Emagtech Wiki - User contributions [en]

Getting Started with EM.Cube

2020-12-14T00:05:13Z

Kazem Sabet: /* Hardware Requirements */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">Visual Electromagnetic Modeling Environment for Simulating Everything from DC to Light<br /></font></strong>
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<td>[[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
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[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
== An EM.Cube Primer ==

=== EM.Cube in a Nutshell ===

[[EM.Cube]] is a visual software environment for electromagnetic (EM) modeling. It features several distinct simulation engines that can solve a wide range of modeling problems such as electromagnetic radiation, scattering, wave propagation in various media, coupling, interference, signal integrity, field interactions with biological systems, etc. Using [[EM.Cube]], you can solve problems of different sizes and length scales, varying from a few microns in MEMS devices to several miles in large urban propagation scenes.

[[EM.Cube]] has a highly integrated modular architecture. Its six computational modules offer a mix of full-wave, static and asymptotic numerical solvers in both time and frequency domains. An intuitive, streamlined user interface is shared among all of [[EM.Cube]]'s computational modules and simulation engines. Once you learn the basics of the software application, you will find enormous computational power at your fingertips. [[EM.Cube]] allows you to plan and execute complex, system-level simulations of multi-scale electromagnetic structures.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[EM.Cube Application Gallery | Examples of EM.Cube's Applications]]'''.

=== EM.Cube's Modular Architecture ===

[[EM.Cube]] brings together several computational modules that can be used to solve a large variety of electromagnetic modeling and RF design problems. Each module revolves around a specific numerical method that is optimized for a certain class of problems or applications. [[EM.Cube]]'s framework is based on total separation of the visual software interface and simulation engines. The numerical solvers communicate with the [[EM.Cube]] application solely through ASCII input and output files. This makes it possible to utilize the same user interface effectively to drive different simulation engines.

At the heart of [[EM.Cube]] is [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], a general-purpose parametric CAD modeling environment. [[EM.Cube]]'s computational modules are all customized variations of [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] equipped with a particular simulation engine. Therefore, they all share the same input utilities (geometry definition and mesh generation) and same output utilities (data visualization and processing). [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] features a powerful 3D CAD modeler with a large selection of native objects (solids, surfaces, curves) and a wide range of object creation, editing and transformation tools. You can import external CAD files with different popular standard formats. [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s intuitive, mouse-driven, point-and-click and drag-and-drop tools let you quickly build very sophisticated structures either from the ground up or by combining native objects with imported external structures. You can also export your projects to a number of popular CAD formats. [[EM.Cube]]'s Data Manager is a versatile utility for processing and plotting your simulation data either as 3D visualizations overlaid on your physical structure or in the form of a variety of graph types.

In addition to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], [[EM.Cube]] currently offers six distinct computational modules:

<table border="1" cellpadding="2" cellspacing="5" style="width: 780px; hight: 40px;">
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<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
CAD Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This is the basic 3D CAD modeling environment for creation, import and export of native and external geometric objects. </td>
</tr>
<tr>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:fdtd-ico.png | link=EM.Tempo]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Tempo]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
FDTD Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features an FDTD simulator for full-wave time domain modeling of 3D objects, circuits, antennas, complex materials and periodic structures. </td>
</tr>
<tr>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:prop-ico.png | link=EM.Terrano]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Terrano]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
Propagation Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features an asymptotic SBR ray tracer for physics-based, site specific modeling of radio wave propagation in urban and natural environments. </td>
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<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:static-ico.png | link=EM.Ferma]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Ferma]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
Static Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features three electrostatic, magnetostatic and steady-state thermal simulation engines that can be used for static or low-frequency analysis of circuits, lumped devices and transmission lines. </td>
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<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:planar-ico.png | link=EM.Picasso]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Picasso]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
Planar Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features a 2.5-D Method of Moments (MoM) solver for full-wave frequency domain modeling of multilayer printed antennas, microwave circuits and periodic planar structures. </td>
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<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:metal-ico.png | link=EM.Libera]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Libera]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
MoM3D Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features two 3D Method of Moments (MoM) solvers for full-wave frequency domain modeling of 3D free-space structures: A Wire MoM simulator and a Surface MoM simulator. </td>
</tr>
<tr>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 50px; background-color: rgb(255, 255, 255);">
[[image:po-ico.png | link=EM.Illumina]] </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
'''[[EM.Illumina]]''' </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; width: 80px; background-color: rgb(255, 255, 255);">
Physical Optics Module </td>
<td style="border-color: rgb(153, 153, 204); padding: 10px; background-color: rgb(255, 255, 255);">
This module features an iterative Physical Optics (PO) solver for asymptotic modeling of electromagnetic scattering from large metallic structures and impedance surfaces in the free space. </td>
</tr>
</table>

Besides sharing a common CAD modeler and common data visualization tools, all computational modules also feature a hierarchy of common elements:

*Physical Structure
*Computational Domain
*Sources
*Observables
*Discretization

The specific contents of each element may vary from module to module depending on the underlying physics. For example, the geometric objects listed under your project's physical structure have different sets of properties in each module. Many source types like plane waves and Hertzian short dipoles or observable types like field sensors, far-field radiation patterns and radar cross section (RCS) are shared among several computational modules. Of [[EM.Cube]]'s computational modules, [[EM.Tempo]] serves as a general-purpose electromagnetic simulator than can handle most types of modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains.

== EM.Cube Installation ==

The [[EM.Cube]] application has been built on a Microsoft Windows platform. While the main program requires a Windows operating system to run, its simulation engines are platform-independent and can be run on Linux platforms or high performance computing (HPC) clusters. If you intend to run one or more of [[EM.Cube]]’s simulation engines on a platform other than Microsoft Windows, please contact our technical support for more information and guidance.

=== Hardware Requirements ===

{| class="wikitable"
|-
! scope="col"|
! scope="col"| RECOMMENDED
! scope="col"| MINIMUM
|-
! scope="row"| Operating System
| Windows 10
| Windows 8.1 or higher
|-
! scope="row"| Processor
| i9 Intel
| i7 or i5 Intel
|-
! scope="row"| RAM
| 32GB
| 8GB
|-
! scope="row"| Graphics Card
| 8GB NVIDIA RTX
| 4GB NVIDIA Quadro
|-
! scope="row"| Display
| Ultra HD
| HD (1080p) 96 DPI
|}

If you have any questions regarding the ability of your system to run [[EM.Cube]], please contact our technical support.

=== Browser Requirements ===

{| class="wikitable"
|-
! scope="col"|
! scope="col"| BROWSER
|-
! scope="row" rowspan="2"| Windows
| Google Chrome, Internet Explorer 8.0 or later with Javascript and Cookies enabled.
|-
| Flash Active X plugin 8.0 or later.
|-
! scope"row" rowspan="2"| Other Platforms
| Google Chrome, Firefox 3.0 or later with Javascript and Cookies enabled.
|-
| Flash Plugin 8.0 or later.
|}

=== Running the Installer ===

#Double click on the installer to begin installing the [[EM.Cube]] software.
#Read and accept the license agreement.
#Follow the prompts until the installation process is completed.

{{Note|You must be an Administrator on your computer to run the installer. If you are using Windows 7, right click the installer and choose "Run as Administrator."}}

=== Placing the EM.Cube License File ===

[[EM.Cube]] Pro requires a valid license to run on any machine. Once you install [[EM.Cube]] on a computer and launch it for the first time, the screen displays a unique EM-ID key, which is made up of a sequence of numbers and letters. You need to write down the EM-ID key and email it to us. We will generate a license file based on the EM-ID key and will email it to you.
You need to place the license file that has a ".lic" file extension in the directory "C:/Program Files (x86)/EMAG/Licenses/".

== Getting to Know EM.Cube's Visual Interface ==

Before you start using [[EM.Cube]], it is important to familiarize yourself with its visual user interface. This is called the [[EM.Cube]] Desktop and consists of a number of visual elements:

*Splash Screen
*Main Window at the center of the screen
*Menu Bar at the top of the screen
*Six horizontal and vertical toolbars scattered at the top, left and right of the screen
*Wide Control Window on the left of the screen with two tabs: Navigation Tree and Python Interpreter
*Status Bar at the bottom of the screen
*Quick Tips on the right of the screen

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[[Image:Desktop_tn_new.png|thumb|left|720px|The visual elements of the [[EM.Cube]] Desktop.]]
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=== Splash Screen ===

The splash screen pops up every time you launch the application. It has four buttons:

*'''New''': Lets you start a brand-new project.
*'''Open''': Lets you open an existing project.
*'''Help''': Opens your browser and takes you the the [[EM.Cube]] Wiki.
*'''Update''': Checks for new updates and alerts you if your [[EM.Cube]] version is no the latest one.

You can click one of the four buttons of the splash screen to proceed. Or you can simply close it using either its "x" button at the upper right corner or using the keyboard's {{key|Esc}} button.

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[[Image:splash1.png|thumb|left|480px|EM.Cube's splash screen.]]
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=== Main Window ===

The main window with a default dark background occupies the largest part of the [[EM.Cube]] desktop. The main window is also referred to as the Project Workspace throughout the [[EM.Cube]] documentation. This is where most of your interaction with [[EM.Cube]] such as CAD construction and data visualization takes place. All the input to [[EM.Cube]]'s simulation engines is created and assembled through the main window, including geometrical and material definitions, sources, boundary conditions, meshes, and observables, <i>i.e.</i> the output quantities you instruct [[EM.Cube]] to generate at the end of a simulation. After a simulation run is completed, the main window is where you view the 3D visualization of the simulation results.

=== Menu Bar ===

[[EM.Cube]]'s standard menus are:

*'''File Menu''': This menu allows you to manage (create, open, save and close) [[EM.Cube]] projects. It also provides the ability to import external CAD files or export CAD files into formats that can be used by other software packages. Printing is accessed from the File Menu.

*'''Edit Menu''': This menu provides Undo, Redo, Cut, Copy, Paste, and Delete – all of which can be used to manage your CAD objects. Through the Preferences dialog, you can set a number of global settings for the [[EM.Cube]] application including color preferences, etc.

*'''View Menu''': The menu lets you hide or show the navigation tree, status bar, and various shortcut toolbars. View Menu also allows you to pan, rotate, and zoom in and out of the current view of the main window. You can change [[EM.Cube]]'s several snap modes from this menu. You can also change the viewing angle of the main window to a variety of pre-selected viewpoints (front, back, perspective, etc.) You can access the Split Viewports option, which splits the main window into a four-port view. You can change the current work plane from View Menu and toggle the grid from the default adaptive type to a fixed custom grid.

*'''Object Menu''': This menu provides one of the several methods for creating geometric objects including solids, surfaces, curves and points.

*'''Tools Menu''': This menu allows you to access all the object editing and transformation tools as well as [[EM.Cube]]'s wizards

*'''Simulate Menu''': This menu contains all the settings, tools and utilities that drive [[EM.Cube]]'s computational modules. From this menu you get access to project units and frequency settings, computational domain, mesh generator, variables, models, custom output, objectives, data manager and simulation Run dialog.

*'''Help Menu''': This menu reports the current version of [[EM.Cube]], displays the current EM-ID and provides a list of all the keyboard shortcuts. From this menu you can access [[EM.Cube]]'s comprehensive documentation including the online manuals and tutorials for all the modules.

=== Toolbars ===

The toolbars can be used in place of the pull-down menus to perform the most commonly used functions with fewer mouse clicks. These functions are grouped into six toolbars:

* '''System Toolbar''': This toolbar is used for general project operations as well as general edit functions.
* '''View Toolbar''': This toolbar provides buttons for most widely used view operation such as zooming and work planes.
* '''Object Toolbar''': This toolbar contains all the tools for drawing [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s native geoemtric object types.
* '''Tools Toolbar''': This toolbar provides a large number of geometric object editing and transformation tools.
* '''Wizard Toolbar''': This toolbar provides easy access to most of [[EM.Cube]]'s preloaded wizards.
* '''Simulate Toolbar''': This toolbar provides access to most important simulation-related functions and operation such as the mesh generator and the simulation run dialog.

<table>
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<td>
[[Image:ToolbarsTop.png|thumb|left|720px|The toolbars allow you to perform the most commonly used functions with fewer mouse clicks.]]
</td>
</tr>
</table>

All the toolbars can be repositioned however you like. Simply grab a toolbar's handle to undock and drag it to any location on the main window. Once undocked, you can also resize a toolbar and make it horizontal or vertical. Move the cursor to the border of the toolbar to turn it into a double arrow. Then drag the mouse until the toolbar gets the right size and appearance. You can dock an undocked toolbar by dragging and dropping it onto the border of the main window. You can show or hide any [[EM.Cube]] toolbar from '''Menu → View → Toolbars'''.

=== Module Bar ===

When you start the [[EM.Cube]] application, it lands you first in [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] by default. The Module Bar located on the left edge of the screen is used to switch among [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] and [[EM.Cube]]'s various computational modules. It consists of eight buttons:

*'''[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]''': [[EM.Cube]]'s 3D CAD modeling environment
*'''[[EM.Tempo]]''': [[EM.Cube]]'s FDTD module
*'''[[EM.Terrano]]''': [[EM.Cube]]'s propagation module
*'''[[EM.Illumina]]''': [[EM.Cube]]'s physical optics module
*'''[[EM.Ferma]]''': [[EM.Cube]]'s static module
*'''[[EM.Picasso]]''': [[EM.Cube]]'s planar module
*'''[[EM.Libera]]''': [[EM.Cube]]'s 3D MoM module
*'''[[RF.Spice A/D]]''': This is a separate stand-alone application that can be used together with [[EM.Cube]]

Clicking on each of the first seven buttons of module bar changes the view to the selected module. Clicking on the [[RF.Spice A/D]] button, opens the [[RF.Spice A/D]] application if you have a valid license of that application.

<table>
<tr>
<td>
[[Image:Modulebar_new.png|thumb|left|450px|The module bar and navigation tree allow you to move among [[EM.Cube]]'s modules and access the properties of the current project's various items in each module.]]
</td>
</tr>
</table>

=== Navigation Tree ===

The Navigation Tree provides all the details of an entire [[EM.Cube]] project. These include the CAD objects and geometric models, material assignments, computational domain and boundary conditions, mesh structure, source information, observable definitions, etc. Besides the menu bar and toolbars, the navigation tree serves as another place from which you can modify most items in your project. Similar to the toolbars, you can undock, move around or hide the module bar and navigation tree.

The contents of the navigation tree vary depending on the selected module. In [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], the navigation tree features two main sections: Geometrical Construction and Data Visualization. The "Geometrical Construction" section holds your geometric objects, while the "Data Visualization" section is used for generation of 3D data visualizations to be displayed in the project workspace. In other modules, the navigation tree typically features five distinct sections:

*Physical Structure
*Computational Domain
*Discretization
*Sources
*Observables

=== Status Bar ===

Underneath the main window and at the bottom of the [[EM.Cube]] desktop, the Status Bar is located. Status Bar displays important information about the current [[EM.Cube]] project including the project unit, frequency, the current coordinate system and state of Snap to Grid and Object Snap modes. Probably the most widely used piece of information on the Status Bar is the current mouse position in the project workspace.

=== Python Command Window ===

On the right of the screen you see the Python command window. There is a Python Command Line at the bottom of this window. This is where you enter your Python commands on line at a time. After entering your command and pressing the keyboard's {{key|Enter}}, the command is executed and is reflected in the larger top part of the window, which maintains a history of your commands during a project session.

== Managing EM.Cube Projects ==

=== Starting a New Project ===

When you start the [[EM.Cube]] application, the splash screen pops up. This screen walks you through the process of setting up a new project if you click its {{key|New}} button. Alternatively, you can close the splash screen without clicking any of its four buttons and land on a blank project workspace in CubeCAD. Here you can start drawing your new geometric objects and build a physical structure for your project.

If you click the {{key|New}} button of the splash screen, the '''New Project''' dialog opens up. You can also open the new project dialog at any time by selecting the menu item '''File → New Project...''', or clicking the '''New''' [[File:New.png]] button of the System Toolbar. The default name of the new project is "UntitledProj" followed by an index. The new project folder by default is created in the "Projects Folder" of your [[EM.Cube]] installation folder. This is normally located in the "EMAG Folder" inside your hard drive's "Documents Folder". From the new project dialog, you can change the location of the new project folder to anywhere on your hard drive using Windows Explorer's folder tree. Before you start the new project, you can change its name to anything you like. Simply type in a new name to replace the default "UntitledProj...".

The problem type is assumed to be "Generic" by default. This creates a blank project in CubeCAD by default. From CubeCAD, you can switch to any of [[EM.Cube]]'s other computational modules and continue to build your project. The new project dialog lets you set the project length units. The default option is '''Millimeters'''. For computational modules, you need to set the operational frequency. The dialog lets you select the frequency unit, which is '''GHz''' (Gigahertz) by default. You can set the project's center frequency and bandwidth. Once you have changed all the settings, click the {{key|Create}} button to make the changes effective and start your new project. Keep in mind that you can always change the center frequency and bandwidth of your project later. However, changing the length units in the middle of a project is highly discouraged after you have already constructed a detailed physical structure.

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<td>
[[Image:Newproj1.png|thumb|left|800px|EM.Cube's New Project dialog.]]
</td>
</tr>
</table>

=== Choosing a Problem Type ===

In most cases, you will prefer to start a generic or blank project and build up your physical structure either in CubeCAD or in one of [[EM.Cube]]'s computational modules. [[EM.Cube]], however, also provides a library of 16 ready-made project templates to get you started as quickly as possible. These projects cover different problem types or applications such as wave propagation, radiation, scattering, circuits, periodic structures, etc. They construct highly parameterized structures in various computational modules. Some of the benefits of the new project templates are:

*You learn how to define variables and parameterzie geometric objects, material groups and other project properties.
*You learn how to define excitation sources and simulation observables in different computational modules.
*You can use a project template as a starting point and then change various parameters or add new geometric objects or other project attributes.
*Each project template has a Python script, which you can access from the models dialog.
*You can learn how to put together simple Python scripts.
*You can use the Python scripts of the existing project templates as a starting point and create more complicated projects scenarios. You can build a library of reusable project templates.

The following table lists [[EM.Cube]]'s new project templates and their purpose:

{| class="wikitable"
|-
! scope="col"|
! scope="col"| Problem Type
! scope="col"| Module
! scope="col"| Python Script
! scope="col"| Notes
! scope="col"| Model
|-
| style="width:10px;" | 1
| style="width:150px;" | Generic
| style="width:50px;" | CubeCAD
| style="width:100px;" | N/A
| style="width:400px;" | Creates a blank project.
| style="width:75px;" | [[image:blank.png|75px]]
|-
| style="width:10px;" | 2
| style="width:150px;" | Simple Outdoor Propagation Scene
| style="width:50px;" | [[EM.Terrano]]
| style="width:100px;" | emag_prop_scene.py
| style="width:400px;" | Creates a two brick buildings with a vertical half-wave dipole transmitter and a grid of isotropic receivers.
| style="width:75px;" | [[image:Ter prop.png|75px]]
|-
| style="width:10px;" | 3
| style="width:150px;" | Simple Indoor Propagation Scene
| style="width:50px;" | [[EM.Terrano]]
| style="width:100px;" | emag_indoor_scene.py
| style="width:400px;" | Creates a brick building with internal wall partitions, a vertical half-wave dipole transmitter and a grid of isotropic receivers.
| style="width:75px;" | [[image:Ter indoor.png|75px]]
|-
| style="width:10px;" | 4
| style="width:150px;" | General Radiation
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_gen_radiation.py
| style="width:400px;" | Creates a wire dipole with a lumped source attached to a square PEC ground plane.
| style="width:75px;" | [[image:Tem rad.png|75px]]
|-
| style="width:10px;" | 5
| style="width:150px;" | General Scattering
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_gen_scattering.py
| style="width:400px;" | Creates a metallic cylinder target with a dielectric coating illuminated by a vertically incident plane wave source.
| style="width:75px;" | [[image:Tem scat.png|75px]]
|-
| style="width:10px;" | 6
| style="width:150px;" | General Periodic Structure
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_gen_periodic.py
| style="width:400px;" | Creates a periodic unit cell containing a metallic cross illuminated by a vertically incident plane wave source.
| style="width:75px;" | [[image:Temp per.png|75px]]
|-
| style="width:10px;" | 7
| style="width:150px;" | General Waveguide Structure
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_gen_waveguide.py
| style="width:400px;" | Creates a vertical rectangular hollow waveguide terminated in a rectangular metallic flange excited using a waveguide port.
| style="width:75px;" | [[image:Tem wg.png|75px]]
|-
| style="width:10px;" | 8
| style="width:150px;" | Finite-Sized Planar Structure
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_finite_planar.py
| style="width:400px;" | Creates a probe-fed square patch on a finite-sized conductor-backed dielectric substrate excited by a lumped source on the vertical probe line.
| style="width:75px;" | [[image:tem_planar.png|75px]]
|-
| style="width:10px;" | 9
| style="width:150px;" | Planar Filter
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_lp_filter.py
| style="width:400px;" | Creates a microstrip lowpass filter excited using two microstrip ports with a Gaussian pulse waveform.
| style="width:75px;" | [[image:Tem lpf.png|75px]]
|-
| style="width:10px;" | 10
| style="width:150px;" | Shielded Resonator
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_shielded_structure.py
| style="width:400px;" | Creates a hemispherical dielectric resonator fed through an extended cylindrical probe in a dielectric substrate at the bottom of a shielded metallic box.
| style="width:75px;" | [[image:Tem shielded.png|75px]]
|-
| style="width:10px;" | 11
| style="width:150px;" | MMIC Circuit
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_mmic.py
| style="width:400px;" | Creates a two-port planar component excited using two microstrip ports on a multilayer substrate inside a shielded metallic box.
| style="width:75px;" | [[image:Tem mmic.png|75px]]
|-
| style="width:10px;" | 12
| style="width:150px;" | Netlist Amplifier Circuit
| style="width:50px;" | [[EM.Tempo]]
| style="width:100px;" | emag_netlist_amp.py
| style="width:400px;" | Creates a linear amplifier circuit containing an active two-port device with a simple Netlist model excited by two microstrip ports.
| style="width:75px;" | [[image:Tem amp.png|75px]]
|-
| style="width:10px;" | 13
| style="width:150px;" | Unbounded Planar Structure
| style="width:50px;" | [[EM.Picasso]]
| style="width:100px;" | emag_unbounded_planar.py
| style="width:400px;" | Creates a probe-fed square patch on a laterally unbounded conductor-backed dielectric substrate excited by a probe gap source.
| style="width:75px;" | [[image:pic_patch.png|75px]]
|-
| style="width:10px;" | 14
| style="width:150px;" | Unbounded Microstrip Structure
| style="width:50px;" | [[EM.Picasso]]
| style="width:100px;" | emag_unbounded_microstrip.py
| style="width:400px;" | Creates a two-port planar microstrip bandpass filter structure excited using two scattering wave ports.
| style="width:75px;" | [[image:pic_mstrip.png|75px]]
|-
| style="width:10px;" | 15
| style="width:150px;" | Unbounded Slot Structure
| style="width:50px;" | [[EM.Picasso]]
| style="width:100px;" | emag_unbounded_slot.py
| style="width:400px;" | Creates a slot structure in an unbounded ground plane excited using an underpassing micrsotrip feed with a shorting pin.
| style="width:75px;" | [[image:pic_slot.png|75px]]
|-
| style="width:10px;" | 16
| style="width:150px;" | Multilayer Periodic Surface
| style="width:50px;" | [[EM.Picasso]]
| style="width:100px;" | emag_netlist_amp.py
| style="width:400px;" | Creates a periodic unit cell using a concentric square loop and patch elements printed on a multilayer dielectric substrate illuminated using a plane wave source.
| style="width:75px;" | [[image:pic_per.png|75px]]
|-
| style="width:10px;" | 17
| style="width:150px;" | Wire Structure
| style="width:50px;" | [[EM.Libera]]
| style="width:100px;" | emag_wire_structure.py
| style="width:400px;" | Creates a multi-wire metal structure including a spiral helix excited by a wire gap source.
| style="width:75px;" | [[image:lib_wire.png|75px]]
|-
| style="width:10px;" | 18
| style="width:150px;" | Air-Filled Capacitor
| style="width:50px;" | [[EM.Ferma]]
| style="width:100px;" | emag_air_capacitor.py
| style="width:400px;" | Creates an air-filled parallel plate capacitor with the top plate connected to a voltage source.
| style="width:75px;" | [[image:fer_cap.png|75px]]
|-
| style="width:10px;" | 19
| style="width:150px;" | Air-Core Solenoid
| style="width:50px;" | [[EM.Ferma]]
| style="width:100px;" | emag_air_solenoid.py
| style="width:400px;" | Creates a current-carrying vertical solenoid with an air core.
| style="width:75px;" | [[image:fer_sol.png|75px]]
|}

=== Opening, Saving & Closing Projects ===

Previously saved projects can be opened using the menu item '''File → Open Project...''', or by clicking the '''Open''' [[File:Open.png]] button of the System Toolbar. If you are in a different project that has been modified, and your changes have not been saved yet, a warning message will appear asking you whether you want to save the current project before opening another project. Once the standard Windows open dialog pops up, you can browse the Windows Explorer and locate any project you wish to open. You have to open the project folder and select the project file with a ".PRJ" file extension.

You can save the current project using the menu item '''File → Save Project''', or by clicking the '''Save''' [[File:Save.png]] button of the System Toolbar. You can save the project under another name using the menu item '''Menu → File → Save Project As...'''. This opens up the standard Windows Save Dialog. The Windows Explorer shows the current location of the project folder. You can type in any name in the provided file path. Or you may change the folder and save the project in another location. "Save As" can be used to make additional copies of the same project under different names.

You can close a project at any time using the menu item '''File → Close Project'''. A message pops up that prompts if you wish to save the existing project. You can quit the [[EM.Cube]] application using the menu item '''File → Quit''' or using the keyboard shortcut {{key|Ctrl+Q}}. Note that when you close a project, you are still in the [[EM.Cube]] application. If you start a new project, you may still carry some of the program settings from the previous project. Quitting and exiting the application ensures that all the default settings would take effect the next time when you start a new project.

[[Image:Info_icon.png|30px]] To find additional details about [[EM.Cube]]'s file operations, see the '''[[Glossary of EM.Cube's Basic File, Edit & View Operations]]'''.

=== Changing Project Settings ===

You can change the project length units and frequency settings at any time after you create a new project. This can be done from the Units and Frequency dialogs. The units dialog can be accessed from '''Menu → Simulate → Project Units''' or by clicking the '''Units''' [[File:Ruler-tool.png]] button of the Simulate Toolbar. You can also open the units dialog by double-clicking the "Units" section of the status bar, which by default displays "mm".

The frequency dialog can be accessed from '''Menu → Simulate → Frequency Settings...''', or by clicking the '''Frequency''' [[File:Frequency-tool.png]] button of the simulate toolbar. The project's current center frequency is displayed on the status bar with the current frequency units. Double-clicking on this value is another way to open up the frequency dialog. From this dialog you can change the values of center frequency and bandwidth as well as the frequency units.

[[Image:Info_icon.png|30px]] To find additional details about these dialogs, see the '''[[Glossary of EM.Cube's Simulation-Related Operations | Glossary of EM.Cube's Simulation-Related Operations]]'''.

=== Handling Project and Data Files ===

All the information about each [[EM.Cube]] project are stored in two files which bear the name of the project and have file extensions ".PRJ" (project file) and ".MDL" (model file). When you run a new simulation, a large number of files of different types are created in the project folder. Some of the output data files have reserved names and are overwritten after each simulation. [[EM.Cube]] deletes most of the files in the project folder before every simulation. The exceptions are the project and model files. It is very important to remember that the project folder is not a place to save your data. Every time you run a simulation, [[EM.Cube]] prompts that you are about to discard all previous results and asks whether you want to proceed.

You can clean up your project folder at any time through '''Menu → Simulate → Delete All Data Files''' or by right-clicking on the '''Data Manager''' item in the "Observables" section of the navigation tree and selecting '''Delete All Data Files''' from the contextual menu. In order to preserve your simulation data, you have to save them in a different folder other than the project folder. One way is to create a subfolder in your project folder. The contents of subfolders are not deleted at the start of a simulation. To save the data in a project subfolder, select the menu item '''Simulate → Save Data As...''' or right-click on the '''Data Manager''' item in the "Observables" section of the navigation tree and select '''Save Data As...''' from the contextual menu. This opens up the Save Data dialog with the default subfolder name "Simulation Data" in your current project folder. You can choose the default subfolder name and location or change the name or browse to another location on your hard drive.

<table>
<tr>
<td>
[[Image:Savedata.png|thumb|left|480px|Saving a project's simulation data into a subfolder.]]
</td>
</tr>
</table>

== Changing EM.Cube's Visual Settings ==

=== Customizing Your Desktop ===

Most of the visual elements of [[EM.Cube]]'s user interface can be customized. [[EM.Cube]] will remember the last state of your visual interface when you exit the application and will restore it the next time you start the application. These information are saved in the Windows registry and remain there until you delete them. You can move the menu bar and the six toolbars around and drop them at any location on the screen. Hover your mouse on the handle of any toolbar and simply drag it. The toolbars become horizontal when they are placed inside the main window. In this case, they are said to be floating inside the main window. If you hover the mouse on one of the four edges of a floating toolbar, its shape changes to a double arrow. You can expand or shrink a floating toolbar horizontally or vertically. When you drop a floating toolbar to an edge of the screen, the toolbar docks onto that edge.

You can customize the [[EM.Cube]] Desktop to your liking in a number of ways. For example, you can change its view mode temporarily, change the background color of your project workspace, and display or hide the grid. These functions can be accessed either through the "View Menu" or "View Toolbar" or through the "Preferences Dialog" of the Edit Menu, which can opened using the menu item '''Edit → Preferences...'''. In general, the changes you make through the menus and toolbars are valid during the session of your project, while the changes you make in the preferences dialog are permanent and are written to the Windows registry. That means your changes persist the next time you open the [[EM.Cube]] application.

Using a number of menu items at the top of the "View Menu", you can turn all the individual toolbars on or off, and show or hide the navigation tree and status bar. Furthermore, you can drag the handle of the navigation tree, Python command window or any of the toolbars and drop them anywhere within the project workspace.

=== The Grid ===

[[EM.Cube]]'s grid is used as a guide for drawing objects. When you start the [[EM.Cube]] applciation, the grid is off by default. However, the '''Snap to Grid''' mode is enabled by default. As you move the mouse in the project workspace, a small white square follows the mouse cursor snapping to the nearest grid node. [[EM.Cube]]'s grid can be turned on or off from the '''Guides''' tab of the preferences dialog. In this tab of the dialog, check the box labeled '''Show Grid Lines''' and click the {{key|Apply}} button of the dialog to display the grid. From this dialog you can also change the color of grid lines. You can show or hide the axis lines in the project workspace.

<table>
<tr>
<td>
[[Image:gridsettings.png|thumb|left|480px|The Guides tab of the Preferences Dialog.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:Enable_Grid.png|thumb|left|640px|Enabling the grid of EM.Cube's project workspace and selection a low-contrast color for the grid.]]
</td>
</tr>
</table>

When the "Snap to Grid" mode is enabled, a text reading like '''Grid Snap: 5''' appears on [[EM.Cube]]'s status bar. This shows the current grid cell size. As you zoom in or zoom out, the grid cell size changes accordingly. You can turn the "Snap to Grid" mode on and off from the status bar by double-clicking on this text to toggle its state. Besides the adaptive grid that is the default grid type, [[EM.Cube]] also offers a fixed grid option, which can be zoomed in or out together with the physical structure in the project workspace.

[[Image:Info_icon.png|30px]] To learn more about [[EM.Cube]]'s grid types, see '''[[Glossary of EM.Cube's Basic File, Edit & View Operations#Grid Properties | EM.Cube's Grid Properties]]'''.

=== Changing the Environment Colors ===

The default background color of the main window is black, but it can easily be changed from the preferences dialog. Select the '''Colors''' tab of the dialog and click the button labeled '''Color''' next to '''Background'''. A color selection window pops up, where you can pick a new background color. Another global color in [[EM.Cube]] is the selection color. When you select an object, its color turns to the selection color. When you hover your mouse on an object without clicking (called the mouse-over state), it becomes translucent with a shade of the selection color. You can snap to the characteristic points of objects (<i>e.g.</i> vertices, edge midpoints, face centers, etc.). These snap points appear in the complementary color of the selection color. By default, [[EM.Cube]]'s selection color is bright yellow, which can also be changed from the '''Colors''' tab of the preferences dialog.

<table>
<tr>
<td>
[[Image:BckColor1.png|thumb|left|360px|The default background and selection colors of EM.Cube's project workspace.]]
</td>
<td>
[[Image:BckColor2.png|thumb|left|360px|Changing the background and selection colors of EM.Cube's project workspace.]]
</td>
</tr>
</table>

=== Basic View Operations ===

When you start [[EM.Cube]], the default grid cell size is set to 5 units. The default view may not be good enough for very small or very large structures. You can easily change the view settings of the project workspace. The simplest view operation is zooming in or out. This can easily be done using the scroll wheel of your mouse. Turning the scroll wheel towards yourself zooms out of a structure, while turning it away from yourself zooms in to the structure. Zooming in and out using the mouse scroll wheel is a temporary operation and does not change the view mode. [[EM.Cube]] provides a number of view modes, which persist until you change the mode or return to the '''Normal Mode'''. You can always return to the normal mode using the {{key|Esc}} (Escape) key of your keyboard. You can also return to the normal mode by clicking the '''Select''' [[File:select-tool_tn.png]] button of the View Toolbar or selecting the menu item '''View → Normal View'''.

The following table summarizes [[EM.Cube]]'s most useful and widely used view operations. "RMB" stands for the right mouse button.

{| class="wikitable"
|-
! scope="col"| View Operation
! scope="col"| Temporary Shortcut
! scope="col"| Persistent Mode: Toolbar
! scope="col"| Persistent Mode: Menu
|-
| Normal View
| style="width:150px;" | {{key|Esc}}
| style="width:200px;" | '''Select''' [[File:select-tool_tn.png]]
| style="width:200px;" | '''View → Select'''
|-
| Pan View
| style="width:150px;" | {{key|Shift+RMB}}
| style="width:200px;" | '''Pan''' [[File:pan-tool_tn.png]]
| style="width:200px;" | '''View → Pan View'''
|-
| Rotate View
| style="width:150px;" | {{key|RMB}} and {{key|Alt+RMB}}
| style="width:200px;" | '''Rotate View''' [[File:rotate-tool_tn.png]]
| style="width:200px;" | '''View → Rotate View'''
|-
| Dynamic Zoom
| style="width:150px;" | mouse scroll wheel and/or {{key|Ctrl+RMB}}
| style="width:200px;" | '''Zoom Dynamic''' [[File:zoom-tool_tn.png]]
| style="width:200px;" | '''View → Zoom → Dynamic'''
|-
| Zoom to Fit
| style="width:150px;" | {{key|Ctrl+E}}
| style="width:200px;" | '''Zoom Extents''' [[File:zoom-to-extent_tn.png]]
| style="width:200px;" | '''View → Zoom → Extents'''
|}

For most of [[EM.Cube]]'s functions, the keyboard shortcuts simply serve as an alternative to a toolbar button or a menu item. In the case of Pan View, Rotate View and Dynamic Zoom, the RMB shortcuts provide temporary functions, while the toolbar buttons or menu item create a persistent view mode. For example, in the rotate view mode, dragging the mouse with the left or right mouse buttons held down results on the rotation of the project workspace's view about different axes of revolution. Once enabled, the rotate view mode stays active until you return to the normal view mode.

[[Image:Info_icon.png|30px]] To find additional details about [[EM.Cube]]'s view operations, see the '''[[Glossary of EM.Cube's Basic File, Edit & View Operations]]'''.

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[Getting_Started_with_EM.Cube#An_EM.Cube_Primer | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:30:37Z

Kazem Sabet:

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R20.1 Release At A Glance ===

The new [[EM.Cube]] R20.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New source arrays of lumped, waveguide, microstrip, CPW and coaxial types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New plots of material parameters vs. frequency for dispersive and gyrotropic material types
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Improved antenna wizards with fast ports acceleration

=== New EM.Terrano (Ray Tracing) Features ===

*Improved ray angular resolution for SBR simulation of large propagation scenes
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with smoothing filters
*Streamlined handling of multi-transmitter scenarios
*New phased array and AESA capability in multi-transmitter and multi-receiver scenarios including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New analog modulation schemes and improved digital waveform capability
*New link margin analysis for both analog and digital modulation schemes
*Definition of connectivity maps based on link margin
*New plane wave source for 3D Field Solver
*New far-field observables for 3D Field Solver including radiation pattern, bistatic and monostatic RCS and polarimetric scattering matrix sweep based on equivalent Huygens surface integration
*Improved radar link solver with a new radar-target positional sweep mode
*Improved scatterer sets with options of spherical targets and imported polarimetric scattering matrix files
*New parameterized PEC and dielectric spherical targets with analytical Mie solutions
*Improved ray visualization of transmitter sweep results
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas
*Improved mobile sweep with varying Eulerian rotation angles of both transmitter and receiver nodes
*New communication link calculator tool
*New radar link calculator tool
*Import of DTED0, DTED1 and DTED2 terrain models
*New Terrain Manager utility with quick view and statistical report capability for importing, cropping, rescaling and repositioning terrain models
*New longitude-latitude (LL) coordinates in the Status Bar and new Python functions for setting and getting the origin’s LL coordinates
*Improved standard atmosphere model
*New non-standard atmosphere models including piecewise linear modified refractivity profiles with one or two break points as well as more general user-defined non-standard M-profiles in the form of piecewise cubic polynomial functions of height
*Analysis of atmospheric propagation through surface and elevated ducts
*New ground database generator for defining the material properties of the earth’s surface using elevation-based or land use map-based classification schemes
*Improved random city, office building, and basic link wizards
*Improved mobile path wizard with new options for monostatic radar and target nodes and template for user-defined cartesian-file-based paths
*New sea surface wizard with different sea states and Douglas and Beaufort scales
*New basic radar wizard
*New Python function for DEM and DTED import
*New Python function for calculating the maximum and RMS height of the terrain
*New Python function for setting the RMS height of rough Earth surface

=== New EM.Picasso (Planar MoM) and EM.Libera (Surface MOM & Wire MOM) Features ===

*New source arrays of strip gap, wire gap, probe gap and scattering port types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New focused Gaussian beam source with higher-order Hermite-Gauss modal profile
*New point transmitter source with user defined radiation pattern
*Multi-transmitter source arrays with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Huygens source arrays with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New option for PO input file to read mesh data from an external MATLAB-generated file
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions

=== New CubeCAD Features ===

*Improved polymesh objects with mesh statistics, better control over primitives and more display options
*New mesh generation scheme in CubeCAD based on the tessellated model of objects for rendering
*Improved STL import of large structures and scenes
*More control over STL export including mesh type and resolution
*Improved parametric surface generator with option to generate a polymesh surface
*Improved parametric curve generator with option to generate a polyline
*New Hilbert space-filling curve option in parametric curve generator
*Improved nodal curves (polyline and NURBS curve) and nodal surfaces (polystrip and NURBS surface) with option for saving and loading the node data
*New Python commands for generating polylines and polystrips from a data file or a text string
*New Python command for extracting part of a nodal curve
*Improved roughen tool with new option to freeze a random rough surface into a tessellated surface object
*Improved random group tool with new option to freeze a random cloud in to a fixed group object
*New parameterization of generic objects resulting from geometric transformations

=== New General Features ===

*New array pattern synthesis tool including Schelkunoff, Sectoral beam, Woodward-Lawson synthesis methods, and particle swarm optimization (PSO)
*New u-v plots of radiation pattern and RCS
*New elevation-azimuth plots of radiation pattern and RCS
*New contour plots of radiation pattern and RCS
*Improved and streamlined interface between [[EM.Cube]] and [[NeoScan]] field measurement data
*[[RF.Spice A/D]] device manager now integrated within [[EM.Cube]] under Tools Menu
*A large number of transmission line calculator and designer tools as part of [[RF.Spice A/D]] device manager
*New capability of generating reusable Touchstone-style S-parameter-based circuit models for use in [[RF.Spice A/D]] from full-wave simulation data
*Capability of designing custom circuit symbols and pin diagrams using [[RF.Spice A/D]] device manager’s symbol editor
*Improved Python interpreter and command line output
*New convenient Python scripting utility in addition to the command line
*New Python command for running Python scripts from the command line
*New Python functions for generating 2D cuts of radiation pattern and RCS
*New amplitude-only graphs of S-parameters
*Improved polar plot capability with user defined dB scale
*Plotting of two and three simultaneous data sets
*Logarithmic scale for the X and Y axes of 2D cartesian graphs
*More control over the default scale settings (linear vs. dB) of 2D and 3D graphs
*New capability of saving and loading individual graph settings and customization of 2D and 3D graphs based on previous templates
*More file operations such as renaming and copying files within Data Manager
*New basic data generator for examining user-defined mathematical and Python functions
*New basic and image-based data generator for importing data from a graph image

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:23:25Z

Kazem Sabet:

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R20.1 Release At A Glance ===

The new [[EM.Cube]] R20.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New source arrays of lumped, waveguide, microstrip, CPW and coaxial types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New plots of material parameters vs. frequency for dispersive and gyrotropic material types
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Improved antenna wizards with fast ports acceleration

=== New EM.Terrano (Ray Tracing) Features ===

*Improved ray angular resolution for SBR simulation of large propagation scenes
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with smoothing filters
*Streamlined handling of multi-transmitter scenarios
*New phased array and AESA capability in multi-transmitter and multi-receiver scenarios including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New analog modulation schemes and improved digital waveform capability
*New link margin analysis for both analog and digital modulation schemes
*Definition of connectivity maps based on link margin
*New plane wave source for 3D Field Solver
*New far-field observables for 3D Field Solver including radiation pattern, bistatic and monostatic RCS and polarimetric scattering matrix sweep based on equivalent Huygens surface integration
*Improved radar link solver with a new radar-target positional sweep mode
*Improved scatterer sets with options of spherical targets and imported polarimetric scattering matrix files
*New parameterized PEC and dielectric spherical targets with analytical Mie solutions
*Improved ray visualization of transmitter sweep results
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas
*Improved mobile sweep with varying Eulerian rotation angles of both transmitter and receiver nodes
*New communication link calculator tool
*New radar link calculator tool
*Import of DTED0, DTED1 and DTED2 terrain models
*New Terrain Manager utility with quick view and statistical report capability for importing, cropping, rescaling and repositioning terrain models
*New longitude-latitude (LL) coordinates in the Status Bar and new Python functions for setting and getting the origin’s LL coordinates
*Improved standard atmosphere model
*New non-standard atmosphere models including piecewise linear modified refractivity profiles with one or two break points as well as more general user-defined non-standard M-profiles in the form of piecewise cubic polynomial functions of height
*Analysis of atmospheric propagation through surface and elevated ducts
*New ground database generator for defining the material properties of the earth’s surface using elevation-based or land use map-based classification schemes
*Improved random city, office building, and basic link wizards
*Improved mobile path wizard with new options for monostatic radar and target nodes and template for user-defined cartesian-file-based paths
*New sea surface wizard with different sea states and Douglas and Beaufort scales
*New basic radar wizard
*New Python function for DEM and DTED import
*New Python function for calculating the maximum and RMS height of the terrain
*New Python function for setting the RMS height of rough Earth surface

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New EM.Picasso (Planar MOM) and EM.Libera (Surface MoM & Wire MOM) Features ===

*New source arrays of strip gap, wire gap, probe gap and scattering port types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:21:27Z

Kazem Sabet:

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R20.1 Release At A Glance ===

The new [[EM.Cube]] R20.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New source arrays of lumped, waveguide, microstrip, CPW and coaxial types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New plots of material parameters vs. frequency for dispersive and gyrotropic material types
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Improved antenna wizards with fast ports acceleration

=== New EM.Terrano (Ray Tracing) Features ===

*Improved ray angular resolution for SBR simulation of large propagation scenes
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with smoothing filters
*Streamlined handling of multi-transmitter scenarios
*New phased array and AESA capability in multi-transmitter and multi-receiver scenarios including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New analog modulation schemes and improved digital waveform capability
*New link margin analysis for both analog and digital modulation schemes
*Definition of connectivity maps based on link margin
*New plane wave source for 3D Field Solver
*New far-field observables for 3D Field Solver including radiation pattern, bistatic and monostatic RCS and polarimetric scattering matrix sweep based on equivalent Huygens surface integration
*Improved radar link solver with a new radar-target positional sweep mode
*Improved scatterer sets with options of spherical targets and imported polarimetric scattering matrix files
*New parameterized PEC and dielectric spherical targets with analytical Mie solutions
*Improved ray visualization of transmitter sweep results
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas
*Improved mobile sweep with varying Eulerian rotation angles of both transmitter and receiver nodes
*New communication link calculator tool
*New radar link calculator tool
*Import of DTED0, DTED1 and DTED2 terrain models
*New Terrain Manager utility with quick view and statistical report capability for importing, cropping, rescaling and repositioning terrain models
*New longitude-latitude (LL) coordinates in the Status Bar and new Python functions for setting and getting the origin’s LL coordinates
*Improved standard atmosphere model
*New non-standard atmosphere models including piecewise linear modified refractivity profiles with one or two break points as well as more general user-defined non-standard M-profiles in the form of piecewise cubic polynomial functions of height
*Analysis of atmospheric propagation through surface and elevated ducts
*New ground database generator for defining the material properties of the earth’s surface using elevation-based or land use map-based classification schemes
*Improved random city, office building, and basic link wizards
*Improved mobile path wizard with new options for monostatic radar and target nodes and template for user-defined cartesian-file-based paths
*New sea surface wizard with different sea states and Douglas and Beaufort scales
*New basic radar wizard
*New Python function for DEM and DTED import
*New Python function for calculating the maximum and RMS height of the terrain
*New Python function for setting the RMS height of rough Earth surface

=== New EM.Ferma (Static) Features ===

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New focused Gaussian beam source with higher-order Hermite-Gauss modal profile
*New point transmitter source with user defined radiation pattern
*Multi-transmitter source arrays with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Huygens source arrays with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New option for PO input file to read mesh data from an external MATLAB-generated file
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:19:31Z

Kazem Sabet:

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R20.1 Release At A Glance ===

The new [[EM.Cube]] R20.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New source arrays of lumped, waveguide, microstrip, CPW and coaxial types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New plots of material parameters vs. frequency for dispersive and gyrotropic material types
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Improved antenna wizards with fast ports acceleration

=== New EM.Terrano (Ray Tracing) Features ===

*Improved ray angular resolution for SBR simulation of large propagation scenes
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with smoothing filters
*Streamlined handling of multi-transmitter scenarios
*New phased array and AESA capability in multi-transmitter and multi-receiver scenarios including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New analog modulation schemes and improved digital waveform capability
*New link margin analysis for both analog and digital modulation schemes
*Definition of connectivity maps based on link margin
*New plane wave source for 3D Field Solver
*New far-field observables for 3D Field Solver including radiation pattern, bistatic and monostatic RCS and polarimetric scattering matrix sweep based on equivalent Huygens surface integration
*Improved radar link solver with a new radar-target positional sweep mode
*Improved scatterer sets with options of spherical targets and imported polarimetric scattering matrix files
*New parameterized PEC and dielectric spherical targets with analytical Mie solutions
*Improved ray visualization of transmitter sweep results
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas
*Improved mobile sweep with varying Eulerian rotation angles of both transmitter and receiver nodes
*New communication link calculator tool
*New radar link calculator tool
*Import of DTED0, DTED1 and DTED2 terrain models
*New Terrain Manager utility with quick view and statistical report capability for importing, cropping, rescaling and repositioning terrain models
*New longitude-latitude (LL) coordinates in the Status Bar and new Python functions for setting and getting the origin’s LL coordinates
*Improved standard atmosphere model
*New non-standard atmosphere models including piecewise linear modified refractivity profiles with one or two break points as well as more general user-defined non-standard M-profiles in the form of piecewise cubic polynomial functions of height
*Analysis of atmospheric propagation through surface and elevated ducts
*New ground database generator for defining the material properties of the earth’s surface using elevation-based or land use map-based classification schemes
*Improved random city, office building, and basic link wizards
*Improved mobile path wizard with new options for monostatic radar and target nodes and template for user-defined cartesian-file-based paths
*New sea surface wizard with different sea states and Douglas and Beaufort scales
*New basic radar wizard
*New Python function for DEM and DTED import
*New Python function for calculating the maximum and RMS height of the terrain
*New Python function for setting the RMS height of rough Earth surface

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:18:49Z

Kazem Sabet: /* New EM.Terrano (Ray Tracing) Features */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R20.1 Release At A Glance ===

The new [[EM.Cube]] R20.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New source arrays of lumped, waveguide, microstrip, CPW and coaxial types with phased array and AESA capability including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New plots of material parameters vs. frequency for dispersive and gyrotropic material types
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable
*Improved radiation pattern and RCS observables with partial elevation and azimuth angle definitions
*Improved array factor definition for the radiation pattern observable with user defined amplitude and phase distribution including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*Improved antenna wizards with fast ports acceleration

=== New EM.Terrano (Ray Tracing) Features ===

*Improved ray angular resolution for SBR simulation of large propagation scenes
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with smoothing filters
*Streamlined handling of multi-transmitter scenarios
*New phased array and AESA capability in multi-transmitter and multi-receiver scenarios including classic weight distribution types (One-Parameter Taylor-Kaiser, Taylor N-bar, Bayliss N-bar, etc.) and user-defined complex weights
*New analog modulation schemes and improved digital waveform capability
*New link margin analysis for both analog and digital modulation schemes
*Definition of connectivity maps based on link margin
*New plane wave source for 3D Field Solver
*New far-field observables for 3D Field Solver including radiation pattern, bistatic and monostatic RCS and polarimetric scattering matrix sweep based on equivalent Huygens surface integration
*Improved radar link solver with a new radar-target positional sweep mode
*Improved scatterer sets with options of spherical targets and imported polarimetric scattering matrix files
*New parameterized PEC and dielectric spherical targets with analytical Mie solutions
*Improved ray visualization of transmitter sweep results
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas
*Improved mobile sweep with varying Eulerian rotation angles of both transmitter and receiver nodes
*New communication link calculator tool
*New radar link calculator tool
*Import of DTED0, DTED1 and DTED2 terrain models
*New Terrain Manager utility with quick view and statistical report capability for importing, cropping, rescaling and repositioning terrain models
*New longitude-latitude (LL) coordinates in the Status Bar and new Python functions for setting and getting the origin’s LL coordinates
*Improved standard atmosphere model
*New non-standard atmosphere models including piecewise linear modified refractivity profiles with one or two break points as well as more general user-defined non-standard M-profiles in the form of piecewise cubic polynomial functions of height
*Analysis of atmospheric propagation through surface and elevated ducts
*New ground database generator for defining the material properties of the earth’s surface using elevation-based or land use map-based classification schemes
*Improved random city, office building, and basic link wizards
*Improved mobile path wizard with new options for monostatic radar and target nodes and template for user-defined cartesian-file-based paths
*New sea surface wizard with different sea states and Douglas and Beaufort scales
*New basic radar wizard
*New Python function for DEM and DTED import
*New Python function for calculating the maximum and RMS height of the terrain
*New Python function for setting the RMS height of rough Earth surface

=== New EM.Ferma (Static) Features ===

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R20.1?

2020-03-30T19:14:30Z

Kazem Sabet:

What's New in EM.Cube R20.1?

2020-03-30T19:12:09Z

Kazem Sabet: /* EM.Cube R19.1 Release At A Glance */

What's New in EM.Cube R20.1?

2020-03-30T18:05:54Z

Kazem Sabet: Created page with "720px <strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong> <strong><font color="#70798..."

New Tutorials

2020-03-30T16:18:54Z

Kazem Sabet:

== EM.Cube Tutorials ==

Each tutorial lesson listed below walks you through the basic features of one of [[EM.Cube]]'s computational modules:

----------------------------------------------------------------------------------------

These are the new pages added or modified for [[EM.Cube]] Release R17:

[[New PO Theory]]

[[What's New in EM.Cube R19.1]]

[[OLD What's New in EM.Cube R18.1?]]

[[What's New in EM.Cube R20.1?]]

[[EM.Terrano Tutorial Lesson 4: Analyzing Indoor Propagation Inside a Building Model with Penetrable Walls]]

[[EM.Terrano Tutorial Lesson 9: A SBR Channel Analysis of An Urban Scene]]

[[EM.Terrano Tutorial Lesson 10: Modeling A Mobile Communications Link]]

----------------------------------------------------------------------------------------

These are the old [[EM.Cube]] documentation pages:

[[The Old EM.Cube Wiki Start Page]]

[[THE OLD Getting Started with EM.Cube]]

[[THE OLD What's New in EM.Cube 2016?]]

[[THE OLD Defining Simulation Observables & Visualizing Output Data]]

---------------------------------

[[V&V Article 6: Using EM.Cube And NeoScan System Together For Antenna Design]]

[[Installing EM.Cube]]

[[EM.Cube FAQ]]

----------------------------------------------------------------------------------------

These are all old stuff:

[[NeoScan_Complete]]

[[NeoScan Manuals]]

[[NeoScan Manual Part A: Getting Started]]

<table>
<tr>
<td>
{|class="wikitable"
|-
! [[EM.Cube]]
|-
|[[File:emcubePAGE.png |225px | link=EM.Cube]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | RF.Spice A/D]]
|-
| [[File:RfspicePAGE New.png |277px | link=RF.Spice A/D | RF.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | B2.Spice A/D]]
|-
| [[File:B2spicePAGE.png |226px | link=RF.Spice A/D | B2.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[NeoScan | NeoScan]]
|-
| [[File:NeoScan_Product.png |245px | link=NeoScan | NeoScan ]]
|-
|}
</td>
</tr>
</table>

----

[[Old Gateway]]

[[Old EM.Cube Page]]

[[Old Digital Glossary]]

----

[[Image:Back_icon.png|40px]] '''[[Main_Page | Back to Emagtech Wiki Gateway]]'''

New Tutorials

2020-03-30T16:15:56Z

Kazem Sabet:

== EM.Cube Tutorials ==

Each tutorial lesson listed below walks you through the basic features of one of [[EM.Cube]]'s computational modules:

----------------------------------------------------------------------------------------

These are the new pages added or modified for [[EM.Cube]] Release R17:

[[New PO Theory]]

[[What's New in EM.Cube R19.1]]

[[EM.Terrano Tutorial Lesson 4: Analyzing Indoor Propagation Inside a Building Model with Penetrable Walls]]

[[EM.Terrano Tutorial Lesson 9: A SBR Channel Analysis of An Urban Scene]]

[[EM.Terrano Tutorial Lesson 10: Modeling A Mobile Communications Link]]

----------------------------------------------------------------------------------------

These are the old [[EM.Cube]] documentation pages:

[[The Old EM.Cube Wiki Start Page]]

[[THE OLD Getting Started with EM.Cube]]

[[THE OLD What's New in EM.Cube 2016?]]

[[THE OLD Defining Simulation Observables & Visualizing Output Data]]

---------------------------------

[[V&V Article 6: Using EM.Cube And NeoScan System Together For Antenna Design]]

[[Installing EM.Cube]]

[[EM.Cube FAQ]]

----------------------------------------------------------------------------------------

These are all old stuff:

[[NeoScan_Complete]]

[[NeoScan Manuals]]

[[NeoScan Manual Part A: Getting Started]]

[[OLD What's New in EM.Cube R18.1?]]

<table>
<tr>
<td>
{|class="wikitable"
|-
! [[EM.Cube]]
|-
|[[File:emcubePAGE.png |225px | link=EM.Cube]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | RF.Spice A/D]]
|-
| [[File:RfspicePAGE New.png |277px | link=RF.Spice A/D | RF.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | B2.Spice A/D]]
|-
| [[File:B2spicePAGE.png |226px | link=RF.Spice A/D | B2.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[NeoScan | NeoScan]]
|-
| [[File:NeoScan_Product.png |245px | link=NeoScan | NeoScan ]]
|-
|}
</td>
</tr>
</table>

----

[[Old Gateway]]

[[Old EM.Cube Page]]

[[Old Digital Glossary]]

----

[[Image:Back_icon.png|40px]] '''[[Main_Page | Back to Emagtech Wiki Gateway]]'''

OLD What's New in EM.Cube R18.1?

2020-03-30T16:13:53Z

Kazem Sabet: Created page with "720px <strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong> <strong><font color="#70798..."

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R18.1 Release At A Glance ===

The new [[EM.Cube]] R18.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New digital modulation schemes with 17 waveform types and computation of Eb/N0 and bit error rate (BER)
*New standard output parameters for SNR, Eb/N0 and BER of the selected receiver with instant update upon changing receiver index
*Fast broadband frequency sweep of the propagation scene with uniformly spaced or discrete frequency samples in a single SBR simulation run
*New option for using multi-frequency radiation patterns in frequency sweeps
*New option for visualizing 3D radiation patterns overlaid on the propagation scene
*Complete polarimetric (theta-phi) characterization of the propagation channel for MIMO analysis
*New "almost real-time" Polarimatrix solver using an existing 3D ray database as an alternative to physical ray tracing
*Real-time transmitter sweep for modeling mobile transmitters using the new Polarimatrix solver
*Real-time rotational sweep for modeling beam scanning using the new Polarimatrix solver
*Real-time mobile (point-to-point) sweep simulation of transmitter-receiver pairs using the new Polarimatrix solver
*New Mobile Path wizard based on existing nodal curves or imported 3D spatial Cartesian data files
*New Point Scatterer sets with imported polarimetric scattering matrix data files
*New Radar Simulator generating a ray tracing solution of bistatic and monostatic radar system configurations
*Improved "Random City" wizard with a larger number of building parameters
*Improved "Basic Link" wizard with parameterized transmitter and receiver heights
*New distributed transmitters and receivers using Huygens sources

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*Improved, more accurate formulation of impedance surfaces in GO-PO and IPO solvers
*Four impedance surface types: dielectric-coated PEC, imperfect conductor, high refractive index medium interface and fixed-impedance surface

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

New Tutorials

2020-03-30T16:13:25Z

Kazem Sabet:

== EM.Cube Tutorials ==

Each tutorial lesson listed below walks you through the basic features of one of [[EM.Cube]]'s computational modules:

----------------------------------------------------------------------------------------

These are the new pages added or modified for [[EM.Cube]] Release R17:

[[New PO Theory]]

[[What's New in EM.Cube R19.1]]

[[EM.Terrano Tutorial Lesson 4: Analyzing Indoor Propagation Inside a Building Model with Penetrable Walls]]

[[EM.Terrano Tutorial Lesson 9: A SBR Channel Analysis of An Urban Scene]]

[[EM.Terrano Tutorial Lesson 10: Modeling A Mobile Communications Link]]

----------------------------------------------------------------------------------------

These are the old [[EM.Cube]] documentation pages:

[[The Old EM.Cube Wiki Start Page]]

[[THE OLD Getting Started with EM.Cube]]

[[THE OLD What's New in EM.Cube 2016?]]

[[THE OLD Defining Simulation Observables & Visualizing Output Data]]

---------------------------------

[[V&V Article 6: Using EM.Cube And NeoScan System Together For Antenna Design]]

[[Installing EM.Cube]]

[[EM.Cube FAQ]]

----------------------------------------------------------------------------------------

These are all old stuff:

[[NeoScan_Complete]]

[[NeoScan Manuals]]

[[NeoScan Manual Part A: Getting Started]]

[[OLD What's New in EM.Cube R18.1?]]

<table>
<tr>
<td>
{|class="wikitable"
|-
! [[EM.Cube]]
|-
|[[File:emcubePAGE.png |225px | link=EM.Cube]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | RF.Spice A/D]]
|-
| [[File:RfspicePAGE New.png |277px | link=RF.Spice A/D | RF.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | B2.Spice A/D]]
|-
| [[File:B2spicePAGE.png |226px | link=RF.Spice A/D | B2.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[NeoScan | NeoScan]]
|-
| [[File:NeoScan_Product.png |245px | link=NeoScan | NeoScan ]]
|-
|}
</td>
</tr>
</table>

----

[[Old Gateway]]

[[Old EM.Cube Page]]

[[Old Digital Glossary]]

----

[[Image:Back_icon.png|40px]] '''[[Main_Page | Back to Emagtech Wiki Gateway]]'''

New Tutorials

2019-10-04T18:36:49Z

Kazem Sabet:

== EM.Cube Tutorials ==

Each tutorial lesson listed below walks you through the basic features of one of [[EM.Cube]]'s computational modules:

----------------------------------------------------------------------------------------

These are the new pages added or modified for [[EM.Cube]] Release R17:

[[New PO Theory]]

[[What's New in EM.Cube R19.1]]

[[EM.Terrano Tutorial Lesson 4: Analyzing Indoor Propagation Inside a Building Model with Penetrable Walls]]

[[EM.Terrano Tutorial Lesson 9: A SBR Channel Analysis of An Urban Scene]]

[[EM.Terrano Tutorial Lesson 10: Modeling A Mobile Communications Link]]

----------------------------------------------------------------------------------------

These are the old [[EM.Cube]] documentation pages:

[[The Old EM.Cube Wiki Start Page]]

[[THE OLD Getting Started with EM.Cube]]

[[THE OLD What's New in EM.Cube 2016?]]

[[THE OLD Defining Simulation Observables & Visualizing Output Data]]

---------------------------------

[[V&V Article 6: Using EM.Cube And NeoScan System Together For Antenna Design]]

[[Installing EM.Cube]]

[[EM.Cube FAQ]]

----------------------------------------------------------------------------------------

These are all old stuff:

[[NeoScan_Complete]]

[[NeoScan Manuals]]

[[NeoScan Manual Part A: Getting Started]]

<table>
<tr>
<td>
{|class="wikitable"
|-
! [[EM.Cube]]
|-
|[[File:emcubePAGE.png |225px | link=EM.Cube]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | RF.Spice A/D]]
|-
| [[File:RfspicePAGE New.png |277px | link=RF.Spice A/D | RF.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | B2.Spice A/D]]
|-
| [[File:B2spicePAGE.png |226px | link=RF.Spice A/D | B2.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[NeoScan | NeoScan]]
|-
| [[File:NeoScan_Product.png |245px | link=NeoScan | NeoScan ]]
|-
|}
</td>
</tr>
</table>

----

[[Old Gateway]]

[[Old EM.Cube Page]]

[[Old Digital Glossary]]

----

[[Image:Back_icon.png|40px]] '''[[Main_Page | Back to Emagtech Wiki Gateway]]'''

File:EM wave.png

2019-07-10T23:16:46Z

Kazem Sabet: Kazem Sabet uploaded a new version of "File:EM wave.png"

File:EM wave.png

2019-07-10T23:14:57Z

Kazem Sabet: Kazem Sabet uploaded a new version of "File:EM wave.png"

What's New in EM.Cube R19.1

2019-05-19T19:20:42Z

Kazem Sabet: /* New EM.Ferma (Static) Features */

What's New in EM.Cube R19.1

2019-05-19T19:13:26Z

Kazem Sabet: /* New EM.Terrano (Ray Tracing) Features */

What's New in EM.Cube R19.1

2019-05-19T19:04:15Z

Kazem Sabet: /* New EM.Tempo (FDTD) Features */

What's New in EM.Cube R19.1

2019-05-19T19:00:08Z

Kazem Sabet: /* New EM.Illumina (Physical Optics) Features */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R19.1 Release At A Glance ===

The new [[EM.Cube]] R19.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New plane wave source in the 3D SBR field solver
*New far-field observables including radiation pattern and bistatic and monostatic RCS in the 3D SBR field solver based on equivalent Huygens surface integration
*Improved ray angular resolution for SBR simulation of large propagation scenes in [[EM.Terrano]]
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with terrain smoothing filters
*New phased array capability at both transmitter and receiver nodes
*Improved digital waveform capability including maximum bit error rate specification
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas using the polarimatrix solver
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R19.1

2019-05-19T18:59:53Z

Kazem Sabet: /* New EM.Terrano (Ray Tracing) Features */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R19.1 Release At A Glance ===

The new [[EM.Cube]] R19.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New plane wave source in the 3D SBR field solver
*New far-field observables including radiation pattern and bistatic and monostatic RCS in the 3D SBR field solver based on equivalent Huygens surface integration
*Improved ray angular resolution for SBR simulation of large propagation scenes in [[EM.Terrano]]
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with terrain smoothing filters
*New phased array capability at both transmitter and receiver nodes
*Improved digital waveform capability including maximum bit error rate specification
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas using the polarimatrix solver
*New polarimetric scattering matrix sweep simulation as a special type of the RCS observable

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R19.1

2019-05-19T18:53:05Z

Kazem Sabet: /* New EM.Illumina (Physical Optics) Features */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R19.1 Release At A Glance ===

The new [[EM.Cube]] R19.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New plane wave source in the 3D SBR field solver
*New far-field observables including radiation pattern and bistatic and monostatic RCS in the 3D SBR field solver based on equivalent Huygens surface integration
*Improved ray angular resolution for SBR simulation of large propagation scenes in [[EM.Terrano]]
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with terrain smoothing filters
*New phased array capability at both transmitter and receiver nodes
*Improved digital waveform capability including maximum bit error rate specification
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas using the polarimatrix solver

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*New improved formulation of lossy dielectric surfaces and dielectric-coated PEC objects based on the method of equivalent current approximation (MECA)
*New Gaussian beam sources
*Huygens source arrays with amplitude and phase distribution

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R19.1

2019-05-19T18:51:10Z

Kazem Sabet: /* New EM.Terrano (Ray Tracing) Features */

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R19.1 Release At A Glance ===

The new [[EM.Cube]] R19.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New plane wave source in the 3D SBR field solver
*New far-field observables including radiation pattern and bistatic and monostatic RCS in the 3D SBR field solver based on equivalent Huygens surface integration
*Improved ray angular resolution for SBR simulation of large propagation scenes in [[EM.Terrano]]
*New 2D long-haul channel analyzer incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler with terrain smoothing filters
*New phased array capability at both transmitter and receiver nodes
*Improved digital waveform capability including maximum bit error rate specification
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas using the polarimatrix solver

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*Improved, more accurate formulation of impedance surfaces in GO-PO and IPO solvers
*Four impedance surface types: dielectric-coated PEC, imperfect conductor, high refractive index medium interface and fixed-impedance surface

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R19.1

2019-05-19T18:47:16Z

Kazem Sabet:

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R19.1 Release At A Glance ===

The new [[EM.Cube]] R19.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New plane wave source in [[EM.Terrano]]’s SBR simulator
*New far-field observables including radiation pattern and bistatic and monostatic RCS in [[EM.Terrano]]’s SBR simulator based on equivalent Huygens surface integration
*Improved ray angular resolution for SBR simulation of large propagation scenes in [[EM.Terrano]]
*New 2D long-haul channel analyzer in [[EM.Terrano]] incorporating spherical earth, knife edge diffraction, rough surface diffusion and atmospheric effects
*New 2D terrain profiler in [[EM.Terrano]] with terrain smoothing filters
*New phased array capability in [[EM.Terrano]] at both transmitter and receiver nodes
*Improved digital waveform capability in [[EM.Terrano]] including maximum bit error rate specification
*Improved rotational sweep with simultaneous rotation of transmit and receive antennas in [[EM.Terrano]]

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*Improved, more accurate formulation of impedance surfaces in GO-PO and IPO solvers
*Four impedance surface types: dielectric-coated PEC, imperfect conductor, high refractive index medium interface and fixed-impedance surface

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

What's New in EM.Cube R19.1

2019-05-19T18:45:46Z

Kazem Sabet: Created page with "720px <strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong> <strong><font color="#70798..."

[[Image:Splash-generic2.jpg|right|720px]]
<strong><font color="#07417e" size="4">MODULAR 3D ELECTROMAGNETIC SIMULATION SUITE <br /></font></strong>
<strong><font color="#707983" size="4">      THAT GROWS WITH YOUR MODELING NEEDS</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

=== EM.Cube R18.1 Release At A Glance ===

The new [[EM.Cube]] R18.1 release is the most powerful electromagnetic simulation suite EMAG Technologies Inc. has ever produced in its history of more than two decades. The new release offers a combination of state-of-the-art simulation capabilities that reflect the latest advances in computational electromagnetics (CEM) as well as productivity features requested by our valued users.

=== New EM.Tempo (FDTD) Features ===

*New gyrotropic materials including biased ferrites and magnetoplasmas
*Conversion of Drude conductors to equivalent isotropic plasmas
*New inhomogeneous dielectric material properties defined as mathematical or Python expressions/functions of 3D spatial coordinates (x,y,z)
*New streamlined way of defining voxel-based dielectric materials using a Python function for retrieving data from a 3D Cartesian (voxel) database
*New arbitrarily oriented Hertzian short dipole sources compatible with [[EM.Cube]]'s other computational modules
*Import of wire current solutions from [[EM.Libera]] as a set of Hertzian short dipole sources
*New wire (filamentary) current sources parallel to one of the principal axes with a uniform, triangular or sinusoidal profile
*Generalized lumped voltage sources on any PEC line object with an arbitrary orientation
*Improved and streamlined multi-plane-wave source excitation including import of 3D polarimetric ray solutions from [[EM.Terrano]]
*Conversion of zero-amplitude sources and ports to resistive termination loads (e.g. for modeling receiver antennas)
*Improved "Fast Ports" capability for accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation/extrapolation
*Extension of "Fast Ports" capability to multiport structures
*Extension of "Fast Ports" to distributed sources and microstrip, CPW, coaxial and waveguide ports
*New collocated series RL and parallel RC lumped devices on PEC lines parallel to one of the principal axes
*New active one-port and two-port Netlist-based lumped circuits on PEC lines parallel to one of the principal axes
*Streamlined Netlist generation for multiple lumped and distributed active one-port and two-port devices
*Allowing subcircuits with local node indexing in Netlist definitions
*New method of using nonlinear dependent B-type sources in Netlist definitions
*Extension of Netlist definitions to all XSPICE parts and subcircuit-model-based devices including system-level behavioral models (virtual blocks)
*Full compatibility with Netlist files generated by [[RF.Spice A/D]] and one-click loading of imported Netlist files
*Allowing Python functions/expressions in the Netlist definition of lumped and distributed active devices
*New distributed Huygens sources
*New fast frequency and angular sweeps of periodic structures with oblique incidence using an existing dispersion sweep database
*New streamlined single-run wideband multi-frequency observables with data management options (field sensors, radiation patterns, RCS and Huygens surfaces)
*New "Polarimetric Scattering Matrix" sweep simulation as a special type of the RCS observable
*Computation of total port voltages, total port currents and total port powers in both time and frequency domains for multiport structures
*New standard output parameters for port voltages, port currents and port powers at the center frequency of the project
*Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes
*New volumetric field sensor observables
*Computation of the total electric and magnetic energy, total dissipated power (Ohmic loss) and total SAR for volumetric field sensors
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene
*New option for sampling the field components of temporal field probes at the boundary of the Yee cell or at its center

=== New EM.Terrano (Ray Tracing) Features ===

*New digital modulation schemes with 17 waveform types and computation of Eb/N0 and bit error rate (BER)
*New standard output parameters for SNR, Eb/N0 and BER of the selected receiver with instant update upon changing receiver index
*Fast broadband frequency sweep of the propagation scene with uniformly spaced or discrete frequency samples in a single SBR simulation run
*New option for using multi-frequency radiation patterns in frequency sweeps
*New option for visualizing 3D radiation patterns overlaid on the propagation scene
*Complete polarimetric (theta-phi) characterization of the propagation channel for MIMO analysis
*New "almost real-time" Polarimatrix solver using an existing 3D ray database as an alternative to physical ray tracing
*Real-time transmitter sweep for modeling mobile transmitters using the new Polarimatrix solver
*Real-time rotational sweep for modeling beam scanning using the new Polarimatrix solver
*Real-time mobile (point-to-point) sweep simulation of transmitter-receiver pairs using the new Polarimatrix solver
*New Mobile Path wizard based on existing nodal curves or imported 3D spatial Cartesian data files
*New Point Scatterer sets with imported polarimetric scattering matrix data files
*New Radar Simulator generating a ray tracing solution of bistatic and monostatic radar system configurations
*Improved "Random City" wizard with a larger number of building parameters
*Improved "Basic Link" wizard with parameterized transmitter and receiver heights
*New distributed transmitters and receivers using Huygens sources

=== New EM.Ferma (Static) Features ===

*New thermal simulation engine (heat conduction and convection) for computation of steady-state temperature distribution and heat flux density
*New inhomogeneous dielectric/magnetic/insulator material properties defined as standard mathematical or Python expressions/functions of 3D spatial coordinates
*New volume heat source defined as a standard mathematical or Python expression/function of 3D spatial coordinates
*Import of SAR or dissipated power density data from [[EM.Tempo]] as a spatially distributed volume heat source
*Computation of electric and magnetic energy densities, dissipated power density (Ohmic loss), and thermal energy density on field sensor planes
*New mutual inductance field integral
*New (alternative) capacitance and inductance field integrals defined based on energy
*New (alternative) resistance field integrals defined based on Ohmic power loss
*New thermal flux and thermal energy field integrals
*New standard output parameters for all the 18 field integral types
*New volumetric field sensor observables
*3D visualization of surface and volumetric spatial Cartesian data overlaid on the scene

=== New EM.Picasso (Planar MoM) Features ===

*Improved planar mesh generation for structures with vertical vias of irregular shape and arrays of via objects
*New capability of handling edge vias and short thin vertical walls (fins)

=== New EM.Illumina (Physical Optics) Features ===

*Improved, more accurate formulation of impedance surfaces in GO-PO and IPO solvers
*Four impedance surface types: dielectric-coated PEC, imperfect conductor, high refractive index medium interface and fixed-impedance surface

=== New Miscellaneous CubeCAD Features ===

*Expanded material list with mechanical and thermal properties
*New list of available standard output parameters based on the project's observables
*Improved and enhanced custom (user-defined) output parameters that can be updated instantly at post-processing
*New functionality added to "Consolidate" tool for converting special transform objects to generic solid, surface or curve objects
*Improved "Random Group (Cloud)" tool for more efficient Monte Carlo simulations
*New capability added to "Roughen" tool for converting random roughened surfaces or objects to Polymesh objects for the purpose of freezing or export
*New expanded graph controls for Matlab-style 2D and 3D plot types
*New option to enable/disable 3D visualization of far-field data during sweep simulations
*New option for arbitrary translation and scaling of 3D radiation and RCS patterns in the scene
*Enhanced array factor with phase progression for the radiation pattern observable associated with a single radiating element

=== New Python Capabilities ===

*New startup Python script
*New Python commands for project and file management
*New Python commands for getting and setting individual properties of geometric objects
*New Python commands for accessing individual objects from the navigation tree
*New Python commands for identifying and accessing material groups and their object members in the navigation tree
*New Python commands for getting the coordinates of nodes of a nodal curve
*New Python command for aligning one of the six faces of the bounding box of an object at a certain coordinate
*New Python commands for retrieving the value of a standard or custom output parameter
*New Python command for setting the boundary conditions of [[EM.Ferma]]
*New Python command for setting up a thermal simulation in [[EM.Ferma]]
*New Python commands for defining all the 18 types of field integrals in [[EM.Ferma]]
*New Python command for creating generic spatial Cartesian data in CubeCAD, [[EM.Tempo]] and [[EM.Ferma]]
*New Python functions for translating, rotating, scaling, aligning and mirroring all the objects in the project workspace
*New Python function for rotating a radiation pattern
*New Python function for computing the radiation pattern of a generalized 3D array
*New Python function for generating the radiation pattern of a Huygens surface data file
*New Python functions for summing, differencing and scaling of .RAD, .RCS, .SEN, .CAR, .HUY and .COV data files
*New Python functions for averaging a set of radiation pattern, RCS or received power coverage data files
*New Python function for extracting a portion of a field sensor or a Cartesian data file
*New Python function for generating a Touchstone file from S-parameter data files
*Improved surrogate model generation based on the high-dimensional model representation (HDMR) technique and association with Python functions of the same name
*Improved Python script for sweeping a Python function or a surrogate model with cubic spline interpolation
*Improved Python script for genetic algorithm (GA) optimization of a Python function or a surrogate model
*Improved Python script for Monte Carlo simulation of a Python function or a surrogate model and generation of probability density functions (PDF) based on Gaussian kernel density estimation (KDE)

=== Integration with NeoScan Field Measurement System ===

*Automated export of [[NeoScan]] field measurement data to [[EM.Cube]]
*Automated near-to-far-field transformation of the near-field data for computation of 3D radiation patterns
*Automated computation of antenna gain and radiation efficiency
*Automated generation of equivalent Huygens sources from measured near-field data
*Matlab-style visualization of measured output signal power in dBm corresponding to individual-component and total field maps

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#EM.Cube R18.1 Release At A Glance | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

New Tutorials

2019-05-19T18:45:10Z

Kazem Sabet: /* EM.Cube Tutorials */

== EM.Cube Tutorials ==

Each tutorial lesson listed below walks you through the basic features of one of [[EM.Cube]]'s computational modules:

----------------------------------------------------------------------------------------

These are the new pages added or modified for [[EM.Cube]] Release R17:

[[New PO Theory]]

[[What's New in EM.Cube R19.1]]

----------------------------------------------------------------------------------------

These are the old [[EM.Cube]] documentation pages:

[[The Old EM.Cube Wiki Start Page]]

[[THE OLD Getting Started with EM.Cube]]

[[THE OLD What's New in EM.Cube 2016?]]

[[THE OLD Defining Simulation Observables & Visualizing Output Data]]

---------------------------------

[[V&V Article 6: Using EM.Cube And NeoScan System Together For Antenna Design]]

[[Installing EM.Cube]]

[[EM.Cube FAQ]]

----------------------------------------------------------------------------------------

These are all old stuff:

[[NeoScan_Complete]]

[[NeoScan Manuals]]

[[NeoScan Manual Part A: Getting Started]]

<table>
<tr>
<td>
{|class="wikitable"
|-
! [[EM.Cube]]
|-
|[[File:emcubePAGE.png |225px | link=EM.Cube]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | RF.Spice A/D]]
|-
| [[File:RfspicePAGE New.png |277px | link=RF.Spice A/D | RF.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[RF.Spice A/D | B2.Spice A/D]]
|-
| [[File:B2spicePAGE.png |226px | link=RF.Spice A/D | B2.Spice A/D]]
|-
|}
</td>
<td>   </td>
<td>
{|class="wikitable"
|-
! [[NeoScan | NeoScan]]
|-
| [[File:NeoScan_Product.png |245px | link=NeoScan | NeoScan ]]
|-
|}
</td>
</tr>
</table>

----

[[Gateway 2015]]

[[Old B2.Spice A/D Site]]

[[Old RF.Spice Site]]

[[Old Gateway]]

[[Old EM.Cube Page]]

[[Old Digital Glossary]]

----

[[Image:Back_icon.png|40px]] '''[[Main_Page | Back to Emagtech Wiki Gateway]]'''

EM.Terrano Tutorial Lesson 1: Analyzing A Basic Line-Of-Sight Propagation Scene

2019-05-18T18:35:56Z

Kazem Sabet: /* What You Will Learn */

{{projectinfo|Tutorial| Analyzing A Basic Line-Of-Sight Propagation Scene|Terrano L1 Fig title.png|In this project, the basic concepts of EM.Terrano are demonstrated, and a simple line-of-sight link will be analyzed in the free space.|

*Point Object
*Array Object
*Base Location Set
*Transmitter Set
*Receiver Set
*Received Power Coverage Map
*Path Loss
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/EMTerrano_Lesson1.zip EMTerrano_Lesson1}} }}

== What You Will Learn ==

In this tutorial you will define transmitter and receiver sets based on point objects and arrays of base points. You will learn how to run an SBR ray tracing analysis of your propagation scene and examine the individual rays received by each receiver. You will learn how to enable and disable the global ground.

{{Note|We strongly recommend that you read through the first few tutorials and study them carefully before setting up your own projects.}}

[[Image:Back_icon.png|30px]] '''[[EM.Terrano | Back to EM.Terrano Manual]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | Back to EM.Terrano Tutorial Gateway]]'''

[[Image:Download2x.png|30px]] '''[http://www.emagtech.com/downloads/ProjectRepo/EMTerrano_Lesson1.zip Download projects related to this tutorial lesson]'''

== Getting Started ==

Open the [[EM.Cube]] application by double-clicking on its icon on your desktop. By default, [[EM.Cube]] opens a blank project with the name “UntitledProj0” in its [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] Module. You can start drawing objects and build up your physical structure right away. Or you can initiate a new project by selecting the <b>New</b> [[Image:fdtd_newb.png]] button of the System Toolbar or using the keyboard shortcut {{key|Ctrl+N}}. This opens up the '''New Project Dialog''', where you can enter a title for your new project and set its path on your hard drive. From the same dialog, you can also set the project’s Length Units, Frequency Units, Center Frequency and Bandwidth.

<table>
<tr>
<td> [[Image:Terrano L1 Fig1.png|thumb|left|720px|The project workspace.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig2.png|thumb|left|720px|The New Project dialog.]] </td>
</tr>
</table>

For this tutorial lesson, set the following parameters in the new project dialog:

<div class="noprint" style="float:left;margin-right:10px">
{| border="1" class="wikitable"
|+ Starting Parameters
|-
! Name
| EMTerrano_Lesson1
|-
! Length Units
| Meters
|-
! Frequency Units
| GHz
|-
! Center Frequency
| 1GHz
|-
! Bandwidth
| 1GHz
|}
</div>

<div class="noprint" style="clear:both"></div>

Click the {{key|Create}} button of the dialog to accept the settings. A new project folder with your given name is immediately created at your specified path.

To navigate to [[EM.Terrano]], simply select its icon from the '''Module Toolbar''' on the left side of the screen. Selecting the module icon changes the contents of the navigation tree to reflect the types of objects supported by the current module.

==Planning the Propagation Scene==

A basic propagation scene in [[EM.Terrano]] involves at least one transmitter and one or more receivers. A transmitter is considered a source, and a receiver is considered an observable. Neither of them is a physical object. In order to define either a transmitter or a receiver in [[EM.Terrano]], first you need to a create a point object in your project workspace. The point object serves as the base location for the transmitter or receiver.

The geometrical objects you draw in the project workspace are grouped together in the navigation tree based on their common properties. The point objects your draw in the project workspace to represent base locations only have a color property and no other physical properties. This means that all the points belonging to the same base location group have the same color. Transmitters or receivers are associated with the existing base point sets already defined in the navigation tree. If a base point set is associated with a transmitter set, then it shouldn't be associated with a receiver set and vice versa.

{{Note|When you start a new project in [[EM.Terrano]] or any other [[EM.Cube]] module, "millimeter" is set as the default project units. In most propagation modeling problems, you will use "meter" or larger units. Make sure to set the proper length units for your project.}}

You can run an SBR ray tracing simulation with only a transmitter and a receiver in the project workspace. You don't need scatterers like buildings or terrain in your scene, although you can always add such items to the project workspace at any time.

== Disabling the Global Ground ==

[[EM.Terrano]] has a default global ground which consists of a dielectric half-space medium at Z < 0. The default material composition of the medium is a typical rock with ε<sub>r</sub> = 5 and σ = 0.005S/m. You can enable or disable the global ground or changes its material properties from [[EM.Terrano]]'s global ground settings dialog. To access this dialog, right-click on the '''Global Environment''' item under '''Computational Domain''' in the navigation tree and select '''Global Environment Settings...''' from the contextual menu. In this tutorial lesson, you are going to have a free-space link. Therefore, remove the check mark from the check box labeled '''Include Half-Space Ground (z<0)'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig7.png|thumb|left|600px|EM.Terrano's global ground settings dialog.]] </td>
</tr>
</table>

==Drawing the Point Sets==

You need to create two sets of point objects to represent base locations for your transmitter and receivers. But first you have to define a base point group in the navigation tree. Right-click on the '''Base Locations''' item under the “Physical Structure” section of the navigation tree and select '''Insert New Point Set…''' from the contextual menu. This opens up the Base Point Set Dialog. You can change the name of the point set or its color from this dialog. Accept the default settings (blue color) and click the {{key|OK}} button to close the dialog. You will notice that the name "BasePointSet_1" in the navigation tree is now displayed in bold letters. This means that this group is the active group in the project workspace. Any object you draw will belong to this group. Also, note that when a base point group is active in the navigation tree, all the buttons of the Object Toolbar are grayed out except for the Point Tool.

<table>
<tr>
<td> [[Image:Terrano L1 Fig8.png|thumb|left|480px|Defining a base location group in EM.Terrano's navigation tree.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig4.png|thumb|left|480px|The Base Point Set dialog.]] </td>
</tr>
</table>

Click the '''Point''' [[File:Point tool tn.png]] button of the Object Toolbar or select the menu item '''Object → Special → Point'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig3.png|thumb|left|720px|Selecting the Point Tool from EM.Terrano's Object Toolbar.]] </td>
</tr>
</table>

With the Point tool activated, click the origin (0,0,0) of the project workspace to place a point. The property dialog of the point object opens up at the lower right corner of the screen. From here you can fine-tune the coordinates of your point object, if necessary. Increase the height of the point to 2m. Click {{key|OK}} to accept the settings. A blue point appears in the project workspace, which has the default blue color of your point set.

<table>
<tr>
<td> [[Image:Terrano L1 Fig5.png|thumb|left|480px|The Point object's Property Dialog.]] </td>
</tr>
</table>

Now, define a second base location set called "BasePointSet_2", and choose an orange color for it. With the new point set group active, draw a point at the location (25m, 0, 2m) just like you did earlier. Next, you will build an array of points using the second orange point object you just created. Click on the point to select it. Its color turns yellow (i.e. the default selection color). Click the {{key|Array}} [[File:Array tool tn.png]] button of the Tools Toolbar or right-click on the object and select '''Array''' from the contextual menu, or simply use the keyboard shortcut {{key|A}}. The Array Dialog opens up. Enter 10, 1 and 1 for the <b>Element Count</b> along the X, Y and Z directions, respectively. Enter 5m, 0 and 0 for <b>Spacing</b> along the three axes, respectively. Click {{key|OK}} to accept the settings and close the Array dialog.

<table>
<tr>
<td> [[Image:Terrano L1 Fig9.png|thumb|left|720px|Selecting the Array Tool from EM.Terrano's Tools Toolbar.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig6.png|thumb|left|480px|The Array dialog.]] </td>
</tr>
</table>

You will see that your original orange point is replaced by a linear array of 10 points uniformly spaced at 5m along the X-axis. You will also notice a rectangular box with a green outline that encloses your point set. This is [[EM.Terrano]]’s domain box that defines the computational domain for ray tracing.

<table>
<tr>
<td> [[Image:Terrano L1 Fig10.png|thumb|left|720px|The geometry of the two point sets in the project workspace.]] </td>
</tr>
</table>

== Defining the Transmitter and Receiver Sets ==

Now you can define transmitter and a receiver sets and associated them with the base point sets you created earlier. Right-click on the '''Transmitters''' item under the '''Sources''' section of the navigation tree and select '''Insert New Transmitter Set...''' from the contextual menu. In the new transmitter set dialog, set "BasePointSet_1" from the drop-down dialog labeled '''Base Point Set'''. Then, Right-click on the '''Receivers''' item under the '''Observables''' section of the navigation tree and select '''Insert New Receiver Set...''' from the contextual menu. In the new receiver set dialog, set "BasePointSet_2" from the drop-down dialog labeled '''Base Point Set'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The transmitter definition dialog.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The receiver definition dialog.]] </td>
</tr>
</table>

You will see that a red ball appears around the blue point representing the transmitter and yellow balls appear around the orange points representing the receivers.

<table>
<tr>
<td> [[Image:Terrano L1 Fig15.png|thumb|left|550px|The free-space propagation scene with the transmitter and receiver sets.]] </td>
</tr>
</table>

Right-click on the '''TransmitterSet_1''' item in the navigation tree and select '''Properties...''' from the contextual menu. Examine the properties of the transmitter set. In the '''Radiator''' section under "Transmitter Properties" of the transmitter dialog, note that the default radiator type of the transmitter is '''Vertical Half-Wave Dipole'''. Similarly, right-click on the '''ReceiverSet_1''' item in the navigation tree and select '''Properties...''' from the contextual menu. Examine the properties of the receiver set. In the '''Radiator''' section of the receiver dialog, note that the default radiator type of the receiver is '''Vertical Half-Wave Dipole'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig13.png|thumb|left|600px|The transmitter set's property dialog.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig14.png|thumb|left|600px|The receiver set's property dialog.]] </td>
</tr>
</table>

== Running an SBR Ray Tracing Analysis ==

At this time, you are ready to run your first SBR simulation. Click the <b>Run</b> [[Image:fdtd_runb.png]] button of the Simulate Toolbar to open up the Simulation Run Dialog. Or alternatively, use the keyboard shortcut {{key|Ctrl+R}}, or the menu item '''Simulate → Run…''' The simplest simulation mode in [[EM.Terrano]] is “Single-Frequency Analysis” (Analysis). In this mode, your physical structure is taken “As Is” and its mesh (none in this case) is passed to the SBR simulation engine along with the necessary information regarding the sources and observables. Keep in mind that an SBR “Analysis” is a single-frequency simulation carried out at the specified center frequency of your project. To run the simulation, click the {{key|Run}} button of the Simulation Run Dialog.

<table>
<tr>
<td> [[Image:Terrano L1 Fig16.png|thumb|left|500px|EM.Terrano's Run Simulation Dialog.]] </td>
</tr>
</table>

A separate window pops up displaying messages from the simulation engine. Once the simulation has been completed, close the message window and return to the project workspace. The navigation tree is now populated with simulation results under the '''Receivers''' node. Go to the “Receivers” section of the navigation tree and click on the '''Rcvd Power''' item under the “ReceiverSet_1” node. This will display the received power coverage map of your receivers in the form of small colored square confetti slightly above the receivers. The color scale on the right shows the minimum and maximum power values of -30.5dBm and -39.5dBm corresponding to the closest and farthest receivers with respect to the transmitter. The legend box also shows the mean and standard deviation of the received powers, which are -35.65dBm and 2.82dBm, respectively.

<table>
<tr>
<td> [[Image:Terrano L1 Fig17.png|thumb|left|720px|The received power coverage map of the receiver set.]] </td>
</tr>
</table>

== Examining the Individual Receivers ==

Open the property dialog of your receiver set and select the first receiver of the array called "ReceiverSet_1_1". Then, click the {{key|Show Ray Data}} button to open up the Ray Data Dialog. You will see a table that lists all the rays received by the selected receiver along with the properties of those rays including their delay in nsec, Theta and Phi angles of arrival and departure in degrees and the amplitude and phase of the Theta and Phi field components of individual rays in dBV/m and degrees, respectively, and the ray's total power in dBm. You will also see two boxes that report the <b>Total Received Power</b> in dBm and the <b>Total Received Field</b> in dBV/m. The computed total received field is reported as -10.28dBV/m. You can change the active receiver index using the drop-down list labeled '''Select Element''' and examine the simulation data for all the receivers in your scene.

<table>
<tr>
<td> [[Image:Terrano L1 Fig20A.png|thumb|left|480px|Selecting receiver No. 1 in the receiver set dialog.]] </td>
<td> [[Image:Terrano L1 Fig20B.png|thumb|left|480px|Selecting receiver No. 10 in the receiver set dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig21A.png|thumb|left|720px|Viewing the properties of the rays of receiver No. 1 in the ray data dialog.]] </td>
</tr>
</table>

== Verifying Your Simulation Results ==

Since your propagation channel is the free space, you can use Friis' transmission formula to validate your simulation results. The Friis transmission formula relates the transmitted and received powers in a line-of-sight (LOS) propagation scenario:

<math> \frac{P_r}{P_t} = G_t G_r \left( \frac{\lambda_0}{4\pi r} \right) ^2 </math>

where r is the distance between the transmitter and receiver and G<sub>T</sub> and G<sub>R</sub> are the gains of the transmitting and receiving antennas, respectively.
According to the property dialog of the transmitter, the effective isotropically radiated power (EIRP) is:

<math> EIRP = P_t G_t = 29.88\text{dBm} </math>

The first receiver is located at a distance of 25m from the transmitter. The received power by this receiver is calculated to be:

<math> P_{r,dB} = EIRP_{dB} + G_{r,dB} + 20log_{10}\left( \frac{\lambda_0}{4\pi r} \right) = 29.88 + 0 + 20log_{10}\left( \frac{0.3}{(4\pi)(25)} \right) = -30.516\text{dBm}</math>

The last receiver is located at a distance of 25m + 9×5m = 70m from the transmitter. The received power by this receiver is calculated to be:

<math> P_{r,dB} = EIRP_{dB} + G_{r,dB} + 20log_{10}\left( \frac{\lambda_0}{4\pi r} \right) = 29.88 + 0 + 20log_{10}\left( \frac{0.3}{(4\pi)(70)} \right) = -39.46\text{dBm}</math>

== Plotting the Channel Path Loss ==

A list of all the 2D and 3D output data files generated at the end of a simulation can be viewed in [[EM.Terrano]]’s Data Manager. To open this dialog, click the <b>Data Manager</b> [[Image:fdtd_datamanagerb.png]] button of Simulate Toolbar, or use the keyboard shortcut {{key|Ctrl+D}}, or select the menu item '''Simulate → Data Manager'''. Select the file "SBR_ReceiverSet_1_PATHLOSS.DAT" from the list by clicking on its name and highlighting its row in the table. Click the {{key|Plot}} button of the dialog. A PyPlot graph window pops up that shows the variation of the path loss as a function of receiver index. If you move the mouse around the graph, you can read the values of the graph on the Status Bar of the graph window.

<table>
<tr>
<td>
[[Image:L1 Fig21B.png|thumb|720px|left|The data manager dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:L1 Fig21C.png|thumb|480px|left|Plot of the path loss vs. receiver index.]]
</td>
</tr>
</table>

The PyPlot window has a number of controls that let you change the settings of your graph using your mouse. For example, using the Pan/Zoom button [[Image:Py zoom icon.png]], you can pan the graph with the left mouse button and zoom it in or out with the right mouse button. A combination of the two operations usually gives you an ideal scaling of your graph.

<table>
<tr>
<td>
[[Image:L1 Fig21D.png|thumb|480px|left|A scaled version of the path loss graph.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#What_You_Will_Learn | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | Back to EM.Terrano Tutorial Gateway]]'''

EM.Terrano Tutorial Lesson 1: Analyzing A Basic Line-Of-Sight Propagation Scene

2019-05-18T18:35:22Z

Kazem Sabet: /* What You Will Learn */

{{projectinfo|Tutorial| Analyzing A Basic Line-Of-Sight Propagation Scene|Terrano L1 Fig title.png|In this project, the basic concepts of EM.Terrano are demonstrated, and a simple line-of-sight link will be analyzed in the free space.|

*Point Object
*Array Object
*Base Location Set
*Transmitter Set
*Receiver Set
*Received Power Coverage Map
*Path Loss
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/EMTerrano_Lesson1.zip EMTerrano_Lesson1}} }}

== What You Will Learn ==

In that tutorial you will define transmitter and receiver sets based on point objects and arrays of base points. You will learn how to run an SBR ray tracing analysis of your propagation scene and examine the individual rays received by each receiver. You will learn how to enable and disable the global ground.

{{Note|We strongly recommend that you read through the first few tutorials and study them carefully before setting up your own projects.}}

[[Image:Back_icon.png|30px]] '''[[EM.Terrano | Back to EM.Terrano Manual]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | Back to EM.Terrano Tutorial Gateway]]'''

[[Image:Download2x.png|30px]] '''[http://www.emagtech.com/downloads/ProjectRepo/EMTerrano_Lesson1.zip Download projects related to this tutorial lesson]'''

== Getting Started ==

Open the [[EM.Cube]] application by double-clicking on its icon on your desktop. By default, [[EM.Cube]] opens a blank project with the name “UntitledProj0” in its [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] Module. You can start drawing objects and build up your physical structure right away. Or you can initiate a new project by selecting the <b>New</b> [[Image:fdtd_newb.png]] button of the System Toolbar or using the keyboard shortcut {{key|Ctrl+N}}. This opens up the '''New Project Dialog''', where you can enter a title for your new project and set its path on your hard drive. From the same dialog, you can also set the project’s Length Units, Frequency Units, Center Frequency and Bandwidth.

<table>
<tr>
<td> [[Image:Terrano L1 Fig1.png|thumb|left|720px|The project workspace.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig2.png|thumb|left|720px|The New Project dialog.]] </td>
</tr>
</table>

For this tutorial lesson, set the following parameters in the new project dialog:

<div class="noprint" style="float:left;margin-right:10px">
{| border="1" class="wikitable"
|+ Starting Parameters
|-
! Name
| EMTerrano_Lesson1
|-
! Length Units
| Meters
|-
! Frequency Units
| GHz
|-
! Center Frequency
| 1GHz
|-
! Bandwidth
| 1GHz
|}
</div>

<div class="noprint" style="clear:both"></div>

Click the {{key|Create}} button of the dialog to accept the settings. A new project folder with your given name is immediately created at your specified path.

To navigate to [[EM.Terrano]], simply select its icon from the '''Module Toolbar''' on the left side of the screen. Selecting the module icon changes the contents of the navigation tree to reflect the types of objects supported by the current module.

==Planning the Propagation Scene==

A basic propagation scene in [[EM.Terrano]] involves at least one transmitter and one or more receivers. A transmitter is considered a source, and a receiver is considered an observable. Neither of them is a physical object. In order to define either a transmitter or a receiver in [[EM.Terrano]], first you need to a create a point object in your project workspace. The point object serves as the base location for the transmitter or receiver.

The geometrical objects you draw in the project workspace are grouped together in the navigation tree based on their common properties. The point objects your draw in the project workspace to represent base locations only have a color property and no other physical properties. This means that all the points belonging to the same base location group have the same color. Transmitters or receivers are associated with the existing base point sets already defined in the navigation tree. If a base point set is associated with a transmitter set, then it shouldn't be associated with a receiver set and vice versa.

{{Note|When you start a new project in [[EM.Terrano]] or any other [[EM.Cube]] module, "millimeter" is set as the default project units. In most propagation modeling problems, you will use "meter" or larger units. Make sure to set the proper length units for your project.}}

You can run an SBR ray tracing simulation with only a transmitter and a receiver in the project workspace. You don't need scatterers like buildings or terrain in your scene, although you can always add such items to the project workspace at any time.

== Disabling the Global Ground ==

[[EM.Terrano]] has a default global ground which consists of a dielectric half-space medium at Z < 0. The default material composition of the medium is a typical rock with ε<sub>r</sub> = 5 and σ = 0.005S/m. You can enable or disable the global ground or changes its material properties from [[EM.Terrano]]'s global ground settings dialog. To access this dialog, right-click on the '''Global Environment''' item under '''Computational Domain''' in the navigation tree and select '''Global Environment Settings...''' from the contextual menu. In this tutorial lesson, you are going to have a free-space link. Therefore, remove the check mark from the check box labeled '''Include Half-Space Ground (z<0)'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig7.png|thumb|left|600px|EM.Terrano's global ground settings dialog.]] </td>
</tr>
</table>

==Drawing the Point Sets==

You need to create two sets of point objects to represent base locations for your transmitter and receivers. But first you have to define a base point group in the navigation tree. Right-click on the '''Base Locations''' item under the “Physical Structure” section of the navigation tree and select '''Insert New Point Set…''' from the contextual menu. This opens up the Base Point Set Dialog. You can change the name of the point set or its color from this dialog. Accept the default settings (blue color) and click the {{key|OK}} button to close the dialog. You will notice that the name "BasePointSet_1" in the navigation tree is now displayed in bold letters. This means that this group is the active group in the project workspace. Any object you draw will belong to this group. Also, note that when a base point group is active in the navigation tree, all the buttons of the Object Toolbar are grayed out except for the Point Tool.

<table>
<tr>
<td> [[Image:Terrano L1 Fig8.png|thumb|left|480px|Defining a base location group in EM.Terrano's navigation tree.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig4.png|thumb|left|480px|The Base Point Set dialog.]] </td>
</tr>
</table>

Click the '''Point''' [[File:Point tool tn.png]] button of the Object Toolbar or select the menu item '''Object → Special → Point'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig3.png|thumb|left|720px|Selecting the Point Tool from EM.Terrano's Object Toolbar.]] </td>
</tr>
</table>

With the Point tool activated, click the origin (0,0,0) of the project workspace to place a point. The property dialog of the point object opens up at the lower right corner of the screen. From here you can fine-tune the coordinates of your point object, if necessary. Increase the height of the point to 2m. Click {{key|OK}} to accept the settings. A blue point appears in the project workspace, which has the default blue color of your point set.

<table>
<tr>
<td> [[Image:Terrano L1 Fig5.png|thumb|left|480px|The Point object's Property Dialog.]] </td>
</tr>
</table>

Now, define a second base location set called "BasePointSet_2", and choose an orange color for it. With the new point set group active, draw a point at the location (25m, 0, 2m) just like you did earlier. Next, you will build an array of points using the second orange point object you just created. Click on the point to select it. Its color turns yellow (i.e. the default selection color). Click the {{key|Array}} [[File:Array tool tn.png]] button of the Tools Toolbar or right-click on the object and select '''Array''' from the contextual menu, or simply use the keyboard shortcut {{key|A}}. The Array Dialog opens up. Enter 10, 1 and 1 for the <b>Element Count</b> along the X, Y and Z directions, respectively. Enter 5m, 0 and 0 for <b>Spacing</b> along the three axes, respectively. Click {{key|OK}} to accept the settings and close the Array dialog.

<table>
<tr>
<td> [[Image:Terrano L1 Fig9.png|thumb|left|720px|Selecting the Array Tool from EM.Terrano's Tools Toolbar.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig6.png|thumb|left|480px|The Array dialog.]] </td>
</tr>
</table>

You will see that your original orange point is replaced by a linear array of 10 points uniformly spaced at 5m along the X-axis. You will also notice a rectangular box with a green outline that encloses your point set. This is [[EM.Terrano]]’s domain box that defines the computational domain for ray tracing.

<table>
<tr>
<td> [[Image:Terrano L1 Fig10.png|thumb|left|720px|The geometry of the two point sets in the project workspace.]] </td>
</tr>
</table>

== Defining the Transmitter and Receiver Sets ==

Now you can define transmitter and a receiver sets and associated them with the base point sets you created earlier. Right-click on the '''Transmitters''' item under the '''Sources''' section of the navigation tree and select '''Insert New Transmitter Set...''' from the contextual menu. In the new transmitter set dialog, set "BasePointSet_1" from the drop-down dialog labeled '''Base Point Set'''. Then, Right-click on the '''Receivers''' item under the '''Observables''' section of the navigation tree and select '''Insert New Receiver Set...''' from the contextual menu. In the new receiver set dialog, set "BasePointSet_2" from the drop-down dialog labeled '''Base Point Set'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The transmitter definition dialog.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The receiver definition dialog.]] </td>
</tr>
</table>

You will see that a red ball appears around the blue point representing the transmitter and yellow balls appear around the orange points representing the receivers.

<table>
<tr>
<td> [[Image:Terrano L1 Fig15.png|thumb|left|550px|The free-space propagation scene with the transmitter and receiver sets.]] </td>
</tr>
</table>

Right-click on the '''TransmitterSet_1''' item in the navigation tree and select '''Properties...''' from the contextual menu. Examine the properties of the transmitter set. In the '''Radiator''' section under "Transmitter Properties" of the transmitter dialog, note that the default radiator type of the transmitter is '''Vertical Half-Wave Dipole'''. Similarly, right-click on the '''ReceiverSet_1''' item in the navigation tree and select '''Properties...''' from the contextual menu. Examine the properties of the receiver set. In the '''Radiator''' section of the receiver dialog, note that the default radiator type of the receiver is '''Vertical Half-Wave Dipole'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig13.png|thumb|left|600px|The transmitter set's property dialog.]] </td>
</tr>
<tr>
<td> [[Image:Terrano L1 Fig14.png|thumb|left|600px|The receiver set's property dialog.]] </td>
</tr>
</table>

== Running an SBR Ray Tracing Analysis ==

At this time, you are ready to run your first SBR simulation. Click the <b>Run</b> [[Image:fdtd_runb.png]] button of the Simulate Toolbar to open up the Simulation Run Dialog. Or alternatively, use the keyboard shortcut {{key|Ctrl+R}}, or the menu item '''Simulate → Run…''' The simplest simulation mode in [[EM.Terrano]] is “Single-Frequency Analysis” (Analysis). In this mode, your physical structure is taken “As Is” and its mesh (none in this case) is passed to the SBR simulation engine along with the necessary information regarding the sources and observables. Keep in mind that an SBR “Analysis” is a single-frequency simulation carried out at the specified center frequency of your project. To run the simulation, click the {{key|Run}} button of the Simulation Run Dialog.

<table>
<tr>
<td> [[Image:Terrano L1 Fig16.png|thumb|left|500px|EM.Terrano's Run Simulation Dialog.]] </td>
</tr>
</table>

A separate window pops up displaying messages from the simulation engine. Once the simulation has been completed, close the message window and return to the project workspace. The navigation tree is now populated with simulation results under the '''Receivers''' node. Go to the “Receivers” section of the navigation tree and click on the '''Rcvd Power''' item under the “ReceiverSet_1” node. This will display the received power coverage map of your receivers in the form of small colored square confetti slightly above the receivers. The color scale on the right shows the minimum and maximum power values of -30.5dBm and -39.5dBm corresponding to the closest and farthest receivers with respect to the transmitter. The legend box also shows the mean and standard deviation of the received powers, which are -35.65dBm and 2.82dBm, respectively.

<table>
<tr>
<td> [[Image:Terrano L1 Fig17.png|thumb|left|720px|The received power coverage map of the receiver set.]] </td>
</tr>
</table>

== Examining the Individual Receivers ==

Open the property dialog of your receiver set and select the first receiver of the array called "ReceiverSet_1_1". Then, click the {{key|Show Ray Data}} button to open up the Ray Data Dialog. You will see a table that lists all the rays received by the selected receiver along with the properties of those rays including their delay in nsec, Theta and Phi angles of arrival and departure in degrees and the amplitude and phase of the Theta and Phi field components of individual rays in dBV/m and degrees, respectively, and the ray's total power in dBm. You will also see two boxes that report the <b>Total Received Power</b> in dBm and the <b>Total Received Field</b> in dBV/m. The computed total received field is reported as -10.28dBV/m. You can change the active receiver index using the drop-down list labeled '''Select Element''' and examine the simulation data for all the receivers in your scene.

<table>
<tr>
<td> [[Image:Terrano L1 Fig20A.png|thumb|left|480px|Selecting receiver No. 1 in the receiver set dialog.]] </td>
<td> [[Image:Terrano L1 Fig20B.png|thumb|left|480px|Selecting receiver No. 10 in the receiver set dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Terrano L1 Fig21A.png|thumb|left|720px|Viewing the properties of the rays of receiver No. 1 in the ray data dialog.]] </td>
</tr>
</table>

== Verifying Your Simulation Results ==

Since your propagation channel is the free space, you can use Friis' transmission formula to validate your simulation results. The Friis transmission formula relates the transmitted and received powers in a line-of-sight (LOS) propagation scenario:

<math> \frac{P_r}{P_t} = G_t G_r \left( \frac{\lambda_0}{4\pi r} \right) ^2 </math>

where r is the distance between the transmitter and receiver and G<sub>T</sub> and G<sub>R</sub> are the gains of the transmitting and receiving antennas, respectively.
According to the property dialog of the transmitter, the effective isotropically radiated power (EIRP) is:

<math> EIRP = P_t G_t = 29.88\text{dBm} </math>

The first receiver is located at a distance of 25m from the transmitter. The received power by this receiver is calculated to be:

<math> P_{r,dB} = EIRP_{dB} + G_{r,dB} + 20log_{10}\left( \frac{\lambda_0}{4\pi r} \right) = 29.88 + 0 + 20log_{10}\left( \frac{0.3}{(4\pi)(25)} \right) = -30.516\text{dBm}</math>

The last receiver is located at a distance of 25m + 9×5m = 70m from the transmitter. The received power by this receiver is calculated to be:

<math> P_{r,dB} = EIRP_{dB} + G_{r,dB} + 20log_{10}\left( \frac{\lambda_0}{4\pi r} \right) = 29.88 + 0 + 20log_{10}\left( \frac{0.3}{(4\pi)(70)} \right) = -39.46\text{dBm}</math>

== Plotting the Channel Path Loss ==

A list of all the 2D and 3D output data files generated at the end of a simulation can be viewed in [[EM.Terrano]]’s Data Manager. To open this dialog, click the <b>Data Manager</b> [[Image:fdtd_datamanagerb.png]] button of Simulate Toolbar, or use the keyboard shortcut {{key|Ctrl+D}}, or select the menu item '''Simulate → Data Manager'''. Select the file "SBR_ReceiverSet_1_PATHLOSS.DAT" from the list by clicking on its name and highlighting its row in the table. Click the {{key|Plot}} button of the dialog. A PyPlot graph window pops up that shows the variation of the path loss as a function of receiver index. If you move the mouse around the graph, you can read the values of the graph on the Status Bar of the graph window.

<table>
<tr>
<td>
[[Image:L1 Fig21B.png|thumb|720px|left|The data manager dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:L1 Fig21C.png|thumb|480px|left|Plot of the path loss vs. receiver index.]]
</td>
</tr>
</table>

The PyPlot window has a number of controls that let you change the settings of your graph using your mouse. For example, using the Pan/Zoom button [[Image:Py zoom icon.png]], you can pan the graph with the left mouse button and zoom it in or out with the right mouse button. A combination of the two operations usually gives you an ideal scaling of your graph.

<table>
<tr>
<td>
[[Image:L1 Fig21D.png|thumb|480px|left|A scaled version of the path loss graph.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#What_You_Will_Learn | Back to the Top of the Page]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | Back to EM.Terrano Tutorial Gateway]]'''

EM.Terrano

2019-04-05T14:18:32Z

Kazem Sabet: /* Wave Propagation Modeling */

[[Image:Splash-prop.jpg|right|720px]]
<strong><font color="#4e1985" size="4">True 3D, Coherent, Polarimetric Ray Tracer That Simulates Very Large Urban Scenes In Just Few Minutes!</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

===EM.Terrano in a Nutshell ===

EM.Terrano is a physics-based, site-specific, wave propagation modeling tool that enables engineers to quickly determine how radio waves propagate in urban, natural or mixed environments. EM.Terrano's simulation engine is equipped with a fully polarimetric, coherent 3D ray tracing solver based on the Shooting-and-Bouncing-Rays (SBR) method, which utilizes geometrical optics (GO) in combination with uniform theory of diffraction (UTD) models of building edges. EM.Terrano lets you analyze and resolve all the rays transmitted from one ore more signal sources, which propagate in a real physical channel made up of buildings, terrain and other obstructing structures. EM.Terrano finds all the rays received by a receiver at a particular location in the physical site and computes their vectorial field and power levels, time delays, angles of arrival and departure, etc. Using EM.Terrano you can examine the connectivity of a communication link between any two points in a real specific propagation site.

Since its introduction in 2002, EM.Terrano has helped wireless engineers around the globe model the physical channel and the mechanisms by which radio signals propagate in various environments. EM.Terrano’s advanced ray tracing simulator finds the dominant propagation paths at each specific physical site. It calculates the true signal characteristics at the actual locations using physical databases of the buildings and terrain at a given site, not those of a statistically average or representative environment. The earlier versions of EM.Terrano's SBR solver relied on certain assumptions and approximations such as the vertical plane launch (VPL) method or 2.5D analysis of urban canyons with prismatic buildings using two separate vertical and horizontal polarizations. In 2014, we introduced a new fully 3D polarimetric SBR solver that accurately traces all the three X, Y and Z components of the electric fields (both amplitude and phase) at every point inside the computational domain. Using a 3D CAD modeler, you can now set up any number of buildings with arbitrary geometries, no longer limited to vertical prismatic shapes. Versatile interior wall arrangements allow indoor propagation modeling inside complex building configurations. The most significant recent development is a multicore parallelized SBR simulation engine that takes advantage of ultrafast k-d tree algorithms borrowed from the field of computer graphics and video gaming to achieve the ultimate speed and efficiency in geometrical optics ray tracing.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Basic Principles of SBR Ray Tracing | Basic SBR Theory]]'''.

<table>
<tr>
<td>
[[Image:Manhattan1.png|thumb|left|420px|A large urban propagation scene featuring lower Manhattan.]]
</td>
</tr>
</table>

=== EM.Terrano as the Propagation Module of EM.Cube ===

EM.Terrano is the ray tracing '''Propagation Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Terrano shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

With the seamless integration of EM.Terrano with [[EM.Cube]]'s other modules, you can now model complex antenna systems in [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]], and generate antenna radiation patterns that can be used to model directional transmitters and receivers at the two ends of your propagation channel. Conversely, you can analyze a propagation scene in EM.Terrano, collect all the rays received at a certain receiver location and import them as coherent plane wave sources to [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]].

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Terrano's SBR Solver ===

EM.Terrano's SBR simulation engine utilizes an intelligent ray tracing algorithm that is based on the concept of k-dimensional trees. A k-d tree is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are particularly useful for searches that involve multidimensional search keys such as range searches and nearest neighbor searches. In a typical large radio propagation scene, there might be a large number of rays emanating from the transmitter that may never hit any obstacles. For example, upward-looking rays in an urban propagation scene quickly exit the computational domain. Rays that hit obstacles on their path, on the other hand, generate new reflected and transmitted rays. The k-d tree algorithm traces all these rays systematically in a very fast and efficient manner. Another major advantage of k-d trees is the fast processing of multi-transmitters scenes.

EM.Terrano performs fully polarimetric and coherent SBR simulations with arbitrary transmitter antenna patterns. Its SBR simulation engine is a true asymptotic "field" solver. The amplitudes and phases of all the three vectorial field components are computed, analyzed and preserved throughout the entire ray tracing process from the source location to the field observation points. You can visualize the magnitude and phase of all six electric and magnetic field components at any point in the computational domain. In most scenes, the buildings and the ground or terrain can be assumed to be made of homogeneous materials. These are represented by their electrical properties such as permittivity ε<sub>r</sub> and electric conductivity σ. More complex scenes may involve a multilayer ground or multilayer building walls. In such cases, one can no longer use the simple reflection or transmission coefficient formulas for homogeneous medium interfaces. EM.Terrano calculates the reflection and transmission coefficients of multilayer structures as functions of incident angle, frequency and polarization and uses them at the respective specular points.

It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD). It is not a "full-wave" technique, and it does not provide a direct numerical solution of Maxwell's equations. SBR makes a number of assumptions, chief among them, a very high operational frequency such that the length scales involved are much larger than the operating wavelength. Under this assumed regime, electromagnetic waves start to behave like optical rays. Virtually all the calculations in SBR are based on far field approximations. In order to maintain a high computational speed for urban propagation problems, EM.Terrano ignores double diffractions. Diffractions from edges give rise to a large number of new secondary rays. The power of diffracted rays drops much faster than reflected rays. In other words, an edge-diffracted ray does not diffract again from another edge in EM.Terrano. However, reflected and penetrated rays do get diffracted from edges just as rays emanated directly from the sources do.

<table>
<tr>
<td>
[[Image:Multipath_Rays.png|thumb|left|500px|A multipath urban propagation scene showing all the rays collected by a receiver.]]
</td>
</tr>
</table>

== EM.Terrano Features at a Glance ==

=== Scene Definition / Construction ===

<ul>
<li>
Buildings/blocks with arbitrary geometries and material properties</li>
<li>
Buildings/blocks with impenetrable surfaces or penetrable surfaces using thin wall approximation</li>
<li>
Multilayer walls for indoor propagation scenes</li>
<li>
Penetrable volume blocks with arbitrary geometries and material properties</li>
<li>
Import of shapefiles and STEP, IGES and STL CAD model files for scene construction</li>
<li>
Terrain surfaces with arbitrary geometries and material properties and random rough surface profiles</li>
<li>
Import of digital elevation map (DEM) terrain models</li>
<li>
Python-based random city wizard with randomized building locations, extents and orientations</li>
<li>
Python-based wizards for generation of parameterized multi-story office buildings and several terrain scene types</li>
<li>
Standard half-wave dipole transmitters and receivers oriented along the principal axes</li>
<li>
Short Hertzian dipole sources with arbitrary orientation</li>
<li>
Isotropic receivers or receiver grids for wireless coverage modeling</li>
<li>
Radiator sets with 3D directional antenna patterns (imported from other modules or external files)</li>
<li>
Full three-axis rotation of imported antenna patterns</li>
<li>
Interchangeable radiator-based definition of transmitters and receivers (networks of transceivers)</li>
</ul>

=== Wave Propagation Modeling ===

<ul>
<li>
Fully 3D polarimetric and coherent Shoot-and-Bounce-Rays (SBR) simulation engine</li>
<li>
GTD/UTD diffraction models for diffraction from building edges and terrain</li>
<li>
Triangular surface mesh generator for discretization of arbitrary block geometries</li>
<li>
Super-fast geometrical/optical ray tracing using advanced k-d tree algorithms</li>
<li>
Intelligent ray tracing with user defined angular extents and resolution</li>
<li>
Ray reflection, edge diffraction and ray transmission through multilayer walls and material volumes</li>
<li>
Communication link analysis for superheterodyne transmitters and receivers</li>
<li>
17 digital modulation waveforms for the calculation of E<sub>b</sub>/N<sub>0</sub> and Bit error rate (BER)</li>
<li>
Incredibly fast frequency sweeps of the entire propagation scene in a single SBR simulation run</li>
<li>
Parametric sweeps of scene elements like building properties, or radiator heights and rotation angles</li>
<li>
Statistical analysis of the propagation scene</li>
<li>
Polarimetric channel characterization for MIMO analysis</li>
<li>
"Almost real-time" Polarimatrix solver using an existing ray database</li>
<li>
"Almost real-time" transmitter sweep using the Polarimatrix solver</li>
<li>
"Almost real-time" rotational sweep for modeling beam steering using the Polarimatrix solver</li>
<li>
"Almost real-time" mobile sweep for modeling mobile communications between Tx-Rx pairs along a mobile path using the Polarimatrix solver</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Standard output parameters for received power, path loss, SNR, E<sub>b</sub>/N<sub>0</sub> and BER at each individual receiver</li>
<li>
Graphical visualization of propagating rays in the scene</li>
<li>
Received power coverage maps</li>
<li>
Link connectivity maps (based on minimum required SNR and BER)</li>
<li>
Color-coded intensity plots of polarimetric electric field distributions</li>
<li>
Incoming ray data analysis at each receiver including delay, angles of arrival and departure</li>
<li>
Cartesian plots of path loss along defined paths</li>
<li>
Power delay profile of the selected receiver</li>
<li>
Polar stem charts of angles of arrival and departure of the selected receiver</li>
</ul>

== Building a Propagation Scene in EM.Terrano ==

=== The Various Elements of a Propagation Scene ===

A typical propagation scene in EM.Terrano consists of several elements. At a minimum, you need a transmitter (Tx) at some location to launch rays into the scene and a receiver (Rx) at another location to receive and collect the incoming rays. A transmitter and a receiver together make the simplest propagation scene, representing a free-space line-of-sight (LOS) channel. In EM.Terrano, a transmitter represents a point source, while a receiver represents a point observable. Both a transmitter and a receiver are associated with point objects, which are one of the many types of geometric objects you can draw in the project workspace. Your scene might involve more than one transmitter and possibly a large grid of receivers.

A more complicated propagation scene usually contains several buildings, walls, or other kinds of scatterers and wave obstructing objects. You model all of these elements by drawing geometric objects in the project workspace or by importing external CAD models. EM.Terrano does not organize the geometric objects of your project workspace by their material composition. Rather, it groups the geometric objects into blocks based on a common type of interaction with incident rays. EM.Terrano offer the following types of object blocks:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Block/Group Type
! scope="col"| Ray Interaction Type
! scope="col"| Object Types Allowed
! scope="col"| Notes
|-
| style="width:30px;" | [[File:impenet_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impenetrable Surface | Impenetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Basic building group for outdoor scenes
|-
| style="width:30px;" | [[File:penet_surf_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Surface | Penetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission in free space
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Behaves similar to impenetrable surface and uses thin wall approximation for generating transmitted rays, used to model hollow buildings with ray penetration, entry and exit
|-
| style="width:30px;" | [[File:terrain_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Terrain Surface | Terrain Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All surface geometric objects, no solid or curve objects
| style="width:300px;" | Behaves exactly like impenetrable surface but can change the elevation of all the buildings and transmitters and receivers located above it
|-
| style="width:30px;" | [[File:penet_vol_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Volume | Penetrable Volume]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission and ray attenuation inside homogeneous material media
| style="width:250px;" | All solid geometric objects, no surface or curve objects
| style="width:300px;" | Used to model wave propagation inside a volumetric material block, also used for creating individual solid walls and interior building partitions and panels in indoor scenes
|-
| style="width:30px;" | [[File:base_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Base Location Set | Base Location Set]]
| style="width:200px;" | Either ray generation or ray reception
| style="width:250px;" | Only point objects
| style="width:300px;" | Required for the definition of transmitters and receivers
|-
| style="width:30px;" | [[File:scatterer_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Scatterer Set | Point Scatterer Set]]
| style="width:200px;" | Ray reception and ray scattering
| style="width:250px;" | Only point, box and sphere objects
| style="width:300px;" | Required for the definition of point scatterers as targets in a radar simulation
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:200px;" | No ray interaction
| style="width:250px;" | All types of objects
| style="width:300px;" | Used for representing non-physical items
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

Impenetrable surfaces, penetrable surfaces, terrain surfaces and penetrable volumes represent all the objects that obstruct the propagation of electromagnetic waves (rays) in the free space. What differentiates them is the types of physical phenomena that are used to model their interaction with the impinging rays. EM.Terrano discretizes geometric objects into a number of flat facets. The field intensity, phase and power of the reflected and transmitted rays depend on the material properties of the obstructing facet. The specular surface of a facet can be modeled locally as a simple homogeneous dielectric half-space or as a multilayer medium. In that respect, all the obstructing objects such as buildings, walls, terrain, etc. behave in a similar way:

* They terminate an impinging ray and replace it with one or more new rays.
* They represent a specular interface between two media of different material compositions for calculating the reflection, transmission or diffraction coefficients.

An outdoor propagation scene typically involves several buildings modeled by impenetrable surfaces. Rays hit the facets of impenetrable buildings and bounce back, but they do not penetrate the object. It is assumed that the interior of such buildings are highly dissipative due to wave absorption or diffusion. An indoor propagation scene typically involves several walls, a ceiling and a floor arranged according to a certain building layout. Penetrable surfaces are used to model the exterior and interior walls of buildings. Rays reflect off these surfaces and diffract off their edges. They also penetrate the thin surface and continue their path in the free space on the other side of the wall. Terrain surfaces with irregular shapes or possibly random rough surfaces are used as an alternative to the flat global ground. You can also build mixed scenes involving both impenetrable and penetrable blocks or irregular terrain. In the context of a propagation scene, penetrable volumes are often used to model block of rain, fog or vegetation. Base location sets are used to geometrically represent point transmitters and point receivers in the project workspace.

Sometimes it is helpful to draw graphical objects as visual clues in the project workspace. These non-physical objects must belong to a virtual object group. Virtual objects are not discretized by EM.Terrano's mesh generator, and they are not passed onto the input data files of the SBR simulation engine.

<table>
<tr>
<td>
[[Image:PROP MAN2.png|thumb|left|720px|An urban propagation scene generated by EM.Terrano's "Random City" and "Basic Link" wizards. It consists of 25 cubic brick buildings, one transmitter and a large two-dimensional array of receivers. ]]
</td>
</tr>
</table>

=== Organizing the Propagation Scene by Block Groups ===

In EM.Terrano, all the geometric objects associated with the various scene elements like buildings, terrain surfaces and base location points are grouped together as blocks based on their common type. All the objects listed under a particular group in the navigation tree share the same color, texture and material properties. Once a new block group has been created in the navigation tree, it becomes the "Active" group of the project workspace, which is always displayed in bold letters. You can draw new objects under the active node. Any block group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.

<table>
<tr>
<td>
[[Image:PROP MAN1.png|thumb|left|480px|EM.Terrano's navigation tree.]]
</td>
</tr>
</table>

It is recommended that you first create block groups, and then draw new objects under the active block group. However, if you start a new EM.Terrano project from scratch, and start drawing a new object without having previously defined any block groups, a new default impenetrable surface group is created and added to the navigation tree to hold your new CAD object. You can always change the properties of a block group later by accessing its property dialog from the contextual menu. You can also delete a block group with all of its objects at any time.

{{Note|You can only import external CAD models (STEP, IGES, STL, DEM, etc.) only to the CubeCAD module. You can then transfer the imported objects from CubeCAD to EM.Terrano.}}

=== Moving Objects Among Different Block Groups ===

You can move any geometric object or a selection of objects from one block group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models of terrain or buildings from CubeCAD to EM.Terrano. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a block group called "Terrain_1" in EM.Terrano, then you have to select the menu item '''Move To → EM.Terrano → Terrain_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.

<table>
<tr>
<td>
[[Image:PROP MAN3.png|thumb|left|720px|Moving the terrain model of Mount Whitney originally imported from an external digital elevation map (DEM) file to EM.Terrano.]]
</td>
</tr>
<tr>
<td>
[[Image:PROP MAN4.png|thumb|left|720px|The imported terrain model of Mount Whitney shown in EM.Terrano's project workspace under a terrain group called "Terrain_1".]]
</td>
</tr>
</table>

=== Adjustment of Block Elevation on Underlying Terrain Surfaces ===

In EM.Terrano, buildings and all other geometric objects are initially drawn on the XY plane. In other words, the Z-coordinates of the local coordinate system (LCS) of all blocks are set to zero until you change them. Since the global ground is located a z = 0, your buildings are seated on the ground. When your propagation scene has an irregular terrain, you would want to place your buildings on the surface of the terrain and not buried under it. This can be done automatically as part of the definition of the block group. Open the property dialog of a block group and check the box labeled '''Adjust Block to Terrain Elevation'''. All the objects belonging to that block are automatically elevated in the Z direction such that their bases sit on the surface of their underlying terrain. In effect, the LCS of each of these individual objects is translated along the global Z-axis by the amount of the Z-elevation of the terrain object at the location of the LCS.

{{Note| You have to make sure that the resolution of your terrain, its variation scale and building dimensions are all comparable. Otherwise, on a rapidly varying high-resolution terrain, you will have buildings whose bottoms touch the terrain only at a few points and parts of them hang in the air.}}

<table>
<tr>
<td>
[[Image:PROP MAN5.png|thumb|left|480px|The property dialog of impenetrable surface showing the terrain elevation adjustment box checked.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN6.png|thumb|left|360px|A set of buildings on an undulating terrain without elevation adjustment.]]
</td>
<td>
[[Image:PROP MAN7.png|thumb|left|360px|The set of buildings on the undulating terrain after elevation adjustment.]]
</td>
</tr>
</table>

== EM.Terrano's Ray Domain & Global Environment ==

=== Why Do You Need a Finite Computational Domain? ===

The SBR simulation engine requires a finite computational domain for ray termination. All the stray rays that emanate from a source inside this finite domain and hit its boundaries are terminated during the simulation process. Such rays exit the computational domain and travel to the infinity, with no chance of ever reaching any receiver in the scene. When you define a propagation scene with various elements like buildings, walls, terrain, etc., a dynamic domain is automatically established and displayed as a green wireframe box that surrounds the entire scene. Every time you create a new object, the domain box is automatically adjusted and extended to enclose all the objects in the scene.

To change the ray domain settings, follow the procedure below:

* Open the Ray Domain Settings Dialog by clicking the '''Domain''' [[File:image025.jpg]] button of the '''Simulate Toolbar''', or by selecting '''Menu > Simulate > Computational Domain > Settings...''', or by right-clicking on the '''Ray Domain''' item of the navigation tree and selecting '''Domain Settings...''' from the contextual menu, or simply using the keyboard shortcut {{key|Ctrl+A}}.
* The size of the Ray domain is specified in terms of six '''Offset''' parameters along the ±X, ±Y and ±Z directions. The default value of all these six offset parameters is 10 project units. Change these values as you like.
* You can also change the color of the domain box using the {{key|Color}} button.
* After changing the settings, use the {{key|Apply}} button to make the changes effective while the dialog is still open.

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[[Image:PROP15.png|thumb|left|480px|EM.Terrano's domain settings dialog.]]
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=== Understanding the Global Ground ===

Most outdoor and indoor propagation scenes include a flat ground at their bottom, which bounces incident rays back into the scene. EM.Terrano provides a global flat ground at z = 0. The global ground indeed acts as an impenetrable surface that blocks the entire computational domain from the z = 0 plane downward. It is displayed as a translucent green plane at z = 0 extending downward. The color of the ground plane is always the same as the color of the ray domain. The global ground is assumed to be made of a homogeneous dielectric material with a specified permittivity ε<sub>r</sub> and electric conductivity σ. By default, a rocky ground is assumed with ε<sub>r</sub> = 5 and σ = 0.005 S/m. You can remove the global ground, in which case, you will have a free space scene. To disable the global ground, open up the "Global Ground Settings" dialog, which can be accessed by right clicking on the '''Global Ground''' item in the Navigation Tree and selecting '''Global Ground Settings... '''Remove the check mark from the box labeled '''"Include Half-Space Ground (z<0)"''' to disable the global ground. This will also remove the green translucent plane from the bottom of your scene. You can also change the material properties of the global ground and set new values for the permittivity and electric conductivity of the impenetrable, half-space, dielectric medium.

Alternatively, you can use EM.Terrano's '''Empirical Soil Model''' to define the material properties of the global ground. This model requires a number of parameters: Temperature in °C, and Volumetric Water Content, Sand Content and Clay Content all as percentage.

{{Note|To model a free-space propagation scene, you have to disable EM.Terrano's default global ground.}}

<table>
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[[Image:Global environ.png|thumb|left|720px|EM.Terrano's Global Environment Settings dialog.]]
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== Defining Point Transmitters & Point Receivers for Your Propagation Scene ==

=== The Nature of Transmitters & Receivers ===

In EM.Terrano, transmitters and receivers are indeed point radiators used for transmitting and receiving signals at different locations of the propagation scene. From a geometric point of view, both transmitters and receivers are represented by point objects or point arrays. These are grouped as base locations in the "Physical Structure" section of the navigation tree. As radiators, transmitters and receivers are defined by a radiator type with a certain far-field radiation pattern. Consistent with [[EM.Cube]]'s other computational modules, transmitters are categorizes as an excitation source, while receivers are categorized as a project observable. In other words, a transmitter is used to generate electromagnetic waves that propagate in the physical scene. A receiver, on the other hand, is used to compute the received fields and received signal power or signal-to-noise ratio (SNR). For this reason, transmitters are defined and listed under the "Sources" sections of the navigation tree, while receivers are defined and listed under the "Observables" section.

EM.Terrano provides three radiator types for point transmitter sets:

#Half-wave dipole oriented along one of the three principal axes
#Two collocated, orthogonally polarized, isotropic radiators
#User defined (arbitrary) antenna with imported far-field radiation pattern

EM.Terrano also provides three radiator types for point receiver sets:

#Half-wave dipole oriented along one of the three principal axes
#Polarization-matched isotropic radiator
#User defined (arbitrary) antenna with imported far-field radiation pattern

The default transmitter and receiver radiator types are both vertical (Z-directed) half-wave dipoles.

There are three different ways to define a transmitter set or a receiver set:

*By defining point objects or point arrays under physical base location sets in the navigation tree and then associating them with a transmitter or receiver set
*Using Python commands emag_tx, emag_rx, emag_tx_array, emag_rx_array, emag_tx_line and emag_rx_line
*Using the "Basic Link" wizard

=== Defining a Point Transmitter Set in the Formal Way ===

Transmitters act as sources in a propagation scene. A transmitter is a point radiator with a fully polarimetric radiation pattern defined over the entire 3D space in the standard spherical coordinate system. EM.Terrano gives you three options for the radiator associated with a point transmitter:

* Half-wave dipole
* Orthogonally polarized isotropic radiators
* User defined antenna pattern

By default, EM.Terrano assumes that your transmitter is a vertically polarized (Z-directed) resonant half-wave dipole antenna. This antenna has an almost omni-directional radiation pattern in all azimuth directions. It also has radiation nulls along the axis of the dipole. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. The second choice of two orthogonally polarized isotropic radiators is an abstract source that is used for polarimetric channel characterization as will be discussed later.

You can override the default radiator option and select any other kind of antenna with a more complicated radiation pattern. For this purpose, you have to import a radiation pattern data file to EM.Terrano. You can model any radiating structure using [[EM.Cube]]'s other computational modules, [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] or [[EM.Illumina]], and generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored in a specially formatted file with a "'''.RAD'''" file extension. This file contains columns of spherical φ and θ angles as well as the real and imaginary parts of the complex-valued far-zone electric field components '''E<sub>θ</sub>''' and '''E<sub>φ</sub>'''. The θ- and φ-components of the far-zone electric field determine the polarization of the transmitting radiator.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point transmitter set.}}

A transmitter set always needs to be associated with an existing base location set with one or more point objects in the project workspace. Therefore, you cannot define a transmitter for your scene before drawing a point object under a base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Point_Transmitter_Set | Point Transmitter Set]]'''.

<table>
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<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The point transmitter set definition dialog.]] </td>
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</table>

Once you define a new transmitter set, its name is added in the '''Transmitters''' section of the navigation tree. The color of all the base points associated with the newly defined transmitter set changes, and an additional little ball with the transmitter color (red by default) appears at the location of each associated base point. You can open the property dialog of the transmitter set and modify a number of parameters including the '''Source Power''' in Watts and the broadcast signal '''Phase''' in degrees. The default transmitter power level is 1W or 30dBm. There is also a check box labeled '''Use Custom Input Power''', which is checked by default. In that case, the power and phase boxes are enabled and you can change the default 1W power and 0° phase values as you wish. [[EM.Cube]]'s ".RAD" radiation pattern files usually contain the value of "Total Radiated Power" in their file header. This quantity is calculated based on the particular excitation mechanism that was used to generate the pattern file in the original [[EM.Cube]] module. When the "Use Custom Input Power" check box is unchecked, EM.Terrano will use the total radiated power value of the radiation file for the SBR simulation.

{{Note|In order to modify any of the transmitter set's parameters, first you need to select the "User Defined Antenna" option, even if you want to keep the vertical half-wave dipole as your radiator.}}

<table>
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[[File:NewTxProp.png|thumb|left|720px|The property dialog of a point transmitter set.]]
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Your transmitter in EM.Teranno is indeed more sophisticated than a simple radiator. It consists of a basic "Transmitter Chain" that contains a voltage source with a series source resistance, and connected via a segment of transmission line to a transmit antenna, which is used to launch the broadcast signal into the free space. The transmitter's property dialog allows you to define the basic transmitter chain. Click the {{key|Transmitter Chain}} button of the Transmitter Set dialog to open the transmitter chain dialog. As shown in the figure below, you can specify the characteristics of the baseband/IF amplifier, mixer and power amplifier (PA) including stage gains and impedance mismatch factors (IMF) as well as the characteristics of the transmission line segment that connects the PA to the antenna. Note that the transmit antenna characteristics are automatically filled using the contents of the imported radiation pattern data file. The transmitter Chain dialog also calculates and reports the "Total Transmitter Chain Gain" based on your input. When you close this dialog and return to the Transmitter Set dialog, you will see the calculated value of the Effective Isotropic Radiated Power (EIRP) of your transmitter in dBm.

{{Note| If you do not modify the default parameters of the transmitter chain, a 50-Ω conjugate match condition is assumed and the power delivered to the antenna will be -3dB lower than your specified baseband power.}}

<table>
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<td> [[File:NewTxChain.png|thumb|left|720px|EM.Terrano's point transmitter chain dialog.]] </td>
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</table>

=== Defining a Point Receiver Set in the Formal Way ===

Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate the far-zone electric fields and the total received power at the location of a receiver. You need to define at least one receiver in the scene before you can run a SBR simulation. Similar to a transmitter, a receiver is a point radiator, too. EM.Terrano gives you three options for the radiator associated with a point receiver set:

* Half-wave dipole
* Polarization matched isotropic radiator
* User defined antenna pattern

By default, EM.Terrano assumes that your receiver is a vertically polarized (Z-directed) resonant half-wave dipole antenna. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. An isotropic radiator has a perfect omni-directional radiation pattern in all azimuth and elevation directions. An isotropic radiator doesn't exist physically in the real world, but it can be used simply as a point in space to compute the electric field.

You may also define a complicated radiation pattern for your receiver set. In that case, you need to import a radiation pattern data file to EM.Terrano similar to the case of a transmitter set.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point receiver set.}}

Similar to transmitter sets, you define a receiver set by associating it with an existing base location set with one or more point objects in the project workspace. All the receivers belonging to the same receiver set have the same radiator type. A typical propagation scene contains one or few transmitters but usually a large number of receivers. To generate a wireless coverage map, you need to define an array of points as your base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Point_Receiver_Set | Point Receiver Set]]'''.

<table>
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<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The point receiver set definition dialog.]] </td>
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</table>

Once you define a new receiver set, its name is added to the '''Receivers''' section of the navigation tree. The color of all the base points associated with the newly defined receiver set changes, and an additional little ball with the receiver color (yellow by default) appears at the location of each associated base point. You can open the property dialog of the receiver set and modify a number of parameters.

<table>
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[[File:NewRxProp.png|thumb|left|720px|The property dialog of a point receiver set.]]
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In the Receiver Set dialog, there is a drop-down list labeled '''Selected Element''', which contains a list of all the individual receivers belonging to the receiver set. At the end of an SBR simulation, the button labeled {{key|Show Ray Data}} becomes enabled. Clicking this button opens the Ray Data dialog, where you can see a list of all the received rays at the selected receiver and their computed characteristics.

If you choose the "user defined antenna" option for your receiver set, it indeed consists of a basic "Receiver Chain" that contains a receive antenna connected via a segment of transmission line to the low-noise amplifier (LNA) that is terminated in a matched load. The receiver set's property dialog allows you to define the basic receiver chain. Click the {{key|Receiver Chain}} button of the Receiver Set dialog to open the receiver chain dialog. As shown in the figure below, you can specify the characteristics of the LNA such as its gain and noise figure in dB as well as the characteristics of the transmission line segment that connects the antenna to the LNA. Note that the receiving antenna characteristics are automatically filled from using contents of the radiation file. You have to enter values for antenna's '''Brightness Temperature''' as well as the temperature of the transmission line and the receiver's ambient temperature. The effective '''Receiver Bandwidth''' is assumed to be 100MHz, which you can change for the purpose of noise calculations. The Receive Chain dialog calculates and reports the "Noise Power" and "Total Receiver Chain Gain" based on your input. At the end of an SBR simulation, the receiver power and signal-noise ratio (SNR) of the selected receiver are calculated and they are reported in the receiver set dialog in dBm and dB, respectively. You can examine the properties of all the individual receivers and all the individual rays received by each receiver in your receiver set using the "Selected Element" drop-down list.

<table>
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<td> [[File:NewRxChain.png|thumb|left|720px|EM.Terrano's point receiver chain dialog.]] </td>
</tr>
</table>

=== Modulation Waveform and Detection ===

EM.Terrano allows you to define a digital modulation scheme for your communication link. There are currently 17 waveforms to choose from in the receiver set property dialog:

*OOK
*M-ary ASK
*Coherent BFSK
*Coherent QFSK
*Coherent M-ary FSK
*Non-Coherent BFSK
*Non-Coherent QFSK
*Non-Coherent M-ary FSK
*BPSK
*QPSK
*Offset QPSK
*M-ary PSK
*DBPSK
*pi/4 Gray-Coded DQPSK
*M-ary QAM
*MSK
*GMSK (BT = 0.3)

In the above list, you need to specify the '''No. Levels (M)''' for the Mary modulation schemes, from which the '''No. Bits per Symbol''' is determined. You can also define a bandwidth for the signal, which has a default value of 100MHz. Once the SNR of the signal is found, given the specified modulation scheme, the E<sub>b</sub>/N<sub>0</sub> parameter is determined, from which the bit error rate (BER) is calculated.

The Shannon – Hartley Equation estimates the channel capacity:

<math> C = B \log_2 \left( 1 + \frac{S}{N} \right) </math>

where B in the bandwidth in Hz, and C is the channel capacity (maximum data rate) expressed in bits/s.

The spectral efficiency of the channel is defined as

<math> \eta = \log_2 \left( 1 + \frac{S}{N} \right) </math>

The quantity E<sub>b</sub>/N<sub>0</sub> is the ratio of energy per bit to noise power spectral density. It is a measure of SNR per bit and is calculated from the following equation:

<math> \frac{E_b}{N_0} = \frac{ 2^\eta - 1}{\eta} </math>

where η is the spectral efficiency.

The relationship between the bit error rate and E<sub>b</sub>/N<sub>0</sub> depends on the modulation scheme and detection type (coherent vs. non-coherent). For example, for coherent QPSK modulation, one can write:

<math> P_b = 0.5 \; \text{erfc} \left( \sqrt{ \frac{E_b}{N_0} } \right) </math>

where P<sub>b</sub> is the bit error rate and erfc(x) is the complementary error function:

<math> \text{erfc}(x) = 1-\text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^2} dt </math>

The '''Minimum Required SNR''' parameter is used to determine link connectivity between each transmitter and receiver pair. If you check the box labeled '''Generate Connectivity Map''' in the receiver set property dialog, a binary map of the propagation scene is generated by EM.Terrano, in which one color represents a closed link and another represent no connection depending on the selected color map type of the graph. EM.Terrano also calculates the '''Max Permissible BER''' corresponding to the specified minimum required SNR and displays it in the receiver set property dialog.

=== A Note on EM.Terrano's Native Dipole Radiators ===

When you define a new transmitter set or a new receiver set, EM.Terrano assigns a vertically polarized half-wave dipole radiator to the set by default. The radiation pattern of this native dipole radiators is calculated using well-know expressions that are derived based on certain assumptions and approximations. For example, the far-zone electric field of a vertically-polarized dipole antenna can be expressed as:

<math> E_\theta(\theta,\phi) \approx j\eta_0 I_0 \frac{e^{-jk_0 r}}{2\pi r} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right] </math>

<math> E_\phi(\theta,\phi) \approx 0 </math>

where k<sub>0</sub> = 2π/λ<sub>0</sub> is the free-space wavenumber, λ<sub>0</sub> is the free-space wavelength, η<sub>0</sub> = 120π Ω is the free-space intrinsic impedance, I<sub>0</sub> is the current on the dipole, and L is the length of the dipole.

The directivity of the dipole antenna is given be the expression:

<math> D_0 \approx \frac{2}{F_1(k_0L) + F_2(k_0L) + F_3(k_0L)} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right]^2 </math>

with

<math> F_1(x) = \gamma + \text{ln}(x) - C_i(x) </math>

<math> F_2(x) = \frac{1}{2} \text{sin}(x) \left[ S_i(2x) - 2S_i(x) \right] </math>

<math> F_3(x) = \frac{1}{2} \text{cos}(x) \left[ \gamma + \text{ln}(x/2) + C_i(2x) - 2C_i(x) \right] </math>

where γ = 0.5772 is the Euler-Mascheroni constant, and C<sub>i</sub>(x) and S<sub>i</sub>(x) are the cosine and sine integrals, respectively:

<math> C_i(x) = - \int_{x}^{\infty} \frac{ \text{cos} \tau}{\tau} d\tau </math>

<math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>

In the case of a half-wave dipole, L = λ<sub>0</sub>/2, and D<sub>0</sub> = 1.643. Moreover, the input impedance of the dipole antenna is Z<sub>A</sub> = 73 + j42.5 Ω. These dipole radiators are connected via 50Ω transmission lines to a 50Ω source or load. Therefore, there is always a certain level of impedance mismatch that violates the conjugate match condition for maximum power.

<table>
<tr>
<td> [[File:Dipole radiators.png|thumb|720px|EM.Terrano's native half-wave dipole transmitter and receiver.]] </td>
</tr>
</table>

On the other hand, we you specify a user-defined antenna pattern for the transmitter or receiver sets, you import a 3D radiation pattern file that contains all the values of E<sub>θ</sub> and E<sub>φ</sub> for all the combinations of (θ, φ) angles. Besides the three native dipole radiators, [[EM.Cube]] also provides 3D radiation pattern files for three X-, Y- and Z-polarized half-wave resonant dipole antennas. These pattern data were generated using a full-wave solver like [[EM.Libera]]'s wire MOM solver. The names of the radiation pattern files are:

* DPL_STD_X.RAD
* DPL_STD_Y.RAD
* DPL_STD_Z.RAD

and they are located in the folder "\Documents\EMAG\Models" on your computer. Note that these are full-wave simulation data and do not involve any approximate assumptions. To use these files as an alternative to the native dipole radiators, you need to select the '''User Defined Antenna Pattern''' radio button as the the radiator type in the transmitter or receiver set property dialog.

=== A Note on the Rotation of Antenna Radiation Patterns ===

EM.Terrano's Transmitter Set dialog and Receiver Set dialog both allow you to rotate an imported radiation pattern. In that case, you need to specify the '''Rotation''' angles in degrees about the X-, Y- and Z-axes. It is important to note that these rotations are performed sequentially and in the following order: first a rotation about the X-axis, then a rotation about the Y-axis, and finally a rotation about the Z-axis. In addition, all the rotations are performed with respect to the "rotated" local coordinate systems (LCS). In other words, the first rotation with respect to the local X-axis transforms the XYZ LCS to a new primed X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS. The second rotation is performed with respect to the new Y<sup>′</sup>-axis and transforms the X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS to a new double-primed X<sup>′′</sup>Y<sup>′′</sup>Z<sup>′′</sup> LCS. The third rotation is finally performed with respect to the new Z<sup>′′</sup>-axis. The figures below shows single and double rotations.

<table>
<tr>
<td> [[File:PROP22B.png|thumb|300px|The local coordinate system of a linear dipole antenna.]] </td>
<td> [[File:PROP22C.png|thumb|600px|Rotating the dipole antenna by +90° about the local Y-axis.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[File:PROP22D.png|thumb|720px|Rotating the dipole antenna by +90° about the local X-axis and then by -45° by the local Y-axis.]] </td>
</tr>
</table>

=== Adjustment of Tx/Rx Elevation above a Terrain Surface ===

When your transmitters or receivers are located above a flat terrain like the global ground, their Z-coordinates are equal to their height above the ground, as the terrain elevation is fixed and equal to zero everywhere. In many propagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across the scene. In that case, you may want to place your transmitters or receivers at a certain height above the underlying ground. The Z-coordinate of a transmitter or receiver is now the sum of the terrain elevation at the base point and the specified height. EM.Terrano gives you the option to adjust the transmitter and receiver sets to the terrain elevation. This is done for individual transmitter sets and individual receiver sets. At the top of the Transmitter Dialog there is a check box labeled "'''Adjust Tx Sets to Terrain Elevation'''". Similarly, at the top of the Receiver Dialog there is a check box labeled "'''Adjust Rx Sets to Terrain Elevation'''". These boxes are unchecked by default. As a result, your transmitter sets or receiver sets coincide with their associated base points in the project workspace. If you check these boxes and place a transmitter set or a receiver set above an irregular terrain, the transmitters or receivers are elevated from the location of their associated base points by the amount of terrain elevation as can be seen in the figure below.

To better understand why there are two separate sets of points in the scene, note that a point array (CAD object) is used to create a uniformly spaced base set. The array object always preserves its grid topology as you move it around the scene. However, the transmitters or receivers associated with this point array object are elevated above the irregular terrain and no longer follow a strictly uniform grid. If you move the base set from its original position to a new location, the base points' topology will stay intact, while the associated transmitters or receivers will be redistributed above the terrain based on their new elevations.

<table>
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<td>
[[Image:PROP MAN8.png|thumb|left|640px|A transmitter (red) and a grid of receivers (yellow) adjusted above a plateau terrain surface. The underlying base point sets (blue and orange dots) associated with the adjusted transmitters and receivers on the terrain are also visible in the figure.]]
</td>
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</table>

== Discretizing the Propagation Scene in EM.Terrano ==

=== Why Do You Need to Discretize the Scene? ===

EM.Terrano's SBR solver uses a method known as Geometrical Optics (GO) in conjunction with the Uniform Theory of Diffraction (UTD) to trace the rays from their originating point at the source to the individual receiver locations. Rays may hit obstructing objects on their way and get reflected, diffracted or transmitted. EM.Terrano's SBR solver can only handle diffraction off linear edges and reflection from and transmission through planar interfaces. When an incident ray hits the surface of the obstructing object, a local planar surface assumption is made at the specular point. The assumptions of linear edges and planar facets obviously work in the case of a scene with cubic buildings and a flat global ground.

In many practical scenarios, however, your buildings may have curved surfaces, or the terrain may be irregular. EM.Terrano allows you to draw any type of surface or solid geometric objects such as cylinders, cones, etc. under impenetrable and penetrable surface groups or penetrable volumes. EM.Terrano's mesh generator creates a triangular surface mesh of all the objects in your propagation scene, which is called a facet mesh. Even the walls of cubic buildings are meshed using triangular cells. This enables EM.Terrano to properly discretize composite buildings made of conjoined cubic objects.

Unlike [[EM.Cube]]'s other computational modules, the density or resolution of EM.Terrano's surface mesh does not depend on the operating frequency and is not expressed in terms of the wavelength. The sole purpose of EM.Terrano's facet mesh is to discretize curved and irregular scatterers into flat facets and linear edges. Therefore, geometrical fidelity is the only criterion for the quality of a facet mesh. It is important to note that discretizing smooth objects using a triangular surface mesh typically creates a large number of small edges among the facets that are simply mesh artifacts and should not be considered as diffracting edges. For example, each rectangular face of a cubic building is subdivided into four triangles along the two diagonals. The four internal edges lying inside the face are obviously not diffracting edges. A lot of subtleties like these must be taken into account by the SBR solver to run accurate and computationally efficient simulations.

=== Generating the Facet Mesh ===

You can view and examine the discretized version of your scene's objects as they are sent to the SBR simulation engine. You can adjust the mesh resolution and increase the geometric fidelity of discretization by creating more and finer triangular facets. On the other hand, you may want to reduce the mesh complexity and send to the SBR engine only a few coarse facets to model your buildings. The resolution of EM.Terrano's facet mesh generator is controlled by the '''Cell Edge Length''' parameter, which is expressed in project length units. The default mesh cell size of 100 units might be too large for non-flat objects. You may have to set a smaller cell edge length in EM.Terrano's Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the curvature of your curved structures adequately.

<table>
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<td>
[[Image:prop_manual-29.png|thumb|left|480px|EM.Terrano's mesh settings dialog.]]
</td>
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</table>

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Facet_Mesh | EM.Terrano's Facet Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:UrbanCanyon2.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 100m.]] </td>
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<td> [[Image:UrbanCanyon3.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 10m.]] </td>
</tr>
</table>

== Running Ray Tracing Simulations in EM.Terrano ==

EM.Terrano provides a number of different simulation or solver types:

* 3D SBR Ray Tracer
* Channel Analyzer
* Polarimatrix Solver
* Radar Simulator

The first three simulation types are described below. For a description of EM.Terrano's Radar Simulator, follow this link.

=== Running a Single-Frequency SBR Analysis ===

Its main solver is the '''3D SBR Ray Tracer'''. Once you have set up your propagation scene in EM.Terrano and have defined sources/transmitters and observables/receivers for your scene, you are ready to run a SBR ray tracing simulation. You set the simulation mode in EM.Terrano's simulation run dialog. A single-frequency SBR analysis is a single-run simulation and the simplest type of ray tracing simulation in EM.Terrano. It involves the following steps:

* Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''. Wireless propagation problems usually require meter, mile or kilometer as the project unit.
* Create the blocks and draw the buildings at the desired locations.
* Keep the default ray domain and accept the default global ground or change its material properties.
* Define an excitation source and observables for your project.
* If you intend to use transmitters and receivers in your scene, first define the required base sets and then define the transmitter and receiver sets based on them.
* Run the SBR simulation engine.
* Visualize the coverage map and plot other data.

You can access EM.Terrano's Simulation Run dialog by clicking the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Simulate → Run...''' or using the keyboard shortcut {{key|Ctrl+R}}. When you click the {{key|Run}} button, a new window opens up that reports the different stages of the SBR simulation and indicates the progress of each stage. After the SBR simulation is successfully completed, a message pops up and prompts the completion of the process.

<table>
<tr>
<td>
[[Image:Terrano L1 Fig16.png|thumb|left|480px|EM.Terrano's simulation run dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN10.png|thumb|left|550px|EM.Terrano's output message window.]]
</td>
</tr>
</table>

=== Changing the SBR Engine Settings ===

There are a number of SBR simulation settings that can be accessed and changed from the Ray Tracing Engine Settings Dialog. To open this dialog, click the button labeled {{key|Settings}} on the right side of the '''Select Simulation or Solver Type''' drop-down list in the Run Dialog. EM.Terrano's SBR simulation engine allows you to separate the physical effects that are calculated during a ray tracing process. You can selectively enable or disable '''Reflection/Transmission''' and '''Edge Diffraction''' in the "Ray-Block Interactions" section of this dialog. By default, ray reflection and transmission and edge diffraction effects are enabled. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in the scene.

EM.Terrano allows a finite number of ray bounces for each original ray emanating from a transmitter. This is very important in situations that may involve resonance effects where rays get trapped among multiple surfaces and may bounce back and forth indefinitely. This is set using the box labeled "'''Max No. Ray Bounces'''", which has a default value of 10. Note that the maximum number of ray bounces directly affects the computation time as well as the size of output simulation data files. This can become critical for indoor propagation scenes, where most of the rays undergo a large number of reflections. Two other parameters control the diffraction computations: '''Max Wedge Angle''' in degrees and '''Min Edge Length''' in project units. The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or coplanar with no diffraction effect. The default value of the maximum wedge angle is 170°. The minimum edge length is size of the common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the minimum edge length is one project units.

<table>
<tr>
<td>
[[Image:PROP MAN11.png|thumb|left|720px|EM.Terrano's SBR simulation engine settings dialog.]]
</td>
</tr>
</table>

As rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish. From a practical point of view, only rays that have power levels above the receiver sensitivity can be effectively received. Therefore, all the rays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default value of -150dBm. Keep in mind that the value of this threshold directly affects the accuracy of the simulation results as well as the size of the output data file.

You can also set the '''Ray Angular Resolution''' of the transmitter rays in degrees. By default, every transmitter emanates equi-angular ray tubes at a resolution of 1 degree. Lower angular resolutions larger than 1° speed up the SBR simulation significantly, but they may compromise the accuracy. Higher angular resolutions less than 1° increase the accuracy of the simulating results, but they also increase the computation time. The SBR Engine Settings dialog also displays the '''Recommended Ray Angular Resolution''' in degrees in a grayed-out box. This number is calculated based on the overall extents of your computational domain as well as the SBR mesh resolution. To see this value, you have to generate the SBR mesh first. Keeping the angular resolution of your project above this threshold value makes sure that the small mesh facets at very large distances from the source would not miss any impinging ray tubes during the simulation.

EM.Terrano gives a few more options for the ray tracing solution of your propagation problem. For instance, it allows you to exclude the direct line-of-sight (LOS) rays from the final solution. There is a check box for this purpose labeled "Exclude direct (LOS) rays from the solution", which is unchecked by default. EM.Terrano also allows you to superpose the received rays incoherently. In that case, the powers of individual ray are simply added to compute that total received power. This option in the check box labeled "Superpose rays incoherently" is disabled by default, too.

At the end of a ray tracing simulation, the electric field of each individual ray is computed and reported. By default, the actual received ray fields are reported, which are independent of the radiation pattern of the receive antennas. EM.Terrano provides a check box labeled "Normalize ray's E-field based on receiver pattern", which is unchecked by default. If this box is checked, the field of each ray is normalized so as to reflect that effect of the receiver antenna's radiation pattern. The received power of each ray is calculated from the following equation:

<math> P_{ray} = \frac{ | \mathbf{E_{norm}} |^2 }{2\eta_0} \frac{\lambda_0^2}{4\pi} </math>

It can be seen that if the ray's E-field is not normalized, the computed ray power will correspond to that of a polarization matched isotropic receiver.

=== Polarimetric Channel Analysis ===

In a 3D SBR simulation, a transmitter shoots a large number of rays in all directions. The electric fields of these rays are polarimetric and their strength and polarization are determined by the designated radiation pattern of the transmit antenna. The rays travel in the propagation scene and bounce from the ground and buildings or other scatterers or get diffracted at the building edges until they reach the location of the receivers. Each individual ray has its own vectorial electric field and power. The electric fields of the received rays are then superposed coherently and polarimetrically to compute the total field at the receiver locations. The designated radiation pattern of the receivers is then used to compute the total received power by each individual receiver.

From a theoretical point of view, the radiation patterns of the transmit and receive antennas are independent of the propagation channel characteristics. For the given locations of the point transmitters and receivers, one can assume ideal isotropic radiators at these points and compute the polarimetric transfer function matrix of the propagation channel. This matrix relates the received electric field at each receiver location to the transmitted electric field at each transmitter location. In general, the vectorial electric field of each individual ray is expressed in the local standard spherical coordinate system at the transmitter and receiver locations. In other words, the polarimetric channel matrix expresses the '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components associated with each ray at the receiver location to its '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components at the transmitter location. Each ray has a delay and θ and φ angles of departure at the transmitter location and θ and φ angles of departure at the receiver location.

To perform a polarimatric channel characterization of your propagation scene, open EM.Terrano's Run Simulation dialog and select '''Channel Analyzer''' from the drop-down list labeled '''Select Simulation or Solver Type'''. At the end of the simulation, a large ray database is generated with two data files called "sbr_channel_matrix.DAT" and "sbr_ray_path.DAT". The former file contains the delay, angles of arrival and departure and complex-valued elements of the channel matrix for all the individual rays that leave each transmitter and arrive at each receiver. The latter file contains the geometric aspects of each ray such as hit point coordinates.

=== The "Almost Real-Time" Polarimatrix Solver ===

After EM.Terrano's channel analyzer generates a ray database that characterizes your propagation channel polarimetrically for all the combinations of transmitter and receiver locations, a ray tracing solution of the propagation problem can readily be found in almost real time by incorporating the effects of the radiation patterns of transmit and receive antennas. This is done using the '''Polarimatrix Solver''', which is the third option of the drop-down list labeled '''Select Simulation or Solver Type''' in EM.Terrano's Run Simulation dialog. The results of the Polarimatrix and 3D SBR solvers must be identical from a theoretical point of view. However, there might be small discrepancies between the two solutions due to roundoff errors.

Using the Polarimatrix solver can lead to a significant reduction of the total simulation time in sweep simulations that involve a large number of transmitters and receivers. Certain simulation modes of EM.Terrano are intended for the Polarimatrix solver only as will be described in the next section.

{{Note| In order to use the Polarimatrix solver, you must first generate a ray database of your propagation scene using EM.Terrano's Channel Analyzer.}}

=== EM.Terrano's Simulation Modes ===

EM.Terrano provides a number of different simulation modes that involve single or multiple simulation runs:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Which Solver?
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Single-Frequency SBR Analysis | Single-Frequency Analysis]]
| style="width:180px;" | Simulates the propagation scene "As Is"
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:180px;" | Varies the operating frequency of the ray tracer
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at a specified set of frequency samples
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:180px;" | Varies the value(s) of one or more project variables
| style="width:150px;" | SBR
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires definition of sweep variables, works only with SBR solver as the physical scene may change during the sweep
|-
| style="width:120px;" | [[#Transmitter_Sweep | Transmitter Sweep]]
| style="width:180px;" | Activates two or more transmitters sequentially with only one transmitter broadcasting at each simulation run
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires at least two transmitters in the scene, works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Rotational_Sweep | Rotational Sweep]]
| style="width:180px;" | Rotates the radiation pattern of the transmit antenna(s) sequentially to model beam steering
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Mobile_Sweep | Mobile Sweep]]
| style="width:180px;" | Considers one pair of active transmitter and receiver at each simulation run to model a mobile communication link
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires the same number of transmitters and receivers, works only with Polarimatrix solver and requires an existing ray database
|}

Click on each item in the above list to learn more about each simulation mode.

You set the simulation mode in EM.Terrano's simulation run dialog using the drop-down list labeled '''Simulation Mode'''. A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can plot the output parameter results on 2D graphs or you can animate the 3D simulation data from the navigation tree.

{{Note| EM.Terrano's frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent.}}

=== Transmitter Sweep ===

When your propagation scene contains two or more transmitters, whether they all belong to the same transmitter set with the same radiation pattern or to different transmitter sets, EM.Terrano assumes all to be coherent with respect to one another. In other words, synchronous transmitters are always assumed. The rays originating from all these transmitters are superposed coherently and vectorially at each receiver. In a transmitter sweep, on the other hand, EM.Terrano assumes only one transmitter broadcasting at a time. The result of the sweep simulation is a number of received power coverage maps, each corresponding to a transmitter in the scene.

{{Note| EM.Terrano's transmitter sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Rotational Sweep ===

You can rotate the 3D radiation patterns of both the transmitters and receivers from the property dialog of the parent transmitter set or receiver set. This is done in advance before a SBR simulation starts. You can define one or more of the rotation angles of a transmitter set or a receiver set as sweep variables and perform a parametric sweep simulation. In that case, the entire scene and all of its buildings are discretized at each simulation run and a complete physical SBR ray tracing simulation is carried out. However, we know that the polarimetric characteristics of the propagation channel are independent of the transmitter or receiver antenna patterns or their rotation angles. A rotational sweep allows you to rotate the radiation pattern of the transmitter(s) about one of the three principal axes sequentially. This is equivalent to the steering of the beam of the transmit antenna either mechanically or electronically. The result of the sweep simulation is a number of received power coverage maps, each corresponding to one of the angular samples. To run a rotational sweep, you must specify the rotation angle.

{{Note| EM.Terrano's rotational sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Mobile Sweep ===

In a mobile sweep, each transmitter is paired with a receiver according to their indices in their parent sets. At each simulation run, only one (Tx, Rx) pair is considered to be active in the scene. As a result, the generated coverage map takes a different meaning implying the sequential movement of the transmitter and receiver pair along their corresponding paths. In other words, the set of point transmitters and the set of point receivers indeed represent the locations of a single transmitter and a single receiver at different instants of time. It is obvious that the total number of transmitters and total number of receivers in the scene must be equal. Otherwise, EM.Terrano will prompt an error message.

[[EM.Cube]] provides a '''Mobile Path Wizard''' that facilitates the creation of a transmitter set or a receiver set along a specified path. This path can be an existing nodal curve (polyline or NURBS curve) or an existing line objects. You can also import a sptial Cartesian data file containing the coordinates of the base location points. For more information, refer to [[Glossary_of_EM.Cube%27s_Wizards#Mobile_Path_Wizard | Mobile Path Wizard]].

{{Note| EM.Terrano's mobile sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Investigating Propagation Effects Selectively One at a Time ===

In a typical SBR ray tracing simulation, EM.Terrano includes all the propagation effects such as direct (LOS) rays, ray reflection and transmission, and edge diffractions. At the end of a SBR simulation, you can visualize the received power coverage map of your propagation scene, which appears under the receiver set item in the navigation tree. The figure below shows the received power coverage map of the random city scene with a vertically polarized half-wave dipole transmitter located 10m above the ground and a large grid of vertically polarized half-wave dipole receivers placed 1.5m above the ground. The legend box shows the limits of the color map between -23dBm as the maximum and -150dB (the default receiver sensitivity value) as the minimum.

<table>
<tr>
<td>
[[Image:UrbanCanyon10.png|thumb|left|640px|The received power coverage map of the random city scene with a dipole transmitter.]]
</td>
</tr>
</table>

Sometime it is helpful to change the scale of the color map to better understand the dynamic range of the coverage map. If you double-click on the legend or right-click on the coverage map's name in the navigation tree and select '''Properties''', the Plot Settings dialog opens up. Select the '''User-Defined''' item and set the lower and upper bounds of color map as you wish.

<table>
<tr>
<td>
[[Image:UrbanCanyon15.png|thumb|left|480px|The plot settings dialog of the coverage map.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon16.png|thumb|left|640px|The received power coverage map of the random city scene with a user-defined color map scale between -80dBm and -20dBm.]]
</td>
</tr>
</table>

To better understand the various propagation effects, EM.Terrano allows you to enable or disable these effects selectively. This is done from the Ray Tracing Simulation Engine Settings dialog using the provided check boxes.

<table>
<tr>
<td>
[[Image:UrbanCanyon14.png|thumb|left|640px|EM.Terrano's simulation run dialog showing the check boxes for controlling various propagation effects.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon11.png|thumb|left|640px|The received power coverage map of the random city scene with direct LOS rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon12.png|thumb|left|640px|The received power coverage map of the random city scene with reflected rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon13.png|thumb|left|640px|The received power coverage map of the random city scene with diffracted rays only.]]
</td>
</tr>
</table>

== Working with EM.Terrano's Simulation Data ==

=== The Ray Tracing Solvers' Output Simulation Data ===

Both the SBR solver and the Polarimatrix solver perform the same type of simulation but in two different ways. The SBR solver discretizes the scene including all the buildings and terrain, shoots a large number of rays from the transmitters and collects the rays at the receivers. The Polarimatrix solver does the same thing using an existing polarimetric ray database that has been previously generated using EM.Terrano's Channel Analyzer. It incorporates the effects of the radiation patterns of the transmit and receive antennas in conjunction with the polarimetric channel characteristics. At the end of a ray tracing simulation, all the polarimetric rays emanating from the transmitter(s) or other sources that are received by the individual receivers are computed, collected, sorted and saved into ASCII data files. From the ray data, the total electric field at the location of receivers as well as the total received power are computed. The individual ray data include the field components of each ray, the ray's elevation and azimuth angles of departure and arrival (departure from the transmitter location and arrival at the receiver location), and time delay of the received ray with respect to the transmitter. If you specify the temperatures, noise figure and transmission line losses in the definition of the receiver sets, the noise power level and signal-to-noise ratio (SNR) at each receiver are also calculated, and so are the E<sub>b</sub>/N<sub>0</sub> and bit error rate (BER) for the selected digital modulation scheme.

=== Visualizing Field & Received Power Coverage Maps ===

In wireless propagation modeling for communication system applications, the received power at the receiver location is more important than the field distributions. In order to compute the received power, you need three pieces of information:

* '''Total Transmitted Power (EIRP)''': This requires knowledge of the baseband signal power, the transmitter chain parameters, the transmission characteristics of the transmission line connecting the transmitter circuit to the transmitting antenna and the radiation characteristics of the transmitting antenna.
* '''Channel Path Loss''': This is computed through SBR simulation.
* '''Receiver Properties''': This includes the radiation characteristics of the receiving antenna, the transmission characteristics of the transmission line connecting the receiving antenna to the receiver circuit and the receiver chain parameters.

In a simple link scenario, the received power P<sub>r</sub> in dBm is found from the following equation:

<math> P_r [dBm] = P_t [dBm] + G_{TC} + G_{TA} - PL + G_{RA} + G_{RC} </math>

where P<sub>t</sub> is the baseband signal power in dBm at the transmitter, G<sub>TC</sub> and G<sub>RC</sub> are the total transmitter and receiver chain gains in dB, respectively, G<sub>TA</sub> and G<sub>RA</sub> are the total transmitting and receiving antenna gains in dB, respectively, and PL is the channel path loss in dB. Keep in mind that EM.Terrano is fully polarimetric. The transmitting and receiving antenna characteristics are specified through the imported radiation pattern files, which are part of the definition of the transmitters and receivers. In particular, the polarization mismatch losses are taken into account through the polarimetric SBR ray tracing analysis.

If you specify the noise-related parameters of your receiver set, the signal-to-noise ratios (SNR) is calculated at each receiver location: SNR = P<sub>r</sub> - P<sub>n</sub>, where P<sub>n</sub> is the noise power level in dB. When planning, designing and deploying a communication system between points A and B, the link is considered to be closes and a connection established if the received signal power at the location of the receiver is above the noise power level by a certain threshold. In other words, the SNR at the receiver must be greater than a certain specified minimum SNR level. You specify (SNR)<sub>min</sub> ss part of the definition of receiver chain in the Receiver Set dialog. In the "Visualization Options" section of this dialog, you can also check the check box labeled '''Generate Connectivity Map'''. This is a binary-level black-and-white map that displays connected receivers in white and disconnected receivers in black. At the end of an SBR simulation, the computed SNR is displayed in the Receiver Set dialog for the selected receiver. The connectivity map is generated and added to the navigation tree underneath the received power coverage map node.

At the end of an SBR simulation, you can visualize the field maps and receiver power coverage map of your receiver sets. A coverage map shows the total '''Received Power''' by each of the receivers and is visualized as a color-coded intensity plot. Under each receiver set node in the navigation tree, a total of seven field maps together with a received power coverage map are added. The field maps include amplitude and phase plots for the three X, Y, Z field components plus a total electric field plot. To display a field or coverage map, simply click on its entry in the navigation tree. The 3D plot appears in the Main Window overlaid on your propagation scene. A legend box on the right shows the color scale and units (dB). The 3D coverage maps are displayed as horizontal confetti above the receivers. You can change the appearance of the receivers and maps from the property dialog of the receiver set. You can further customize the settings of the 3D field and coverage plots.

<table>
<tr>
<td>
[[Image:AnnArbor Scene1.png|thumb|left|640px|The downtown Ann Arbor propagation scene.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene2.png|thumb|left|640px|The electric field distribution map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene3.png|thumb|left|640px|The received power coverage map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene4.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 3dB with the basic color map option.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene5.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 20dB with the basic color map option.]]
</td>
</tr>
</table>

=== Visualizing the Rays in the Scene ===

At the end of a SBR simulation, each receiver receives a number of rays. Some receivers may not receive any rays at all. You can visualize all the rays received by a certain receiver from the active transmitter of the scene. To do this, right click the '''Receivers''' item of the Navigation Tree. From the context menu select '''Show Received Rays'''. All the rays received by the currently selected receiver of the scene are displayed in the scene. The rays are identified by labels, are ordered by their power and have different colors for better visualization. You can display the rays for only one receiver at a time. The receiver set property dialog has a list of all the individual receivers belonging to that set. To display the rays received by another receiver, you have to change the '''Selected Receiver''' in the receiver set's property dialog. If you keep the mouse focus on this dropdown list and roll your mouse scroll wheel, you can scan the selected receivers and move the rays from one receiver to the next in the list. To remove the visualized rays from the scene, right click the Receivers item of the Navigation Tree again and from the context menu select '''Hide Received Rays'''.

You can also view the ray parameters by opening the property dialog of a receiver set. By default, the first receiver of the set is always selected. You can select any other receiver from the drop-down list labeled '''Selected Receiver'''. If you click the button labeled '''Show Ray Data''', a new dialog opens up with a table that contains all the received rays at the selected receiver and their parameters:

* Delay is the total time delay that a ray experiences travelling from the transmitter to the receiver after all the reflections, transmissions and diffractions and is expressed in nanoseconds.
* Ray Field is the received electric field at the receiver location due to a specific ray and is given in dBV/m.
* Ray Power is the received power at the receiver due to a specific ray and is given in dBm.
* Angles of Arrival are the θ and φ angles of the incoming ray at the local spherical coordinate system of the receiver.

<table>
<tr>
<td>
[[Image:UrbanCanyon17.png|thumb|left|720px|EM.Terrano's ray data dialog showing a selected ray.]]
</td>
</tr>
</table>

The Ray Data Dialog also shows the '''Total Received Power''' in dBm and '''Total Received Field''' in dBV/m due to all the rays received by the receiver. You can sort the rays based on their delay, field, power, etc. To do so, simply click on the grey column label in the table to sort the rays in ascending order based on the selected parameter. You can also select any ray by clicking on its '''ID''' and highlighting its row in the table. In that case, the selected rays is highlighted in the Project Workspace and all the other rays become thin (faded).

{{Note|All the received rays are summed up coherently in a vectorial manner at the receiver location.}}

<table>
<tr>
<td> [[Image:UrbanCanyon18.png|thumb|left|640px|Visualization of received rays at the location of a selected receiver in the random city scene.]] </td>
</tr>
</table>

=== The Standard Output Data File ===

At the end of an SBR simulation, EM.Terrano writes a number of ASCII data files to your project folder. The main output data file is called "sbr_results.RTOUT". This file contains all the information about individual receivers and the parameters of each ray that is received by each individual receiver.
At the end of an SBR simulation, the results are written into a main output data file with the reserved name of SBR_Results.RTOUT. This file has the following format:

Each receiver line has the following information:

* Receiver ID
* Receiver X, Y, Z coordinates
* Total received power in dBm
* Total number of received rays

Each rays line received by a receiver has the following information:

* Ray Index
* Delay in nsec
* θ and φ Angles of Arrival in deg
* θ and φ Angles of Departure in deg
* Real and imaginary parts of the three E<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub> components
* Number of ray hit points
* Coordinates of individual hit points

The angles of arrival are the θ and φ angles of a received ray measured in degrees and are referenced in the local spherical coordinate systems centered at the location of the receiver. The angles of departure for a received ray are the θ and φ angles of the originating transmitter ray, measured in degrees and referenced in the local spherical coordinate systems centered at the location of the active transmitter, which eventually arrives at the receiver. The total time delay is measured in nanoseconds between t = 0 nsec at the time of launch from the transmitter location till being received at the receiver location.

<table>
<tr>
<td>
[[Image:prop_run8_tn.png|thumb|left|720px|A typical SBR output data file.]]
</td>
</tr>
</table>

=== Plotting Other Simulation Results ===

Besides "sbr_results.out", [[EM.Terrano]] writes a number of other ASCII data files to your project folder. You can view or plot these data in [[EM.Cube]]'s Data Manager. You can open data manager by clicking the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Menu > Simulate > Data Manager''' from the menu bar or by right-clicking on the '''Data Manager''' item of the navigation tree and selecting '''Open Data Manager...''' from the contextual menu or by using the keyboard shortcut {{key|Ctrl+D}}.

The available data files in the "2D Data Files" tab of Data Manger include:

* '''Path Loss''': The channel path loss is defined as PL = P<sub>r</sub> - EIRP. The path loss data are stored in a file called "SBR_receiver_set_name_PATHLOSS.DAT" as a function of the receiver index. The path loss data make sense only if your receiver set has the default isotropic radiator.
* '''Power Delay Profile''': The delays of the individual rays received by the selected receiver with respect to the transmitter are expressed in ns and tabulated together with the power of each ray in the file "SBR_receiver_set_name_DELAY.DAT". You can plot these data from the Data Manager as a bar chart called the power delay profile. The bars indeed correspond to the difference between the ray power in dBm and the minimum power threshold level in dBm, which makes them a positive quantity.
* '''Angles of Arrival''': These are the Theta and Phi angles of the individual rays received by the selected receiver and saved to the files "SBR_receiver_set_name_ThetaARRIVAL.ANG" and "SBR_receiver_set_name_PhiARRIVAL.ANG". You can plot them in the Data Manager in polar stem charts.

When you run a frequency or parametric sweep in [[EM.Terrano]], a tremendous amount of data may be generated. [[EM.Terrano]] only stores the '''Received Power''', '''Path Loss''' and '''SNR''' of the selected receiver
in ASCII data files called "PREC_i.DAT", "PL_i.DAT" and "SNR_i.DAT", where is the index of the receiver set in your scene. These quantities are tabulated vs. the sweep variable's samples. You can plot these files in EM.Grid.

[[Image:Info_icon.png|40px]] Click here to learn more about working with data filed and plotting graphs in [[EM.Cube]]'s '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#The_Data_Manager | Data Manager]]'''.

<table>
<tr>
<td> [[Image:Terrano pathloss.png|thumb|360px|Cartesian graph of path loss.]] </td>
<td> [[Image:Terrano delay.png|thumb|360px|Bar graph of power delay profile.]] </td>
</tr>
<tr>
<td> [[Image:Terrano ARR phi.png|thumb|360px|Polar stem graph of Phi angle of arrival.]] </td>
<td> [[Image:Terrano ARR theta.png|thumb|360px|Polar stem graph of Theta angle of arrival.]] </td>
</tr>
<tr>
<td> [[Image:Terrano DEP phi.png|thumb|360px|Polar stem graph of Phi angle of departure.]] </td>
<td> [[Image:Terrano DEP theta.png|thumb|360px|Polar stem graph of Theta angle of departure.]] </td>
</tr>
</table>

=== Visualizing 3D Radiation Patterns of Transmit and Receive Antennas in the Scene ===

When you designate a "User Defined Antenna Pattern" as the radiator type of a transmitter set or a receiver set, EM.Terrano copies the imported radiation pattern data file from its original folder to the current project folder. The name of the ".RAD" file is listed under the '''3D Data Files''' tab of the data manager. Sometimes it might be desired to visualize these radiation patterns in your propagation scene at the actual location of the transmitter or receiver. To do so, you have to define a new '''Radiation Pattern''' observable in the navigation tree. The label of the new observable must be identical to the name of the ".RAD" data file. In addition, the Theta and Phi angle increments of the new radiation pattern observable (expressed in degrees) must be identical to the Theta and Phi angular resolutions of the imported pattern file. If all these conditions are met, then go to the '''Simulate Menu''' and select the item '''Update All 3D Visualization'''. The contents of the 3D radiation patterns are added to the navigation tree. Click on one of the radiation pattern items in the navigation tree and it will be displayed in the scene.

<table>
<tr>
<td>
[[Image:UrbanCanyon6.png|thumb|left|640px|The received power coverage map of the random city scene with a highly directional dipole array transmitter.]]
</td>
</tr>
</table>

By Default, [[EM.Cube]] always visualizes the 3D radiation patterns at the origin of coordinates, i.e. at (0, 0, 0). This is because that radiation pattern data are computed in the standard spherical coordinate system centered at (0, 0, 0). The theta and phi components of the far-zone electric fields are defined with respect to the X, Y and Z axes of this system. When visualizing the 3D radiation pattern data in a propagation scene, it is more intuitive to display the pattern at the location of the transmitter or receiver. The Radiation Pattern dialog allows you to translate the pattern visualization to any arbitrary point in the project workspace. It also allows you to scale up or scale down the pattern visualization with respect to the background scene.

In the example shown above, the imported pattern data file is called "Dipole_Array1.RAD". Therefore, the label of the radiation pattern observable is chosen to be "Dipole_Array1". The theta and phi angle increments are both 1° in this case. The radiation pattern has been elevated by 10m to be positioned at the location of the transmitter and a scaling factor of 0.3 has been used.

<table>
<tr>
<td>
[[Image:UrbanCanyon8.png|thumb|left|640px|Setting the pattern parameters in the radiation pattern dialog.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon7.png|thumb|left|720px|Visualization of the 3D radiation pattern of the directional transmitter in the random city scene.]]
</td>
</tr>
</table>

There is an important catch to remember here. When you define a radiation pattern observable for your project, EM.Terrano will attempt to compute the overall effective radiation pattern of the entire physical structure. However, in this case, you defined the radiation pattern observable merely for visualization purposes. To stop EM.Terrano from computing the actual radiation pattern of your entire scene, there is a check box in EM.Terrano's Ray Tracer Simulation Engine Settings dialog that is labeled '''Do not compute new radiation patterns'''. This box is checked by default, which means the actual radiation pattern of your entire scene will not be computed automatically. But you need to remember to uncheck this box if you ever need to compute a new radiation pattern using EM.Terrano's SBR solver as an asymptotic EM solver (see next section).

<table>
<tr>
<td>
[[Image:UrbanCanyon9.png|thumb|left|640px|EM.Terrano's Run Simulation dialog.]]
</td>
</tr>
</table>

== Using EM.Terrano as an Asymptotic Field Solver ==

Like every other electromagnetic solver, EM.Terrano's SBR ray tracer requires an excitation source and one or more observables for the generation of simulation data. EM.Terrano offers several types of sources and observables for a SBR simulation. You already learned about the transmitter set as a source and the receiver set as an observable. You can mix and match different source types and observable types depending on the requirements of your modeling problem.

The available source types in EM.Terrano are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:transmitter_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Transmitter Set | Point Transmitter Set]]
| style="width:250px;" | Modeling realsitic antennas & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source | Hertzian Short Dipole]]
| style="width:250px;" | Almost omni-directional physical radiator
| style="width:250px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source | Huygens Source]]
| style="width:250px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

The available observables types in [[EM.Terrano]] are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:receiver_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Point Receiver Set | Point Receiver Set]]
| style="width:250px;" | Generating received power coverage maps & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:Distr Rx icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Distributed Receiver Set | Distributed Receiver Set]]
| style="width:250px;" | Computing received power at a receiver characterized by Huygens surface data
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor Observable | Near-Field Sensor]]
| style="width:250px;" | Generating electric and magnetic field distribution maps
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern Observable | Far-Field Radiation Pattern]]
| style="width:250px;" | Computing the effective radiation pattern of a radiator in the presence of a large scattering scene
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface Observable | Huygens Surface]]
| style="width:250px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone observable
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

When you define a far-field observable in EM.Terrano, a collection of invisible, isotropic receivers are placed on the surface of a large sphere that encircles your propagation scene and all of its geometric objects. These receivers are placed uniformly on the spherical surface at a spacing that is determined by your specified angular resolutions. In most cases, you need to define angular resolutions of at least 1° or smaller. Note that this is different than the transmitter rays' angular resolution. You may have a large number of transmitted rays but not enough receivers to compute the effective radiation pattern at all azimuth and elevation angles. Also keep in mind that with 1° Theta and Phi angle increments, you will have a total of 181 × 361 = 65,341 spherically placed receivers in your scene.

{{Note| Computing radiation patterns using EM.Terrano's SBR solver typically takes much longer computation times than using [[EM.Cube]]'s other computational modules.}}

<table>
<tr>
<td> [[Image:SBR pattern.png|thumb|540px|Computed 3D radiation pattern of two vertical short dipole radiators placed 1m apart in the free space at 1GHz.]] </td>
</tr>
</table>

== Statistical Analysis of Propagation Scene ==

EM.Terrano's coverage maps display the received power at the location of all the receivers. The receivers together from a set/ensemble, which might be uniformly spaced or distributed across the propagation scene or may consist of randomly scattered radiators. Every coverage map shows the '''Mean''' and '''Standard Deviation''' of the received power for all the receivers involved. These information are displayed at the bottom of the coverage map's legend box and are expressed in dB.

When you run either a frequency sweep or a parametric sweep simulation in EM.Terrano, you have the option to generate two additional coverage maps: one for the mean of all the individual sample coverage maps and another for their standard deviation. To do so, in the '''Run Dialog''', check the box labeled '''"Create Mean and Standard Deviation received power coverage maps"'''. Note that the mean and standard deviation values displayed on the individual coverage maps correspond to the spatial statistics of the receivers in the scene, while the mean and standard deviation coverage maps show the statistics with respect to the frequency or other sweep variable sets at each point in the site. Also, note that both of the mean and standard deviation coverage maps have their own spatial mean and standard deviation values expressed in dB at the bottom of their legend box.

<table>
<tr>
<td>
[[Image:PROP MAN12.png|thumb|left|480px|EM.Terrano's simulation run dialog showing frequency sweep as the simulation mode along with statistical analysis.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon4.png|thumb|left|640px|The mean coverage map at the end of a frequency sweep.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon5.png|thumb|left|640px|The standard deviation coverage map at the end of a frequency sweep.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Terrano#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

EM.Terrano

2019-04-05T14:16:44Z

Kazem Sabet: /* Scene Definition / Construction */

[[Image:Splash-prop.jpg|right|720px]]
<strong><font color="#4e1985" size="4">True 3D, Coherent, Polarimetric Ray Tracer That Simulates Very Large Urban Scenes In Just Few Minutes!</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

===EM.Terrano in a Nutshell ===

EM.Terrano is a physics-based, site-specific, wave propagation modeling tool that enables engineers to quickly determine how radio waves propagate in urban, natural or mixed environments. EM.Terrano's simulation engine is equipped with a fully polarimetric, coherent 3D ray tracing solver based on the Shooting-and-Bouncing-Rays (SBR) method, which utilizes geometrical optics (GO) in combination with uniform theory of diffraction (UTD) models of building edges. EM.Terrano lets you analyze and resolve all the rays transmitted from one ore more signal sources, which propagate in a real physical channel made up of buildings, terrain and other obstructing structures. EM.Terrano finds all the rays received by a receiver at a particular location in the physical site and computes their vectorial field and power levels, time delays, angles of arrival and departure, etc. Using EM.Terrano you can examine the connectivity of a communication link between any two points in a real specific propagation site.

Since its introduction in 2002, EM.Terrano has helped wireless engineers around the globe model the physical channel and the mechanisms by which radio signals propagate in various environments. EM.Terrano’s advanced ray tracing simulator finds the dominant propagation paths at each specific physical site. It calculates the true signal characteristics at the actual locations using physical databases of the buildings and terrain at a given site, not those of a statistically average or representative environment. The earlier versions of EM.Terrano's SBR solver relied on certain assumptions and approximations such as the vertical plane launch (VPL) method or 2.5D analysis of urban canyons with prismatic buildings using two separate vertical and horizontal polarizations. In 2014, we introduced a new fully 3D polarimetric SBR solver that accurately traces all the three X, Y and Z components of the electric fields (both amplitude and phase) at every point inside the computational domain. Using a 3D CAD modeler, you can now set up any number of buildings with arbitrary geometries, no longer limited to vertical prismatic shapes. Versatile interior wall arrangements allow indoor propagation modeling inside complex building configurations. The most significant recent development is a multicore parallelized SBR simulation engine that takes advantage of ultrafast k-d tree algorithms borrowed from the field of computer graphics and video gaming to achieve the ultimate speed and efficiency in geometrical optics ray tracing.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Basic Principles of SBR Ray Tracing | Basic SBR Theory]]'''.

<table>
<tr>
<td>
[[Image:Manhattan1.png|thumb|left|420px|A large urban propagation scene featuring lower Manhattan.]]
</td>
</tr>
</table>

=== EM.Terrano as the Propagation Module of EM.Cube ===

EM.Terrano is the ray tracing '''Propagation Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Terrano shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

With the seamless integration of EM.Terrano with [[EM.Cube]]'s other modules, you can now model complex antenna systems in [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]], and generate antenna radiation patterns that can be used to model directional transmitters and receivers at the two ends of your propagation channel. Conversely, you can analyze a propagation scene in EM.Terrano, collect all the rays received at a certain receiver location and import them as coherent plane wave sources to [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]].

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Terrano's SBR Solver ===

EM.Terrano's SBR simulation engine utilizes an intelligent ray tracing algorithm that is based on the concept of k-dimensional trees. A k-d tree is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are particularly useful for searches that involve multidimensional search keys such as range searches and nearest neighbor searches. In a typical large radio propagation scene, there might be a large number of rays emanating from the transmitter that may never hit any obstacles. For example, upward-looking rays in an urban propagation scene quickly exit the computational domain. Rays that hit obstacles on their path, on the other hand, generate new reflected and transmitted rays. The k-d tree algorithm traces all these rays systematically in a very fast and efficient manner. Another major advantage of k-d trees is the fast processing of multi-transmitters scenes.

EM.Terrano performs fully polarimetric and coherent SBR simulations with arbitrary transmitter antenna patterns. Its SBR simulation engine is a true asymptotic "field" solver. The amplitudes and phases of all the three vectorial field components are computed, analyzed and preserved throughout the entire ray tracing process from the source location to the field observation points. You can visualize the magnitude and phase of all six electric and magnetic field components at any point in the computational domain. In most scenes, the buildings and the ground or terrain can be assumed to be made of homogeneous materials. These are represented by their electrical properties such as permittivity ε<sub>r</sub> and electric conductivity σ. More complex scenes may involve a multilayer ground or multilayer building walls. In such cases, one can no longer use the simple reflection or transmission coefficient formulas for homogeneous medium interfaces. EM.Terrano calculates the reflection and transmission coefficients of multilayer structures as functions of incident angle, frequency and polarization and uses them at the respective specular points.

It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD). It is not a "full-wave" technique, and it does not provide a direct numerical solution of Maxwell's equations. SBR makes a number of assumptions, chief among them, a very high operational frequency such that the length scales involved are much larger than the operating wavelength. Under this assumed regime, electromagnetic waves start to behave like optical rays. Virtually all the calculations in SBR are based on far field approximations. In order to maintain a high computational speed for urban propagation problems, EM.Terrano ignores double diffractions. Diffractions from edges give rise to a large number of new secondary rays. The power of diffracted rays drops much faster than reflected rays. In other words, an edge-diffracted ray does not diffract again from another edge in EM.Terrano. However, reflected and penetrated rays do get diffracted from edges just as rays emanated directly from the sources do.

<table>
<tr>
<td>
[[Image:Multipath_Rays.png|thumb|left|500px|A multipath urban propagation scene showing all the rays collected by a receiver.]]
</td>
</tr>
</table>

== EM.Terrano Features at a Glance ==

=== Scene Definition / Construction ===

<ul>
<li>
Buildings/blocks with arbitrary geometries and material properties</li>
<li>
Buildings/blocks with impenetrable surfaces or penetrable surfaces using thin wall approximation</li>
<li>
Multilayer walls for indoor propagation scenes</li>
<li>
Penetrable volume blocks with arbitrary geometries and material properties</li>
<li>
Import of shapefiles and STEP, IGES and STL CAD model files for scene construction</li>
<li>
Terrain surfaces with arbitrary geometries and material properties and random rough surface profiles</li>
<li>
Import of digital elevation map (DEM) terrain models</li>
<li>
Python-based random city wizard with randomized building locations, extents and orientations</li>
<li>
Python-based wizards for generation of parameterized multi-story office buildings and several terrain scene types</li>
<li>
Standard half-wave dipole transmitters and receivers oriented along the principal axes</li>
<li>
Short Hertzian dipole sources with arbitrary orientation</li>
<li>
Isotropic receivers or receiver grids for wireless coverage modeling</li>
<li>
Radiator sets with 3D directional antenna patterns (imported from other modules or external files)</li>
<li>
Full three-axis rotation of imported antenna patterns</li>
<li>
Interchangeable radiator-based definition of transmitters and receivers (networks of transceivers)</li>
</ul>

=== Wave Propagation Modeling ===

<ul>
<li>
Fully 3D polarimetric and coherent Shoot-and-Bounce-Rays (SBR) simulation engine</li>
<li>
GTD/UTD diffraction models for diffraction from building edges and terrain</li>
<li>
Triangular surface mesh generator for discretization of arbitrary block geometries</li>
<li>
Super-fast geometrical/optical ray tracing using advanced k-d tree algorithms</li>
<li>
Intelligent ray tracing with user defined angular extents and resolution</li>
<li>
Ray reflection, edge diffraction and ray transmission through multilayer walls and material volumes</li>
<li>
Communication link analysis for superheterodyne transmitters and receivers</li>
<li>
17 digital modulation waveforms for the calculation of E<sub>b</sub>/N<sub>0</sub> and Bit error rate (BER)</li>
<li>
Incredibly fast frequency sweeps of the entire propagation scene in a single SBR simulation run</li>
<li>
Parametric sweeps of scene elements like building properties, or radiator heights and rotation angles</li>
<li>
Statistical analsyis of the propagation scene</li>
<li>
Polarimetric channel characterization for MIMO analysis</li>
<li>
"Almost real-time" Polarimatrix solver using an existing ray database</li>
<li>
"Almost real-time" transmitter sweep using the Polarimatrix solver</li>
<li>
"Almost real-time" rotational sweep for modeling beam steering using the Polarimatrix solver</li>
<li>
"Almost real-time" mobile sweep for modeling mobile communications between Tx-Rx pairs along a mobile path using the Polarimatrix solver</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Standard output parameters for received power, path loss, SNR, E<sub>b</sub>/N<sub>0</sub> and BER at each individual receiver</li>
<li>
Graphical visualization of propagating rays in the scene</li>
<li>
Received power coverage maps</li>
<li>
Link connectivity maps (based on minimum required SNR and BER)</li>
<li>
Color-coded intensity plots of polarimetric electric field distributions</li>
<li>
Incoming ray data analysis at each receiver including delay, angles of arrival and departure</li>
<li>
Cartesian plots of path loss along defined paths</li>
<li>
Power delay profile of the selected receiver</li>
<li>
Polar stem charts of angles of arrival and departure of the selected receiver</li>
</ul>

== Building a Propagation Scene in EM.Terrano ==

=== The Various Elements of a Propagation Scene ===

A typical propagation scene in EM.Terrano consists of several elements. At a minimum, you need a transmitter (Tx) at some location to launch rays into the scene and a receiver (Rx) at another location to receive and collect the incoming rays. A transmitter and a receiver together make the simplest propagation scene, representing a free-space line-of-sight (LOS) channel. In EM.Terrano, a transmitter represents a point source, while a receiver represents a point observable. Both a transmitter and a receiver are associated with point objects, which are one of the many types of geometric objects you can draw in the project workspace. Your scene might involve more than one transmitter and possibly a large grid of receivers.

A more complicated propagation scene usually contains several buildings, walls, or other kinds of scatterers and wave obstructing objects. You model all of these elements by drawing geometric objects in the project workspace or by importing external CAD models. EM.Terrano does not organize the geometric objects of your project workspace by their material composition. Rather, it groups the geometric objects into blocks based on a common type of interaction with incident rays. EM.Terrano offer the following types of object blocks:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Block/Group Type
! scope="col"| Ray Interaction Type
! scope="col"| Object Types Allowed
! scope="col"| Notes
|-
| style="width:30px;" | [[File:impenet_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impenetrable Surface | Impenetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Basic building group for outdoor scenes
|-
| style="width:30px;" | [[File:penet_surf_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Surface | Penetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission in free space
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Behaves similar to impenetrable surface and uses thin wall approximation for generating transmitted rays, used to model hollow buildings with ray penetration, entry and exit
|-
| style="width:30px;" | [[File:terrain_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Terrain Surface | Terrain Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All surface geometric objects, no solid or curve objects
| style="width:300px;" | Behaves exactly like impenetrable surface but can change the elevation of all the buildings and transmitters and receivers located above it
|-
| style="width:30px;" | [[File:penet_vol_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Volume | Penetrable Volume]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission and ray attenuation inside homogeneous material media
| style="width:250px;" | All solid geometric objects, no surface or curve objects
| style="width:300px;" | Used to model wave propagation inside a volumetric material block, also used for creating individual solid walls and interior building partitions and panels in indoor scenes
|-
| style="width:30px;" | [[File:base_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Base Location Set | Base Location Set]]
| style="width:200px;" | Either ray generation or ray reception
| style="width:250px;" | Only point objects
| style="width:300px;" | Required for the definition of transmitters and receivers
|-
| style="width:30px;" | [[File:scatterer_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Scatterer Set | Point Scatterer Set]]
| style="width:200px;" | Ray reception and ray scattering
| style="width:250px;" | Only point, box and sphere objects
| style="width:300px;" | Required for the definition of point scatterers as targets in a radar simulation
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:200px;" | No ray interaction
| style="width:250px;" | All types of objects
| style="width:300px;" | Used for representing non-physical items
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

Impenetrable surfaces, penetrable surfaces, terrain surfaces and penetrable volumes represent all the objects that obstruct the propagation of electromagnetic waves (rays) in the free space. What differentiates them is the types of physical phenomena that are used to model their interaction with the impinging rays. EM.Terrano discretizes geometric objects into a number of flat facets. The field intensity, phase and power of the reflected and transmitted rays depend on the material properties of the obstructing facet. The specular surface of a facet can be modeled locally as a simple homogeneous dielectric half-space or as a multilayer medium. In that respect, all the obstructing objects such as buildings, walls, terrain, etc. behave in a similar way:

* They terminate an impinging ray and replace it with one or more new rays.
* They represent a specular interface between two media of different material compositions for calculating the reflection, transmission or diffraction coefficients.

An outdoor propagation scene typically involves several buildings modeled by impenetrable surfaces. Rays hit the facets of impenetrable buildings and bounce back, but they do not penetrate the object. It is assumed that the interior of such buildings are highly dissipative due to wave absorption or diffusion. An indoor propagation scene typically involves several walls, a ceiling and a floor arranged according to a certain building layout. Penetrable surfaces are used to model the exterior and interior walls of buildings. Rays reflect off these surfaces and diffract off their edges. They also penetrate the thin surface and continue their path in the free space on the other side of the wall. Terrain surfaces with irregular shapes or possibly random rough surfaces are used as an alternative to the flat global ground. You can also build mixed scenes involving both impenetrable and penetrable blocks or irregular terrain. In the context of a propagation scene, penetrable volumes are often used to model block of rain, fog or vegetation. Base location sets are used to geometrically represent point transmitters and point receivers in the project workspace.

Sometimes it is helpful to draw graphical objects as visual clues in the project workspace. These non-physical objects must belong to a virtual object group. Virtual objects are not discretized by EM.Terrano's mesh generator, and they are not passed onto the input data files of the SBR simulation engine.

<table>
<tr>
<td>
[[Image:PROP MAN2.png|thumb|left|720px|An urban propagation scene generated by EM.Terrano's "Random City" and "Basic Link" wizards. It consists of 25 cubic brick buildings, one transmitter and a large two-dimensional array of receivers. ]]
</td>
</tr>
</table>

=== Organizing the Propagation Scene by Block Groups ===

In EM.Terrano, all the geometric objects associated with the various scene elements like buildings, terrain surfaces and base location points are grouped together as blocks based on their common type. All the objects listed under a particular group in the navigation tree share the same color, texture and material properties. Once a new block group has been created in the navigation tree, it becomes the "Active" group of the project workspace, which is always displayed in bold letters. You can draw new objects under the active node. Any block group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.

<table>
<tr>
<td>
[[Image:PROP MAN1.png|thumb|left|480px|EM.Terrano's navigation tree.]]
</td>
</tr>
</table>

It is recommended that you first create block groups, and then draw new objects under the active block group. However, if you start a new EM.Terrano project from scratch, and start drawing a new object without having previously defined any block groups, a new default impenetrable surface group is created and added to the navigation tree to hold your new CAD object. You can always change the properties of a block group later by accessing its property dialog from the contextual menu. You can also delete a block group with all of its objects at any time.

{{Note|You can only import external CAD models (STEP, IGES, STL, DEM, etc.) only to the CubeCAD module. You can then transfer the imported objects from CubeCAD to EM.Terrano.}}

=== Moving Objects Among Different Block Groups ===

You can move any geometric object or a selection of objects from one block group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models of terrain or buildings from CubeCAD to EM.Terrano. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a block group called "Terrain_1" in EM.Terrano, then you have to select the menu item '''Move To → EM.Terrano → Terrain_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.

<table>
<tr>
<td>
[[Image:PROP MAN3.png|thumb|left|720px|Moving the terrain model of Mount Whitney originally imported from an external digital elevation map (DEM) file to EM.Terrano.]]
</td>
</tr>
<tr>
<td>
[[Image:PROP MAN4.png|thumb|left|720px|The imported terrain model of Mount Whitney shown in EM.Terrano's project workspace under a terrain group called "Terrain_1".]]
</td>
</tr>
</table>

=== Adjustment of Block Elevation on Underlying Terrain Surfaces ===

In EM.Terrano, buildings and all other geometric objects are initially drawn on the XY plane. In other words, the Z-coordinates of the local coordinate system (LCS) of all blocks are set to zero until you change them. Since the global ground is located a z = 0, your buildings are seated on the ground. When your propagation scene has an irregular terrain, you would want to place your buildings on the surface of the terrain and not buried under it. This can be done automatically as part of the definition of the block group. Open the property dialog of a block group and check the box labeled '''Adjust Block to Terrain Elevation'''. All the objects belonging to that block are automatically elevated in the Z direction such that their bases sit on the surface of their underlying terrain. In effect, the LCS of each of these individual objects is translated along the global Z-axis by the amount of the Z-elevation of the terrain object at the location of the LCS.

{{Note| You have to make sure that the resolution of your terrain, its variation scale and building dimensions are all comparable. Otherwise, on a rapidly varying high-resolution terrain, you will have buildings whose bottoms touch the terrain only at a few points and parts of them hang in the air.}}

<table>
<tr>
<td>
[[Image:PROP MAN5.png|thumb|left|480px|The property dialog of impenetrable surface showing the terrain elevation adjustment box checked.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN6.png|thumb|left|360px|A set of buildings on an undulating terrain without elevation adjustment.]]
</td>
<td>
[[Image:PROP MAN7.png|thumb|left|360px|The set of buildings on the undulating terrain after elevation adjustment.]]
</td>
</tr>
</table>

== EM.Terrano's Ray Domain & Global Environment ==

=== Why Do You Need a Finite Computational Domain? ===

The SBR simulation engine requires a finite computational domain for ray termination. All the stray rays that emanate from a source inside this finite domain and hit its boundaries are terminated during the simulation process. Such rays exit the computational domain and travel to the infinity, with no chance of ever reaching any receiver in the scene. When you define a propagation scene with various elements like buildings, walls, terrain, etc., a dynamic domain is automatically established and displayed as a green wireframe box that surrounds the entire scene. Every time you create a new object, the domain box is automatically adjusted and extended to enclose all the objects in the scene.

To change the ray domain settings, follow the procedure below:

* Open the Ray Domain Settings Dialog by clicking the '''Domain''' [[File:image025.jpg]] button of the '''Simulate Toolbar''', or by selecting '''Menu > Simulate > Computational Domain > Settings...''', or by right-clicking on the '''Ray Domain''' item of the navigation tree and selecting '''Domain Settings...''' from the contextual menu, or simply using the keyboard shortcut {{key|Ctrl+A}}.
* The size of the Ray domain is specified in terms of six '''Offset''' parameters along the ±X, ±Y and ±Z directions. The default value of all these six offset parameters is 10 project units. Change these values as you like.
* You can also change the color of the domain box using the {{key|Color}} button.
* After changing the settings, use the {{key|Apply}} button to make the changes effective while the dialog is still open.

<table>
<tr>
<td>
[[Image:PROP15.png|thumb|left|480px|EM.Terrano's domain settings dialog.]]
</td>
</tr>
</table>

=== Understanding the Global Ground ===

Most outdoor and indoor propagation scenes include a flat ground at their bottom, which bounces incident rays back into the scene. EM.Terrano provides a global flat ground at z = 0. The global ground indeed acts as an impenetrable surface that blocks the entire computational domain from the z = 0 plane downward. It is displayed as a translucent green plane at z = 0 extending downward. The color of the ground plane is always the same as the color of the ray domain. The global ground is assumed to be made of a homogeneous dielectric material with a specified permittivity ε<sub>r</sub> and electric conductivity σ. By default, a rocky ground is assumed with ε<sub>r</sub> = 5 and σ = 0.005 S/m. You can remove the global ground, in which case, you will have a free space scene. To disable the global ground, open up the "Global Ground Settings" dialog, which can be accessed by right clicking on the '''Global Ground''' item in the Navigation Tree and selecting '''Global Ground Settings... '''Remove the check mark from the box labeled '''"Include Half-Space Ground (z<0)"''' to disable the global ground. This will also remove the green translucent plane from the bottom of your scene. You can also change the material properties of the global ground and set new values for the permittivity and electric conductivity of the impenetrable, half-space, dielectric medium.

Alternatively, you can use EM.Terrano's '''Empirical Soil Model''' to define the material properties of the global ground. This model requires a number of parameters: Temperature in °C, and Volumetric Water Content, Sand Content and Clay Content all as percentage.

{{Note|To model a free-space propagation scene, you have to disable EM.Terrano's default global ground.}}

<table>
<tr>
<td>
[[Image:Global environ.png|thumb|left|720px|EM.Terrano's Global Environment Settings dialog.]]
</td>
</tr>
</table>

== Defining Point Transmitters & Point Receivers for Your Propagation Scene ==

=== The Nature of Transmitters & Receivers ===

In EM.Terrano, transmitters and receivers are indeed point radiators used for transmitting and receiving signals at different locations of the propagation scene. From a geometric point of view, both transmitters and receivers are represented by point objects or point arrays. These are grouped as base locations in the "Physical Structure" section of the navigation tree. As radiators, transmitters and receivers are defined by a radiator type with a certain far-field radiation pattern. Consistent with [[EM.Cube]]'s other computational modules, transmitters are categorizes as an excitation source, while receivers are categorized as a project observable. In other words, a transmitter is used to generate electromagnetic waves that propagate in the physical scene. A receiver, on the other hand, is used to compute the received fields and received signal power or signal-to-noise ratio (SNR). For this reason, transmitters are defined and listed under the "Sources" sections of the navigation tree, while receivers are defined and listed under the "Observables" section.

EM.Terrano provides three radiator types for point transmitter sets:

#Half-wave dipole oriented along one of the three principal axes
#Two collocated, orthogonally polarized, isotropic radiators
#User defined (arbitrary) antenna with imported far-field radiation pattern

EM.Terrano also provides three radiator types for point receiver sets:

#Half-wave dipole oriented along one of the three principal axes
#Polarization-matched isotropic radiator
#User defined (arbitrary) antenna with imported far-field radiation pattern

The default transmitter and receiver radiator types are both vertical (Z-directed) half-wave dipoles.

There are three different ways to define a transmitter set or a receiver set:

*By defining point objects or point arrays under physical base location sets in the navigation tree and then associating them with a transmitter or receiver set
*Using Python commands emag_tx, emag_rx, emag_tx_array, emag_rx_array, emag_tx_line and emag_rx_line
*Using the "Basic Link" wizard

=== Defining a Point Transmitter Set in the Formal Way ===

Transmitters act as sources in a propagation scene. A transmitter is a point radiator with a fully polarimetric radiation pattern defined over the entire 3D space in the standard spherical coordinate system. EM.Terrano gives you three options for the radiator associated with a point transmitter:

* Half-wave dipole
* Orthogonally polarized isotropic radiators
* User defined antenna pattern

By default, EM.Terrano assumes that your transmitter is a vertically polarized (Z-directed) resonant half-wave dipole antenna. This antenna has an almost omni-directional radiation pattern in all azimuth directions. It also has radiation nulls along the axis of the dipole. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. The second choice of two orthogonally polarized isotropic radiators is an abstract source that is used for polarimetric channel characterization as will be discussed later.

You can override the default radiator option and select any other kind of antenna with a more complicated radiation pattern. For this purpose, you have to import a radiation pattern data file to EM.Terrano. You can model any radiating structure using [[EM.Cube]]'s other computational modules, [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] or [[EM.Illumina]], and generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored in a specially formatted file with a "'''.RAD'''" file extension. This file contains columns of spherical φ and θ angles as well as the real and imaginary parts of the complex-valued far-zone electric field components '''E<sub>θ</sub>''' and '''E<sub>φ</sub>'''. The θ- and φ-components of the far-zone electric field determine the polarization of the transmitting radiator.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point transmitter set.}}

A transmitter set always needs to be associated with an existing base location set with one or more point objects in the project workspace. Therefore, you cannot define a transmitter for your scene before drawing a point object under a base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Point_Transmitter_Set | Point Transmitter Set]]'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The point transmitter set definition dialog.]] </td>
</tr>
</table>

Once you define a new transmitter set, its name is added in the '''Transmitters''' section of the navigation tree. The color of all the base points associated with the newly defined transmitter set changes, and an additional little ball with the transmitter color (red by default) appears at the location of each associated base point. You can open the property dialog of the transmitter set and modify a number of parameters including the '''Source Power''' in Watts and the broadcast signal '''Phase''' in degrees. The default transmitter power level is 1W or 30dBm. There is also a check box labeled '''Use Custom Input Power''', which is checked by default. In that case, the power and phase boxes are enabled and you can change the default 1W power and 0° phase values as you wish. [[EM.Cube]]'s ".RAD" radiation pattern files usually contain the value of "Total Radiated Power" in their file header. This quantity is calculated based on the particular excitation mechanism that was used to generate the pattern file in the original [[EM.Cube]] module. When the "Use Custom Input Power" check box is unchecked, EM.Terrano will use the total radiated power value of the radiation file for the SBR simulation.

{{Note|In order to modify any of the transmitter set's parameters, first you need to select the "User Defined Antenna" option, even if you want to keep the vertical half-wave dipole as your radiator.}}

<table>
<tr>
<td>
[[File:NewTxProp.png|thumb|left|720px|The property dialog of a point transmitter set.]]
</td>
</tr>
</table>

Your transmitter in EM.Teranno is indeed more sophisticated than a simple radiator. It consists of a basic "Transmitter Chain" that contains a voltage source with a series source resistance, and connected via a segment of transmission line to a transmit antenna, which is used to launch the broadcast signal into the free space. The transmitter's property dialog allows you to define the basic transmitter chain. Click the {{key|Transmitter Chain}} button of the Transmitter Set dialog to open the transmitter chain dialog. As shown in the figure below, you can specify the characteristics of the baseband/IF amplifier, mixer and power amplifier (PA) including stage gains and impedance mismatch factors (IMF) as well as the characteristics of the transmission line segment that connects the PA to the antenna. Note that the transmit antenna characteristics are automatically filled using the contents of the imported radiation pattern data file. The transmitter Chain dialog also calculates and reports the "Total Transmitter Chain Gain" based on your input. When you close this dialog and return to the Transmitter Set dialog, you will see the calculated value of the Effective Isotropic Radiated Power (EIRP) of your transmitter in dBm.

{{Note| If you do not modify the default parameters of the transmitter chain, a 50-Ω conjugate match condition is assumed and the power delivered to the antenna will be -3dB lower than your specified baseband power.}}

<table>
<tr>
<td> [[File:NewTxChain.png|thumb|left|720px|EM.Terrano's point transmitter chain dialog.]] </td>
</tr>
</table>

=== Defining a Point Receiver Set in the Formal Way ===

Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate the far-zone electric fields and the total received power at the location of a receiver. You need to define at least one receiver in the scene before you can run a SBR simulation. Similar to a transmitter, a receiver is a point radiator, too. EM.Terrano gives you three options for the radiator associated with a point receiver set:

* Half-wave dipole
* Polarization matched isotropic radiator
* User defined antenna pattern

By default, EM.Terrano assumes that your receiver is a vertically polarized (Z-directed) resonant half-wave dipole antenna. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. An isotropic radiator has a perfect omni-directional radiation pattern in all azimuth and elevation directions. An isotropic radiator doesn't exist physically in the real world, but it can be used simply as a point in space to compute the electric field.

You may also define a complicated radiation pattern for your receiver set. In that case, you need to import a radiation pattern data file to EM.Terrano similar to the case of a transmitter set.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point receiver set.}}

Similar to transmitter sets, you define a receiver set by associating it with an existing base location set with one or more point objects in the project workspace. All the receivers belonging to the same receiver set have the same radiator type. A typical propagation scene contains one or few transmitters but usually a large number of receivers. To generate a wireless coverage map, you need to define an array of points as your base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Point_Receiver_Set | Point Receiver Set]]'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The point receiver set definition dialog.]] </td>
</tr>
</table>

Once you define a new receiver set, its name is added to the '''Receivers''' section of the navigation tree. The color of all the base points associated with the newly defined receiver set changes, and an additional little ball with the receiver color (yellow by default) appears at the location of each associated base point. You can open the property dialog of the receiver set and modify a number of parameters.

<table>
<tr>
<td>
[[File:NewRxProp.png|thumb|left|720px|The property dialog of a point receiver set.]]
</td>
</tr>
</table>

In the Receiver Set dialog, there is a drop-down list labeled '''Selected Element''', which contains a list of all the individual receivers belonging to the receiver set. At the end of an SBR simulation, the button labeled {{key|Show Ray Data}} becomes enabled. Clicking this button opens the Ray Data dialog, where you can see a list of all the received rays at the selected receiver and their computed characteristics.

If you choose the "user defined antenna" option for your receiver set, it indeed consists of a basic "Receiver Chain" that contains a receive antenna connected via a segment of transmission line to the low-noise amplifier (LNA) that is terminated in a matched load. The receiver set's property dialog allows you to define the basic receiver chain. Click the {{key|Receiver Chain}} button of the Receiver Set dialog to open the receiver chain dialog. As shown in the figure below, you can specify the characteristics of the LNA such as its gain and noise figure in dB as well as the characteristics of the transmission line segment that connects the antenna to the LNA. Note that the receiving antenna characteristics are automatically filled from using contents of the radiation file. You have to enter values for antenna's '''Brightness Temperature''' as well as the temperature of the transmission line and the receiver's ambient temperature. The effective '''Receiver Bandwidth''' is assumed to be 100MHz, which you can change for the purpose of noise calculations. The Receive Chain dialog calculates and reports the "Noise Power" and "Total Receiver Chain Gain" based on your input. At the end of an SBR simulation, the receiver power and signal-noise ratio (SNR) of the selected receiver are calculated and they are reported in the receiver set dialog in dBm and dB, respectively. You can examine the properties of all the individual receivers and all the individual rays received by each receiver in your receiver set using the "Selected Element" drop-down list.

<table>
<tr>
<td> [[File:NewRxChain.png|thumb|left|720px|EM.Terrano's point receiver chain dialog.]] </td>
</tr>
</table>

=== Modulation Waveform and Detection ===

EM.Terrano allows you to define a digital modulation scheme for your communication link. There are currently 17 waveforms to choose from in the receiver set property dialog:

*OOK
*M-ary ASK
*Coherent BFSK
*Coherent QFSK
*Coherent M-ary FSK
*Non-Coherent BFSK
*Non-Coherent QFSK
*Non-Coherent M-ary FSK
*BPSK
*QPSK
*Offset QPSK
*M-ary PSK
*DBPSK
*pi/4 Gray-Coded DQPSK
*M-ary QAM
*MSK
*GMSK (BT = 0.3)

In the above list, you need to specify the '''No. Levels (M)''' for the Mary modulation schemes, from which the '''No. Bits per Symbol''' is determined. You can also define a bandwidth for the signal, which has a default value of 100MHz. Once the SNR of the signal is found, given the specified modulation scheme, the E<sub>b</sub>/N<sub>0</sub> parameter is determined, from which the bit error rate (BER) is calculated.

The Shannon – Hartley Equation estimates the channel capacity:

<math> C = B \log_2 \left( 1 + \frac{S}{N} \right) </math>

where B in the bandwidth in Hz, and C is the channel capacity (maximum data rate) expressed in bits/s.

The spectral efficiency of the channel is defined as

<math> \eta = \log_2 \left( 1 + \frac{S}{N} \right) </math>

The quantity E<sub>b</sub>/N<sub>0</sub> is the ratio of energy per bit to noise power spectral density. It is a measure of SNR per bit and is calculated from the following equation:

<math> \frac{E_b}{N_0} = \frac{ 2^\eta - 1}{\eta} </math>

where η is the spectral efficiency.

The relationship between the bit error rate and E<sub>b</sub>/N<sub>0</sub> depends on the modulation scheme and detection type (coherent vs. non-coherent). For example, for coherent QPSK modulation, one can write:

<math> P_b = 0.5 \; \text{erfc} \left( \sqrt{ \frac{E_b}{N_0} } \right) </math>

where P<sub>b</sub> is the bit error rate and erfc(x) is the complementary error function:

<math> \text{erfc}(x) = 1-\text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^2} dt </math>

The '''Minimum Required SNR''' parameter is used to determine link connectivity between each transmitter and receiver pair. If you check the box labeled '''Generate Connectivity Map''' in the receiver set property dialog, a binary map of the propagation scene is generated by EM.Terrano, in which one color represents a closed link and another represent no connection depending on the selected color map type of the graph. EM.Terrano also calculates the '''Max Permissible BER''' corresponding to the specified minimum required SNR and displays it in the receiver set property dialog.

=== A Note on EM.Terrano's Native Dipole Radiators ===

When you define a new transmitter set or a new receiver set, EM.Terrano assigns a vertically polarized half-wave dipole radiator to the set by default. The radiation pattern of this native dipole radiators is calculated using well-know expressions that are derived based on certain assumptions and approximations. For example, the far-zone electric field of a vertically-polarized dipole antenna can be expressed as:

<math> E_\theta(\theta,\phi) \approx j\eta_0 I_0 \frac{e^{-jk_0 r}}{2\pi r} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right] </math>

<math> E_\phi(\theta,\phi) \approx 0 </math>

where k<sub>0</sub> = 2π/λ<sub>0</sub> is the free-space wavenumber, λ<sub>0</sub> is the free-space wavelength, η<sub>0</sub> = 120π Ω is the free-space intrinsic impedance, I<sub>0</sub> is the current on the dipole, and L is the length of the dipole.

The directivity of the dipole antenna is given be the expression:

<math> D_0 \approx \frac{2}{F_1(k_0L) + F_2(k_0L) + F_3(k_0L)} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right]^2 </math>

with

<math> F_1(x) = \gamma + \text{ln}(x) - C_i(x) </math>

<math> F_2(x) = \frac{1}{2} \text{sin}(x) \left[ S_i(2x) - 2S_i(x) \right] </math>

<math> F_3(x) = \frac{1}{2} \text{cos}(x) \left[ \gamma + \text{ln}(x/2) + C_i(2x) - 2C_i(x) \right] </math>

where γ = 0.5772 is the Euler-Mascheroni constant, and C<sub>i</sub>(x) and S<sub>i</sub>(x) are the cosine and sine integrals, respectively:

<math> C_i(x) = - \int_{x}^{\infty} \frac{ \text{cos} \tau}{\tau} d\tau </math>

<math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>

In the case of a half-wave dipole, L = λ<sub>0</sub>/2, and D<sub>0</sub> = 1.643. Moreover, the input impedance of the dipole antenna is Z<sub>A</sub> = 73 + j42.5 Ω. These dipole radiators are connected via 50Ω transmission lines to a 50Ω source or load. Therefore, there is always a certain level of impedance mismatch that violates the conjugate match condition for maximum power.

<table>
<tr>
<td> [[File:Dipole radiators.png|thumb|720px|EM.Terrano's native half-wave dipole transmitter and receiver.]] </td>
</tr>
</table>

On the other hand, we you specify a user-defined antenna pattern for the transmitter or receiver sets, you import a 3D radiation pattern file that contains all the values of E<sub>θ</sub> and E<sub>φ</sub> for all the combinations of (θ, φ) angles. Besides the three native dipole radiators, [[EM.Cube]] also provides 3D radiation pattern files for three X-, Y- and Z-polarized half-wave resonant dipole antennas. These pattern data were generated using a full-wave solver like [[EM.Libera]]'s wire MOM solver. The names of the radiation pattern files are:

* DPL_STD_X.RAD
* DPL_STD_Y.RAD
* DPL_STD_Z.RAD

and they are located in the folder "\Documents\EMAG\Models" on your computer. Note that these are full-wave simulation data and do not involve any approximate assumptions. To use these files as an alternative to the native dipole radiators, you need to select the '''User Defined Antenna Pattern''' radio button as the the radiator type in the transmitter or receiver set property dialog.

=== A Note on the Rotation of Antenna Radiation Patterns ===

EM.Terrano's Transmitter Set dialog and Receiver Set dialog both allow you to rotate an imported radiation pattern. In that case, you need to specify the '''Rotation''' angles in degrees about the X-, Y- and Z-axes. It is important to note that these rotations are performed sequentially and in the following order: first a rotation about the X-axis, then a rotation about the Y-axis, and finally a rotation about the Z-axis. In addition, all the rotations are performed with respect to the "rotated" local coordinate systems (LCS). In other words, the first rotation with respect to the local X-axis transforms the XYZ LCS to a new primed X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS. The second rotation is performed with respect to the new Y<sup>′</sup>-axis and transforms the X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS to a new double-primed X<sup>′′</sup>Y<sup>′′</sup>Z<sup>′′</sup> LCS. The third rotation is finally performed with respect to the new Z<sup>′′</sup>-axis. The figures below shows single and double rotations.

<table>
<tr>
<td> [[File:PROP22B.png|thumb|300px|The local coordinate system of a linear dipole antenna.]] </td>
<td> [[File:PROP22C.png|thumb|600px|Rotating the dipole antenna by +90° about the local Y-axis.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[File:PROP22D.png|thumb|720px|Rotating the dipole antenna by +90° about the local X-axis and then by -45° by the local Y-axis.]] </td>
</tr>
</table>

=== Adjustment of Tx/Rx Elevation above a Terrain Surface ===

When your transmitters or receivers are located above a flat terrain like the global ground, their Z-coordinates are equal to their height above the ground, as the terrain elevation is fixed and equal to zero everywhere. In many propagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across the scene. In that case, you may want to place your transmitters or receivers at a certain height above the underlying ground. The Z-coordinate of a transmitter or receiver is now the sum of the terrain elevation at the base point and the specified height. EM.Terrano gives you the option to adjust the transmitter and receiver sets to the terrain elevation. This is done for individual transmitter sets and individual receiver sets. At the top of the Transmitter Dialog there is a check box labeled "'''Adjust Tx Sets to Terrain Elevation'''". Similarly, at the top of the Receiver Dialog there is a check box labeled "'''Adjust Rx Sets to Terrain Elevation'''". These boxes are unchecked by default. As a result, your transmitter sets or receiver sets coincide with their associated base points in the project workspace. If you check these boxes and place a transmitter set or a receiver set above an irregular terrain, the transmitters or receivers are elevated from the location of their associated base points by the amount of terrain elevation as can be seen in the figure below.

To better understand why there are two separate sets of points in the scene, note that a point array (CAD object) is used to create a uniformly spaced base set. The array object always preserves its grid topology as you move it around the scene. However, the transmitters or receivers associated with this point array object are elevated above the irregular terrain and no longer follow a strictly uniform grid. If you move the base set from its original position to a new location, the base points' topology will stay intact, while the associated transmitters or receivers will be redistributed above the terrain based on their new elevations.

<table>
<tr>
<td>
[[Image:PROP MAN8.png|thumb|left|640px|A transmitter (red) and a grid of receivers (yellow) adjusted above a plateau terrain surface. The underlying base point sets (blue and orange dots) associated with the adjusted transmitters and receivers on the terrain are also visible in the figure.]]
</td>
</tr>
</table>

== Discretizing the Propagation Scene in EM.Terrano ==

=== Why Do You Need to Discretize the Scene? ===

EM.Terrano's SBR solver uses a method known as Geometrical Optics (GO) in conjunction with the Uniform Theory of Diffraction (UTD) to trace the rays from their originating point at the source to the individual receiver locations. Rays may hit obstructing objects on their way and get reflected, diffracted or transmitted. EM.Terrano's SBR solver can only handle diffraction off linear edges and reflection from and transmission through planar interfaces. When an incident ray hits the surface of the obstructing object, a local planar surface assumption is made at the specular point. The assumptions of linear edges and planar facets obviously work in the case of a scene with cubic buildings and a flat global ground.

In many practical scenarios, however, your buildings may have curved surfaces, or the terrain may be irregular. EM.Terrano allows you to draw any type of surface or solid geometric objects such as cylinders, cones, etc. under impenetrable and penetrable surface groups or penetrable volumes. EM.Terrano's mesh generator creates a triangular surface mesh of all the objects in your propagation scene, which is called a facet mesh. Even the walls of cubic buildings are meshed using triangular cells. This enables EM.Terrano to properly discretize composite buildings made of conjoined cubic objects.

Unlike [[EM.Cube]]'s other computational modules, the density or resolution of EM.Terrano's surface mesh does not depend on the operating frequency and is not expressed in terms of the wavelength. The sole purpose of EM.Terrano's facet mesh is to discretize curved and irregular scatterers into flat facets and linear edges. Therefore, geometrical fidelity is the only criterion for the quality of a facet mesh. It is important to note that discretizing smooth objects using a triangular surface mesh typically creates a large number of small edges among the facets that are simply mesh artifacts and should not be considered as diffracting edges. For example, each rectangular face of a cubic building is subdivided into four triangles along the two diagonals. The four internal edges lying inside the face are obviously not diffracting edges. A lot of subtleties like these must be taken into account by the SBR solver to run accurate and computationally efficient simulations.

=== Generating the Facet Mesh ===

You can view and examine the discretized version of your scene's objects as they are sent to the SBR simulation engine. You can adjust the mesh resolution and increase the geometric fidelity of discretization by creating more and finer triangular facets. On the other hand, you may want to reduce the mesh complexity and send to the SBR engine only a few coarse facets to model your buildings. The resolution of EM.Terrano's facet mesh generator is controlled by the '''Cell Edge Length''' parameter, which is expressed in project length units. The default mesh cell size of 100 units might be too large for non-flat objects. You may have to set a smaller cell edge length in EM.Terrano's Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the curvature of your curved structures adequately.

<table>
<tr>
<td>
[[Image:prop_manual-29.png|thumb|left|480px|EM.Terrano's mesh settings dialog.]]
</td>
</tr>
</table>

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Facet_Mesh | EM.Terrano's Facet Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:UrbanCanyon2.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 100m.]] </td>
</tr>
<tr>
<td> [[Image:UrbanCanyon3.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 10m.]] </td>
</tr>
</table>

== Running Ray Tracing Simulations in EM.Terrano ==

EM.Terrano provides a number of different simulation or solver types:

* 3D SBR Ray Tracer
* Channel Analyzer
* Polarimatrix Solver
* Radar Simulator

The first three simulation types are described below. For a description of EM.Terrano's Radar Simulator, follow this link.

=== Running a Single-Frequency SBR Analysis ===

Its main solver is the '''3D SBR Ray Tracer'''. Once you have set up your propagation scene in EM.Terrano and have defined sources/transmitters and observables/receivers for your scene, you are ready to run a SBR ray tracing simulation. You set the simulation mode in EM.Terrano's simulation run dialog. A single-frequency SBR analysis is a single-run simulation and the simplest type of ray tracing simulation in EM.Terrano. It involves the following steps:

* Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''. Wireless propagation problems usually require meter, mile or kilometer as the project unit.
* Create the blocks and draw the buildings at the desired locations.
* Keep the default ray domain and accept the default global ground or change its material properties.
* Define an excitation source and observables for your project.
* If you intend to use transmitters and receivers in your scene, first define the required base sets and then define the transmitter and receiver sets based on them.
* Run the SBR simulation engine.
* Visualize the coverage map and plot other data.

You can access EM.Terrano's Simulation Run dialog by clicking the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Simulate → Run...''' or using the keyboard shortcut {{key|Ctrl+R}}. When you click the {{key|Run}} button, a new window opens up that reports the different stages of the SBR simulation and indicates the progress of each stage. After the SBR simulation is successfully completed, a message pops up and prompts the completion of the process.

<table>
<tr>
<td>
[[Image:Terrano L1 Fig16.png|thumb|left|480px|EM.Terrano's simulation run dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN10.png|thumb|left|550px|EM.Terrano's output message window.]]
</td>
</tr>
</table>

=== Changing the SBR Engine Settings ===

There are a number of SBR simulation settings that can be accessed and changed from the Ray Tracing Engine Settings Dialog. To open this dialog, click the button labeled {{key|Settings}} on the right side of the '''Select Simulation or Solver Type''' drop-down list in the Run Dialog. EM.Terrano's SBR simulation engine allows you to separate the physical effects that are calculated during a ray tracing process. You can selectively enable or disable '''Reflection/Transmission''' and '''Edge Diffraction''' in the "Ray-Block Interactions" section of this dialog. By default, ray reflection and transmission and edge diffraction effects are enabled. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in the scene.

EM.Terrano allows a finite number of ray bounces for each original ray emanating from a transmitter. This is very important in situations that may involve resonance effects where rays get trapped among multiple surfaces and may bounce back and forth indefinitely. This is set using the box labeled "'''Max No. Ray Bounces'''", which has a default value of 10. Note that the maximum number of ray bounces directly affects the computation time as well as the size of output simulation data files. This can become critical for indoor propagation scenes, where most of the rays undergo a large number of reflections. Two other parameters control the diffraction computations: '''Max Wedge Angle''' in degrees and '''Min Edge Length''' in project units. The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or coplanar with no diffraction effect. The default value of the maximum wedge angle is 170°. The minimum edge length is size of the common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the minimum edge length is one project units.

<table>
<tr>
<td>
[[Image:PROP MAN11.png|thumb|left|720px|EM.Terrano's SBR simulation engine settings dialog.]]
</td>
</tr>
</table>

As rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish. From a practical point of view, only rays that have power levels above the receiver sensitivity can be effectively received. Therefore, all the rays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default value of -150dBm. Keep in mind that the value of this threshold directly affects the accuracy of the simulation results as well as the size of the output data file.

You can also set the '''Ray Angular Resolution''' of the transmitter rays in degrees. By default, every transmitter emanates equi-angular ray tubes at a resolution of 1 degree. Lower angular resolutions larger than 1° speed up the SBR simulation significantly, but they may compromise the accuracy. Higher angular resolutions less than 1° increase the accuracy of the simulating results, but they also increase the computation time. The SBR Engine Settings dialog also displays the '''Recommended Ray Angular Resolution''' in degrees in a grayed-out box. This number is calculated based on the overall extents of your computational domain as well as the SBR mesh resolution. To see this value, you have to generate the SBR mesh first. Keeping the angular resolution of your project above this threshold value makes sure that the small mesh facets at very large distances from the source would not miss any impinging ray tubes during the simulation.

EM.Terrano gives a few more options for the ray tracing solution of your propagation problem. For instance, it allows you to exclude the direct line-of-sight (LOS) rays from the final solution. There is a check box for this purpose labeled "Exclude direct (LOS) rays from the solution", which is unchecked by default. EM.Terrano also allows you to superpose the received rays incoherently. In that case, the powers of individual ray are simply added to compute that total received power. This option in the check box labeled "Superpose rays incoherently" is disabled by default, too.

At the end of a ray tracing simulation, the electric field of each individual ray is computed and reported. By default, the actual received ray fields are reported, which are independent of the radiation pattern of the receive antennas. EM.Terrano provides a check box labeled "Normalize ray's E-field based on receiver pattern", which is unchecked by default. If this box is checked, the field of each ray is normalized so as to reflect that effect of the receiver antenna's radiation pattern. The received power of each ray is calculated from the following equation:

<math> P_{ray} = \frac{ | \mathbf{E_{norm}} |^2 }{2\eta_0} \frac{\lambda_0^2}{4\pi} </math>

It can be seen that if the ray's E-field is not normalized, the computed ray power will correspond to that of a polarization matched isotropic receiver.

=== Polarimetric Channel Analysis ===

In a 3D SBR simulation, a transmitter shoots a large number of rays in all directions. The electric fields of these rays are polarimetric and their strength and polarization are determined by the designated radiation pattern of the transmit antenna. The rays travel in the propagation scene and bounce from the ground and buildings or other scatterers or get diffracted at the building edges until they reach the location of the receivers. Each individual ray has its own vectorial electric field and power. The electric fields of the received rays are then superposed coherently and polarimetrically to compute the total field at the receiver locations. The designated radiation pattern of the receivers is then used to compute the total received power by each individual receiver.

From a theoretical point of view, the radiation patterns of the transmit and receive antennas are independent of the propagation channel characteristics. For the given locations of the point transmitters and receivers, one can assume ideal isotropic radiators at these points and compute the polarimetric transfer function matrix of the propagation channel. This matrix relates the received electric field at each receiver location to the transmitted electric field at each transmitter location. In general, the vectorial electric field of each individual ray is expressed in the local standard spherical coordinate system at the transmitter and receiver locations. In other words, the polarimetric channel matrix expresses the '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components associated with each ray at the receiver location to its '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components at the transmitter location. Each ray has a delay and θ and φ angles of departure at the transmitter location and θ and φ angles of departure at the receiver location.

To perform a polarimatric channel characterization of your propagation scene, open EM.Terrano's Run Simulation dialog and select '''Channel Analyzer''' from the drop-down list labeled '''Select Simulation or Solver Type'''. At the end of the simulation, a large ray database is generated with two data files called "sbr_channel_matrix.DAT" and "sbr_ray_path.DAT". The former file contains the delay, angles of arrival and departure and complex-valued elements of the channel matrix for all the individual rays that leave each transmitter and arrive at each receiver. The latter file contains the geometric aspects of each ray such as hit point coordinates.

=== The "Almost Real-Time" Polarimatrix Solver ===

After EM.Terrano's channel analyzer generates a ray database that characterizes your propagation channel polarimetrically for all the combinations of transmitter and receiver locations, a ray tracing solution of the propagation problem can readily be found in almost real time by incorporating the effects of the radiation patterns of transmit and receive antennas. This is done using the '''Polarimatrix Solver''', which is the third option of the drop-down list labeled '''Select Simulation or Solver Type''' in EM.Terrano's Run Simulation dialog. The results of the Polarimatrix and 3D SBR solvers must be identical from a theoretical point of view. However, there might be small discrepancies between the two solutions due to roundoff errors.

Using the Polarimatrix solver can lead to a significant reduction of the total simulation time in sweep simulations that involve a large number of transmitters and receivers. Certain simulation modes of EM.Terrano are intended for the Polarimatrix solver only as will be described in the next section.

{{Note| In order to use the Polarimatrix solver, you must first generate a ray database of your propagation scene using EM.Terrano's Channel Analyzer.}}

=== EM.Terrano's Simulation Modes ===

EM.Terrano provides a number of different simulation modes that involve single or multiple simulation runs:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Which Solver?
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Single-Frequency SBR Analysis | Single-Frequency Analysis]]
| style="width:180px;" | Simulates the propagation scene "As Is"
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:180px;" | Varies the operating frequency of the ray tracer
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at a specified set of frequency samples
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:180px;" | Varies the value(s) of one or more project variables
| style="width:150px;" | SBR
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires definition of sweep variables, works only with SBR solver as the physical scene may change during the sweep
|-
| style="width:120px;" | [[#Transmitter_Sweep | Transmitter Sweep]]
| style="width:180px;" | Activates two or more transmitters sequentially with only one transmitter broadcasting at each simulation run
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires at least two transmitters in the scene, works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Rotational_Sweep | Rotational Sweep]]
| style="width:180px;" | Rotates the radiation pattern of the transmit antenna(s) sequentially to model beam steering
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Mobile_Sweep | Mobile Sweep]]
| style="width:180px;" | Considers one pair of active transmitter and receiver at each simulation run to model a mobile communication link
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires the same number of transmitters and receivers, works only with Polarimatrix solver and requires an existing ray database
|}

Click on each item in the above list to learn more about each simulation mode.

You set the simulation mode in EM.Terrano's simulation run dialog using the drop-down list labeled '''Simulation Mode'''. A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can plot the output parameter results on 2D graphs or you can animate the 3D simulation data from the navigation tree.

{{Note| EM.Terrano's frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent.}}

=== Transmitter Sweep ===

When your propagation scene contains two or more transmitters, whether they all belong to the same transmitter set with the same radiation pattern or to different transmitter sets, EM.Terrano assumes all to be coherent with respect to one another. In other words, synchronous transmitters are always assumed. The rays originating from all these transmitters are superposed coherently and vectorially at each receiver. In a transmitter sweep, on the other hand, EM.Terrano assumes only one transmitter broadcasting at a time. The result of the sweep simulation is a number of received power coverage maps, each corresponding to a transmitter in the scene.

{{Note| EM.Terrano's transmitter sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Rotational Sweep ===

You can rotate the 3D radiation patterns of both the transmitters and receivers from the property dialog of the parent transmitter set or receiver set. This is done in advance before a SBR simulation starts. You can define one or more of the rotation angles of a transmitter set or a receiver set as sweep variables and perform a parametric sweep simulation. In that case, the entire scene and all of its buildings are discretized at each simulation run and a complete physical SBR ray tracing simulation is carried out. However, we know that the polarimetric characteristics of the propagation channel are independent of the transmitter or receiver antenna patterns or their rotation angles. A rotational sweep allows you to rotate the radiation pattern of the transmitter(s) about one of the three principal axes sequentially. This is equivalent to the steering of the beam of the transmit antenna either mechanically or electronically. The result of the sweep simulation is a number of received power coverage maps, each corresponding to one of the angular samples. To run a rotational sweep, you must specify the rotation angle.

{{Note| EM.Terrano's rotational sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Mobile Sweep ===

In a mobile sweep, each transmitter is paired with a receiver according to their indices in their parent sets. At each simulation run, only one (Tx, Rx) pair is considered to be active in the scene. As a result, the generated coverage map takes a different meaning implying the sequential movement of the transmitter and receiver pair along their corresponding paths. In other words, the set of point transmitters and the set of point receivers indeed represent the locations of a single transmitter and a single receiver at different instants of time. It is obvious that the total number of transmitters and total number of receivers in the scene must be equal. Otherwise, EM.Terrano will prompt an error message.

[[EM.Cube]] provides a '''Mobile Path Wizard''' that facilitates the creation of a transmitter set or a receiver set along a specified path. This path can be an existing nodal curve (polyline or NURBS curve) or an existing line objects. You can also import a sptial Cartesian data file containing the coordinates of the base location points. For more information, refer to [[Glossary_of_EM.Cube%27s_Wizards#Mobile_Path_Wizard | Mobile Path Wizard]].

{{Note| EM.Terrano's mobile sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Investigating Propagation Effects Selectively One at a Time ===

In a typical SBR ray tracing simulation, EM.Terrano includes all the propagation effects such as direct (LOS) rays, ray reflection and transmission, and edge diffractions. At the end of a SBR simulation, you can visualize the received power coverage map of your propagation scene, which appears under the receiver set item in the navigation tree. The figure below shows the received power coverage map of the random city scene with a vertically polarized half-wave dipole transmitter located 10m above the ground and a large grid of vertically polarized half-wave dipole receivers placed 1.5m above the ground. The legend box shows the limits of the color map between -23dBm as the maximum and -150dB (the default receiver sensitivity value) as the minimum.

<table>
<tr>
<td>
[[Image:UrbanCanyon10.png|thumb|left|640px|The received power coverage map of the random city scene with a dipole transmitter.]]
</td>
</tr>
</table>

Sometime it is helpful to change the scale of the color map to better understand the dynamic range of the coverage map. If you double-click on the legend or right-click on the coverage map's name in the navigation tree and select '''Properties''', the Plot Settings dialog opens up. Select the '''User-Defined''' item and set the lower and upper bounds of color map as you wish.

<table>
<tr>
<td>
[[Image:UrbanCanyon15.png|thumb|left|480px|The plot settings dialog of the coverage map.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon16.png|thumb|left|640px|The received power coverage map of the random city scene with a user-defined color map scale between -80dBm and -20dBm.]]
</td>
</tr>
</table>

To better understand the various propagation effects, EM.Terrano allows you to enable or disable these effects selectively. This is done from the Ray Tracing Simulation Engine Settings dialog using the provided check boxes.

<table>
<tr>
<td>
[[Image:UrbanCanyon14.png|thumb|left|640px|EM.Terrano's simulation run dialog showing the check boxes for controlling various propagation effects.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon11.png|thumb|left|640px|The received power coverage map of the random city scene with direct LOS rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon12.png|thumb|left|640px|The received power coverage map of the random city scene with reflected rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon13.png|thumb|left|640px|The received power coverage map of the random city scene with diffracted rays only.]]
</td>
</tr>
</table>

== Working with EM.Terrano's Simulation Data ==

=== The Ray Tracing Solvers' Output Simulation Data ===

Both the SBR solver and the Polarimatrix solver perform the same type of simulation but in two different ways. The SBR solver discretizes the scene including all the buildings and terrain, shoots a large number of rays from the transmitters and collects the rays at the receivers. The Polarimatrix solver does the same thing using an existing polarimetric ray database that has been previously generated using EM.Terrano's Channel Analyzer. It incorporates the effects of the radiation patterns of the transmit and receive antennas in conjunction with the polarimetric channel characteristics. At the end of a ray tracing simulation, all the polarimetric rays emanating from the transmitter(s) or other sources that are received by the individual receivers are computed, collected, sorted and saved into ASCII data files. From the ray data, the total electric field at the location of receivers as well as the total received power are computed. The individual ray data include the field components of each ray, the ray's elevation and azimuth angles of departure and arrival (departure from the transmitter location and arrival at the receiver location), and time delay of the received ray with respect to the transmitter. If you specify the temperatures, noise figure and transmission line losses in the definition of the receiver sets, the noise power level and signal-to-noise ratio (SNR) at each receiver are also calculated, and so are the E<sub>b</sub>/N<sub>0</sub> and bit error rate (BER) for the selected digital modulation scheme.

=== Visualizing Field & Received Power Coverage Maps ===

In wireless propagation modeling for communication system applications, the received power at the receiver location is more important than the field distributions. In order to compute the received power, you need three pieces of information:

* '''Total Transmitted Power (EIRP)''': This requires knowledge of the baseband signal power, the transmitter chain parameters, the transmission characteristics of the transmission line connecting the transmitter circuit to the transmitting antenna and the radiation characteristics of the transmitting antenna.
* '''Channel Path Loss''': This is computed through SBR simulation.
* '''Receiver Properties''': This includes the radiation characteristics of the receiving antenna, the transmission characteristics of the transmission line connecting the receiving antenna to the receiver circuit and the receiver chain parameters.

In a simple link scenario, the received power P<sub>r</sub> in dBm is found from the following equation:

<math> P_r [dBm] = P_t [dBm] + G_{TC} + G_{TA} - PL + G_{RA} + G_{RC} </math>

where P<sub>t</sub> is the baseband signal power in dBm at the transmitter, G<sub>TC</sub> and G<sub>RC</sub> are the total transmitter and receiver chain gains in dB, respectively, G<sub>TA</sub> and G<sub>RA</sub> are the total transmitting and receiving antenna gains in dB, respectively, and PL is the channel path loss in dB. Keep in mind that EM.Terrano is fully polarimetric. The transmitting and receiving antenna characteristics are specified through the imported radiation pattern files, which are part of the definition of the transmitters and receivers. In particular, the polarization mismatch losses are taken into account through the polarimetric SBR ray tracing analysis.

If you specify the noise-related parameters of your receiver set, the signal-to-noise ratios (SNR) is calculated at each receiver location: SNR = P<sub>r</sub> - P<sub>n</sub>, where P<sub>n</sub> is the noise power level in dB. When planning, designing and deploying a communication system between points A and B, the link is considered to be closes and a connection established if the received signal power at the location of the receiver is above the noise power level by a certain threshold. In other words, the SNR at the receiver must be greater than a certain specified minimum SNR level. You specify (SNR)<sub>min</sub> ss part of the definition of receiver chain in the Receiver Set dialog. In the "Visualization Options" section of this dialog, you can also check the check box labeled '''Generate Connectivity Map'''. This is a binary-level black-and-white map that displays connected receivers in white and disconnected receivers in black. At the end of an SBR simulation, the computed SNR is displayed in the Receiver Set dialog for the selected receiver. The connectivity map is generated and added to the navigation tree underneath the received power coverage map node.

At the end of an SBR simulation, you can visualize the field maps and receiver power coverage map of your receiver sets. A coverage map shows the total '''Received Power''' by each of the receivers and is visualized as a color-coded intensity plot. Under each receiver set node in the navigation tree, a total of seven field maps together with a received power coverage map are added. The field maps include amplitude and phase plots for the three X, Y, Z field components plus a total electric field plot. To display a field or coverage map, simply click on its entry in the navigation tree. The 3D plot appears in the Main Window overlaid on your propagation scene. A legend box on the right shows the color scale and units (dB). The 3D coverage maps are displayed as horizontal confetti above the receivers. You can change the appearance of the receivers and maps from the property dialog of the receiver set. You can further customize the settings of the 3D field and coverage plots.

<table>
<tr>
<td>
[[Image:AnnArbor Scene1.png|thumb|left|640px|The downtown Ann Arbor propagation scene.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene2.png|thumb|left|640px|The electric field distribution map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene3.png|thumb|left|640px|The received power coverage map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene4.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 3dB with the basic color map option.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene5.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 20dB with the basic color map option.]]
</td>
</tr>
</table>

=== Visualizing the Rays in the Scene ===

At the end of a SBR simulation, each receiver receives a number of rays. Some receivers may not receive any rays at all. You can visualize all the rays received by a certain receiver from the active transmitter of the scene. To do this, right click the '''Receivers''' item of the Navigation Tree. From the context menu select '''Show Received Rays'''. All the rays received by the currently selected receiver of the scene are displayed in the scene. The rays are identified by labels, are ordered by their power and have different colors for better visualization. You can display the rays for only one receiver at a time. The receiver set property dialog has a list of all the individual receivers belonging to that set. To display the rays received by another receiver, you have to change the '''Selected Receiver''' in the receiver set's property dialog. If you keep the mouse focus on this dropdown list and roll your mouse scroll wheel, you can scan the selected receivers and move the rays from one receiver to the next in the list. To remove the visualized rays from the scene, right click the Receivers item of the Navigation Tree again and from the context menu select '''Hide Received Rays'''.

You can also view the ray parameters by opening the property dialog of a receiver set. By default, the first receiver of the set is always selected. You can select any other receiver from the drop-down list labeled '''Selected Receiver'''. If you click the button labeled '''Show Ray Data''', a new dialog opens up with a table that contains all the received rays at the selected receiver and their parameters:

* Delay is the total time delay that a ray experiences travelling from the transmitter to the receiver after all the reflections, transmissions and diffractions and is expressed in nanoseconds.
* Ray Field is the received electric field at the receiver location due to a specific ray and is given in dBV/m.
* Ray Power is the received power at the receiver due to a specific ray and is given in dBm.
* Angles of Arrival are the θ and φ angles of the incoming ray at the local spherical coordinate system of the receiver.

<table>
<tr>
<td>
[[Image:UrbanCanyon17.png|thumb|left|720px|EM.Terrano's ray data dialog showing a selected ray.]]
</td>
</tr>
</table>

The Ray Data Dialog also shows the '''Total Received Power''' in dBm and '''Total Received Field''' in dBV/m due to all the rays received by the receiver. You can sort the rays based on their delay, field, power, etc. To do so, simply click on the grey column label in the table to sort the rays in ascending order based on the selected parameter. You can also select any ray by clicking on its '''ID''' and highlighting its row in the table. In that case, the selected rays is highlighted in the Project Workspace and all the other rays become thin (faded).

{{Note|All the received rays are summed up coherently in a vectorial manner at the receiver location.}}

<table>
<tr>
<td> [[Image:UrbanCanyon18.png|thumb|left|640px|Visualization of received rays at the location of a selected receiver in the random city scene.]] </td>
</tr>
</table>

=== The Standard Output Data File ===

At the end of an SBR simulation, EM.Terrano writes a number of ASCII data files to your project folder. The main output data file is called "sbr_results.RTOUT". This file contains all the information about individual receivers and the parameters of each ray that is received by each individual receiver.
At the end of an SBR simulation, the results are written into a main output data file with the reserved name of SBR_Results.RTOUT. This file has the following format:

Each receiver line has the following information:

* Receiver ID
* Receiver X, Y, Z coordinates
* Total received power in dBm
* Total number of received rays

Each rays line received by a receiver has the following information:

* Ray Index
* Delay in nsec
* θ and φ Angles of Arrival in deg
* θ and φ Angles of Departure in deg
* Real and imaginary parts of the three E<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub> components
* Number of ray hit points
* Coordinates of individual hit points

The angles of arrival are the θ and φ angles of a received ray measured in degrees and are referenced in the local spherical coordinate systems centered at the location of the receiver. The angles of departure for a received ray are the θ and φ angles of the originating transmitter ray, measured in degrees and referenced in the local spherical coordinate systems centered at the location of the active transmitter, which eventually arrives at the receiver. The total time delay is measured in nanoseconds between t = 0 nsec at the time of launch from the transmitter location till being received at the receiver location.

<table>
<tr>
<td>
[[Image:prop_run8_tn.png|thumb|left|720px|A typical SBR output data file.]]
</td>
</tr>
</table>

=== Plotting Other Simulation Results ===

Besides "sbr_results.out", [[EM.Terrano]] writes a number of other ASCII data files to your project folder. You can view or plot these data in [[EM.Cube]]'s Data Manager. You can open data manager by clicking the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Menu > Simulate > Data Manager''' from the menu bar or by right-clicking on the '''Data Manager''' item of the navigation tree and selecting '''Open Data Manager...''' from the contextual menu or by using the keyboard shortcut {{key|Ctrl+D}}.

The available data files in the "2D Data Files" tab of Data Manger include:

* '''Path Loss''': The channel path loss is defined as PL = P<sub>r</sub> - EIRP. The path loss data are stored in a file called "SBR_receiver_set_name_PATHLOSS.DAT" as a function of the receiver index. The path loss data make sense only if your receiver set has the default isotropic radiator.
* '''Power Delay Profile''': The delays of the individual rays received by the selected receiver with respect to the transmitter are expressed in ns and tabulated together with the power of each ray in the file "SBR_receiver_set_name_DELAY.DAT". You can plot these data from the Data Manager as a bar chart called the power delay profile. The bars indeed correspond to the difference between the ray power in dBm and the minimum power threshold level in dBm, which makes them a positive quantity.
* '''Angles of Arrival''': These are the Theta and Phi angles of the individual rays received by the selected receiver and saved to the files "SBR_receiver_set_name_ThetaARRIVAL.ANG" and "SBR_receiver_set_name_PhiARRIVAL.ANG". You can plot them in the Data Manager in polar stem charts.

When you run a frequency or parametric sweep in [[EM.Terrano]], a tremendous amount of data may be generated. [[EM.Terrano]] only stores the '''Received Power''', '''Path Loss''' and '''SNR''' of the selected receiver
in ASCII data files called "PREC_i.DAT", "PL_i.DAT" and "SNR_i.DAT", where is the index of the receiver set in your scene. These quantities are tabulated vs. the sweep variable's samples. You can plot these files in EM.Grid.

[[Image:Info_icon.png|40px]] Click here to learn more about working with data filed and plotting graphs in [[EM.Cube]]'s '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#The_Data_Manager | Data Manager]]'''.

<table>
<tr>
<td> [[Image:Terrano pathloss.png|thumb|360px|Cartesian graph of path loss.]] </td>
<td> [[Image:Terrano delay.png|thumb|360px|Bar graph of power delay profile.]] </td>
</tr>
<tr>
<td> [[Image:Terrano ARR phi.png|thumb|360px|Polar stem graph of Phi angle of arrival.]] </td>
<td> [[Image:Terrano ARR theta.png|thumb|360px|Polar stem graph of Theta angle of arrival.]] </td>
</tr>
<tr>
<td> [[Image:Terrano DEP phi.png|thumb|360px|Polar stem graph of Phi angle of departure.]] </td>
<td> [[Image:Terrano DEP theta.png|thumb|360px|Polar stem graph of Theta angle of departure.]] </td>
</tr>
</table>

=== Visualizing 3D Radiation Patterns of Transmit and Receive Antennas in the Scene ===

When you designate a "User Defined Antenna Pattern" as the radiator type of a transmitter set or a receiver set, EM.Terrano copies the imported radiation pattern data file from its original folder to the current project folder. The name of the ".RAD" file is listed under the '''3D Data Files''' tab of the data manager. Sometimes it might be desired to visualize these radiation patterns in your propagation scene at the actual location of the transmitter or receiver. To do so, you have to define a new '''Radiation Pattern''' observable in the navigation tree. The label of the new observable must be identical to the name of the ".RAD" data file. In addition, the Theta and Phi angle increments of the new radiation pattern observable (expressed in degrees) must be identical to the Theta and Phi angular resolutions of the imported pattern file. If all these conditions are met, then go to the '''Simulate Menu''' and select the item '''Update All 3D Visualization'''. The contents of the 3D radiation patterns are added to the navigation tree. Click on one of the radiation pattern items in the navigation tree and it will be displayed in the scene.

<table>
<tr>
<td>
[[Image:UrbanCanyon6.png|thumb|left|640px|The received power coverage map of the random city scene with a highly directional dipole array transmitter.]]
</td>
</tr>
</table>

By Default, [[EM.Cube]] always visualizes the 3D radiation patterns at the origin of coordinates, i.e. at (0, 0, 0). This is because that radiation pattern data are computed in the standard spherical coordinate system centered at (0, 0, 0). The theta and phi components of the far-zone electric fields are defined with respect to the X, Y and Z axes of this system. When visualizing the 3D radiation pattern data in a propagation scene, it is more intuitive to display the pattern at the location of the transmitter or receiver. The Radiation Pattern dialog allows you to translate the pattern visualization to any arbitrary point in the project workspace. It also allows you to scale up or scale down the pattern visualization with respect to the background scene.

In the example shown above, the imported pattern data file is called "Dipole_Array1.RAD". Therefore, the label of the radiation pattern observable is chosen to be "Dipole_Array1". The theta and phi angle increments are both 1° in this case. The radiation pattern has been elevated by 10m to be positioned at the location of the transmitter and a scaling factor of 0.3 has been used.

<table>
<tr>
<td>
[[Image:UrbanCanyon8.png|thumb|left|640px|Setting the pattern parameters in the radiation pattern dialog.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon7.png|thumb|left|720px|Visualization of the 3D radiation pattern of the directional transmitter in the random city scene.]]
</td>
</tr>
</table>

There is an important catch to remember here. When you define a radiation pattern observable for your project, EM.Terrano will attempt to compute the overall effective radiation pattern of the entire physical structure. However, in this case, you defined the radiation pattern observable merely for visualization purposes. To stop EM.Terrano from computing the actual radiation pattern of your entire scene, there is a check box in EM.Terrano's Ray Tracer Simulation Engine Settings dialog that is labeled '''Do not compute new radiation patterns'''. This box is checked by default, which means the actual radiation pattern of your entire scene will not be computed automatically. But you need to remember to uncheck this box if you ever need to compute a new radiation pattern using EM.Terrano's SBR solver as an asymptotic EM solver (see next section).

<table>
<tr>
<td>
[[Image:UrbanCanyon9.png|thumb|left|640px|EM.Terrano's Run Simulation dialog.]]
</td>
</tr>
</table>

== Using EM.Terrano as an Asymptotic Field Solver ==

Like every other electromagnetic solver, EM.Terrano's SBR ray tracer requires an excitation source and one or more observables for the generation of simulation data. EM.Terrano offers several types of sources and observables for a SBR simulation. You already learned about the transmitter set as a source and the receiver set as an observable. You can mix and match different source types and observable types depending on the requirements of your modeling problem.

The available source types in EM.Terrano are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:transmitter_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Transmitter Set | Point Transmitter Set]]
| style="width:250px;" | Modeling realsitic antennas & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source | Hertzian Short Dipole]]
| style="width:250px;" | Almost omni-directional physical radiator
| style="width:250px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source | Huygens Source]]
| style="width:250px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

The available observables types in [[EM.Terrano]] are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:receiver_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Point Receiver Set | Point Receiver Set]]
| style="width:250px;" | Generating received power coverage maps & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:Distr Rx icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Distributed Receiver Set | Distributed Receiver Set]]
| style="width:250px;" | Computing received power at a receiver characterized by Huygens surface data
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor Observable | Near-Field Sensor]]
| style="width:250px;" | Generating electric and magnetic field distribution maps
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern Observable | Far-Field Radiation Pattern]]
| style="width:250px;" | Computing the effective radiation pattern of a radiator in the presence of a large scattering scene
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface Observable | Huygens Surface]]
| style="width:250px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone observable
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

When you define a far-field observable in EM.Terrano, a collection of invisible, isotropic receivers are placed on the surface of a large sphere that encircles your propagation scene and all of its geometric objects. These receivers are placed uniformly on the spherical surface at a spacing that is determined by your specified angular resolutions. In most cases, you need to define angular resolutions of at least 1° or smaller. Note that this is different than the transmitter rays' angular resolution. You may have a large number of transmitted rays but not enough receivers to compute the effective radiation pattern at all azimuth and elevation angles. Also keep in mind that with 1° Theta and Phi angle increments, you will have a total of 181 × 361 = 65,341 spherically placed receivers in your scene.

{{Note| Computing radiation patterns using EM.Terrano's SBR solver typically takes much longer computation times than using [[EM.Cube]]'s other computational modules.}}

<table>
<tr>
<td> [[Image:SBR pattern.png|thumb|540px|Computed 3D radiation pattern of two vertical short dipole radiators placed 1m apart in the free space at 1GHz.]] </td>
</tr>
</table>

== Statistical Analysis of Propagation Scene ==

EM.Terrano's coverage maps display the received power at the location of all the receivers. The receivers together from a set/ensemble, which might be uniformly spaced or distributed across the propagation scene or may consist of randomly scattered radiators. Every coverage map shows the '''Mean''' and '''Standard Deviation''' of the received power for all the receivers involved. These information are displayed at the bottom of the coverage map's legend box and are expressed in dB.

When you run either a frequency sweep or a parametric sweep simulation in EM.Terrano, you have the option to generate two additional coverage maps: one for the mean of all the individual sample coverage maps and another for their standard deviation. To do so, in the '''Run Dialog''', check the box labeled '''"Create Mean and Standard Deviation received power coverage maps"'''. Note that the mean and standard deviation values displayed on the individual coverage maps correspond to the spatial statistics of the receivers in the scene, while the mean and standard deviation coverage maps show the statistics with respect to the frequency or other sweep variable sets at each point in the site. Also, note that both of the mean and standard deviation coverage maps have their own spatial mean and standard deviation values expressed in dB at the bottom of their legend box.

<table>
<tr>
<td>
[[Image:PROP MAN12.png|thumb|left|480px|EM.Terrano's simulation run dialog showing frequency sweep as the simulation mode along with statistical analysis.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon4.png|thumb|left|640px|The mean coverage map at the end of a frequency sweep.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon5.png|thumb|left|640px|The standard deviation coverage map at the end of a frequency sweep.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Terrano#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

EM.Terrano

2019-04-05T14:15:26Z

Kazem Sabet: /* Scene Definition / Construction */

[[Image:Splash-prop.jpg|right|720px]]
<strong><font color="#4e1985" size="4">True 3D, Coherent, Polarimetric Ray Tracer That Simulates Very Large Urban Scenes In Just Few Minutes!</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

===EM.Terrano in a Nutshell ===

EM.Terrano is a physics-based, site-specific, wave propagation modeling tool that enables engineers to quickly determine how radio waves propagate in urban, natural or mixed environments. EM.Terrano's simulation engine is equipped with a fully polarimetric, coherent 3D ray tracing solver based on the Shooting-and-Bouncing-Rays (SBR) method, which utilizes geometrical optics (GO) in combination with uniform theory of diffraction (UTD) models of building edges. EM.Terrano lets you analyze and resolve all the rays transmitted from one ore more signal sources, which propagate in a real physical channel made up of buildings, terrain and other obstructing structures. EM.Terrano finds all the rays received by a receiver at a particular location in the physical site and computes their vectorial field and power levels, time delays, angles of arrival and departure, etc. Using EM.Terrano you can examine the connectivity of a communication link between any two points in a real specific propagation site.

Since its introduction in 2002, EM.Terrano has helped wireless engineers around the globe model the physical channel and the mechanisms by which radio signals propagate in various environments. EM.Terrano’s advanced ray tracing simulator finds the dominant propagation paths at each specific physical site. It calculates the true signal characteristics at the actual locations using physical databases of the buildings and terrain at a given site, not those of a statistically average or representative environment. The earlier versions of EM.Terrano's SBR solver relied on certain assumptions and approximations such as the vertical plane launch (VPL) method or 2.5D analysis of urban canyons with prismatic buildings using two separate vertical and horizontal polarizations. In 2014, we introduced a new fully 3D polarimetric SBR solver that accurately traces all the three X, Y and Z components of the electric fields (both amplitude and phase) at every point inside the computational domain. Using a 3D CAD modeler, you can now set up any number of buildings with arbitrary geometries, no longer limited to vertical prismatic shapes. Versatile interior wall arrangements allow indoor propagation modeling inside complex building configurations. The most significant recent development is a multicore parallelized SBR simulation engine that takes advantage of ultrafast k-d tree algorithms borrowed from the field of computer graphics and video gaming to achieve the ultimate speed and efficiency in geometrical optics ray tracing.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Basic Principles of SBR Ray Tracing | Basic SBR Theory]]'''.

<table>
<tr>
<td>
[[Image:Manhattan1.png|thumb|left|420px|A large urban propagation scene featuring lower Manhattan.]]
</td>
</tr>
</table>

=== EM.Terrano as the Propagation Module of EM.Cube ===

EM.Terrano is the ray tracing '''Propagation Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Terrano shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

With the seamless integration of EM.Terrano with [[EM.Cube]]'s other modules, you can now model complex antenna systems in [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]], and generate antenna radiation patterns that can be used to model directional transmitters and receivers at the two ends of your propagation channel. Conversely, you can analyze a propagation scene in EM.Terrano, collect all the rays received at a certain receiver location and import them as coherent plane wave sources to [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]].

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Terrano's SBR Solver ===

EM.Terrano's SBR simulation engine utilizes an intelligent ray tracing algorithm that is based on the concept of k-dimensional trees. A k-d tree is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are particularly useful for searches that involve multidimensional search keys such as range searches and nearest neighbor searches. In a typical large radio propagation scene, there might be a large number of rays emanating from the transmitter that may never hit any obstacles. For example, upward-looking rays in an urban propagation scene quickly exit the computational domain. Rays that hit obstacles on their path, on the other hand, generate new reflected and transmitted rays. The k-d tree algorithm traces all these rays systematically in a very fast and efficient manner. Another major advantage of k-d trees is the fast processing of multi-transmitters scenes.

EM.Terrano performs fully polarimetric and coherent SBR simulations with arbitrary transmitter antenna patterns. Its SBR simulation engine is a true asymptotic "field" solver. The amplitudes and phases of all the three vectorial field components are computed, analyzed and preserved throughout the entire ray tracing process from the source location to the field observation points. You can visualize the magnitude and phase of all six electric and magnetic field components at any point in the computational domain. In most scenes, the buildings and the ground or terrain can be assumed to be made of homogeneous materials. These are represented by their electrical properties such as permittivity ε<sub>r</sub> and electric conductivity σ. More complex scenes may involve a multilayer ground or multilayer building walls. In such cases, one can no longer use the simple reflection or transmission coefficient formulas for homogeneous medium interfaces. EM.Terrano calculates the reflection and transmission coefficients of multilayer structures as functions of incident angle, frequency and polarization and uses them at the respective specular points.

It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD). It is not a "full-wave" technique, and it does not provide a direct numerical solution of Maxwell's equations. SBR makes a number of assumptions, chief among them, a very high operational frequency such that the length scales involved are much larger than the operating wavelength. Under this assumed regime, electromagnetic waves start to behave like optical rays. Virtually all the calculations in SBR are based on far field approximations. In order to maintain a high computational speed for urban propagation problems, EM.Terrano ignores double diffractions. Diffractions from edges give rise to a large number of new secondary rays. The power of diffracted rays drops much faster than reflected rays. In other words, an edge-diffracted ray does not diffract again from another edge in EM.Terrano. However, reflected and penetrated rays do get diffracted from edges just as rays emanated directly from the sources do.

<table>
<tr>
<td>
[[Image:Multipath_Rays.png|thumb|left|500px|A multipath urban propagation scene showing all the rays collected by a receiver.]]
</td>
</tr>
</table>

== EM.Terrano Features at a Glance ==

=== Scene Definition / Construction ===

<ul>
<li>
Buildings/blocks with arbitrary geometries and material properties</li>
<li>
Buildings/blocks with impenetrable surfaces or penetrable surfaces using thin wall approximation</li>
<li>
Multilayer walls for indoor propagation scenes</li>
<li>
Penetrable volume blocks with arbitrary geometries and material properties</li>
<li>
Import of shapefiles and STEP, IGES and STL CAD model files for scene construction</li>
<li>
Terrain surfaces with arbitrary geometries and material properties and random rough surface profiles</li>
<li>
Import of digital elevation map (DEM) terrain models</li>
<li>
Python-based random city wizard with randomized building locations, extents and orientations</li>
<li>
Python-based wizards for generation of parameterized multi-story office bulidings and several terrain scene types</li>
<li>
Standard half-wave dipole transmitters and receivers orinted along the principal axes</li>
<li>
Short Hertzian dipole sources with arbitrary orientation</li>
<li>
Isotropic receivers or receiver grids for wireless coverage modeling</li>
<li>
Radiator sets with 3D directional antenna patterns (imported from other modules or external files)</li>
<li>
Full three-axis rotation of imported antenna patterns</li>
<li>
Interchangeable radiator-based definition of transmitters and receivers (networks of transceivers)</li>
</ul>

=== Wave Propagation Modeling ===

<ul>
<li>
Fully 3D polarimetric and coherent Shoot-and-Bounce-Rays (SBR) simulation engine</li>
<li>
GTD/UTD diffraction models for diffraction from building edges and terrain</li>
<li>
Triangular surface mesh generator for discretization of arbitrary block geometries</li>
<li>
Super-fast geometrical/optical ray tracing using advanced k-d tree algorithms</li>
<li>
Intelligent ray tracing with user defined angular extents and resolution</li>
<li>
Ray reflection, edge diffraction and ray transmission through multilayer walls and material volumes</li>
<li>
Communication link analysis for superheterodyne transmitters and receivers</li>
<li>
17 digital modulation waveforms for the calculation of E<sub>b</sub>/N<sub>0</sub> and Bit error rate (BER)</li>
<li>
Incredibly fast frequency sweeps of the entire propagation scene in a single SBR simulation run</li>
<li>
Parametric sweeps of scene elements like building properties, or radiator heights and rotation angles</li>
<li>
Statistical analsyis of the propagation scene</li>
<li>
Polarimetric channel characterization for MIMO analysis</li>
<li>
"Almost real-time" Polarimatrix solver using an existing ray database</li>
<li>
"Almost real-time" transmitter sweep using the Polarimatrix solver</li>
<li>
"Almost real-time" rotational sweep for modeling beam steering using the Polarimatrix solver</li>
<li>
"Almost real-time" mobile sweep for modeling mobile communications between Tx-Rx pairs along a mobile path using the Polarimatrix solver</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Standard output parameters for received power, path loss, SNR, E<sub>b</sub>/N<sub>0</sub> and BER at each individual receiver</li>
<li>
Graphical visualization of propagating rays in the scene</li>
<li>
Received power coverage maps</li>
<li>
Link connectivity maps (based on minimum required SNR and BER)</li>
<li>
Color-coded intensity plots of polarimetric electric field distributions</li>
<li>
Incoming ray data analysis at each receiver including delay, angles of arrival and departure</li>
<li>
Cartesian plots of path loss along defined paths</li>
<li>
Power delay profile of the selected receiver</li>
<li>
Polar stem charts of angles of arrival and departure of the selected receiver</li>
</ul>

== Building a Propagation Scene in EM.Terrano ==

=== The Various Elements of a Propagation Scene ===

A typical propagation scene in EM.Terrano consists of several elements. At a minimum, you need a transmitter (Tx) at some location to launch rays into the scene and a receiver (Rx) at another location to receive and collect the incoming rays. A transmitter and a receiver together make the simplest propagation scene, representing a free-space line-of-sight (LOS) channel. In EM.Terrano, a transmitter represents a point source, while a receiver represents a point observable. Both a transmitter and a receiver are associated with point objects, which are one of the many types of geometric objects you can draw in the project workspace. Your scene might involve more than one transmitter and possibly a large grid of receivers.

A more complicated propagation scene usually contains several buildings, walls, or other kinds of scatterers and wave obstructing objects. You model all of these elements by drawing geometric objects in the project workspace or by importing external CAD models. EM.Terrano does not organize the geometric objects of your project workspace by their material composition. Rather, it groups the geometric objects into blocks based on a common type of interaction with incident rays. EM.Terrano offer the following types of object blocks:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Block/Group Type
! scope="col"| Ray Interaction Type
! scope="col"| Object Types Allowed
! scope="col"| Notes
|-
| style="width:30px;" | [[File:impenet_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impenetrable Surface | Impenetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Basic building group for outdoor scenes
|-
| style="width:30px;" | [[File:penet_surf_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Surface | Penetrable Surface]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission in free space
| style="width:250px;" | All solid & surface geometric objects, no curve objects
| style="width:300px;" | Behaves similar to impenetrable surface and uses thin wall approximation for generating transmitted rays, used to model hollow buildings with ray penetration, entry and exit
|-
| style="width:30px;" | [[File:terrain_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Terrain Surface | Terrain Surface]]
| style="width:200px;" | Ray reflection, ray diffraction
| style="width:250px;" | All surface geometric objects, no solid or curve objects
| style="width:300px;" | Behaves exactly like impenetrable surface but can change the elevation of all the buildings and transmitters and receivers located above it
|-
| style="width:30px;" | [[File:penet_vol_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Volume | Penetrable Volume]]
| style="width:200px;" | Ray reflection, ray diffraction, ray transmission and ray attenuation inside homogeneous material media
| style="width:250px;" | All solid geometric objects, no surface or curve objects
| style="width:300px;" | Used to model wave propagation inside a volumetric material block, also used for creating individual solid walls and interior building partitions and panels in indoor scenes
|-
| style="width:30px;" | [[File:base_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Base Location Set | Base Location Set]]
| style="width:200px;" | Either ray generation or ray reception
| style="width:250px;" | Only point objects
| style="width:300px;" | Required for the definition of transmitters and receivers
|-
| style="width:30px;" | [[File:scatterer_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Scatterer Set | Point Scatterer Set]]
| style="width:200px;" | Ray reception and ray scattering
| style="width:250px;" | Only point, box and sphere objects
| style="width:300px;" | Required for the definition of point scatterers as targets in a radar simulation
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:200px;" | No ray interaction
| style="width:250px;" | All types of objects
| style="width:300px;" | Used for representing non-physical items
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

Impenetrable surfaces, penetrable surfaces, terrain surfaces and penetrable volumes represent all the objects that obstruct the propagation of electromagnetic waves (rays) in the free space. What differentiates them is the types of physical phenomena that are used to model their interaction with the impinging rays. EM.Terrano discretizes geometric objects into a number of flat facets. The field intensity, phase and power of the reflected and transmitted rays depend on the material properties of the obstructing facet. The specular surface of a facet can be modeled locally as a simple homogeneous dielectric half-space or as a multilayer medium. In that respect, all the obstructing objects such as buildings, walls, terrain, etc. behave in a similar way:

* They terminate an impinging ray and replace it with one or more new rays.
* They represent a specular interface between two media of different material compositions for calculating the reflection, transmission or diffraction coefficients.

An outdoor propagation scene typically involves several buildings modeled by impenetrable surfaces. Rays hit the facets of impenetrable buildings and bounce back, but they do not penetrate the object. It is assumed that the interior of such buildings are highly dissipative due to wave absorption or diffusion. An indoor propagation scene typically involves several walls, a ceiling and a floor arranged according to a certain building layout. Penetrable surfaces are used to model the exterior and interior walls of buildings. Rays reflect off these surfaces and diffract off their edges. They also penetrate the thin surface and continue their path in the free space on the other side of the wall. Terrain surfaces with irregular shapes or possibly random rough surfaces are used as an alternative to the flat global ground. You can also build mixed scenes involving both impenetrable and penetrable blocks or irregular terrain. In the context of a propagation scene, penetrable volumes are often used to model block of rain, fog or vegetation. Base location sets are used to geometrically represent point transmitters and point receivers in the project workspace.

Sometimes it is helpful to draw graphical objects as visual clues in the project workspace. These non-physical objects must belong to a virtual object group. Virtual objects are not discretized by EM.Terrano's mesh generator, and they are not passed onto the input data files of the SBR simulation engine.

<table>
<tr>
<td>
[[Image:PROP MAN2.png|thumb|left|720px|An urban propagation scene generated by EM.Terrano's "Random City" and "Basic Link" wizards. It consists of 25 cubic brick buildings, one transmitter and a large two-dimensional array of receivers. ]]
</td>
</tr>
</table>

=== Organizing the Propagation Scene by Block Groups ===

In EM.Terrano, all the geometric objects associated with the various scene elements like buildings, terrain surfaces and base location points are grouped together as blocks based on their common type. All the objects listed under a particular group in the navigation tree share the same color, texture and material properties. Once a new block group has been created in the navigation tree, it becomes the "Active" group of the project workspace, which is always displayed in bold letters. You can draw new objects under the active node. Any block group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.

<table>
<tr>
<td>
[[Image:PROP MAN1.png|thumb|left|480px|EM.Terrano's navigation tree.]]
</td>
</tr>
</table>

It is recommended that you first create block groups, and then draw new objects under the active block group. However, if you start a new EM.Terrano project from scratch, and start drawing a new object without having previously defined any block groups, a new default impenetrable surface group is created and added to the navigation tree to hold your new CAD object. You can always change the properties of a block group later by accessing its property dialog from the contextual menu. You can also delete a block group with all of its objects at any time.

{{Note|You can only import external CAD models (STEP, IGES, STL, DEM, etc.) only to the CubeCAD module. You can then transfer the imported objects from CubeCAD to EM.Terrano.}}

=== Moving Objects Among Different Block Groups ===

You can move any geometric object or a selection of objects from one block group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models of terrain or buildings from CubeCAD to EM.Terrano. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a block group called "Terrain_1" in EM.Terrano, then you have to select the menu item '''Move To → EM.Terrano → Terrain_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.

<table>
<tr>
<td>
[[Image:PROP MAN3.png|thumb|left|720px|Moving the terrain model of Mount Whitney originally imported from an external digital elevation map (DEM) file to EM.Terrano.]]
</td>
</tr>
<tr>
<td>
[[Image:PROP MAN4.png|thumb|left|720px|The imported terrain model of Mount Whitney shown in EM.Terrano's project workspace under a terrain group called "Terrain_1".]]
</td>
</tr>
</table>

=== Adjustment of Block Elevation on Underlying Terrain Surfaces ===

In EM.Terrano, buildings and all other geometric objects are initially drawn on the XY plane. In other words, the Z-coordinates of the local coordinate system (LCS) of all blocks are set to zero until you change them. Since the global ground is located a z = 0, your buildings are seated on the ground. When your propagation scene has an irregular terrain, you would want to place your buildings on the surface of the terrain and not buried under it. This can be done automatically as part of the definition of the block group. Open the property dialog of a block group and check the box labeled '''Adjust Block to Terrain Elevation'''. All the objects belonging to that block are automatically elevated in the Z direction such that their bases sit on the surface of their underlying terrain. In effect, the LCS of each of these individual objects is translated along the global Z-axis by the amount of the Z-elevation of the terrain object at the location of the LCS.

{{Note| You have to make sure that the resolution of your terrain, its variation scale and building dimensions are all comparable. Otherwise, on a rapidly varying high-resolution terrain, you will have buildings whose bottoms touch the terrain only at a few points and parts of them hang in the air.}}

<table>
<tr>
<td>
[[Image:PROP MAN5.png|thumb|left|480px|The property dialog of impenetrable surface showing the terrain elevation adjustment box checked.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN6.png|thumb|left|360px|A set of buildings on an undulating terrain without elevation adjustment.]]
</td>
<td>
[[Image:PROP MAN7.png|thumb|left|360px|The set of buildings on the undulating terrain after elevation adjustment.]]
</td>
</tr>
</table>

== EM.Terrano's Ray Domain & Global Environment ==

=== Why Do You Need a Finite Computational Domain? ===

The SBR simulation engine requires a finite computational domain for ray termination. All the stray rays that emanate from a source inside this finite domain and hit its boundaries are terminated during the simulation process. Such rays exit the computational domain and travel to the infinity, with no chance of ever reaching any receiver in the scene. When you define a propagation scene with various elements like buildings, walls, terrain, etc., a dynamic domain is automatically established and displayed as a green wireframe box that surrounds the entire scene. Every time you create a new object, the domain box is automatically adjusted and extended to enclose all the objects in the scene.

To change the ray domain settings, follow the procedure below:

* Open the Ray Domain Settings Dialog by clicking the '''Domain''' [[File:image025.jpg]] button of the '''Simulate Toolbar''', or by selecting '''Menu > Simulate > Computational Domain > Settings...''', or by right-clicking on the '''Ray Domain''' item of the navigation tree and selecting '''Domain Settings...''' from the contextual menu, or simply using the keyboard shortcut {{key|Ctrl+A}}.
* The size of the Ray domain is specified in terms of six '''Offset''' parameters along the ±X, ±Y and ±Z directions. The default value of all these six offset parameters is 10 project units. Change these values as you like.
* You can also change the color of the domain box using the {{key|Color}} button.
* After changing the settings, use the {{key|Apply}} button to make the changes effective while the dialog is still open.

<table>
<tr>
<td>
[[Image:PROP15.png|thumb|left|480px|EM.Terrano's domain settings dialog.]]
</td>
</tr>
</table>

=== Understanding the Global Ground ===

Most outdoor and indoor propagation scenes include a flat ground at their bottom, which bounces incident rays back into the scene. EM.Terrano provides a global flat ground at z = 0. The global ground indeed acts as an impenetrable surface that blocks the entire computational domain from the z = 0 plane downward. It is displayed as a translucent green plane at z = 0 extending downward. The color of the ground plane is always the same as the color of the ray domain. The global ground is assumed to be made of a homogeneous dielectric material with a specified permittivity ε<sub>r</sub> and electric conductivity σ. By default, a rocky ground is assumed with ε<sub>r</sub> = 5 and σ = 0.005 S/m. You can remove the global ground, in which case, you will have a free space scene. To disable the global ground, open up the "Global Ground Settings" dialog, which can be accessed by right clicking on the '''Global Ground''' item in the Navigation Tree and selecting '''Global Ground Settings... '''Remove the check mark from the box labeled '''"Include Half-Space Ground (z<0)"''' to disable the global ground. This will also remove the green translucent plane from the bottom of your scene. You can also change the material properties of the global ground and set new values for the permittivity and electric conductivity of the impenetrable, half-space, dielectric medium.

Alternatively, you can use EM.Terrano's '''Empirical Soil Model''' to define the material properties of the global ground. This model requires a number of parameters: Temperature in °C, and Volumetric Water Content, Sand Content and Clay Content all as percentage.

{{Note|To model a free-space propagation scene, you have to disable EM.Terrano's default global ground.}}

<table>
<tr>
<td>
[[Image:Global environ.png|thumb|left|720px|EM.Terrano's Global Environment Settings dialog.]]
</td>
</tr>
</table>

== Defining Point Transmitters & Point Receivers for Your Propagation Scene ==

=== The Nature of Transmitters & Receivers ===

In EM.Terrano, transmitters and receivers are indeed point radiators used for transmitting and receiving signals at different locations of the propagation scene. From a geometric point of view, both transmitters and receivers are represented by point objects or point arrays. These are grouped as base locations in the "Physical Structure" section of the navigation tree. As radiators, transmitters and receivers are defined by a radiator type with a certain far-field radiation pattern. Consistent with [[EM.Cube]]'s other computational modules, transmitters are categorizes as an excitation source, while receivers are categorized as a project observable. In other words, a transmitter is used to generate electromagnetic waves that propagate in the physical scene. A receiver, on the other hand, is used to compute the received fields and received signal power or signal-to-noise ratio (SNR). For this reason, transmitters are defined and listed under the "Sources" sections of the navigation tree, while receivers are defined and listed under the "Observables" section.

EM.Terrano provides three radiator types for point transmitter sets:

#Half-wave dipole oriented along one of the three principal axes
#Two collocated, orthogonally polarized, isotropic radiators
#User defined (arbitrary) antenna with imported far-field radiation pattern

EM.Terrano also provides three radiator types for point receiver sets:

#Half-wave dipole oriented along one of the three principal axes
#Polarization-matched isotropic radiator
#User defined (arbitrary) antenna with imported far-field radiation pattern

The default transmitter and receiver radiator types are both vertical (Z-directed) half-wave dipoles.

There are three different ways to define a transmitter set or a receiver set:

*By defining point objects or point arrays under physical base location sets in the navigation tree and then associating them with a transmitter or receiver set
*Using Python commands emag_tx, emag_rx, emag_tx_array, emag_rx_array, emag_tx_line and emag_rx_line
*Using the "Basic Link" wizard

=== Defining a Point Transmitter Set in the Formal Way ===

Transmitters act as sources in a propagation scene. A transmitter is a point radiator with a fully polarimetric radiation pattern defined over the entire 3D space in the standard spherical coordinate system. EM.Terrano gives you three options for the radiator associated with a point transmitter:

* Half-wave dipole
* Orthogonally polarized isotropic radiators
* User defined antenna pattern

By default, EM.Terrano assumes that your transmitter is a vertically polarized (Z-directed) resonant half-wave dipole antenna. This antenna has an almost omni-directional radiation pattern in all azimuth directions. It also has radiation nulls along the axis of the dipole. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. The second choice of two orthogonally polarized isotropic radiators is an abstract source that is used for polarimetric channel characterization as will be discussed later.

You can override the default radiator option and select any other kind of antenna with a more complicated radiation pattern. For this purpose, you have to import a radiation pattern data file to EM.Terrano. You can model any radiating structure using [[EM.Cube]]'s other computational modules, [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] or [[EM.Illumina]], and generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored in a specially formatted file with a "'''.RAD'''" file extension. This file contains columns of spherical φ and θ angles as well as the real and imaginary parts of the complex-valued far-zone electric field components '''E<sub>θ</sub>''' and '''E<sub>φ</sub>'''. The θ- and φ-components of the far-zone electric field determine the polarization of the transmitting radiator.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point transmitter set.}}

A transmitter set always needs to be associated with an existing base location set with one or more point objects in the project workspace. Therefore, you cannot define a transmitter for your scene before drawing a point object under a base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Point_Transmitter_Set | Point Transmitter Set]]'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The point transmitter set definition dialog.]] </td>
</tr>
</table>

Once you define a new transmitter set, its name is added in the '''Transmitters''' section of the navigation tree. The color of all the base points associated with the newly defined transmitter set changes, and an additional little ball with the transmitter color (red by default) appears at the location of each associated base point. You can open the property dialog of the transmitter set and modify a number of parameters including the '''Source Power''' in Watts and the broadcast signal '''Phase''' in degrees. The default transmitter power level is 1W or 30dBm. There is also a check box labeled '''Use Custom Input Power''', which is checked by default. In that case, the power and phase boxes are enabled and you can change the default 1W power and 0° phase values as you wish. [[EM.Cube]]'s ".RAD" radiation pattern files usually contain the value of "Total Radiated Power" in their file header. This quantity is calculated based on the particular excitation mechanism that was used to generate the pattern file in the original [[EM.Cube]] module. When the "Use Custom Input Power" check box is unchecked, EM.Terrano will use the total radiated power value of the radiation file for the SBR simulation.

{{Note|In order to modify any of the transmitter set's parameters, first you need to select the "User Defined Antenna" option, even if you want to keep the vertical half-wave dipole as your radiator.}}

<table>
<tr>
<td>
[[File:NewTxProp.png|thumb|left|720px|The property dialog of a point transmitter set.]]
</td>
</tr>
</table>

Your transmitter in EM.Teranno is indeed more sophisticated than a simple radiator. It consists of a basic "Transmitter Chain" that contains a voltage source with a series source resistance, and connected via a segment of transmission line to a transmit antenna, which is used to launch the broadcast signal into the free space. The transmitter's property dialog allows you to define the basic transmitter chain. Click the {{key|Transmitter Chain}} button of the Transmitter Set dialog to open the transmitter chain dialog. As shown in the figure below, you can specify the characteristics of the baseband/IF amplifier, mixer and power amplifier (PA) including stage gains and impedance mismatch factors (IMF) as well as the characteristics of the transmission line segment that connects the PA to the antenna. Note that the transmit antenna characteristics are automatically filled using the contents of the imported radiation pattern data file. The transmitter Chain dialog also calculates and reports the "Total Transmitter Chain Gain" based on your input. When you close this dialog and return to the Transmitter Set dialog, you will see the calculated value of the Effective Isotropic Radiated Power (EIRP) of your transmitter in dBm.

{{Note| If you do not modify the default parameters of the transmitter chain, a 50-Ω conjugate match condition is assumed and the power delivered to the antenna will be -3dB lower than your specified baseband power.}}

<table>
<tr>
<td> [[File:NewTxChain.png|thumb|left|720px|EM.Terrano's point transmitter chain dialog.]] </td>
</tr>
</table>

=== Defining a Point Receiver Set in the Formal Way ===

Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate the far-zone electric fields and the total received power at the location of a receiver. You need to define at least one receiver in the scene before you can run a SBR simulation. Similar to a transmitter, a receiver is a point radiator, too. EM.Terrano gives you three options for the radiator associated with a point receiver set:

* Half-wave dipole
* Polarization matched isotropic radiator
* User defined antenna pattern

By default, EM.Terrano assumes that your receiver is a vertically polarized (Z-directed) resonant half-wave dipole antenna. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. An isotropic radiator has a perfect omni-directional radiation pattern in all azimuth and elevation directions. An isotropic radiator doesn't exist physically in the real world, but it can be used simply as a point in space to compute the electric field.

You may also define a complicated radiation pattern for your receiver set. In that case, you need to import a radiation pattern data file to EM.Terrano similar to the case of a transmitter set.

{{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point receiver set.}}

Similar to transmitter sets, you define a receiver set by associating it with an existing base location set with one or more point objects in the project workspace. All the receivers belonging to the same receiver set have the same radiator type. A typical propagation scene contains one or few transmitters but usually a large number of receivers. To generate a wireless coverage map, you need to define an array of points as your base location set.

[[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Point_Receiver_Set | Point Receiver Set]]'''.

<table>
<tr>
<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The point receiver set definition dialog.]] </td>
</tr>
</table>

Once you define a new receiver set, its name is added to the '''Receivers''' section of the navigation tree. The color of all the base points associated with the newly defined receiver set changes, and an additional little ball with the receiver color (yellow by default) appears at the location of each associated base point. You can open the property dialog of the receiver set and modify a number of parameters.

<table>
<tr>
<td>
[[File:NewRxProp.png|thumb|left|720px|The property dialog of a point receiver set.]]
</td>
</tr>
</table>

In the Receiver Set dialog, there is a drop-down list labeled '''Selected Element''', which contains a list of all the individual receivers belonging to the receiver set. At the end of an SBR simulation, the button labeled {{key|Show Ray Data}} becomes enabled. Clicking this button opens the Ray Data dialog, where you can see a list of all the received rays at the selected receiver and their computed characteristics.

If you choose the "user defined antenna" option for your receiver set, it indeed consists of a basic "Receiver Chain" that contains a receive antenna connected via a segment of transmission line to the low-noise amplifier (LNA) that is terminated in a matched load. The receiver set's property dialog allows you to define the basic receiver chain. Click the {{key|Receiver Chain}} button of the Receiver Set dialog to open the receiver chain dialog. As shown in the figure below, you can specify the characteristics of the LNA such as its gain and noise figure in dB as well as the characteristics of the transmission line segment that connects the antenna to the LNA. Note that the receiving antenna characteristics are automatically filled from using contents of the radiation file. You have to enter values for antenna's '''Brightness Temperature''' as well as the temperature of the transmission line and the receiver's ambient temperature. The effective '''Receiver Bandwidth''' is assumed to be 100MHz, which you can change for the purpose of noise calculations. The Receive Chain dialog calculates and reports the "Noise Power" and "Total Receiver Chain Gain" based on your input. At the end of an SBR simulation, the receiver power and signal-noise ratio (SNR) of the selected receiver are calculated and they are reported in the receiver set dialog in dBm and dB, respectively. You can examine the properties of all the individual receivers and all the individual rays received by each receiver in your receiver set using the "Selected Element" drop-down list.

<table>
<tr>
<td> [[File:NewRxChain.png|thumb|left|720px|EM.Terrano's point receiver chain dialog.]] </td>
</tr>
</table>

=== Modulation Waveform and Detection ===

EM.Terrano allows you to define a digital modulation scheme for your communication link. There are currently 17 waveforms to choose from in the receiver set property dialog:

*OOK
*M-ary ASK
*Coherent BFSK
*Coherent QFSK
*Coherent M-ary FSK
*Non-Coherent BFSK
*Non-Coherent QFSK
*Non-Coherent M-ary FSK
*BPSK
*QPSK
*Offset QPSK
*M-ary PSK
*DBPSK
*pi/4 Gray-Coded DQPSK
*M-ary QAM
*MSK
*GMSK (BT = 0.3)

In the above list, you need to specify the '''No. Levels (M)''' for the Mary modulation schemes, from which the '''No. Bits per Symbol''' is determined. You can also define a bandwidth for the signal, which has a default value of 100MHz. Once the SNR of the signal is found, given the specified modulation scheme, the E<sub>b</sub>/N<sub>0</sub> parameter is determined, from which the bit error rate (BER) is calculated.

The Shannon – Hartley Equation estimates the channel capacity:

<math> C = B \log_2 \left( 1 + \frac{S}{N} \right) </math>

where B in the bandwidth in Hz, and C is the channel capacity (maximum data rate) expressed in bits/s.

The spectral efficiency of the channel is defined as

<math> \eta = \log_2 \left( 1 + \frac{S}{N} \right) </math>

The quantity E<sub>b</sub>/N<sub>0</sub> is the ratio of energy per bit to noise power spectral density. It is a measure of SNR per bit and is calculated from the following equation:

<math> \frac{E_b}{N_0} = \frac{ 2^\eta - 1}{\eta} </math>

where η is the spectral efficiency.

The relationship between the bit error rate and E<sub>b</sub>/N<sub>0</sub> depends on the modulation scheme and detection type (coherent vs. non-coherent). For example, for coherent QPSK modulation, one can write:

<math> P_b = 0.5 \; \text{erfc} \left( \sqrt{ \frac{E_b}{N_0} } \right) </math>

where P<sub>b</sub> is the bit error rate and erfc(x) is the complementary error function:

<math> \text{erfc}(x) = 1-\text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^2} dt </math>

The '''Minimum Required SNR''' parameter is used to determine link connectivity between each transmitter and receiver pair. If you check the box labeled '''Generate Connectivity Map''' in the receiver set property dialog, a binary map of the propagation scene is generated by EM.Terrano, in which one color represents a closed link and another represent no connection depending on the selected color map type of the graph. EM.Terrano also calculates the '''Max Permissible BER''' corresponding to the specified minimum required SNR and displays it in the receiver set property dialog.

=== A Note on EM.Terrano's Native Dipole Radiators ===

When you define a new transmitter set or a new receiver set, EM.Terrano assigns a vertically polarized half-wave dipole radiator to the set by default. The radiation pattern of this native dipole radiators is calculated using well-know expressions that are derived based on certain assumptions and approximations. For example, the far-zone electric field of a vertically-polarized dipole antenna can be expressed as:

<math> E_\theta(\theta,\phi) \approx j\eta_0 I_0 \frac{e^{-jk_0 r}}{2\pi r} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right] </math>

<math> E_\phi(\theta,\phi) \approx 0 </math>

where k<sub>0</sub> = 2π/λ<sub>0</sub> is the free-space wavenumber, λ<sub>0</sub> is the free-space wavelength, η<sub>0</sub> = 120π Ω is the free-space intrinsic impedance, I<sub>0</sub> is the current on the dipole, and L is the length of the dipole.

The directivity of the dipole antenna is given be the expression:

<math> D_0 \approx \frac{2}{F_1(k_0L) + F_2(k_0L) + F_3(k_0L)} \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right]^2 </math>

with

<math> F_1(x) = \gamma + \text{ln}(x) - C_i(x) </math>

<math> F_2(x) = \frac{1}{2} \text{sin}(x) \left[ S_i(2x) - 2S_i(x) \right] </math>

<math> F_3(x) = \frac{1}{2} \text{cos}(x) \left[ \gamma + \text{ln}(x/2) + C_i(2x) - 2C_i(x) \right] </math>

where γ = 0.5772 is the Euler-Mascheroni constant, and C<sub>i</sub>(x) and S<sub>i</sub>(x) are the cosine and sine integrals, respectively:

<math> C_i(x) = - \int_{x}^{\infty} \frac{ \text{cos} \tau}{\tau} d\tau </math>

<math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>

In the case of a half-wave dipole, L = λ<sub>0</sub>/2, and D<sub>0</sub> = 1.643. Moreover, the input impedance of the dipole antenna is Z<sub>A</sub> = 73 + j42.5 Ω. These dipole radiators are connected via 50Ω transmission lines to a 50Ω source or load. Therefore, there is always a certain level of impedance mismatch that violates the conjugate match condition for maximum power.

<table>
<tr>
<td> [[File:Dipole radiators.png|thumb|720px|EM.Terrano's native half-wave dipole transmitter and receiver.]] </td>
</tr>
</table>

On the other hand, we you specify a user-defined antenna pattern for the transmitter or receiver sets, you import a 3D radiation pattern file that contains all the values of E<sub>θ</sub> and E<sub>φ</sub> for all the combinations of (θ, φ) angles. Besides the three native dipole radiators, [[EM.Cube]] also provides 3D radiation pattern files for three X-, Y- and Z-polarized half-wave resonant dipole antennas. These pattern data were generated using a full-wave solver like [[EM.Libera]]'s wire MOM solver. The names of the radiation pattern files are:

* DPL_STD_X.RAD
* DPL_STD_Y.RAD
* DPL_STD_Z.RAD

and they are located in the folder "\Documents\EMAG\Models" on your computer. Note that these are full-wave simulation data and do not involve any approximate assumptions. To use these files as an alternative to the native dipole radiators, you need to select the '''User Defined Antenna Pattern''' radio button as the the radiator type in the transmitter or receiver set property dialog.

=== A Note on the Rotation of Antenna Radiation Patterns ===

EM.Terrano's Transmitter Set dialog and Receiver Set dialog both allow you to rotate an imported radiation pattern. In that case, you need to specify the '''Rotation''' angles in degrees about the X-, Y- and Z-axes. It is important to note that these rotations are performed sequentially and in the following order: first a rotation about the X-axis, then a rotation about the Y-axis, and finally a rotation about the Z-axis. In addition, all the rotations are performed with respect to the "rotated" local coordinate systems (LCS). In other words, the first rotation with respect to the local X-axis transforms the XYZ LCS to a new primed X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS. The second rotation is performed with respect to the new Y<sup>′</sup>-axis and transforms the X<sup>′</sup>Y<sup>′</sup>Z<sup>′</sup> LCS to a new double-primed X<sup>′′</sup>Y<sup>′′</sup>Z<sup>′′</sup> LCS. The third rotation is finally performed with respect to the new Z<sup>′′</sup>-axis. The figures below shows single and double rotations.

<table>
<tr>
<td> [[File:PROP22B.png|thumb|300px|The local coordinate system of a linear dipole antenna.]] </td>
<td> [[File:PROP22C.png|thumb|600px|Rotating the dipole antenna by +90° about the local Y-axis.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[File:PROP22D.png|thumb|720px|Rotating the dipole antenna by +90° about the local X-axis and then by -45° by the local Y-axis.]] </td>
</tr>
</table>

=== Adjustment of Tx/Rx Elevation above a Terrain Surface ===

When your transmitters or receivers are located above a flat terrain like the global ground, their Z-coordinates are equal to their height above the ground, as the terrain elevation is fixed and equal to zero everywhere. In many propagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across the scene. In that case, you may want to place your transmitters or receivers at a certain height above the underlying ground. The Z-coordinate of a transmitter or receiver is now the sum of the terrain elevation at the base point and the specified height. EM.Terrano gives you the option to adjust the transmitter and receiver sets to the terrain elevation. This is done for individual transmitter sets and individual receiver sets. At the top of the Transmitter Dialog there is a check box labeled "'''Adjust Tx Sets to Terrain Elevation'''". Similarly, at the top of the Receiver Dialog there is a check box labeled "'''Adjust Rx Sets to Terrain Elevation'''". These boxes are unchecked by default. As a result, your transmitter sets or receiver sets coincide with their associated base points in the project workspace. If you check these boxes and place a transmitter set or a receiver set above an irregular terrain, the transmitters or receivers are elevated from the location of their associated base points by the amount of terrain elevation as can be seen in the figure below.

To better understand why there are two separate sets of points in the scene, note that a point array (CAD object) is used to create a uniformly spaced base set. The array object always preserves its grid topology as you move it around the scene. However, the transmitters or receivers associated with this point array object are elevated above the irregular terrain and no longer follow a strictly uniform grid. If you move the base set from its original position to a new location, the base points' topology will stay intact, while the associated transmitters or receivers will be redistributed above the terrain based on their new elevations.

<table>
<tr>
<td>
[[Image:PROP MAN8.png|thumb|left|640px|A transmitter (red) and a grid of receivers (yellow) adjusted above a plateau terrain surface. The underlying base point sets (blue and orange dots) associated with the adjusted transmitters and receivers on the terrain are also visible in the figure.]]
</td>
</tr>
</table>

== Discretizing the Propagation Scene in EM.Terrano ==

=== Why Do You Need to Discretize the Scene? ===

EM.Terrano's SBR solver uses a method known as Geometrical Optics (GO) in conjunction with the Uniform Theory of Diffraction (UTD) to trace the rays from their originating point at the source to the individual receiver locations. Rays may hit obstructing objects on their way and get reflected, diffracted or transmitted. EM.Terrano's SBR solver can only handle diffraction off linear edges and reflection from and transmission through planar interfaces. When an incident ray hits the surface of the obstructing object, a local planar surface assumption is made at the specular point. The assumptions of linear edges and planar facets obviously work in the case of a scene with cubic buildings and a flat global ground.

In many practical scenarios, however, your buildings may have curved surfaces, or the terrain may be irregular. EM.Terrano allows you to draw any type of surface or solid geometric objects such as cylinders, cones, etc. under impenetrable and penetrable surface groups or penetrable volumes. EM.Terrano's mesh generator creates a triangular surface mesh of all the objects in your propagation scene, which is called a facet mesh. Even the walls of cubic buildings are meshed using triangular cells. This enables EM.Terrano to properly discretize composite buildings made of conjoined cubic objects.

Unlike [[EM.Cube]]'s other computational modules, the density or resolution of EM.Terrano's surface mesh does not depend on the operating frequency and is not expressed in terms of the wavelength. The sole purpose of EM.Terrano's facet mesh is to discretize curved and irregular scatterers into flat facets and linear edges. Therefore, geometrical fidelity is the only criterion for the quality of a facet mesh. It is important to note that discretizing smooth objects using a triangular surface mesh typically creates a large number of small edges among the facets that are simply mesh artifacts and should not be considered as diffracting edges. For example, each rectangular face of a cubic building is subdivided into four triangles along the two diagonals. The four internal edges lying inside the face are obviously not diffracting edges. A lot of subtleties like these must be taken into account by the SBR solver to run accurate and computationally efficient simulations.

=== Generating the Facet Mesh ===

You can view and examine the discretized version of your scene's objects as they are sent to the SBR simulation engine. You can adjust the mesh resolution and increase the geometric fidelity of discretization by creating more and finer triangular facets. On the other hand, you may want to reduce the mesh complexity and send to the SBR engine only a few coarse facets to model your buildings. The resolution of EM.Terrano's facet mesh generator is controlled by the '''Cell Edge Length''' parameter, which is expressed in project length units. The default mesh cell size of 100 units might be too large for non-flat objects. You may have to set a smaller cell edge length in EM.Terrano's Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the curvature of your curved structures adequately.

<table>
<tr>
<td>
[[Image:prop_manual-29.png|thumb|left|480px|EM.Terrano's mesh settings dialog.]]
</td>
</tr>
</table>

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Facet_Mesh | EM.Terrano's Facet Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:UrbanCanyon2.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 100m.]] </td>
</tr>
<tr>
<td> [[Image:UrbanCanyon3.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 10m.]] </td>
</tr>
</table>

== Running Ray Tracing Simulations in EM.Terrano ==

EM.Terrano provides a number of different simulation or solver types:

* 3D SBR Ray Tracer
* Channel Analyzer
* Polarimatrix Solver
* Radar Simulator

The first three simulation types are described below. For a description of EM.Terrano's Radar Simulator, follow this link.

=== Running a Single-Frequency SBR Analysis ===

Its main solver is the '''3D SBR Ray Tracer'''. Once you have set up your propagation scene in EM.Terrano and have defined sources/transmitters and observables/receivers for your scene, you are ready to run a SBR ray tracing simulation. You set the simulation mode in EM.Terrano's simulation run dialog. A single-frequency SBR analysis is a single-run simulation and the simplest type of ray tracing simulation in EM.Terrano. It involves the following steps:

* Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''. Wireless propagation problems usually require meter, mile or kilometer as the project unit.
* Create the blocks and draw the buildings at the desired locations.
* Keep the default ray domain and accept the default global ground or change its material properties.
* Define an excitation source and observables for your project.
* If you intend to use transmitters and receivers in your scene, first define the required base sets and then define the transmitter and receiver sets based on them.
* Run the SBR simulation engine.
* Visualize the coverage map and plot other data.

You can access EM.Terrano's Simulation Run dialog by clicking the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Simulate → Run...''' or using the keyboard shortcut {{key|Ctrl+R}}. When you click the {{key|Run}} button, a new window opens up that reports the different stages of the SBR simulation and indicates the progress of each stage. After the SBR simulation is successfully completed, a message pops up and prompts the completion of the process.

<table>
<tr>
<td>
[[Image:Terrano L1 Fig16.png|thumb|left|480px|EM.Terrano's simulation run dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:PROP MAN10.png|thumb|left|550px|EM.Terrano's output message window.]]
</td>
</tr>
</table>

=== Changing the SBR Engine Settings ===

There are a number of SBR simulation settings that can be accessed and changed from the Ray Tracing Engine Settings Dialog. To open this dialog, click the button labeled {{key|Settings}} on the right side of the '''Select Simulation or Solver Type''' drop-down list in the Run Dialog. EM.Terrano's SBR simulation engine allows you to separate the physical effects that are calculated during a ray tracing process. You can selectively enable or disable '''Reflection/Transmission''' and '''Edge Diffraction''' in the "Ray-Block Interactions" section of this dialog. By default, ray reflection and transmission and edge diffraction effects are enabled. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in the scene.

EM.Terrano allows a finite number of ray bounces for each original ray emanating from a transmitter. This is very important in situations that may involve resonance effects where rays get trapped among multiple surfaces and may bounce back and forth indefinitely. This is set using the box labeled "'''Max No. Ray Bounces'''", which has a default value of 10. Note that the maximum number of ray bounces directly affects the computation time as well as the size of output simulation data files. This can become critical for indoor propagation scenes, where most of the rays undergo a large number of reflections. Two other parameters control the diffraction computations: '''Max Wedge Angle''' in degrees and '''Min Edge Length''' in project units. The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or coplanar with no diffraction effect. The default value of the maximum wedge angle is 170°. The minimum edge length is size of the common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the minimum edge length is one project units.

<table>
<tr>
<td>
[[Image:PROP MAN11.png|thumb|left|720px|EM.Terrano's SBR simulation engine settings dialog.]]
</td>
</tr>
</table>

As rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish. From a practical point of view, only rays that have power levels above the receiver sensitivity can be effectively received. Therefore, all the rays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default value of -150dBm. Keep in mind that the value of this threshold directly affects the accuracy of the simulation results as well as the size of the output data file.

You can also set the '''Ray Angular Resolution''' of the transmitter rays in degrees. By default, every transmitter emanates equi-angular ray tubes at a resolution of 1 degree. Lower angular resolutions larger than 1° speed up the SBR simulation significantly, but they may compromise the accuracy. Higher angular resolutions less than 1° increase the accuracy of the simulating results, but they also increase the computation time. The SBR Engine Settings dialog also displays the '''Recommended Ray Angular Resolution''' in degrees in a grayed-out box. This number is calculated based on the overall extents of your computational domain as well as the SBR mesh resolution. To see this value, you have to generate the SBR mesh first. Keeping the angular resolution of your project above this threshold value makes sure that the small mesh facets at very large distances from the source would not miss any impinging ray tubes during the simulation.

EM.Terrano gives a few more options for the ray tracing solution of your propagation problem. For instance, it allows you to exclude the direct line-of-sight (LOS) rays from the final solution. There is a check box for this purpose labeled "Exclude direct (LOS) rays from the solution", which is unchecked by default. EM.Terrano also allows you to superpose the received rays incoherently. In that case, the powers of individual ray are simply added to compute that total received power. This option in the check box labeled "Superpose rays incoherently" is disabled by default, too.

At the end of a ray tracing simulation, the electric field of each individual ray is computed and reported. By default, the actual received ray fields are reported, which are independent of the radiation pattern of the receive antennas. EM.Terrano provides a check box labeled "Normalize ray's E-field based on receiver pattern", which is unchecked by default. If this box is checked, the field of each ray is normalized so as to reflect that effect of the receiver antenna's radiation pattern. The received power of each ray is calculated from the following equation:

<math> P_{ray} = \frac{ | \mathbf{E_{norm}} |^2 }{2\eta_0} \frac{\lambda_0^2}{4\pi} </math>

It can be seen that if the ray's E-field is not normalized, the computed ray power will correspond to that of a polarization matched isotropic receiver.

=== Polarimetric Channel Analysis ===

In a 3D SBR simulation, a transmitter shoots a large number of rays in all directions. The electric fields of these rays are polarimetric and their strength and polarization are determined by the designated radiation pattern of the transmit antenna. The rays travel in the propagation scene and bounce from the ground and buildings or other scatterers or get diffracted at the building edges until they reach the location of the receivers. Each individual ray has its own vectorial electric field and power. The electric fields of the received rays are then superposed coherently and polarimetrically to compute the total field at the receiver locations. The designated radiation pattern of the receivers is then used to compute the total received power by each individual receiver.

From a theoretical point of view, the radiation patterns of the transmit and receive antennas are independent of the propagation channel characteristics. For the given locations of the point transmitters and receivers, one can assume ideal isotropic radiators at these points and compute the polarimetric transfer function matrix of the propagation channel. This matrix relates the received electric field at each receiver location to the transmitted electric field at each transmitter location. In general, the vectorial electric field of each individual ray is expressed in the local standard spherical coordinate system at the transmitter and receiver locations. In other words, the polarimetric channel matrix expresses the '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components associated with each ray at the receiver location to its '''E<sub>θ</sub>''' and '''E<sub>φ</sub>''' field components at the transmitter location. Each ray has a delay and θ and φ angles of departure at the transmitter location and θ and φ angles of departure at the receiver location.

To perform a polarimatric channel characterization of your propagation scene, open EM.Terrano's Run Simulation dialog and select '''Channel Analyzer''' from the drop-down list labeled '''Select Simulation or Solver Type'''. At the end of the simulation, a large ray database is generated with two data files called "sbr_channel_matrix.DAT" and "sbr_ray_path.DAT". The former file contains the delay, angles of arrival and departure and complex-valued elements of the channel matrix for all the individual rays that leave each transmitter and arrive at each receiver. The latter file contains the geometric aspects of each ray such as hit point coordinates.

=== The "Almost Real-Time" Polarimatrix Solver ===

After EM.Terrano's channel analyzer generates a ray database that characterizes your propagation channel polarimetrically for all the combinations of transmitter and receiver locations, a ray tracing solution of the propagation problem can readily be found in almost real time by incorporating the effects of the radiation patterns of transmit and receive antennas. This is done using the '''Polarimatrix Solver''', which is the third option of the drop-down list labeled '''Select Simulation or Solver Type''' in EM.Terrano's Run Simulation dialog. The results of the Polarimatrix and 3D SBR solvers must be identical from a theoretical point of view. However, there might be small discrepancies between the two solutions due to roundoff errors.

Using the Polarimatrix solver can lead to a significant reduction of the total simulation time in sweep simulations that involve a large number of transmitters and receivers. Certain simulation modes of EM.Terrano are intended for the Polarimatrix solver only as will be described in the next section.

{{Note| In order to use the Polarimatrix solver, you must first generate a ray database of your propagation scene using EM.Terrano's Channel Analyzer.}}

=== EM.Terrano's Simulation Modes ===

EM.Terrano provides a number of different simulation modes that involve single or multiple simulation runs:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Which Solver?
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Single-Frequency SBR Analysis | Single-Frequency Analysis]]
| style="width:180px;" | Simulates the propagation scene "As Is"
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:180px;" | Varies the operating frequency of the ray tracer
| style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator
| style="width:120px;" | Runs at a specified set of frequency samples
| style="width:300px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:180px;" | Varies the value(s) of one or more project variables
| style="width:150px;" | SBR
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires definition of sweep variables, works only with SBR solver as the physical scene may change during the sweep
|-
| style="width:120px;" | [[#Transmitter_Sweep | Transmitter Sweep]]
| style="width:180px;" | Activates two or more transmitters sequentially with only one transmitter broadcasting at each simulation run
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires at least two transmitters in the scene, works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Rotational_Sweep | Rotational Sweep]]
| style="width:180px;" | Rotates the radiation pattern of the transmit antenna(s) sequentially to model beam steering
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Works only with Polarimatrix solver and requires an existing ray database
|-
| style="width:120px;" | [[#Mobile_Sweep | Mobile Sweep]]
| style="width:180px;" | Considers one pair of active transmitter and receiver at each simulation run to model a mobile communication link
| style="width:150px;" | Polarimatrix
| style="width:120px;" | Runs at the center frequency fc
| style="width:300px;" | Requires the same number of transmitters and receivers, works only with Polarimatrix solver and requires an existing ray database
|}

Click on each item in the above list to learn more about each simulation mode.

You set the simulation mode in EM.Terrano's simulation run dialog using the drop-down list labeled '''Simulation Mode'''. A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can plot the output parameter results on 2D graphs or you can animate the 3D simulation data from the navigation tree.

{{Note| EM.Terrano's frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent.}}

=== Transmitter Sweep ===

When your propagation scene contains two or more transmitters, whether they all belong to the same transmitter set with the same radiation pattern or to different transmitter sets, EM.Terrano assumes all to be coherent with respect to one another. In other words, synchronous transmitters are always assumed. The rays originating from all these transmitters are superposed coherently and vectorially at each receiver. In a transmitter sweep, on the other hand, EM.Terrano assumes only one transmitter broadcasting at a time. The result of the sweep simulation is a number of received power coverage maps, each corresponding to a transmitter in the scene.

{{Note| EM.Terrano's transmitter sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Rotational Sweep ===

You can rotate the 3D radiation patterns of both the transmitters and receivers from the property dialog of the parent transmitter set or receiver set. This is done in advance before a SBR simulation starts. You can define one or more of the rotation angles of a transmitter set or a receiver set as sweep variables and perform a parametric sweep simulation. In that case, the entire scene and all of its buildings are discretized at each simulation run and a complete physical SBR ray tracing simulation is carried out. However, we know that the polarimetric characteristics of the propagation channel are independent of the transmitter or receiver antenna patterns or their rotation angles. A rotational sweep allows you to rotate the radiation pattern of the transmitter(s) about one of the three principal axes sequentially. This is equivalent to the steering of the beam of the transmit antenna either mechanically or electronically. The result of the sweep simulation is a number of received power coverage maps, each corresponding to one of the angular samples. To run a rotational sweep, you must specify the rotation angle.

{{Note| EM.Terrano's rotational sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Mobile Sweep ===

In a mobile sweep, each transmitter is paired with a receiver according to their indices in their parent sets. At each simulation run, only one (Tx, Rx) pair is considered to be active in the scene. As a result, the generated coverage map takes a different meaning implying the sequential movement of the transmitter and receiver pair along their corresponding paths. In other words, the set of point transmitters and the set of point receivers indeed represent the locations of a single transmitter and a single receiver at different instants of time. It is obvious that the total number of transmitters and total number of receivers in the scene must be equal. Otherwise, EM.Terrano will prompt an error message.

[[EM.Cube]] provides a '''Mobile Path Wizard''' that facilitates the creation of a transmitter set or a receiver set along a specified path. This path can be an existing nodal curve (polyline or NURBS curve) or an existing line objects. You can also import a sptial Cartesian data file containing the coordinates of the base location points. For more information, refer to [[Glossary_of_EM.Cube%27s_Wizards#Mobile_Path_Wizard | Mobile Path Wizard]].

{{Note| EM.Terrano's mobile sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}}

=== Investigating Propagation Effects Selectively One at a Time ===

In a typical SBR ray tracing simulation, EM.Terrano includes all the propagation effects such as direct (LOS) rays, ray reflection and transmission, and edge diffractions. At the end of a SBR simulation, you can visualize the received power coverage map of your propagation scene, which appears under the receiver set item in the navigation tree. The figure below shows the received power coverage map of the random city scene with a vertically polarized half-wave dipole transmitter located 10m above the ground and a large grid of vertically polarized half-wave dipole receivers placed 1.5m above the ground. The legend box shows the limits of the color map between -23dBm as the maximum and -150dB (the default receiver sensitivity value) as the minimum.

<table>
<tr>
<td>
[[Image:UrbanCanyon10.png|thumb|left|640px|The received power coverage map of the random city scene with a dipole transmitter.]]
</td>
</tr>
</table>

Sometime it is helpful to change the scale of the color map to better understand the dynamic range of the coverage map. If you double-click on the legend or right-click on the coverage map's name in the navigation tree and select '''Properties''', the Plot Settings dialog opens up. Select the '''User-Defined''' item and set the lower and upper bounds of color map as you wish.

<table>
<tr>
<td>
[[Image:UrbanCanyon15.png|thumb|left|480px|The plot settings dialog of the coverage map.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon16.png|thumb|left|640px|The received power coverage map of the random city scene with a user-defined color map scale between -80dBm and -20dBm.]]
</td>
</tr>
</table>

To better understand the various propagation effects, EM.Terrano allows you to enable or disable these effects selectively. This is done from the Ray Tracing Simulation Engine Settings dialog using the provided check boxes.

<table>
<tr>
<td>
[[Image:UrbanCanyon14.png|thumb|left|640px|EM.Terrano's simulation run dialog showing the check boxes for controlling various propagation effects.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon11.png|thumb|left|640px|The received power coverage map of the random city scene with direct LOS rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon12.png|thumb|left|640px|The received power coverage map of the random city scene with reflected rays only.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon13.png|thumb|left|640px|The received power coverage map of the random city scene with diffracted rays only.]]
</td>
</tr>
</table>

== Working with EM.Terrano's Simulation Data ==

=== The Ray Tracing Solvers' Output Simulation Data ===

Both the SBR solver and the Polarimatrix solver perform the same type of simulation but in two different ways. The SBR solver discretizes the scene including all the buildings and terrain, shoots a large number of rays from the transmitters and collects the rays at the receivers. The Polarimatrix solver does the same thing using an existing polarimetric ray database that has been previously generated using EM.Terrano's Channel Analyzer. It incorporates the effects of the radiation patterns of the transmit and receive antennas in conjunction with the polarimetric channel characteristics. At the end of a ray tracing simulation, all the polarimetric rays emanating from the transmitter(s) or other sources that are received by the individual receivers are computed, collected, sorted and saved into ASCII data files. From the ray data, the total electric field at the location of receivers as well as the total received power are computed. The individual ray data include the field components of each ray, the ray's elevation and azimuth angles of departure and arrival (departure from the transmitter location and arrival at the receiver location), and time delay of the received ray with respect to the transmitter. If you specify the temperatures, noise figure and transmission line losses in the definition of the receiver sets, the noise power level and signal-to-noise ratio (SNR) at each receiver are also calculated, and so are the E<sub>b</sub>/N<sub>0</sub> and bit error rate (BER) for the selected digital modulation scheme.

=== Visualizing Field & Received Power Coverage Maps ===

In wireless propagation modeling for communication system applications, the received power at the receiver location is more important than the field distributions. In order to compute the received power, you need three pieces of information:

* '''Total Transmitted Power (EIRP)''': This requires knowledge of the baseband signal power, the transmitter chain parameters, the transmission characteristics of the transmission line connecting the transmitter circuit to the transmitting antenna and the radiation characteristics of the transmitting antenna.
* '''Channel Path Loss''': This is computed through SBR simulation.
* '''Receiver Properties''': This includes the radiation characteristics of the receiving antenna, the transmission characteristics of the transmission line connecting the receiving antenna to the receiver circuit and the receiver chain parameters.

In a simple link scenario, the received power P<sub>r</sub> in dBm is found from the following equation:

<math> P_r [dBm] = P_t [dBm] + G_{TC} + G_{TA} - PL + G_{RA} + G_{RC} </math>

where P<sub>t</sub> is the baseband signal power in dBm at the transmitter, G<sub>TC</sub> and G<sub>RC</sub> are the total transmitter and receiver chain gains in dB, respectively, G<sub>TA</sub> and G<sub>RA</sub> are the total transmitting and receiving antenna gains in dB, respectively, and PL is the channel path loss in dB. Keep in mind that EM.Terrano is fully polarimetric. The transmitting and receiving antenna characteristics are specified through the imported radiation pattern files, which are part of the definition of the transmitters and receivers. In particular, the polarization mismatch losses are taken into account through the polarimetric SBR ray tracing analysis.

If you specify the noise-related parameters of your receiver set, the signal-to-noise ratios (SNR) is calculated at each receiver location: SNR = P<sub>r</sub> - P<sub>n</sub>, where P<sub>n</sub> is the noise power level in dB. When planning, designing and deploying a communication system between points A and B, the link is considered to be closes and a connection established if the received signal power at the location of the receiver is above the noise power level by a certain threshold. In other words, the SNR at the receiver must be greater than a certain specified minimum SNR level. You specify (SNR)<sub>min</sub> ss part of the definition of receiver chain in the Receiver Set dialog. In the "Visualization Options" section of this dialog, you can also check the check box labeled '''Generate Connectivity Map'''. This is a binary-level black-and-white map that displays connected receivers in white and disconnected receivers in black. At the end of an SBR simulation, the computed SNR is displayed in the Receiver Set dialog for the selected receiver. The connectivity map is generated and added to the navigation tree underneath the received power coverage map node.

At the end of an SBR simulation, you can visualize the field maps and receiver power coverage map of your receiver sets. A coverage map shows the total '''Received Power''' by each of the receivers and is visualized as a color-coded intensity plot. Under each receiver set node in the navigation tree, a total of seven field maps together with a received power coverage map are added. The field maps include amplitude and phase plots for the three X, Y, Z field components plus a total electric field plot. To display a field or coverage map, simply click on its entry in the navigation tree. The 3D plot appears in the Main Window overlaid on your propagation scene. A legend box on the right shows the color scale and units (dB). The 3D coverage maps are displayed as horizontal confetti above the receivers. You can change the appearance of the receivers and maps from the property dialog of the receiver set. You can further customize the settings of the 3D field and coverage plots.

<table>
<tr>
<td>
[[Image:AnnArbor Scene1.png|thumb|left|640px|The downtown Ann Arbor propagation scene.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene2.png|thumb|left|640px|The electric field distribution map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene3.png|thumb|left|640px|The received power coverage map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene4.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 3dB with the basic color map option.]]
</td>
</tr>
<tr>
<td>
[[Image:AnnArbor Scene5.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR<sub>min</sub> = 20dB with the basic color map option.]]
</td>
</tr>
</table>

=== Visualizing the Rays in the Scene ===

At the end of a SBR simulation, each receiver receives a number of rays. Some receivers may not receive any rays at all. You can visualize all the rays received by a certain receiver from the active transmitter of the scene. To do this, right click the '''Receivers''' item of the Navigation Tree. From the context menu select '''Show Received Rays'''. All the rays received by the currently selected receiver of the scene are displayed in the scene. The rays are identified by labels, are ordered by their power and have different colors for better visualization. You can display the rays for only one receiver at a time. The receiver set property dialog has a list of all the individual receivers belonging to that set. To display the rays received by another receiver, you have to change the '''Selected Receiver''' in the receiver set's property dialog. If you keep the mouse focus on this dropdown list and roll your mouse scroll wheel, you can scan the selected receivers and move the rays from one receiver to the next in the list. To remove the visualized rays from the scene, right click the Receivers item of the Navigation Tree again and from the context menu select '''Hide Received Rays'''.

You can also view the ray parameters by opening the property dialog of a receiver set. By default, the first receiver of the set is always selected. You can select any other receiver from the drop-down list labeled '''Selected Receiver'''. If you click the button labeled '''Show Ray Data''', a new dialog opens up with a table that contains all the received rays at the selected receiver and their parameters:

* Delay is the total time delay that a ray experiences travelling from the transmitter to the receiver after all the reflections, transmissions and diffractions and is expressed in nanoseconds.
* Ray Field is the received electric field at the receiver location due to a specific ray and is given in dBV/m.
* Ray Power is the received power at the receiver due to a specific ray and is given in dBm.
* Angles of Arrival are the θ and φ angles of the incoming ray at the local spherical coordinate system of the receiver.

<table>
<tr>
<td>
[[Image:UrbanCanyon17.png|thumb|left|720px|EM.Terrano's ray data dialog showing a selected ray.]]
</td>
</tr>
</table>

The Ray Data Dialog also shows the '''Total Received Power''' in dBm and '''Total Received Field''' in dBV/m due to all the rays received by the receiver. You can sort the rays based on their delay, field, power, etc. To do so, simply click on the grey column label in the table to sort the rays in ascending order based on the selected parameter. You can also select any ray by clicking on its '''ID''' and highlighting its row in the table. In that case, the selected rays is highlighted in the Project Workspace and all the other rays become thin (faded).

{{Note|All the received rays are summed up coherently in a vectorial manner at the receiver location.}}

<table>
<tr>
<td> [[Image:UrbanCanyon18.png|thumb|left|640px|Visualization of received rays at the location of a selected receiver in the random city scene.]] </td>
</tr>
</table>

=== The Standard Output Data File ===

At the end of an SBR simulation, EM.Terrano writes a number of ASCII data files to your project folder. The main output data file is called "sbr_results.RTOUT". This file contains all the information about individual receivers and the parameters of each ray that is received by each individual receiver.
At the end of an SBR simulation, the results are written into a main output data file with the reserved name of SBR_Results.RTOUT. This file has the following format:

Each receiver line has the following information:

* Receiver ID
* Receiver X, Y, Z coordinates
* Total received power in dBm
* Total number of received rays

Each rays line received by a receiver has the following information:

* Ray Index
* Delay in nsec
* θ and φ Angles of Arrival in deg
* θ and φ Angles of Departure in deg
* Real and imaginary parts of the three E<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub> components
* Number of ray hit points
* Coordinates of individual hit points

The angles of arrival are the θ and φ angles of a received ray measured in degrees and are referenced in the local spherical coordinate systems centered at the location of the receiver. The angles of departure for a received ray are the θ and φ angles of the originating transmitter ray, measured in degrees and referenced in the local spherical coordinate systems centered at the location of the active transmitter, which eventually arrives at the receiver. The total time delay is measured in nanoseconds between t = 0 nsec at the time of launch from the transmitter location till being received at the receiver location.

<table>
<tr>
<td>
[[Image:prop_run8_tn.png|thumb|left|720px|A typical SBR output data file.]]
</td>
</tr>
</table>

=== Plotting Other Simulation Results ===

Besides "sbr_results.out", [[EM.Terrano]] writes a number of other ASCII data files to your project folder. You can view or plot these data in [[EM.Cube]]'s Data Manager. You can open data manager by clicking the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Menu > Simulate > Data Manager''' from the menu bar or by right-clicking on the '''Data Manager''' item of the navigation tree and selecting '''Open Data Manager...''' from the contextual menu or by using the keyboard shortcut {{key|Ctrl+D}}.

The available data files in the "2D Data Files" tab of Data Manger include:

* '''Path Loss''': The channel path loss is defined as PL = P<sub>r</sub> - EIRP. The path loss data are stored in a file called "SBR_receiver_set_name_PATHLOSS.DAT" as a function of the receiver index. The path loss data make sense only if your receiver set has the default isotropic radiator.
* '''Power Delay Profile''': The delays of the individual rays received by the selected receiver with respect to the transmitter are expressed in ns and tabulated together with the power of each ray in the file "SBR_receiver_set_name_DELAY.DAT". You can plot these data from the Data Manager as a bar chart called the power delay profile. The bars indeed correspond to the difference between the ray power in dBm and the minimum power threshold level in dBm, which makes them a positive quantity.
* '''Angles of Arrival''': These are the Theta and Phi angles of the individual rays received by the selected receiver and saved to the files "SBR_receiver_set_name_ThetaARRIVAL.ANG" and "SBR_receiver_set_name_PhiARRIVAL.ANG". You can plot them in the Data Manager in polar stem charts.

When you run a frequency or parametric sweep in [[EM.Terrano]], a tremendous amount of data may be generated. [[EM.Terrano]] only stores the '''Received Power''', '''Path Loss''' and '''SNR''' of the selected receiver
in ASCII data files called "PREC_i.DAT", "PL_i.DAT" and "SNR_i.DAT", where is the index of the receiver set in your scene. These quantities are tabulated vs. the sweep variable's samples. You can plot these files in EM.Grid.

[[Image:Info_icon.png|40px]] Click here to learn more about working with data filed and plotting graphs in [[EM.Cube]]'s '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#The_Data_Manager | Data Manager]]'''.

<table>
<tr>
<td> [[Image:Terrano pathloss.png|thumb|360px|Cartesian graph of path loss.]] </td>
<td> [[Image:Terrano delay.png|thumb|360px|Bar graph of power delay profile.]] </td>
</tr>
<tr>
<td> [[Image:Terrano ARR phi.png|thumb|360px|Polar stem graph of Phi angle of arrival.]] </td>
<td> [[Image:Terrano ARR theta.png|thumb|360px|Polar stem graph of Theta angle of arrival.]] </td>
</tr>
<tr>
<td> [[Image:Terrano DEP phi.png|thumb|360px|Polar stem graph of Phi angle of departure.]] </td>
<td> [[Image:Terrano DEP theta.png|thumb|360px|Polar stem graph of Theta angle of departure.]] </td>
</tr>
</table>

=== Visualizing 3D Radiation Patterns of Transmit and Receive Antennas in the Scene ===

When you designate a "User Defined Antenna Pattern" as the radiator type of a transmitter set or a receiver set, EM.Terrano copies the imported radiation pattern data file from its original folder to the current project folder. The name of the ".RAD" file is listed under the '''3D Data Files''' tab of the data manager. Sometimes it might be desired to visualize these radiation patterns in your propagation scene at the actual location of the transmitter or receiver. To do so, you have to define a new '''Radiation Pattern''' observable in the navigation tree. The label of the new observable must be identical to the name of the ".RAD" data file. In addition, the Theta and Phi angle increments of the new radiation pattern observable (expressed in degrees) must be identical to the Theta and Phi angular resolutions of the imported pattern file. If all these conditions are met, then go to the '''Simulate Menu''' and select the item '''Update All 3D Visualization'''. The contents of the 3D radiation patterns are added to the navigation tree. Click on one of the radiation pattern items in the navigation tree and it will be displayed in the scene.

<table>
<tr>
<td>
[[Image:UrbanCanyon6.png|thumb|left|640px|The received power coverage map of the random city scene with a highly directional dipole array transmitter.]]
</td>
</tr>
</table>

By Default, [[EM.Cube]] always visualizes the 3D radiation patterns at the origin of coordinates, i.e. at (0, 0, 0). This is because that radiation pattern data are computed in the standard spherical coordinate system centered at (0, 0, 0). The theta and phi components of the far-zone electric fields are defined with respect to the X, Y and Z axes of this system. When visualizing the 3D radiation pattern data in a propagation scene, it is more intuitive to display the pattern at the location of the transmitter or receiver. The Radiation Pattern dialog allows you to translate the pattern visualization to any arbitrary point in the project workspace. It also allows you to scale up or scale down the pattern visualization with respect to the background scene.

In the example shown above, the imported pattern data file is called "Dipole_Array1.RAD". Therefore, the label of the radiation pattern observable is chosen to be "Dipole_Array1". The theta and phi angle increments are both 1° in this case. The radiation pattern has been elevated by 10m to be positioned at the location of the transmitter and a scaling factor of 0.3 has been used.

<table>
<tr>
<td>
[[Image:UrbanCanyon8.png|thumb|left|640px|Setting the pattern parameters in the radiation pattern dialog.]]
</td>
</tr>
</table>
<table>
<tr>
<td>
[[Image:UrbanCanyon7.png|thumb|left|720px|Visualization of the 3D radiation pattern of the directional transmitter in the random city scene.]]
</td>
</tr>
</table>

There is an important catch to remember here. When you define a radiation pattern observable for your project, EM.Terrano will attempt to compute the overall effective radiation pattern of the entire physical structure. However, in this case, you defined the radiation pattern observable merely for visualization purposes. To stop EM.Terrano from computing the actual radiation pattern of your entire scene, there is a check box in EM.Terrano's Ray Tracer Simulation Engine Settings dialog that is labeled '''Do not compute new radiation patterns'''. This box is checked by default, which means the actual radiation pattern of your entire scene will not be computed automatically. But you need to remember to uncheck this box if you ever need to compute a new radiation pattern using EM.Terrano's SBR solver as an asymptotic EM solver (see next section).

<table>
<tr>
<td>
[[Image:UrbanCanyon9.png|thumb|left|640px|EM.Terrano's Run Simulation dialog.]]
</td>
</tr>
</table>

== Using EM.Terrano as an Asymptotic Field Solver ==

Like every other electromagnetic solver, EM.Terrano's SBR ray tracer requires an excitation source and one or more observables for the generation of simulation data. EM.Terrano offers several types of sources and observables for a SBR simulation. You already learned about the transmitter set as a source and the receiver set as an observable. You can mix and match different source types and observable types depending on the requirements of your modeling problem.

The available source types in EM.Terrano are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:transmitter_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Transmitter Set | Point Transmitter Set]]
| style="width:250px;" | Modeling realsitic antennas & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source | Hertzian Short Dipole]]
| style="width:250px;" | Almost omni-directional physical radiator
| style="width:250px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source | Huygens Source]]
| style="width:250px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

The available observables types in [[EM.Terrano]] are:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:receiver_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Point Receiver Set | Point Receiver Set]]
| style="width:250px;" | Generating received power coverage maps & link budget calculations
| style="width:250px;" | Requires to be associated with a base location point set
|-
| style="width:30px;" | [[File:Distr Rx icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Distributed Receiver Set | Distributed Receiver Set]]
| style="width:250px;" | Computing received power at a receiver characterized by Huygens surface data
| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor Observable | Near-Field Sensor]]
| style="width:250px;" | Generating electric and magnetic field distribution maps
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern Observable | Far-Field Radiation Pattern]]
| style="width:250px;" | Computing the effective radiation pattern of a radiator in the presence of a large scattering scene
| style="width:250px;" | None, stand-alone observable
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface Observable | Huygens Surface]]
| style="width:250px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None, stand-alone observable
|}

Click on each type to learn more about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

When you define a far-field observable in EM.Terrano, a collection of invisible, isotropic receivers are placed on the surface of a large sphere that encircles your propagation scene and all of its geometric objects. These receivers are placed uniformly on the spherical surface at a spacing that is determined by your specified angular resolutions. In most cases, you need to define angular resolutions of at least 1° or smaller. Note that this is different than the transmitter rays' angular resolution. You may have a large number of transmitted rays but not enough receivers to compute the effective radiation pattern at all azimuth and elevation angles. Also keep in mind that with 1° Theta and Phi angle increments, you will have a total of 181 × 361 = 65,341 spherically placed receivers in your scene.

{{Note| Computing radiation patterns using EM.Terrano's SBR solver typically takes much longer computation times than using [[EM.Cube]]'s other computational modules.}}

<table>
<tr>
<td> [[Image:SBR pattern.png|thumb|540px|Computed 3D radiation pattern of two vertical short dipole radiators placed 1m apart in the free space at 1GHz.]] </td>
</tr>
</table>

== Statistical Analysis of Propagation Scene ==

EM.Terrano's coverage maps display the received power at the location of all the receivers. The receivers together from a set/ensemble, which might be uniformly spaced or distributed across the propagation scene or may consist of randomly scattered radiators. Every coverage map shows the '''Mean''' and '''Standard Deviation''' of the received power for all the receivers involved. These information are displayed at the bottom of the coverage map's legend box and are expressed in dB.

When you run either a frequency sweep or a parametric sweep simulation in EM.Terrano, you have the option to generate two additional coverage maps: one for the mean of all the individual sample coverage maps and another for their standard deviation. To do so, in the '''Run Dialog''', check the box labeled '''"Create Mean and Standard Deviation received power coverage maps"'''. Note that the mean and standard deviation values displayed on the individual coverage maps correspond to the spatial statistics of the receivers in the scene, while the mean and standard deviation coverage maps show the statistics with respect to the frequency or other sweep variable sets at each point in the site. Also, note that both of the mean and standard deviation coverage maps have their own spatial mean and standard deviation values expressed in dB at the bottom of their legend box.

<table>
<tr>
<td>
[[Image:PROP MAN12.png|thumb|left|480px|EM.Terrano's simulation run dialog showing frequency sweep as the simulation mode along with statistical analysis.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:UrbanCanyon4.png|thumb|left|640px|The mean coverage map at the end of a frequency sweep.]]
</td>
</tr>
<tr>
<td>
[[Image:UrbanCanyon5.png|thumb|left|640px|The standard deviation coverage map at the end of a frequency sweep.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Terrano#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

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Glossary of Generic Analog & Mixed-Mode Devices & Sources

2018-10-11T16:54:00Z

Kazem Sabet: /* Nonlinear Dependent Sources */

==4-Bit ADC Bridge==

[[File:GK44.png]]

This 8-pin device is simply a bundle of 4 1-bit ADC bridges. Each analog input pin has a corresponding digital output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|}

==4-Bit DAC Bridge==

[[File:GK45.png]]

This 8-pin device is simply a bundle of 4 1-bit DAC bridges. Each digital input pin has a corresponding analog output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|}

== AC/RF Current Source ==

[[File:GL11.png]]

This is a simplified version of the standard Current Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak current amplitude||A||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal current||A||0||
|-
|}

== AC/RF Voltage Source ==

[[File:GL10.png]]

This is a simplified version of the standard Voltage Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak voltage amplitude||V||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal voltage||V||0||
|-
|}

==Alternate Ferrite Core Transformer==

[[File:GK96.png]]

The alternate ferrite core transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ferrite_Core_Transformer | Ferrite Core Transformer]], except for the reversed polarity of its secondary port.

==Alternate Ideal Transformer==

[[File:XFMR2.png]]

The alternate ideal transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ideal_Transformer | Ideal Transformer]], except for the reversed polarity of its secondary port.

== AM Modulated Source ==

[[File:GL23.png]]

This is a voltage source with a single-tone amplitude modulated waveform. The AM modulation index MDI is defined as the ratio of maximum amplitude deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Analog Clock ==

[[File:GL30.png]]

This is a periodic pulse generator with a default 0V low output level and a default 5V high output level.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|delay||delay time||sec||0||
|-
|rise||rise time||sec||0.1n||
|-
|fall||fall time||sec||0.1n||
|-
|pulse_wid||clock pulse width||sec||1u||required
|-
|period||clock period||-||2u||required
|-
|out_low||low output voltage level||V||0||
|-|-
|out_high||high output voltage level||V||5||
|-
|}

==Analog-to-Digital Converter (ADC) Bridge==
[[File:GK42.png]]

The ADC Bridge takes an analog value from an analog node and may be in the form of a voltage or current.
If the input is less than or equal to "in_low", then a digital "0" is generated. If
the input is greater than or equal to "in_high", a digital "1" is generated. Otherwise,
a digital "UNKNOWN" is the output value. Unlike the DAC Bridge, ramping or delay is not applicable.
Rather, the continuous ramping of the input provides for any associated delays in the digitized signal.

This model also posts an input load value based on the parameter input_load.

Model Identifier: adc_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> adc_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] adc_bridge

.model adc_bridge adc_bridge in_low = .1 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|rise_delay||L-to-H delay time||sec||1n||
|-
|fall_delay||H-to-L delay time||sec||1n||
|-
|}

== Arbitrary Temporal Waveform Generator ==

[[File:GL17.png]]

This is a voltage source with an arbitrary waveform defined by a mathematical expression. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(t)" standing for time.

Examples:

* v(t) is equivalent to f(t) = t.
* 0.1*(v(t))^2 is equivalent to f(t) = 0.1t^2.
* sin(2*pi*v(t)) is equivalent to f(t) = sin(2πt).

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Tmax||maximum signal duration||sec||1e6||required
|-
|}

==Auto-Transformer==

[[File:GK102.png]]

This 3-pin device models an auto-transformer with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lp||primary inductance||H||1m||
|-
|Ls||secondary inductance||H||1m||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Bipolar Junction Transistor (BJT)==
[[File:G11.png]]

The BJT is an active device which has up to 4 pins. The three standard pins are base, emitter, and collector. These are given in the default symbol. The substrate, which is grounded by default, is the fourth pin. To use the BJT with the substrate, create a new 4-pin BJT using the Device Editor and Symbol Editor.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

Area factor scales the model parameters RE and RC. IC VBE is the initial voltage from base emitter. IC VCE is the initial voltage from collector to emitter. TEMP is the overriding temperature. These parameters are based on the Gummel and Poon integral-charge model. If these parameters are not specified, then it will reduce to the simpler Ebers-Moll model.

The process model is mandatory for the BJT. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|IS||transport saturation current||A||1.0e-16||1.0e-15
|-
|BF||ideal maximum forward beta|| ||100||100
|-
|NF||forward current emission coefficient|| ||1.0||1
|-
|VAF||forward Early voltage||V||infinite||200
|-
|IKF||corner forward beta high current roll-off||A||infinite||0.01
|-
|ISE||B-E leakage saturation current||A||0||1.0e-13
|-
|NE||B-E leakage emission coefficient|| ||1.5||2
|-
|BR||ideal maximum reverse beta|| ||1||0.1
|-
|NR||reverse current emission coefficient|| ||1||1
|-
|VAR||reverse Early voltage||V||infinite||200
|-
|IKR||corner reverse beta high current roll-off||A||infinite||0.01
|-
|ISC||B-C leakage saturation current||A||0||1.0e-13
|-
|NC||B-C leakage emission coefficient|| ||2||1.5
|-
|RB||zero bias base resistance||ohms||0||100
|-
|IRB||current where base resistance falls halfway to minimum value||A||infinite||0.1
|-
|RBM||minimum base resistance at high currents||ohms||RB||10
|-
|RE||emitter resistance||ohms||0||1
|-
|RC||collector resistance||ohms||0||10
|-
|CJE||B-E zero bias depletion capacitance||F||0||2pF
|-
|VJE||B-E built-in potential||V||0.75||0.6
|-
|MJE||B-E junction exponential factor|| ||0.33||0.33
|-
|TF||ideal forward transit time||sec||0||0.1ns
|-
|XTF||coefficient for bias dependence of TF|| ||0||
|-
|VTF||voltage describing VBC dependence of TF||V||infinite||
|-
|ITF||high-current parameter for effect on TF||A||0||
|-
|PTF||excess phase at freq=1.0/(TF*2PI)Hz||degree||0||
|-
|CJC||B-C zero bias depletion capacitance||F||0||2pF
|-
|VJC||B-C built-in potential||V||0.75||0.5
|-
|MJC||B-C junction exponential factor|| ||0.33||0.5
|-
|XCJC||fraction of B-C depletion capacitance connected to internal base node|| ||1||
|-
|TR||ideal reverse transit time||sec||0||10ns
|-
|CJS||zero bias collector-substrate capacitance||F||0||2pF
|-
|VJS||substrate junction built-in potential||V||0.75||
|-
|MJS||substrate junction exponential factor|| ||0||0.5
|-
|XTB||forward and reverse beta temp. exponent|| ||0||
|-
|EG||energy gap for temperature effect on IS||eV||1.11||
|-
|XTI||temperature exponent for effect on IS|| ||3||
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

==Capacitance Meter==
[[File:G37.png]]

The Capacitance Meter measures the total capacitance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total capacitance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense a capacitance value and alter their behavior based upon it.

Model Identifier: cmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> cmeter {<gain = value>}

Example:

A1 1 2 cap_meter

.model cap_meter cmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Capacitor==
[[File:GK120.png]]

Capacitors are used to store electrical energy. They can filter or remove AC signals or block DC current without disrupting AC signals. A capacitor's ability to store energy is termed capacitance and is measured in Farads, with values from pF to mF. The only time current flows through a capacitor is when the charge is collected on, or is removed from, its parallel plates. This means that the voltage across the capacitor is changing, which doesn't conform to DC analysis. In a physical circuit, there is a transition stage during which capacitors charge up to their final values. The result is the same as if these capacitors did not exist and the connections to them were left dangling. In other words, in a (steady-state) DC analysis, a capacitor behaves like an open circuit. Therefore, it is important that no section of the circuit is isolated from the capacitors. Every circuit node needs some path for DC current to the ground.

A capacitor's transient behavior is described by the equation:

i(t) = C * (dv(t)/dt)

Its initial voltage is only important when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An capacitor's AC behavior is described by the equation:

i = j ω * C * v

All capacitor names must begin with C.

Netlist Format:

C<device_name> <N+> <N-> <value>

Example:

C1 1 2 10p

[[RF.Spice A/D]] provides three types of capacitors: simple, user-defined (or real) and semiconductor. The standard capacitor parameters are N+, N-, VALUE, and IC. In a simple capacitor, VALUE must
be specified for the capacitance in Farads. IC is the (optional) initial condition for the capacitor voltage.

==Center-Tapped Ferrite Core Transformer==

[[File:GK97.png]]

This five-pin three-port device models a center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

==Controlled Sine Wave Oscillator==

[[File:G24.png]]

This is a four-terminal function generator with a sinusoidal wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.
This function has parameterizable values of low and high peak output voltage.

Model Identifier: sine

Netlist Form:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> sine cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) sine

.model sine sine cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[1 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|}

==Controlled Sources==

Circuits can contain linear dependent sources characterized by one of the following equations (where g,
e, f, and h are constants representing transconductance, voltage gain, current gain, and transresistance,
respectively):

<SPAN STYLE="font-size: 9pt ; ">i<sub>out</sub> = g v<sub>in</sub>
     v<sub>out</sub> = e v<sub>in</sub>
     i<sub>out</sub> = f i<sub>in</sub>
     v<sub>out</sub> = h i<sub>in</sub></SPAN>
<P CLASS="Bodytext" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; ">
For further information, refer to:</P>

Linear Current Controlled Current Source (CCCS)

Linear Voltage Controlled Current Source (VCCS)

Linear Current Controlled Voltage Source (CCVS)

Linear Voltage Controlled Voltage Source (VCVS)

==Controlled Square Wave Oscillator==

[[File:G25.png]]

This is a four-terminal function generator with a square wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: square

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> square cntl_array = [<value1> <value2>] freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) square

.model square square cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Duty_cycle||Duty cycle||-||0.5||
|-
|Rise_time||Output rise time||sec||1.0e-9||
|-
|Fall_time||Output fall time||sec||1.0e-9||
|-
|}

==Controlled Triangle Wave Oscillator==

[[File:G26.png]]

This is a four-terminal function generator with a triangle wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defined voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: triangle

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> tirangle cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>]{<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 4) %vd(2 3) triangle

.model triangle triangle cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Rise_duty||Rise time duty cycle||0.5||
|-
|}

== Crystal ==

[[File:GK78.png]]

This is a 2-pin parameterized crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CM||motional capacitance||F||10f||
|-
|C0||shunt capacitance||F||1p||
|-
|RM||motional resistance||Ohms||100||
|-
|LM||motional inductance||H||100m||
|-
|}

==Current Noise Source==

[[File:GL16.png]]

This is a current noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the [[parameters]] of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise current||A/√Hz||1p||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Current Source==

[[File:G17B.png]]

Current source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a current source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset current. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==Current-Controlled Switch==

[[File:G20.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Current-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the turn-on and turn-off currents in Amperes and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the rest of [[parameters]]. When the current through the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the current through the switch or controlling device is less than or equal to the turn off current, the switch opens.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|I_ON||turn-on current||A||0.0||
|-
|I_OFF||turn-off current||A||0.0||
|-
|RON||closed resistance||Ohms||1.0||
|-
|ROFF||open resistance||Ohms||1/GMIN||
|-
|}

==Darlington Pair==

[[File:GK108.png]]

A Darlington pair is a three-pin device that consists of two interconnected BJT transistors of the same type. The collectors of two transistors are connected together to provide the "Collector" pin of the pair. The base of the first BJT acts the "Base" pin of the pair. The emitter of the first BJT is internally connected to the base of the second BJT. The emitter of the second BJT acts as the "Emitter" pin of the pair. There are two types of Darlington pair: NPN and PNP. The parameterized generic Darlington pair also contains a diode connected between the collector and emitter pin as well as two base-emitter resistors, one across each BJT.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|is_bjt||bjt saturation current||A||1.0e-12||
|-
|bf_bjt||bjt forward beta||-||150||
|-
|nf_bjt||bjt forward emission coefficient||-||1||
|-
|ise_bjt||B-E leakage saturation current||A||0||
|-
|ne_bjt||B-E leakage emission coefficient||-||1||
|-
|br_bjt||ideal maximum reverse beta||-||1||
|-
|nr_bjt||reverse current emission coefficient||-||1||
|-
|isc_bjt||B-C leakage saturation current||A||0||
|-
|nc_bjt||B-C leakage emission coefficient||-||1||
|-
|rb_bjt||zero bias base resistance||Ohms||0||
|-
|irb_bjt||current where base resistance falls halfway to minimum value||A||inf||
|-
|rbm_bjt||minimum base resistance at high currents||ohms||0||
|-
|re_bjt||emitter resistance||Ohms||0||
|-
|rc_bjt||collector resistance||Ohms||0||
|-
|cje_bjt||B-E zero bias depletion capacitance||F||0||
|-
|vje_bjt||B-E built-in potential||V||0.75||
|-
|mje_bjt||B-E junction grading coefficient||-||0.33||
|-
|cjc_bjt||B-C zero bias depletion capacitance||F||0||
|-
|vjc_bjt||B-C built-in potential||V||0.75||
|-
|mjc_bjt||B-C junction exponential factor||-||0.33||
|-
|tf_bjt||ideal forward transit time||sec||0||
|-
|tr_bjt||ideal reverse transit time||sec||0||
|-
|is_d||diode saturation current||A||1.0e-12||
|-
|rs_d||diode resistance||Ohms||0||
|-
|n_d||diode emission coefficient||-||1||
|-
|cjo_d||diode junction capacitance||F||0||
|-
|vj_d||diode junction potential||V||1||
|-
|m_d||diode grading coefficient|| ||0.5||
|-
|tnom||parameter measurement temperature||deg C||27||
|-
|r1||first base-emitter resistance||Ohms||1k||
|-
|r2||second base-emitter resistance||Ohms||1k||
|-
|}

== DC Bias Sources Vcc, Vee, Vdd, Vss ==

[[File:GL12.png]]

These are simple 1-pin DC voltage sources. Vcc and Vdd provide a positive voltage, while Vee and Vss provide a negative voltage

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|vcc||bias voltage||V||+15||required
|-
|vee||bias voltage||V||-15||required
|-
|vdd||bias voltage||V||+15||required
|-
|vss||bias voltage||V||-15||required
|-
|}

==Digital-to-Analog Converter (DAC) Bridge==

[[File:GK43.png]]

The DAC Bridge takes a digital value from a digital node and can only be eiter "0", "1",
or "U". It then outputs the value "out_low", "out_high" or "out_udndef",
or ramps linearly toward one of these "final" values from its curent analog output level. This
ramping speed depends on the values of "t_rise" and "t_fall".

Model Identifier: dac_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> dac_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] dac_bridge

.model dac_bridge dac_bridge out_low = 0 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|out_undef||analog output for undefined digital input||V||0.5||required
|-
|input_load||capacitive input load||F||1p||
|-
|t_rise||L-to-H delay time||sec||1n||
|-
|t_fall||H-to-L delay time||sec||1n||
|-
|}

==Diode==

[[File:G9.png]]

Diodes allow current flow only in one direction, following their symbol's arrow, and thus can be used as simple solid
state switches in AC circuits.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process models can be either junction diodes or Schottky barrier diodes. Area factor scales the model parameters
IS, RS, CJO, and IBV. VD is the initial voltage, and TEMP is the overriding temperature. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||0||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|EG||activation energy||eV||1.11||
|-
|XTI||saturation current temp. exp.||-||3.0||
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||forward bias junction fit parameter||-||0.5||
|-
|BV||reverse breakdown voltage||V||inf||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|}

==Diode Bridge==

[[File:GK107.png]]

This four-pin device is a bridge configuration of four generic diodes.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||10p||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|BV||reverse breakdown voltage||V||1000||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|}

==Doubly Center-Tapped Ferrite Core Transformer==

[[File:GK98.png]]

This six-pin four-port device models a doubly center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of full-winding primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== DPDT Switch ==

[[File:GK74.png]]

This is an 8-pin device that models a double-pole double-throw switch. It has two input signals and four output pins. When the control voltage is at the high state, the first and second input voltages are transferred to the first and third output pins, respectively. When the control voltage is at the low state, the first and second input voltages are transferred to the second and fourth output pins, respectively.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== DPST Switch ==

[[File:GK73.png]]

This is a 6-pin device that models a double-pole single-throw switch. It has two input signals and two output signals. When the switch on, the first and second input voltages are transferred to the first and second output pins, respectively. When the switch is off, the output pin do not receive any input signals.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Ferrite Core Transformer==

[[File:GK95.png]]

This four-pin two-port device models a physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary turns||-||100||required
|-
|n_sec||number of secondary turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== FM Modulated Source ==

[[File:GL24.png]]

This is a voltage source with a single-tone frequency modulated waveform. The FM modulation index MDI is defined as the ratio of maximum frequency deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

==Frequency Meter==
[[File:G114.png]]

The Frequency Meter is a four-pin shunt device that is connected in parallel with an AC source just like a voltmeter and measures the operating frequency of the AC circuit. The input pins are connected across the AC source. The voltage across the output pins is equal to the frequency of the source in Hertz within a scale factor SF. Note that the Frequency Meter is designed to work with a single-tone AC source of unit amplitude. If the amplitude of the source is not one, multiply the SF parameter by the non-unit source amplitude value. The output voltage of the Frequency Meter can be used in conjunction with linear or nonlinear dependent sources to model frequency-dependent quantities.

Model Identifier: fmeter

Parameters:

The only parameter is the scale factor SF with a default value of 1.0. Set SF = 1e-6 to read out the frequency in MHz. Set SF = 1e-9 to read out the frequency in GHz. Set SF = 6.283185 (2*pi) to read out the angular frequency ω in radian/s.

== Fuse ==

[[File:GK76.png]]

This is a 2-pin interactive current-controlled switch. If the current passing through the fuse is less than a specified threshold current, the switch is closed. If the current exceeds the threshold level, the fuse breaks and remains open thereafter. The device's symbol changes to display its state.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|r||resistance when intact||Ohms||1.0||
|-
|i_thresh||threshold current||A||1.0||
|-
|}

==Ground==

[[File:G15.png]]

Ground has a voltage of zero (0) and is used as a reference to compute electrical values in the circuit.
All circuits <B>must</B> be grounded to be properly simulated. There is no limit on the number of grounds
you may use in a circuit. All components connected to ground are referenced to a common point and treated
as linked through ground.

==Hysteresis Block (XSPICE)==

[[File:G37.png]]

The Hysteresis block is a simple buffer stage that provides hysteresis of the output with respect to the
input. The in_low and in_high parameter values. The output values are limited to out_lower_limit and
out_upper_limit. The value of \93hyst\94 is added to the in_low and in_high points in order to specify the
points at which the slope of the hysteresis function would normally change abruptly as the input transitions
from a low to a high value. Likewise, the value of \93hyst\94 is subtracted from the in_high and in_low values
in order to specify the points at which the slope of the hysteresis function would normally change abruptly
as the input transitions from a high to a low value. In fact, the slope of the hysteresis function is
never allowed to change abruptly but is smoothly varied whenever the input_dowmain smoothing parameter
is set greater than zero.

Model Identifier: hyst

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> hyst {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 hysteresis_block

.model hysteresis_block hyst in_low = 0.0 in_high = 1.0

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default
|-
|In_low||input low value||0.0
|-
|in_high||input high value||1.0
|-
|hyst||hysteresis||0.1
|-
|out_lower_limit||output lower limit||0.0
|-
|out_upper_limit||output upper limit||1.0
|-
|input_domain||input smoothing domain||0.01
|-
|fraction||smoothing fraction/absolute value switch||true
|-
|}

==Ideal Center-Tapped Transformer with Push-Pull Input==

[[File:XFMR4.png]]

The ideal center-tapped transformer with push-pull input is a five-pin three-port device with two primary input ports and one secondary output port. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P1}{v_S} = \frac{v_P2}{v_S} = n </math>

where v<sub>S</sub> is the secondary voltage, v<sub>P1</sub> is measured between the top primary pin P1 and the center tap pin, and v<sub>P2</sub> is measured between the center tap pin and the bottom primary pin P2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P1</sub>/N<sub>S</sub> = N<sub>P2</sub>/N<sub>S</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Center-Tapped Transformer with Push-Pull Output==

[[File:XFMR3.png]]

The ideal center-tapped transformer with push-pull output is a five-pin three-port device with one primary input port and two secondary output ports. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P}{v_{S1}} = \frac{v_P}{v_{S2}} = n </math>

where v<sub>P</sub> is the primary voltage, v<sub>S1</sub> is measured between the top secondary pin S1 and the center tap pin, and v<sub>S2</sub> is measured between the center tap pin and the bottom secondary pin S2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S1</sub> = N<sub>P</sub>/N<sub>S2</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Diode==

[[File:GK106.png]]

This 2-pin device is a very basic and primitive model of a diode as a rectifier or switch. When the voltage across the device's terminals is positive, it acts as a short circuit. When the voltage across the device's terminals is negative, it acts as an open circuit.

Parameters:

None

==Ideal Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This is a very basic and primitive model of an operational amplifier. It has only one parameter, open loop gain with a default value of 50,000, which is adequate for most cases. The ideal Op-Amp device doesn't require any DC bias voltages.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|A||open loop gain||-||50,000||
|-
|}

==Ideal Transformer==

[[File:XFMR1.png]]

The ideal transformer is a four-pin two-port device with the following relationship between the voltages and currents at its primary and secondary ports:

<math> \frac{v_P}{v_S} = - \frac{i_S}{i_P} = \frac{N_P}{N_S} = n </math>

where v<sub>P</sub>, i<sub>P</sub>, N<sub>P</sub> are the primary voltage, current and number of turns, respectively, and v<sub>S</sub>, i<sub>S</sub>, N<sub>S</sub> are the secondary voltage, current and number of turns, respectively. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S</sub>, which represents the primary-to-secondary turns ratio. Note that the ideal transformer model is defined based on controlled sources and does not involve any magnetic physical parameters as opposed to mutual inductors or ferrite core transformer.

==Inductance Meter==

[[File:G37.png]]

The Inductance Meter measures the total inductance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total inductance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense an inductance value and alter their behavior based upon it. Care must be exercised when connecting an Inductance Meter to the inductors of a circuit. This is due to the fact that inductors are treated by SPICE as current sources. This can cause a problem when an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor.

Model Identifier: lmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> imeter {<gain = value>}

Example:

A1 1 2 inductance_meter

.model inductance_meter lmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Inductive Coupler Block==

[[File:GK99.png]]

The Inductive Coupler Block couples any two existing inductors. This block doesn't have any pins because it doesn't actually represent inductors, only the coupling between them. This is useful if you want to
couple two inductors that are in different parts of the circuit, or if you want to couple more than two inductors together. In the latter case, use more than one of these, with each one coupling a pair of inductors.

The standard parameters are Inductor1, Inductor2, and k. Inductor1 is the name of first inductor, Inductor2 is the name of the second inductor, and k is the coefficient of coupling, 0 < k ≤ 1.

==Inductive Coupling (XSPICE)==

[[File:G41.png]]

This function is a conceptual model which is used as a building block to create a wide variety of inductive and magnetic circuit models. This function is normally used in
conjunction with the “core” model, but it can also be used with resistors, hysteresis blocks, etc. to build up systems which mock the behavior of linear and nonlinear components.
The lcouple takes as an input (on the “l” port) a current. This current value is multiplied by the num_turns value, N, to produce an output value (a voltage value which appears on the
mmf_out port). The mmf_out acts similar to a magnetomotive force in a magnetic circuit;
when the lcouple is connected to the “core” model, or to some other resistive device, a current will flow. This current value (which is modulated by whatever the lcouple is
connected to) is then used by the lcouple to calculate a voltage “seen” at the “l” port. The voltage is a function of the derivative with respect to time of the current value seen at mmf_out.

The most common use for lcouple will be as a building block in the construction of transformer models. To create a transformer with a single input and a single output, you
would require two lcouple models plus one “core” model.

Example:

A1 (1 0) (2 3) lcouple1

.model lcouple1 lcouple ( num_turns = 10 )

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|num_turns||number of turns||-||1||required
|-
|}

==Inductor==

[[File:GK121.png]]

Inductors are used to store magnetic energy. An inductor's ability to counteract current changes passing through it is called its inductance (L), which is
measured in Henrys. In a (steady-state) DC analysis, the inductor acts like a short circuit. It is indeed treated as a current source, which can be problematic if an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor. The resistor may be of negligible value or one that accounts for the coil resistance of the inductor. In AC and transient analyses, the inductor develops a voltage across it in response to the changing magnetic
flux within its coil.

An inductor's transient behavior is described by the equation:

v(t) = L*(di(t)/dt)

The inductor's initial condition is optional. It is the initial value of the inductor current in Amperes that flows from node N+ through the inductor to node N-. The only time that the initial current matters is when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An inductor's AC behavior is described by the equation:

v = j ω * L * i

All inductor names must begin with L.

Netlist Format:

L<device_name> <N+> <N-> <value>

Example:

L1 1 2 10u

==Inductor with Ferrite Core==

[[File:GK94.png]]

This 2-pin device models a physical inductor with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. Unlike the standard inductor device, you do not specify an inductance value for the inductor with ferrite core. Rather, you specify physical parameters like cross sectional area, core length and number of turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_turns||number of turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== Insulated Gate Bipolar Transistor (IGBT)==

[[File:GK111.png]]

This is a 3-pin parameterized Insulated Gate Bipolar Transistor (IGBT) device with three pins: Collector(C), Gate (G), and Emitter (E). It is primarily used as a fast electronic switch. The IGBT combines the simple gate-drive characteristics of MOSFETs with the high-current and low-saturation-voltage capability of bipolar transistors. The device's model consists of an isolated gate FET for the control input, and a PNP bipolar power transistor as a switch. To further modify the internal device models, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|cap||parasitic capacitance||F||1n||
|-
|rg||gate resistance||Ohms||5||
|-
|re||emitter resistance||Ohms||0.05||
|-
|bf||pnp transistor forward beta||-||1||
|-
|vto||MOSFET threshold voltage||V||5||
|-
|kt||MOSFET transconductance||-||2.99||
|-
|cgso||MOSFET voltage gate-source overlap capacitance||F||5u||
|-
|nd||diode emission coefficient||-||50||
|-
|cjo||diode junction capacitance||F||1n||
|-
|}

==Interactive Switch==

[[File:GK75.png]]

This device is an interactive switch that can be closed or opened either directly from the Schematic Editor by clicking on its symbol or from the Instrument Panel.

==Junction Field Effect Transistor (JFET)==

[[File:G12.png]]

The JFET is the simplest transistor device and has three pins: gate, drain and source. The JFET defaults are based on the Shichman and Hodges FET model. This is a square-law device because of the expression relating the drain current to the gate-to-source voltage:
Idrain=*(VGS-Vthreshold)2. In real JFETs, near the saturation point, the drain currents vary with the drain voltages. This can be modeled by the following formula: Idrain=*(VGS-VTO)2*(1+*VDS), which yields an increasing
drain current for increasing values of VDS.

The gate-to-source and gate-to-drain junctions each have a nonlinear capacitor. The zero-bias capacitance value is selected for each junction.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process model parameters are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||threshold voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||ohms||0||100
|-
|RS||source ohmic resistance||ohms||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|IS||gate junction saturation current||A||1.0e-14||1.0e-14
|-
|B||doping tail parameter|| ||1||1.1
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

== Light Emitting Diode (LED) ==

[[File:GK114.png]]

This is a two-pin parameterized diode device that emits light of a certain wavelength when it is forward-biased.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rs||ohmic resistance||Ohms||10||
|-
|vj||junction potential||V||0.6||
|-
|cjo||zero bias junction capacitance||F||10p||
|-
|tt||transit time||sec||0.1n||
|-
|}

==Linear Current-Controlled Current Source (CCCS)==

[[File:G2.png]]

The CCCS is a current source whose current is directly proportional to the current across a controlling Ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the current gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the current gain.

Model Identifier: cccs

Netlist Format:

F<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

F1 1 0 V1 1.0

==Linear Current-Controlled Voltage Source (CCVS)==

[[File:G4.png]]

The CCVS is a voltage source whose voltage is directly proportional to the current through a controlling ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the trans-resistance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the trans-resistance gain.

Model Identifier: ccvs

Netlist Format:

H<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

H1 1 0 V1 1.0

==Linear Voltage-Controlled Current Source (VCCS)==

[[File:G3.png]]

The VCCS is a current source whose current is directly proportional to the voltage across a controlling voltmeter or the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the trans-conductance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the trans-conductance gain.

Model Identifier: vccs

Netlist Format:

G<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

G1 1 0 2 0 1.0

==Linear Voltage-Controlled Voltage Source (VCVS)==

[[File:G1.png]]

The VCVS is a voltage source whose voltage is directly proportional to the voltage across a controlling voltmeter of the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the voltage gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the voltage gain.

Model Identifier: vcvs

Netlist Format:

E<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

E1 1 0 2 0 1.0

==Lossless Transmission Line==

[[File:G21.png]]

The lossless transmission line is a four-pin two-port device that models only one propagating mode of an ideal transmission line. When using this SPICE model, should all four nodes of the actual circuit be distinct, two modes may be activated, and this device would be insufficient for that purpose. To circumvent this potential problem, two transmission line devices would be required. Due to the implementation details, you may produce more accurate simulation results with a lossy transmission line device with zero loss.

Optional initial condition parameters are the voltage and current at each of the transmission line ports.

The standard device parameters are Z0, TD, F, NL, IC, described below:

{| class="wikitable"
|-
|Z0||characteristic impedance
|-
|TD||transmission delay
|-
|F||frequency
|-
|NL||normalized electrical length of the transmission line with respect to the wavelength in the line at frequency F. (If F is specified, but NL is not, the default is 0.25.)
|-
|IC||initial condition (Specifies the voltage and current at each of the transmission line ports.)
|-
|}

==Lossy Transmission Line==

[[File:G22.png]]

The lossy transmission line is a four-pin two-port convolution model for uniform constant-parameter distributed lines. MNAME is the process model name, which
includes a set of pre-specified options as described below.

The device model [[parameters]] are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|R||resistance /length||Ohm /m||0.0||0.2
|-
|L||inductance/length||henrys/m||0.0||9.13e-9
|-
|C||capacitance/length||farads/m||0.0||3.65e-12
|-
|LEN||length of line||m||none||1.0
|-
|LININTERP||use linear interpolation||flag||not set||set
|-
|QUADINTERP||use quadratic interpolation||flag||not set||set
|-
|MIXEDINTERP||use linear when quadratic seems bad||flag||not set||set
|-
|COMPACTREL||special reltol for straight line checking||flag||RETOL||1.0e-3
|-
|COMPACTABS||special abstol for straight line checking||flag||ABSTOL||1.0e-9
|-
|NOCONTROL||don't do complex time control||flag||not set||set
|-
|STEPLIMIT||always limit timestep to 0.8*(delay of line)|| || ||
|-
|NOSTEPLIMIT||don't always limit timestep to 0.8*(delay of line)||flag||not set||set
|-
|TRUNCNR||use Newton-Raphson method for timestep calculation in LTRAtrunc||flag||not set||set
|-
|TRUNCDONTCUT||don't limit timestep to keep impulse-response errors low||flag||not set||set
|-
|}

<P CLASS="Normal-1">
The RLC (uniform transmission line with series loss only), RC (uniform RC line), LC (lossless transmission
line), and RG (distributed series resistance and parallel conductance only) lines have been implemented.
The length (LEN) must be given. COMPACTREL and COMPACTABS control the compaction of past history values
used in convolution. Larger values for these lower accuracy but improve speed. These are used with the
TRYTOCOMPACT option. </P>

==Magnetic Core (XSPICE)==

[[File:G42.png]]

This device is used as a building block to create a wide variety of inductive and magnetic circuit models. It is almost always to be used in conjunction with the "lcouple" model to build up systems which simulate the behavior of linear and nonlinear magnetic components. There are two fundamental modes of operation for the core model. These are the "PWL" mode (which is the default and most
likely to be of use to you) and the "Hysteresis" mode.

<b>PWL Mode (mode = 1)</b>

In the PWL mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf) value. This value is divided by the total effective length of the core to produce a value for the Magnetic Field Intensity, H, which is then used to find the corresponding Flux Density, B, using the piecewise linear relationship described by you in the H_array / B_array coordinate pairs. B is then multiplied by the cross-sectional area of the core to find the Flux value, which is output as a current. The pertinent mathematical equations are:

H = mmf / L, where L = Length (in apmere-turns/meter)

B = f(H)

Φ = B * A, where A = Area

The B value is derived from a piecewise linear transfer function described to the model by the H_array and B_array coordinate pairs. This transfer function does not include hysteretic effects; for that, you would need to substitute a HYST model for the core. The magnetic flux value Φ in turn is used by the "lcouple"
code model to obtain a value for the voltage reflected back across its terminals to the driving electrical circuit.

<b>Hysteresis Mode (mode = 2)</b>

In the Hysteresis mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf)
value. This value is used as input to the equivalent of a hysteresis code model block. The parameters
defining the input low and high values, the output low and high values, and the amount of hysteresis are
as in that model. The output from this mode, as in PWL mode, is a current value which is seen across the magnetic core port.

One final note to be made about the two core models is that certain parameters are specific to one or the other. In particular, the in_low, in_high, out_lower_limit, out_upper_limit, and hysteresis parameters are not available in PWL mode. Likewise, the H_array, B_array, area, ad length values are unavailable
in Hysteresis mode. The input_domain and fraction parameters are common to both modes (though their behavior is somewhat different; for explanation of the input_domain and fraction values for the Hysteresis mode, please refer to the Hysteresis Block discussion.

Model Identifier: core

Netlist Format:

A<device_name> <mc1 _pin> <mc2_pin> <model_name>

.model <model_name> core area = <value> length = <value> H_array = [<value1> <value2>] B_array = [<value1> <value2>]
{<param1 = value> < param2 = value> ...}

Example:

A1 1 2 core

.model core core area = 1 length = 1 H_array = [0 1] B_array = [0 1]

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|H_array||magnetic field array||[0 1]||required
|-
|B_array||flux density array||[0 1]||required
|-
|Area||cross-sectional area||1||required
|-
|Length||core length||1||required
|-
|Input_domain||input smoothing domain||0.01||
|-
|Fraction||smoothing fraction/abs switch||True||
|-
|Mode||mode switch (1=pwl, 2=hyst)||1||
|-
|In_low||input low value||0.0||
|-
|In_high||input high value||1.0||
|-
|Hyst||hysteresis||0.1||
|-
|Out_lower_limit||output lower limit||0.0||
|-
|Out_upper_limit||output upper limit||1.0||
|-
|}

==Marker==

[[File:G16.png]]

The marker serves several purposes:

* It can appear as a default plot in simulations if the "Voltage Probe" box is checked.

* It can be used to set the initial voltage or voltage guess at the node it is connected to.

* It can be used as a port for a subcircuit when you choose the checkbox labeled "Use as Subcircuit Port" is checked.

* It can be used to explicitly set a node number in place of the arbitrarily assigned node number by the program. In this case, make sure the "Set Node Index" box is checked. Otherwise, it will act as just a voltage probe.

* It can be used to connect different parts of a circuit in place of wires. To use markers as virtual connectors, place them at points where wires would otherwise connect. Then set the Part Title of the two (or more) markers to the same name, and they will act as a single circuit node.

==MESFET==

[[File:G14.png]]

The MESFET is a Schottky-barrier gate FET with six times greater electron mobility than silicon. MESFETs are important devices for creating high frequency circuits. They function by creating a potential barrier between the gate and the channel when the metal gate
contacts the gallium-arsenide substrate. Electron velocity saturates for fields approximately ten times lower than with silicon. The Curtice model includes linear and saturated operation.

The standard parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

All the MESFET process model parameters are described in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||pinch-off voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|B||doping tail extending parameter||1/V||0.3||0.3
|-
|ALPHA||saturation voltage parameter||1/V||2||2
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||Ohm||0||100
|-
|RS||source ohmic resistance||Ohm||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula||-||0.5||
|-
|}

==MOSFET==

[[File:G13.png]]

The MOSFET is an active device that has up to 4 pins. The three standard pins are gate, drain, and source. These are given in the default symbol. The bulk node, which is grounded by default, is the fourth pin. The MOSFET with the bulk is named mos_n_lvl1_4 (the lvl1 is for level 1, the n for nmos, and the 4 for 4 pins.)

The standard [[parameters]] are L, W, AD, AS, PD, PS, NRD, NRS, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|L||channel length, in meters
|-
|W||channel width, in meters
|-
|AD,AS||areas of the drain and source diffusions, in meters2
|-
|PD,PS||perimeters of drain and source junctions, in meters(They default to 0.0.)
|-
|NRD,NRS||equivalent number of squares of the drain and source diffusions (These values multiply the sheet resistance for an accurate representation of parasitic series drain and source resistance of each transistor. The default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

There are five different default models: square-law I-V characteristic, analytical, semi-empirical, and BSIM and BSIM2 (Berkeley Short-channel IGFET Model), which include second-order effects such as channel-length
modulation, subthreshold conduction, scattering-limited velocity saturation, small-size effects, and charge-controlled capacitance. The process parameter LEVEL specifies which of the models is chosen as indicated below:

{| class="wikitable"
|-
|LEVEL 1||Schichman-Hodges
|-
|LEVEL 2||MOS2
|-
|LEVEL 3||MOS3
|-
|LEVEL 4||BSIM
|-
|LEVEL 5||BSIM2
|-
|LEVEL 6||MOS6
|-
|}

The process model [[parameters]] for levels 1,2,3, and 6 are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|LEVEL||model index|| ||1||
|-
|VTO||zero-bias threshold voltage||V||0.0||1.0
|-
|KP||transconductance parameter||A/V2||2e-5||3.1e-5
|-
|GAMMA||bulk threshold parameter||V1/2||0.0||0.37
|-
|PHI||surface potential||V||0.6||0.65
|-
|LAMBDA||channel-length modulation (level 1 & 2 only)||1/V||0.0||0.02
|-
|RD||drain ohmic resistance||ohms||0.0||1.0
|-
|RS||source ohmic resistance||ohms||0.0||1.0
|-
|CBD||zero-bias B-D junction capacitance||F||0.0||20fF
|-
|CBS||zero-bias B-S junction capacitance||F||0.0||20fF
|-
|IS||bulk junction saturation current||A||1.0e-14||1.0e-15
|-
|PB||bulk junction potential||V||0.8||0.87
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m||0.0||2e-10
|-
|RSH||drain & source diffusion sheet resistance||ohm/area||0.0||10.0
|-
|CJ||zero-bias bulk junction bottom capacitance per meter2 junction area||F/m2||0.0||2e-4
|-
|MJ||bulk junction bottom grading coefficient|| ||0.5||0.5
|-
|CJSW||zero-bias bulk junction sidewall capacitance per meter junction perimeter||F/m||0.0||1.0e-9
|-
|MJSW||bulk junction sidewall grading coefficient|| ||0.5, 0.33 (level1), (level2,3)||
|-
|JS||bulk junction saturation current per meter2 of junction area||A/m2|| ||1.0e-8
|-
|TOX||oxide thickness||meter||1.0e-7||1.0e-7
|-
|NSUB||substrate doping||1/cm3||0.0||4.0e15
|-
|NSS||surface state density||1/cm2||0.0||1.0e10
|-
|NFS||fast surface state density||1/cm2||0.0||1.0e10
|-
|TPG||type gate material(+1 if opp. substrate, 0 if A1 gate, -1 if same as substrate)|| ||1.0||
|-
|XJ||metallurgical junction depth||meter||0.0||1
|-
|LD||lateral diffusion||meter||0.0||0.8
|-
|UO||surface mobility||cm2/Vs||600||700
|-
|UCRIT||critical field for mobility degradation (level2 only)||V/cm||1.0e4||1.0e4
|-
|UEXP||critical field exponent in mobility degradation (level2 only)|| ||0.0||0.1
|-
|UTRA||transverse field coefficient (deleted for level2)|| ||0.0||0.3
|-
|VMAX||maximum drift velocity of carriers||m/s||0.0||5.0e4
|-
|NEFF||total channel-charge (fixed and mobile) coefficient (level2 only)|| ||1.0||5.0
|-
|KF||flicker noise coefficient|| ||0.0||1.0e-26
|-
|AF||flicker noise exponent|| ||1.0||1.2
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|DELTA||width effect on threshold voltage (level2,3)|| ||0.0||1.0
|-
|THETA||mobility modulation (level3 only)||1/V||0.0||0.1
|-
|ETA||static feedback (level3 only)|| ||0.0||1.0
|-
|KAPPA||saturation field factor (level3 only)|| ||0.2||0.5
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

The BSIM model has no default parameters, and leaving one out is considered an error. The additional process model parameters for level 4 and 5 models are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS
|-
|VFB||flat-band voltage||V
|-
|PHI||surface inversion potential||V
|-
|K1||body effect coefficient||V1/2
|-
|K2||drain/source depletion charge-sharing coefficient||
|-
|ETA||zero-bias drain-induced barrier-lowering coefficient||
|-
|MUZ||zero-bias mobility||cm2/V-s
|-
|DL||shortening of channel||m
|-
|DW||narrowing of channel||m
|-
|U0||zero-bias transverse-field mobility degradation coefficient||V-1
|-
|U1||zero-bias velocity saturation coefficient||m/V
|-
|X2MZ||sens. of mobility to substrate bias at Vds=0||cm2/V2-s
|-
|X2E||sens. of drain-induced barrier lowering effect to substrate bias||V-1
|-
|X3E||sens. of drain-induced barrier lowering effect to drain bias at Vds= Vdd||V-1
|-
|X2U0||sens. of transverse field mobility degradation to substrate bias||V-2
|-
|X2U1||sens. of velocity saturation effect to substrate bias||mV-2
|-
|MUS||mobility at zero substrate bias and at Vds= Vdd||cm2/V2-s
|-
|X2MS||sens. of mobility to substrate bias at Vds= Vdd||cm2/V2-s
|-
|X3MS||sens. of mobility to drain bias at Vds= Vdd||cm2/V2-s
|-
|X3U1||sens. of velocity saturation effect on drain bias at Vds= Vdd||mV-2
|-
|TOX||gate oxide thickness||m
|-
|TEMP||temperature at which [[parameters]] were measured||deg. C
|-
|VDD||measurement bias range||V
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m
|-
|XPART||gate-oxide capacitance-charge model flag||
|-
|N0||zero-bias subthreshold slope coefficient||
|-
|NB||sens. of subthreshold slope to substrate bias||
|-
|ND||sens. of subthreshold slope to drain bias||
|-
|RSH||drain and source diffusion sheet resistance||ohms/area
|-
|JS||source drain junction current density||A/m2
|-
|PB||built-in potential of source drain junction||V
|-
|MJ||grading coefficient of source drain junction||
|-
|PBSW||built-in potential of source drain junction sidewall||V
|-
|MJSW||grading coefficient of source drain junction sidewall||
|-
|CJ||source drain junction capacitance per unit area||F/ m2
|-
|CJSW||source drain junction sidewall capacitance per unit length||F/m
|-
|WDF||source drain junction default width||m
|-
|DELL||source drain junction length reduction||m
|-
|}

XPART=0 selects a 40/60 drain/source charge partition; XPART=1 selects a 0/100 partition.

==Mutual Inductors==

[[File:GK100.png]]

The mutual inductors device is a pair of inductors that are coupled to each other. L1 and L2 are the names of two inductors. You have to specify the inductance of inductor L1, the inductance of inductor L2, the initial current through each, and the coupling coefficient k, 0 ≤ k ≤ 1. The mutual inductance M expressed in units of H can be calculated using the following definition:

<math> k = \frac{M}{\sqrt{L_1 L_2}} </math>

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|inductance1||inductance of inductor 1||H||1||
|-
|inductance2||inductance of inductor 2||H||1||
|-
|ic1||initial current through inductor 1||A||0||
|-
|ic2||initial current through inductor 2||A||0||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Non-Ideal Current Transformer==

[[File:GK104.png]]

This 8-pin device models a non-ideal lossy current transformer. Its model consists of an ideal transformer with more secondary turns than primary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. on each side of the internal ideal transformer, there is a series leakage inductance LL<sub>k</sub>, followed by a shunt winding capacitance CW<sub>k</sub> and a series winding resistance RW<sub>k</sub>, which connects to the exterior positive pin on that side. The inter-winding resistance R<sub>12</sub> is connected across the negative pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||secondary-to-primary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary leakage inductance||H||1m||
|-
|ll2||secondary leakage inductance||H||1m||
|-
|cw1||primary winding capacitance||F||1p||
|-
|cw2||secondary winding capacitance||F||1p||
|-
|r12||inter-winding resistance||Ohms||10Meg||
|-
|}

==Non-Ideal Diode==

[[File:G9.png]]

This 2-pin device is a basic simplified model of a diode as a rectifier or switch. When forward-biased, it acts as a low-valued voltage source. When reverse-biased, it acts as an open circuit until the reverse voltage exceeds the specified breakdown voltage. Then it acts as a high-valued voltage source of the reverse polarity.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|vf||forward drop voltage||V||0.5||required
|-
|vr||reverse breakdown voltage||V||100||required
|-
|}

==Non-Ideal Voltage Transformer==

[[File:GK103.png]]

This 8-pin device models a non-ideal lossy voltage transformer. Its model consists of an ideal transformer with more primary turns than secondary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. There are series combinations of a winding resistance RW<sub>k</sub> and a leakage inductance LL<sub>k</sub> on the primary and secondary sides. These are connected between the positive interior and exterior pins on each side. There are also two shunt branches at the inputs of the primary and secondary sides (connected between the positive and negative exterior pins), each consisting of a distributed turn-to-turn winding resistance RDC<sub>k</sub> in series with a distributed turn-to-turn winding capacitance CW<sub>k</sub>. The inter-winding capacitance CWW<sub>12</sub> is connected across the positive pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||primary-to-secondary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary winding leakage inductance||H||1m||
|-
|ll2||secondary winding leakage inductance||H||1m||
|-
|rdc1||primary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw1||primary distributed turn-to-turn winding capacitance||F||1p||
|-
|rdc2||secondary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw2||secondary distributed turn-to-turn winding capacitance||F||1p||
|-
|cww12||inter-winding capacitance||F||1p||
|-
|}

==Nonlinear Capacitor==

[[File:GK89.png]]

The nonlinear capacitor model allows the capacitor to be described by an arbitrary relationship between the capacitor's charge Q and the voltage V across the capacitor. In other words, Q = f(V). The nonlinear capacitance is then defined as C(V) = dQ/dV. You need to define the charge Q by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ C_DEF } * v(pos,neg)

which implies a linear capacitor, where Q = C<sub>DEF</sub> V. Therefore, C = C(V) = dQ/dV = C<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|C_DEF||default capacitance||F||1||
|-
|}

==Nonlinear Conductor==

[[File:GK88.png]]

The nonlinear conductor model allows the conductor to be described by an arbitrary relationship between the conductor's current I and the voltage V across the conductor. In other words, I = f(V). The nonlinear conductance is then defined as G(V) = dI/dV. You need to define the current I by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ G_DEF } * v(pos,neg)

which implies a linear conductor, where I = G<sub>DEF</sub> V. Therefore, G = G(V) = dI/dV = G<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|G_DEF||default capacitance||S||1||
|-
|}

==Nonlinear Dependent Sources==

[[File:G18.png]]

Nonlinear dependent (arbitrary) sources use an equation or mathematical expression to describe their behavior. One and only one of the two forms: V=<expr> or I=<expr> must be given.

Netlist Format:

B<device_name> v = <expression>

B<device_name> i = <expression>

Examples:

v = I(v1) + 3* I(v2)

I = v(i1) + 3* v(2) + 5 * v(3) ^2

The first example is a current-controlled voltage source. The v on the left side of the equation
indicates that it is a voltage source. I(v1) and I(v2) are the currents through voltage sources named v1 and v2, respectively.

The second example is a voltage-controlled current source. v(2) and v(3) represents the voltages at nodes 2 and 3, respectively, and v(i1) represents the voltage across a current source named i1.

The following mathematical functions defined for real variables can be used in the expressions:

abs(x), acos(x), acosh(x), asin(x), asinh(x), atan(x), atanh(x), cos(x), cosh(x), exp(x), ln(x), log(x), max(x,y), min(x,y), pwr(x,y), pwrs(x,y), sgn(x), sin(x), sinh(x), sqrt(x), tan(x), tanh(x), u(x), uramp(x).

The function "sgn" is the signum function and its value is 1 if the argument is positive or zero and -1 if the argument is negative.
The function "u(x)" is the unit step and "uramp(x)" is the integral of the unit step. The
unit step is one if its argument is greater than zero and zero if its argument is less than zero. The
ramp function (uramp) is 0 for argument values less than zero and equal to the argument for argument values
greater than zero.

The following operators are permissible: +, -, *, /, and ^.

The power functions have equivalent expressions: pwr(x,y) = x^y and pwrs(x,y) = sgn(x)*abs(x)^y.

Two constants can also be used in expressions: pi = 3.1415926 and e = 2.7182818.

There is a conditional function with the syntax IF(Condition, Expression1, Expression2). If "Condition" is met, then the return value of the function is Expression1; otherwise, it is Expression2. An example of this type of function is IF(v(1)>=0,1,-1), which is equivalent to sgn(v(1)).

To get time into an expression, integrate the current from a constant current source with a capacitor
and use the voltage across the capacitor.

Note: All the functions and expressions are case-insensitive.

==Nonlinear Inductor==

[[File:GK90.png]]

The nonlinear inductor model allows the inductor to be described by an arbitrary relationship between the inductor's magnetic flux Φ and the current I flowing through the inductor . In other words, Φ = f(I). The nonlinear inductance is then defined as L(I) = dΦ/dI. You need to define the flux Φ by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ L_DEF } * i(vx)

which implies a linear inductor, where Φ = L<sub>DEF</sub> I. Therefore, L = L(I) = dΦ/dI = L<sub>DEF</sub>.

Another example is 1e-4*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|L_DEF||default inductance||H||1||
|-
|}

==Nonlinear Resistor==

[[File:GK87.png]]

The nonlinear resistor model allows the resistor to be described by an arbitrary relationship between the voltage V across the resistor and its current I. In other words, V = f(I). The nonlinear resistance is then defined as R(I) = dV/dI. You need to define the voltage V by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ R_DEF } * i(vx)

which implies a linear resistor, where V = R<sub>DEF</sub> I. Therefore, R = R(I) = dV/dI = R<sub>DEF</sub>.

Another example is 10*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R_DEF||default resistance||Ω||1||
|-
|}

==Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This three-pin device models a parameterized operational amplifier with a very high voltage gain, a very high input impedance and a very low output impedance. The behavioral model of the parameterized Op-Amp device is based on the algorithm found in the book <B>Macromodeling with Spice</B>,
authored by Connelly & Choi, published by Prentice Hall. The default parameters are those of the 741 Op-Amp. This device doesn't require external DC bias voltage sources. Its positive and negative DC bias voltages are specified as its parameters. Sometimes the simulation doesn't converge if there is no DC path from the output of the Op-Amp to the ground.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|r_in_dm||differential mode input resistance||Ohms||2Meg||
|-
|r_in_cm||common mode input resistance||Ohms||2G||
|-
|Avd0||differential mode DC gain||dB||106||
|-
|CMRR||common mode rejection ratio||dB||90||
|-
|r_out||output resistance||Ohms||75||
|-
|c_in||input capacitance||F||1.4p||
|-
|ios||input offset current||A||20n||
|-
|ib||input bias current||A||80n||
|-
|vio||input offset voltage||V||1m||
|-
|slew_pos||positive slew rate||V/s||0.5e6||
|-
|slew_neg||negative slew rate||V/s||0.5e6||
|-
|curr_src_max||maximum output source current||A||25m||
|-
|curr_sink_||maximum output sink current||A25m||
|-
|fp1||dominant pole frequency||Hz||5||
|-
|fp2||second pole frequency||Hz||2Meg||
|-
|fp3||third pole frequency||Hz||20Meg||
|-
|fp4||fourth pole frequency||Hz||100Meg||
|-
|fz||first zero frequency||Hz||5Meg||
|-
|vcc_pos||positive dc voltage source||V||12||
|-
|vcc_neg||negative dc voltage source||V||12||
|-
|}

== Optocoupler ==

[[File:GK115.png]]

This is a five-pin parameterized optocoupler device. Its model consists of an ideal diode device in series with an Ohmic resistance connected between the Anode (A) and Cathode (K) pins together with a bipolar junction transistor device with three accessible pins, Collector (C), Base (B) and Emitter (E). A current-controlled current source is connected between base and collector of the BJT, whose current is controlled by the current passing through the diode. The proportionality constant is twice the specified value of the current transfer ratio (ctr) parameter.

You can change or enhance the models of the diode and BJT by adding more parameters. To do so, you have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ctr||current transfer ratio||-||0.5||
|-
|rd||diode ohmic resistance||Ohms||0.1||
|-
|}

== Overtone Crystal ==

[[File:GK79.png]]

This is a 2-pin parameterized overtone crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|LM||fundamental motional inductance||H||250m||
|-
|CM1||fundamental motional capacitance||F||10f||
|-
|RM1||fundamental motional resistance||Ohms||20||
|-
|RM3||3rd overtone motional resistance||Ohms||50||
|-
|RM5||5th overtone motional resistance||Ohms||100||
|-
|RM7||7th overtone motional resistance||Ohms||150||
|-
|C0||shunt capacitance||F||3p||
|-
|}

== Photodiode ==

[[File:GK113.png]]

This is a 4-pin parameterized photodiode device. A pair of pins, Anode (A) and Cathode (K), represent the physical terminals of the photodiode. The photodiode model connected between the anode and cathode pins consists of the parallel connection of an ideal diode, a dark current source, a noise current source, a current-controlled current source, a diode capacitance, a shunt resistance altogether with a series resistance.

Another pair of pins IS+ and IS- act as an ammeter that must be inserted in a control circuit. The current passing through this ammeter controls the current of the photodiode. The default proportionality constant is unity. The controlling current is typically a function of light intensity incident on the surface of the photodiode.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|id||dark current||A||1n||
|-
|ir||noise current||A||1p||
|-
|cd||diode capacitance||F||10p||
|-
|rs||series resistance||Ohms||1m||
|-
|rp||parallel resistance||Ohms||1Meg||
|-
|}

==Piecewise Linear (PWL) Controlled Source==

[[File:GL49.png]]

The Piecewise Linear (PWL) Controlled Source is a single-input and single-output function generator whose output is not necessarily
linear for all input values. Instead, it follows an I/O relationship that is specified by the x_array and y_array coordinates. The x_array and y_array values represent vectors of coordinate points on the x and y axes, respectively. The x_array values are progressively increasing input coordinate points, and the associated y_array values represent the outputs at those points. There may be as few as two pairs specified, or as many as memory and simulation speed allow.

In order to fully specify outputs for values of Vin outside of the bounds of the PWL function, the PWL
controlled source model extends the slope found between the lowest two coordinate pairs and the highest
two coordinate pairs. This has the effect of making the transfer function completely linear for Vin
less than x_array[0] and Vin greater than x_array[n]. It also has the potentially subtle effect of unrealistically
causing an output to reach a very large or small value for large inputs. You should thus keep in mind
that the PWL Source does not inherently provide a limiting capability.

In order to diminish the potential for divergence of simulations when using the PWL block, a form
of smoothing around the x_array and y_array coordinate points is necessary. This is due to the iterative
nature of the simulator and its reliance on smooth first derivatives of transfer functions in order to
arrive at a matrix solution. Consequently, the two parameters "input_domain" and "fraction" are included
to allow you some control over the amount and nature o the smoothing performed.

Fraction is a switch that is either TRUE or FALSE. When TRUE (the default setting), the simulator assumes
that the specified input_domain value is to be interpreted as a fractional figure. Otherwise, it is interpreted
as an absolute value. Thus, if fraction = TRUE and input_domain = 0.10, the simulator assumes that the smoothing
radius about each coordinate point is to be set equal to 10% of the length of either the x_array segment
above each coordinate point, or the x_array segment below each coordinate point. The specific segment
length chosen will be the smallest of these two for each coordinate point.

If fraction = FALSE and input_domain = 0.10, then the simulator will begin smoothing the transfer function at 0.10
volts (or amperes) below each x_array coordinate and will continue the smoothing process for another 0.10
volts (or amperes) above each x_array coordinate point.

Model Identifier: pwl

Netlist Format:

A<device_name> %vd(<in_pin> <in_ref_pin>) %vd(<out_pin> <out_ref_pin>) <model_name>

.model <model_name> pwl x_array = [<value1> <value2> ...] y_array = [<value1>
<value2> ...] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(2 3) %vd(1 4) pwl
.model pwl pwl x_array = [0 1] y_array = [0 1]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|x_array||x-element array||V||[0 1]||required
|-
|y_array||y-element array||V||[0 1]||required
|-
|input_domain||input smoothing domain||-||0.01||
|-
|fraction||smoothing %/abs switch||-||True||
|-
|}

== PM Modulated Source ==

[[File:GL25.png]]

This is a voltage source with a single-tone phase modulated waveform. The PM modulation index MDI is defined as the ratio of maximum phase deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Potentiometer ==

[[File:GK77.png]]

This is a 3-pin device that models a potentiometer with options for either linear or logarithmic resistance. position = 0 corresponds to the wiper being at the extreme left and position = 1 corresponds to the wiper being at the extreme right. With the default position = 0.5 corresponding to the midpoint, this device functions as a one-half voltage divider.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|position||position of wiper connection||-||0.5||Must be between 0.0 and 1.0.
|-
|log||log-linear switch||-||False||Select False for linear and True for logarithmic.
|-
|r||total resistance||Ohms||0.1u||
|-
|log_multiplier||multiplier constant for log resistance||-||1.0||
|-
|}

== Programmable Unijunction Transistor (PUT)==

[[File:GK112.png]]

This is a 3-pin parameterized Programmable Unijunction Transistor (PUT) device with three pins: Base 1 (B1), Base 2 (B2) and Emitter (E). It is biased with a positive voltage between the two bases. This device has a unique characteristic that when it is triggered, its emitter current increases regeneratively until it is restricted by emitter power supply. It exhibits a negative resistance characteristic and so it can be employed as an oscillator. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To change these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|eta||-||-||0.6||
|-
|rbb||total base-to-base resistance||Ohms||40k||
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

==Random Resistor==

[[File:GK93.png]]

The random resistor device models a resistor whose resistance is a random number between 0 and a maximum specified value.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|max_val||maximum resistance value||Ω||1k||
|-
|}

==Real Capacitor==

[[File:GK117.png]]

This is primarily a non-ideal, temperature-dependent capacitor model. You can access it from the Parts Menu as '''User-Defined Capacitor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent capacitance is computed using the quadratic equation:

C(T) = C(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance and a series inductance together with the capacitor, all in parallel with a shunt resistance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Resr||series resistance||Ω||10||
|-
|Ls||inductance||H||1p||
|-
|C||capacitance||F||1n||
|-
|Rp||parallel resistance||Ω||1G||
|-
|ic||voltage initial condition||V||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||F/°C||0.1||
|-
|tc2||second-order temperature coefficient||F/°C<sup>2</sup>||0.01||
|-
|}

==Real Inductor==

[[File:GK118.png]]

This is primarily a non-ideal inductor model. You can access it from the Parts Menu as '''User-Defined Inductor'''. Its series resistor has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance together with the inductor, and the combination in parallel with a shunt capacitance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Rdc||series resistance||Ω||10||
|-
|L||inductance||H||1||
|-
|Cp||capacitance||F||1p||
|-
|ic||current initial condition||A||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Real Resistor==

[[File:GK116.png]]

This is primarily a non-ideal, temperature-dependent resistor model. You can access it from the Parts Menu as '''User-Defined Resistor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series inductance together with the resistor.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R||resistance||Ω||1k||
|-
|Ls||inductance||H||1n||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Resistor==

[[File:GK119.png]]

Resistors are passive devices that dissipate power. Their resistance value varies depending on how much power they can dissipate and is measured
in Ohms. The transient, DC and AC behaviors of a resistor are all described by the same equation:

v = R * i

where v is the voltage across the resistor, i is the current passing through the resistor, and R is the resistance. The value of R must be nonzero.

All resistor names must begin with R.

Netlist Format:

R<device_name> <N+> <N-> <value>

Example:

R1 1 2 1k

[[RF.Spice A/D]] provides three types of resistor: Simple, User-Defined (Real Resistor) and Semiconductor. The resistance of the simple resistor is a single value expressed in Ohms. You can also set the Monte Carlo tolerance for this resistor.

==Schottky Diode==

[[File:GK80.png]]

The Schottky diode has the same model as the generic diode with a nonzero transit time (tt), a nonzero junction capacitance (cjo) and a typically larger saturation current (is), a lower junction potential (vj) and a smaller grading coefficient (m).

==Semiconducting Capacitor==

[[File:GK83.png]]

This is the more general form of the Capacitor model and allows for the calculation of the actual capacitance value from strictly geometric information and the specifications of the process.

General Form:

CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>

If VALUE is specified, it defines the capacitance. If MNAME is specified, then the capacitance is calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. Either VALUE or MNAME, LENGTH, and WIDTH may be specified, but not both sets. The optional initial condition "IC" is the initial voltage across the capacitor for transient simulations.

The capacitance is computed as:

CAP = CJ * (LENGTH - NARROW) * (WIDTH - NARROW)+ 2 * CJSW * (LENGTH + WIDTH - 2NARROW) * CAP

To modify the model parameters, first double click on the capacitor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit CJ, CJSW, NARROW, DEFW, and CAP.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CJ||junction bottom capacitance||F/m<sup>2</sup>||-||
|-
|CJSW||junction sidewall capacitance||F/m ||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|CAP||nominal capacitance for Monte Carlo simulation||F||1||
|-
|}

== Semiconductor Resistor ==

[[File:GK82.png]]

This is the more general form of the resistor model and allows for the modeling of temperature effects and for the calculation of the actual resistance value from strictly geometric information and the specifications of the process.

General Form:

RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>

If VALUE is specified, it overrides the geometric information and defines the resistance. If MNAME is specified, then the resistance may be calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. The (optional) TEMP value is the temperature at which this device is to operate, and overrides the temperature specification in the SPICE Options Dialog.

The resistance is computed as:

R(T0) = (RSH) * [(L - NARROW) / (W - NARROW)] * RES

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

To modify the model parameters, first double click on the resistor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit TC1, TC2, RSH, RES, etc.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|TC1||first order temperature coefficient||Ω/°C||-||
|-
|TC2||second order temperature coefficient||Ω/°C<sup>2</sup>||-||
|-
|RSH||sheet resistance||Ω/sq||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|TNOM||the parameter measurement temperature||deg C ||27||
|-
|RES||resistance multiplier for Monte Carlo simulation||Ohms||1||
|-
|}

== Silicon-Controlled Rectifier (SCR)==

[[File:GK109.png]]

This is a 3-pin parameterized Silicon-Controlled Rectifier (SCR) device with three pins: Anode (A), Cathode (K) and Gate (G). It is a unidirectional device which can conduct current only in one direction. The SCR can be triggered only by a positive current going into its gate. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

== SPDT Switch ==

[[File:GK72.png]]

This is a 5-pin device that models a single-pole double-throw switch. The input voltage is transferred to the first output pin if the control voltage is at a high state. Otherwise, its is transferred to the second output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== SPST Switch ==

[[File:GK71.png]]

This is a 4-pin device that models a single-pole single-throw switch. It is virtually equivalent of the standard voltage-controlled switch.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Tabulated Conductor==

[[File:GK92.png]]

The tabulated conductor model allows the conductance to be described by a table relating the device's current i(t) to its terminal voltage v(t). In effect, the conductance is defined as G = di(t)/dv(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (v,i) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tabulated Resistor==

[[File:GK91.png]]

The tabulated resistor model allows the resistance to be described by a table relating the device's terminal voltage v(t) to its current i(t). In effect, the resistance is defined as R = dv(t)/di(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (i,v) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tapped Inductor==

[[File:GK101.png]]

This 3-pin device models a tapped inductor with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lt||total inductance||H||1m||
|-
|ratio||ratio of number of turns between positive terminal and tap to total number of turns||-||0.5||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

== Temperature-Dependent Current Source ==

[[File:GL14.png]]

This is a current source whose current is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

== Temperature-Dependent Voltage Source ==

[[File:GL13.png]]

This is a voltage source whose voltage is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

==Thermometer==
[[File:G115.png]]

The Thermometer is a two-pin device that measures the operating temperature of a circuit. The voltage across the device pins is equal to SPICE's operating temperature in degrees centigrade. The output voltage of the Thermometer can be used in conjunction with linear or nonlinear dependent sources to model temperature-dependent quantities.

Model Identifier: thermo

Parameters:

This device has no parameters.

== Triac Thyristor ==

[[File:GK110.png]]

This is a 3-pin bidirectional thyristor device that conducts current in either direction when triggered. A thyristor is analogous to a relay in that a small voltage and current can control a much larger voltage and current. The triac has two anode pins termed Main Terminal 1 (MT1) and Main Terminal 2 (MT2) and a Gate (G) pin. In order to create a triggering current for a triac, either a positive or negative voltage can be applied to the gate. Once triggered, the thyristor continues to conduct, even if the gate current ceases, until the main current drops below a certain level called the holding current. The device's model involves two NPN BJT transistors and two PNP BJT transistors. The forward beta parameters of the NPN and PNP transistors are set equal to 20 and 5, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|bvf||breakdown voltage of forward diodes||V||100||
|-
|rh||resistance controlling reverse holding current||Ohms||100||
|-
|rgp||resistance controlling forward holding current and trigger current||Ohms||50||
|-
|}

==Uniform RC Transmission Line==

[[File:G23.png]]

The standard parameters are L, and N. They are described below:

Two of the nodes are the element nodes connected by the RC line. The third is the node to which the capacitances
are connected. L is the length of the RC line in meters. N is the number of lumped segments to use in
modeling the RC line.

This device is derived from a model proposed by Gertzberrg. It expands the URC line into a network of
lumped RC segments with internally generated nodes. These segments increase toward the middle of the
URC line in a geometric progression with K as the proportionality constant.

The URC line is made up entirely of resistor and capacitor segments, unless the ISPERL parameter has a
non-zero value. In this case, capacitors are replaced by reverse biased diodes with an equivalent zero-bias
junction capacitance, a saturation current of ISPERL amps per meter of transmission line, and optional
series resistance of RSPERL ohms per meter.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|K||propagation constant||-||2||1.2
|-
|FMAX||maximum frequency of interest||Hz||1.0G||6.5Meg
|-
|RPERL||resistance per unit length||Ohm /m||1000||10
|-
|CPERL||capacitance per unit length||F/m||1.0e-15||1pF
|-
|ISPERL||saturation current per unit length||A/m||0||-
|-
|RSPERL||diode resistance per unit length||Ohm/m||0||-
|-
|}

==Varactor Diode==

[[File:GK81.png]]

A varactor diode is a combination of the generic diode with additional package inductance, package capacitance and a series resistance. This diode device has a typically large value of junction capacitance (cjo).

Parameters (in addition to standard diode parameters):

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|q||quality factor||-||5000||
|-
|f0||frequency of Q-factor specification||Hz||50Meg||
|-
|ls||package inductance||H||0.5n||
|-
|cp||package capacitance ||F||0.05p||
|-
|}

==Voltage-Controlled Capacitor==

[[File:GK85.png]]

This 3-pin device models a voltage-controlled two-terminal capacitor whose capacitance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in F/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_C||conversion factor||F/V||1.0||
|-
|}

==Voltage-Controlled Inductor==

[[File:GK86.png]]

This 3-pin device models a voltage-controlled two-terminal inductor whose inductance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in H/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_L||conversion factor||H/V||1.0||
|-
|}

==Voltage-Controlled Resistor==

[[File:GK84.png]]

This 3-pin device models a voltage-controlled two-terminal resistor whose resistance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in Ω/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_r||conversion factor||Ω/V||1.0||
|-
|}

==Voltage-Controlled Switch==

[[File:G19.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Voltage-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Voltmeter or controlling voltage nodes, as well as the turn-on and turn-off voltages in Volts and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the rest of [[parameters]]. When the voltage across the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the voltage across the switch or controlling device is less than or equal to the turn off current, the switch opens.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|V_ON||turn-on voltage||V||0.5||
|-
|V_OFF||turn-off voltage||V||0.0||
|-
|RON||on resistance||Ohms||1.0||
|-
|ROFF||off resistance||Ohms||1G||
|-
|}

==Voltage Noise Source==

[[File:GL15.png]]

This is a voltage noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the parameters of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise voltage||V/√Hz||1n||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Voltage Source==

[[File:G17A.png]]

A voltage source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a voltage source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset voltage. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==XSpice Devices and their models==

XSpice devices have the following form:
<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 4pt 0pt 1px 0pt ; font-family: 02070309020205020404,sans-serif; ">
A<device_name> <node1> <node2> ... <model_name></P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., A2 1 2 transfer_function

Note that XSpice devices must start with the "A" designation, much as a resistor starts with
an "R". Some devices will have grouped (or vector) pins and are designated by being placed
inside square brackets. In the example shown below, the 1 and 2 pins are grouped. Pin 3 is not. </P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 [1 2] 3 summer </P>

Some models will have voltage differential pairs of pins and will be denoted by a %vd( ). In the following
example pins 1 and 4 are differential pairs, as well as pins 2 and 3. Differential pairs must go between
parentheses ().

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 %vd(1 4) %vd(2 3) triangle </P>

Refer to individual devices for more information.

Each XSpice device will also have a model associated with it. Each model will have the following form:

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
.model <model_name> <model_identifier> {<pname1 = pval1>} {<pname2 = pval2>}
...</P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., .model transfer_function s_xfer in_offset = 0.0 gain = 1.0</P>

Model_name refers to the name given in the device line. Model_identifier is an internal designation and
must be of an existing designation Refer to each device's example for the correct designation.

Parameter values are optional. If they aren't specified, then the default will be used. Some devices
have parameters that require a value and must be specified. Refer to individual devices for any required parameters.

==Zener Diode==

[[File:G10.png]]

The Zener Diode models the DC characteristics of most zeners. Since most data sheets for zener diodes do
not give detailed characteristics in the forward region, only a single point defines the forward characteristicThe
saturation current refers to the relatively constant reverse current that is produced when the voltage
across the zener is negative, but breakdown has not been reached. The reverse leakage current determines
the slight increase in reverse current as the voltage across the zener becomes more negative. It is modeled
as a resistance parallel to the zener with value v_breakdown / i_rev.

Note that the limt_switch parameter engages an internal limiting function for the zener. This can, in
some cases, prevent the simulator from converging to an unrealistic solution if the voltage across or
current into the device is excessive. If use of this feature fails to yield acceptable results, the convlimit
option should be tried (add the following statement to the SPICE input deck: .options convlimit)

Model Identifier: zener

Netlist Format:

A<device_name> <z_pin> <z_out_pin> <model_name>

.model <model_name> zener v_breakdown = 1 {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 zener

.model zener zener v_breakdown = 1

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|v_breakdown||breakdown voltage||1||required
|-
|i_breakdown||breakdown current||2.0e-2||
|-
|i_sat||saturation current||1.0e-12||
|-
|N_forward||forward emission coefficient||1.0||
|-
|limit_switch||switch for on-board limiting (convergence aid)||False||
|-
|}

<p> </p>
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D | Back to RF.Spice A/D Wiki Gateway]]'''

Glossary of Generic Analog & Mixed-Mode Devices & Sources

2018-10-11T16:52:00Z

Kazem Sabet: /* Nonlinear Dependent Sources */

==4-Bit ADC Bridge==

[[File:GK44.png]]

This 8-pin device is simply a bundle of 4 1-bit ADC bridges. Each analog input pin has a corresponding digital output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|}

==4-Bit DAC Bridge==

[[File:GK45.png]]

This 8-pin device is simply a bundle of 4 1-bit DAC bridges. Each digital input pin has a corresponding analog output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|}

== AC/RF Current Source ==

[[File:GL11.png]]

This is a simplified version of the standard Current Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak current amplitude||A||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal current||A||0||
|-
|}

== AC/RF Voltage Source ==

[[File:GL10.png]]

This is a simplified version of the standard Voltage Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak voltage amplitude||V||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal voltage||V||0||
|-
|}

==Alternate Ferrite Core Transformer==

[[File:GK96.png]]

The alternate ferrite core transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ferrite_Core_Transformer | Ferrite Core Transformer]], except for the reversed polarity of its secondary port.

==Alternate Ideal Transformer==

[[File:XFMR2.png]]

The alternate ideal transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ideal_Transformer | Ideal Transformer]], except for the reversed polarity of its secondary port.

== AM Modulated Source ==

[[File:GL23.png]]

This is a voltage source with a single-tone amplitude modulated waveform. The AM modulation index MDI is defined as the ratio of maximum amplitude deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Analog Clock ==

[[File:GL30.png]]

This is a periodic pulse generator with a default 0V low output level and a default 5V high output level.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|delay||delay time||sec||0||
|-
|rise||rise time||sec||0.1n||
|-
|fall||fall time||sec||0.1n||
|-
|pulse_wid||clock pulse width||sec||1u||required
|-
|period||clock period||-||2u||required
|-
|out_low||low output voltage level||V||0||
|-|-
|out_high||high output voltage level||V||5||
|-
|}

==Analog-to-Digital Converter (ADC) Bridge==
[[File:GK42.png]]

The ADC Bridge takes an analog value from an analog node and may be in the form of a voltage or current.
If the input is less than or equal to "in_low", then a digital "0" is generated. If
the input is greater than or equal to "in_high", a digital "1" is generated. Otherwise,
a digital "UNKNOWN" is the output value. Unlike the DAC Bridge, ramping or delay is not applicable.
Rather, the continuous ramping of the input provides for any associated delays in the digitized signal.

This model also posts an input load value based on the parameter input_load.

Model Identifier: adc_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> adc_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] adc_bridge

.model adc_bridge adc_bridge in_low = .1 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|rise_delay||L-to-H delay time||sec||1n||
|-
|fall_delay||H-to-L delay time||sec||1n||
|-
|}

== Arbitrary Temporal Waveform Generator ==

[[File:GL17.png]]

This is a voltage source with an arbitrary waveform defined by a mathematical expression. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(t)" standing for time.

Examples:

* v(t) is equivalent to f(t) = t.
* 0.1*(v(t))^2 is equivalent to f(t) = 0.1t^2.
* sin(2*pi*v(t)) is equivalent to f(t) = sin(2πt).

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Tmax||maximum signal duration||sec||1e6||required
|-
|}

==Auto-Transformer==

[[File:GK102.png]]

This 3-pin device models an auto-transformer with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lp||primary inductance||H||1m||
|-
|Ls||secondary inductance||H||1m||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Bipolar Junction Transistor (BJT)==
[[File:G11.png]]

The BJT is an active device which has up to 4 pins. The three standard pins are base, emitter, and collector. These are given in the default symbol. The substrate, which is grounded by default, is the fourth pin. To use the BJT with the substrate, create a new 4-pin BJT using the Device Editor and Symbol Editor.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

Area factor scales the model parameters RE and RC. IC VBE is the initial voltage from base emitter. IC VCE is the initial voltage from collector to emitter. TEMP is the overriding temperature. These parameters are based on the Gummel and Poon integral-charge model. If these parameters are not specified, then it will reduce to the simpler Ebers-Moll model.

The process model is mandatory for the BJT. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|IS||transport saturation current||A||1.0e-16||1.0e-15
|-
|BF||ideal maximum forward beta|| ||100||100
|-
|NF||forward current emission coefficient|| ||1.0||1
|-
|VAF||forward Early voltage||V||infinite||200
|-
|IKF||corner forward beta high current roll-off||A||infinite||0.01
|-
|ISE||B-E leakage saturation current||A||0||1.0e-13
|-
|NE||B-E leakage emission coefficient|| ||1.5||2
|-
|BR||ideal maximum reverse beta|| ||1||0.1
|-
|NR||reverse current emission coefficient|| ||1||1
|-
|VAR||reverse Early voltage||V||infinite||200
|-
|IKR||corner reverse beta high current roll-off||A||infinite||0.01
|-
|ISC||B-C leakage saturation current||A||0||1.0e-13
|-
|NC||B-C leakage emission coefficient|| ||2||1.5
|-
|RB||zero bias base resistance||ohms||0||100
|-
|IRB||current where base resistance falls halfway to minimum value||A||infinite||0.1
|-
|RBM||minimum base resistance at high currents||ohms||RB||10
|-
|RE||emitter resistance||ohms||0||1
|-
|RC||collector resistance||ohms||0||10
|-
|CJE||B-E zero bias depletion capacitance||F||0||2pF
|-
|VJE||B-E built-in potential||V||0.75||0.6
|-
|MJE||B-E junction exponential factor|| ||0.33||0.33
|-
|TF||ideal forward transit time||sec||0||0.1ns
|-
|XTF||coefficient for bias dependence of TF|| ||0||
|-
|VTF||voltage describing VBC dependence of TF||V||infinite||
|-
|ITF||high-current parameter for effect on TF||A||0||
|-
|PTF||excess phase at freq=1.0/(TF*2PI)Hz||degree||0||
|-
|CJC||B-C zero bias depletion capacitance||F||0||2pF
|-
|VJC||B-C built-in potential||V||0.75||0.5
|-
|MJC||B-C junction exponential factor|| ||0.33||0.5
|-
|XCJC||fraction of B-C depletion capacitance connected to internal base node|| ||1||
|-
|TR||ideal reverse transit time||sec||0||10ns
|-
|CJS||zero bias collector-substrate capacitance||F||0||2pF
|-
|VJS||substrate junction built-in potential||V||0.75||
|-
|MJS||substrate junction exponential factor|| ||0||0.5
|-
|XTB||forward and reverse beta temp. exponent|| ||0||
|-
|EG||energy gap for temperature effect on IS||eV||1.11||
|-
|XTI||temperature exponent for effect on IS|| ||3||
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

==Capacitance Meter==
[[File:G37.png]]

The Capacitance Meter measures the total capacitance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total capacitance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense a capacitance value and alter their behavior based upon it.

Model Identifier: cmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> cmeter {<gain = value>}

Example:

A1 1 2 cap_meter

.model cap_meter cmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Capacitor==
[[File:GK120.png]]

Capacitors are used to store electrical energy. They can filter or remove AC signals or block DC current without disrupting AC signals. A capacitor's ability to store energy is termed capacitance and is measured in Farads, with values from pF to mF. The only time current flows through a capacitor is when the charge is collected on, or is removed from, its parallel plates. This means that the voltage across the capacitor is changing, which doesn't conform to DC analysis. In a physical circuit, there is a transition stage during which capacitors charge up to their final values. The result is the same as if these capacitors did not exist and the connections to them were left dangling. In other words, in a (steady-state) DC analysis, a capacitor behaves like an open circuit. Therefore, it is important that no section of the circuit is isolated from the capacitors. Every circuit node needs some path for DC current to the ground.

A capacitor's transient behavior is described by the equation:

i(t) = C * (dv(t)/dt)

Its initial voltage is only important when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An capacitor's AC behavior is described by the equation:

i = j ω * C * v

All capacitor names must begin with C.

Netlist Format:

C<device_name> <N+> <N-> <value>

Example:

C1 1 2 10p

[[RF.Spice A/D]] provides three types of capacitors: simple, user-defined (or real) and semiconductor. The standard capacitor parameters are N+, N-, VALUE, and IC. In a simple capacitor, VALUE must
be specified for the capacitance in Farads. IC is the (optional) initial condition for the capacitor voltage.

==Center-Tapped Ferrite Core Transformer==

[[File:GK97.png]]

This five-pin three-port device models a center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

==Controlled Sine Wave Oscillator==

[[File:G24.png]]

This is a four-terminal function generator with a sinusoidal wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.
This function has parameterizable values of low and high peak output voltage.

Model Identifier: sine

Netlist Form:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> sine cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) sine

.model sine sine cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[1 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|}

==Controlled Sources==

Circuits can contain linear dependent sources characterized by one of the following equations (where g,
e, f, and h are constants representing transconductance, voltage gain, current gain, and transresistance,
respectively):

<SPAN STYLE="font-size: 9pt ; ">i<sub>out</sub> = g v<sub>in</sub>
     v<sub>out</sub> = e v<sub>in</sub>
     i<sub>out</sub> = f i<sub>in</sub>
     v<sub>out</sub> = h i<sub>in</sub></SPAN>
<P CLASS="Bodytext" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; ">
For further information, refer to:</P>

Linear Current Controlled Current Source (CCCS)

Linear Voltage Controlled Current Source (VCCS)

Linear Current Controlled Voltage Source (CCVS)

Linear Voltage Controlled Voltage Source (VCVS)

==Controlled Square Wave Oscillator==

[[File:G25.png]]

This is a four-terminal function generator with a square wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: square

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> square cntl_array = [<value1> <value2>] freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) square

.model square square cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Duty_cycle||Duty cycle||-||0.5||
|-
|Rise_time||Output rise time||sec||1.0e-9||
|-
|Fall_time||Output fall time||sec||1.0e-9||
|-
|}

==Controlled Triangle Wave Oscillator==

[[File:G26.png]]

This is a four-terminal function generator with a triangle wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defined voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: triangle

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> tirangle cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>]{<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 4) %vd(2 3) triangle

.model triangle triangle cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Rise_duty||Rise time duty cycle||0.5||
|-
|}

== Crystal ==

[[File:GK78.png]]

This is a 2-pin parameterized crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CM||motional capacitance||F||10f||
|-
|C0||shunt capacitance||F||1p||
|-
|RM||motional resistance||Ohms||100||
|-
|LM||motional inductance||H||100m||
|-
|}

==Current Noise Source==

[[File:GL16.png]]

This is a current noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the [[parameters]] of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise current||A/√Hz||1p||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Current Source==

[[File:G17B.png]]

Current source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a current source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset current. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==Current-Controlled Switch==

[[File:G20.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Current-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the turn-on and turn-off currents in Amperes and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the rest of [[parameters]]. When the current through the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the current through the switch or controlling device is less than or equal to the turn off current, the switch opens.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|I_ON||turn-on current||A||0.0||
|-
|I_OFF||turn-off current||A||0.0||
|-
|RON||closed resistance||Ohms||1.0||
|-
|ROFF||open resistance||Ohms||1/GMIN||
|-
|}

==Darlington Pair==

[[File:GK108.png]]

A Darlington pair is a three-pin device that consists of two interconnected BJT transistors of the same type. The collectors of two transistors are connected together to provide the "Collector" pin of the pair. The base of the first BJT acts the "Base" pin of the pair. The emitter of the first BJT is internally connected to the base of the second BJT. The emitter of the second BJT acts as the "Emitter" pin of the pair. There are two types of Darlington pair: NPN and PNP. The parameterized generic Darlington pair also contains a diode connected between the collector and emitter pin as well as two base-emitter resistors, one across each BJT.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|is_bjt||bjt saturation current||A||1.0e-12||
|-
|bf_bjt||bjt forward beta||-||150||
|-
|nf_bjt||bjt forward emission coefficient||-||1||
|-
|ise_bjt||B-E leakage saturation current||A||0||
|-
|ne_bjt||B-E leakage emission coefficient||-||1||
|-
|br_bjt||ideal maximum reverse beta||-||1||
|-
|nr_bjt||reverse current emission coefficient||-||1||
|-
|isc_bjt||B-C leakage saturation current||A||0||
|-
|nc_bjt||B-C leakage emission coefficient||-||1||
|-
|rb_bjt||zero bias base resistance||Ohms||0||
|-
|irb_bjt||current where base resistance falls halfway to minimum value||A||inf||
|-
|rbm_bjt||minimum base resistance at high currents||ohms||0||
|-
|re_bjt||emitter resistance||Ohms||0||
|-
|rc_bjt||collector resistance||Ohms||0||
|-
|cje_bjt||B-E zero bias depletion capacitance||F||0||
|-
|vje_bjt||B-E built-in potential||V||0.75||
|-
|mje_bjt||B-E junction grading coefficient||-||0.33||
|-
|cjc_bjt||B-C zero bias depletion capacitance||F||0||
|-
|vjc_bjt||B-C built-in potential||V||0.75||
|-
|mjc_bjt||B-C junction exponential factor||-||0.33||
|-
|tf_bjt||ideal forward transit time||sec||0||
|-
|tr_bjt||ideal reverse transit time||sec||0||
|-
|is_d||diode saturation current||A||1.0e-12||
|-
|rs_d||diode resistance||Ohms||0||
|-
|n_d||diode emission coefficient||-||1||
|-
|cjo_d||diode junction capacitance||F||0||
|-
|vj_d||diode junction potential||V||1||
|-
|m_d||diode grading coefficient|| ||0.5||
|-
|tnom||parameter measurement temperature||deg C||27||
|-
|r1||first base-emitter resistance||Ohms||1k||
|-
|r2||second base-emitter resistance||Ohms||1k||
|-
|}

== DC Bias Sources Vcc, Vee, Vdd, Vss ==

[[File:GL12.png]]

These are simple 1-pin DC voltage sources. Vcc and Vdd provide a positive voltage, while Vee and Vss provide a negative voltage

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|vcc||bias voltage||V||+15||required
|-
|vee||bias voltage||V||-15||required
|-
|vdd||bias voltage||V||+15||required
|-
|vss||bias voltage||V||-15||required
|-
|}

==Digital-to-Analog Converter (DAC) Bridge==

[[File:GK43.png]]

The DAC Bridge takes a digital value from a digital node and can only be eiter "0", "1",
or "U". It then outputs the value "out_low", "out_high" or "out_udndef",
or ramps linearly toward one of these "final" values from its curent analog output level. This
ramping speed depends on the values of "t_rise" and "t_fall".

Model Identifier: dac_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> dac_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] dac_bridge

.model dac_bridge dac_bridge out_low = 0 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|out_undef||analog output for undefined digital input||V||0.5||required
|-
|input_load||capacitive input load||F||1p||
|-
|t_rise||L-to-H delay time||sec||1n||
|-
|t_fall||H-to-L delay time||sec||1n||
|-
|}

==Diode==

[[File:G9.png]]

Diodes allow current flow only in one direction, following their symbol's arrow, and thus can be used as simple solid
state switches in AC circuits.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process models can be either junction diodes or Schottky barrier diodes. Area factor scales the model parameters
IS, RS, CJO, and IBV. VD is the initial voltage, and TEMP is the overriding temperature. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||0||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|EG||activation energy||eV||1.11||
|-
|XTI||saturation current temp. exp.||-||3.0||
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||forward bias junction fit parameter||-||0.5||
|-
|BV||reverse breakdown voltage||V||inf||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|}

==Diode Bridge==

[[File:GK107.png]]

This four-pin device is a bridge configuration of four generic diodes.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||10p||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|BV||reverse breakdown voltage||V||1000||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|}

==Doubly Center-Tapped Ferrite Core Transformer==

[[File:GK98.png]]

This six-pin four-port device models a doubly center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of full-winding primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== DPDT Switch ==

[[File:GK74.png]]

This is an 8-pin device that models a double-pole double-throw switch. It has two input signals and four output pins. When the control voltage is at the high state, the first and second input voltages are transferred to the first and third output pins, respectively. When the control voltage is at the low state, the first and second input voltages are transferred to the second and fourth output pins, respectively.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== DPST Switch ==

[[File:GK73.png]]

This is a 6-pin device that models a double-pole single-throw switch. It has two input signals and two output signals. When the switch on, the first and second input voltages are transferred to the first and second output pins, respectively. When the switch is off, the output pin do not receive any input signals.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Ferrite Core Transformer==

[[File:GK95.png]]

This four-pin two-port device models a physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary turns||-||100||required
|-
|n_sec||number of secondary turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== FM Modulated Source ==

[[File:GL24.png]]

This is a voltage source with a single-tone frequency modulated waveform. The FM modulation index MDI is defined as the ratio of maximum frequency deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

==Frequency Meter==
[[File:G114.png]]

The Frequency Meter is a four-pin shunt device that is connected in parallel with an AC source just like a voltmeter and measures the operating frequency of the AC circuit. The input pins are connected across the AC source. The voltage across the output pins is equal to the frequency of the source in Hertz within a scale factor SF. Note that the Frequency Meter is designed to work with a single-tone AC source of unit amplitude. If the amplitude of the source is not one, multiply the SF parameter by the non-unit source amplitude value. The output voltage of the Frequency Meter can be used in conjunction with linear or nonlinear dependent sources to model frequency-dependent quantities.

Model Identifier: fmeter

Parameters:

The only parameter is the scale factor SF with a default value of 1.0. Set SF = 1e-6 to read out the frequency in MHz. Set SF = 1e-9 to read out the frequency in GHz. Set SF = 6.283185 (2*pi) to read out the angular frequency ω in radian/s.

== Fuse ==

[[File:GK76.png]]

This is a 2-pin interactive current-controlled switch. If the current passing through the fuse is less than a specified threshold current, the switch is closed. If the current exceeds the threshold level, the fuse breaks and remains open thereafter. The device's symbol changes to display its state.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|r||resistance when intact||Ohms||1.0||
|-
|i_thresh||threshold current||A||1.0||
|-
|}

==Ground==

[[File:G15.png]]

Ground has a voltage of zero (0) and is used as a reference to compute electrical values in the circuit.
All circuits <B>must</B> be grounded to be properly simulated. There is no limit on the number of grounds
you may use in a circuit. All components connected to ground are referenced to a common point and treated
as linked through ground.

==Hysteresis Block (XSPICE)==

[[File:G37.png]]

The Hysteresis block is a simple buffer stage that provides hysteresis of the output with respect to the
input. The in_low and in_high parameter values. The output values are limited to out_lower_limit and
out_upper_limit. The value of \93hyst\94 is added to the in_low and in_high points in order to specify the
points at which the slope of the hysteresis function would normally change abruptly as the input transitions
from a low to a high value. Likewise, the value of \93hyst\94 is subtracted from the in_high and in_low values
in order to specify the points at which the slope of the hysteresis function would normally change abruptly
as the input transitions from a high to a low value. In fact, the slope of the hysteresis function is
never allowed to change abruptly but is smoothly varied whenever the input_dowmain smoothing parameter
is set greater than zero.

Model Identifier: hyst

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> hyst {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 hysteresis_block

.model hysteresis_block hyst in_low = 0.0 in_high = 1.0

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default
|-
|In_low||input low value||0.0
|-
|in_high||input high value||1.0
|-
|hyst||hysteresis||0.1
|-
|out_lower_limit||output lower limit||0.0
|-
|out_upper_limit||output upper limit||1.0
|-
|input_domain||input smoothing domain||0.01
|-
|fraction||smoothing fraction/absolute value switch||true
|-
|}

==Ideal Center-Tapped Transformer with Push-Pull Input==

[[File:XFMR4.png]]

The ideal center-tapped transformer with push-pull input is a five-pin three-port device with two primary input ports and one secondary output port. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P1}{v_S} = \frac{v_P2}{v_S} = n </math>

where v<sub>S</sub> is the secondary voltage, v<sub>P1</sub> is measured between the top primary pin P1 and the center tap pin, and v<sub>P2</sub> is measured between the center tap pin and the bottom primary pin P2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P1</sub>/N<sub>S</sub> = N<sub>P2</sub>/N<sub>S</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Center-Tapped Transformer with Push-Pull Output==

[[File:XFMR3.png]]

The ideal center-tapped transformer with push-pull output is a five-pin three-port device with one primary input port and two secondary output ports. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P}{v_{S1}} = \frac{v_P}{v_{S2}} = n </math>

where v<sub>P</sub> is the primary voltage, v<sub>S1</sub> is measured between the top secondary pin S1 and the center tap pin, and v<sub>S2</sub> is measured between the center tap pin and the bottom secondary pin S2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S1</sub> = N<sub>P</sub>/N<sub>S2</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Diode==

[[File:GK106.png]]

This 2-pin device is a very basic and primitive model of a diode as a rectifier or switch. When the voltage across the device's terminals is positive, it acts as a short circuit. When the voltage across the device's terminals is negative, it acts as an open circuit.

Parameters:

None

==Ideal Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This is a very basic and primitive model of an operational amplifier. It has only one parameter, open loop gain with a default value of 50,000, which is adequate for most cases. The ideal Op-Amp device doesn't require any DC bias voltages.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|A||open loop gain||-||50,000||
|-
|}

==Ideal Transformer==

[[File:XFMR1.png]]

The ideal transformer is a four-pin two-port device with the following relationship between the voltages and currents at its primary and secondary ports:

<math> \frac{v_P}{v_S} = - \frac{i_S}{i_P} = \frac{N_P}{N_S} = n </math>

where v<sub>P</sub>, i<sub>P</sub>, N<sub>P</sub> are the primary voltage, current and number of turns, respectively, and v<sub>S</sub>, i<sub>S</sub>, N<sub>S</sub> are the secondary voltage, current and number of turns, respectively. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S</sub>, which represents the primary-to-secondary turns ratio. Note that the ideal transformer model is defined based on controlled sources and does not involve any magnetic physical parameters as opposed to mutual inductors or ferrite core transformer.

==Inductance Meter==

[[File:G37.png]]

The Inductance Meter measures the total inductance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total inductance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense an inductance value and alter their behavior based upon it. Care must be exercised when connecting an Inductance Meter to the inductors of a circuit. This is due to the fact that inductors are treated by SPICE as current sources. This can cause a problem when an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor.

Model Identifier: lmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> imeter {<gain = value>}

Example:

A1 1 2 inductance_meter

.model inductance_meter lmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Inductive Coupler Block==

[[File:GK99.png]]

The Inductive Coupler Block couples any two existing inductors. This block doesn't have any pins because it doesn't actually represent inductors, only the coupling between them. This is useful if you want to
couple two inductors that are in different parts of the circuit, or if you want to couple more than two inductors together. In the latter case, use more than one of these, with each one coupling a pair of inductors.

The standard parameters are Inductor1, Inductor2, and k. Inductor1 is the name of first inductor, Inductor2 is the name of the second inductor, and k is the coefficient of coupling, 0 < k ≤ 1.

==Inductive Coupling (XSPICE)==

[[File:G41.png]]

This function is a conceptual model which is used as a building block to create a wide variety of inductive and magnetic circuit models. This function is normally used in
conjunction with the “core” model, but it can also be used with resistors, hysteresis blocks, etc. to build up systems which mock the behavior of linear and nonlinear components.
The lcouple takes as an input (on the “l” port) a current. This current value is multiplied by the num_turns value, N, to produce an output value (a voltage value which appears on the
mmf_out port). The mmf_out acts similar to a magnetomotive force in a magnetic circuit;
when the lcouple is connected to the “core” model, or to some other resistive device, a current will flow. This current value (which is modulated by whatever the lcouple is
connected to) is then used by the lcouple to calculate a voltage “seen” at the “l” port. The voltage is a function of the derivative with respect to time of the current value seen at mmf_out.

The most common use for lcouple will be as a building block in the construction of transformer models. To create a transformer with a single input and a single output, you
would require two lcouple models plus one “core” model.

Example:

A1 (1 0) (2 3) lcouple1

.model lcouple1 lcouple ( num_turns = 10 )

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|num_turns||number of turns||-||1||required
|-
|}

==Inductor==

[[File:GK121.png]]

Inductors are used to store magnetic energy. An inductor's ability to counteract current changes passing through it is called its inductance (L), which is
measured in Henrys. In a (steady-state) DC analysis, the inductor acts like a short circuit. It is indeed treated as a current source, which can be problematic if an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor. The resistor may be of negligible value or one that accounts for the coil resistance of the inductor. In AC and transient analyses, the inductor develops a voltage across it in response to the changing magnetic
flux within its coil.

An inductor's transient behavior is described by the equation:

v(t) = L*(di(t)/dt)

The inductor's initial condition is optional. It is the initial value of the inductor current in Amperes that flows from node N+ through the inductor to node N-. The only time that the initial current matters is when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An inductor's AC behavior is described by the equation:

v = j ω * L * i

All inductor names must begin with L.

Netlist Format:

L<device_name> <N+> <N-> <value>

Example:

L1 1 2 10u

==Inductor with Ferrite Core==

[[File:GK94.png]]

This 2-pin device models a physical inductor with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. Unlike the standard inductor device, you do not specify an inductance value for the inductor with ferrite core. Rather, you specify physical parameters like cross sectional area, core length and number of turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_turns||number of turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== Insulated Gate Bipolar Transistor (IGBT)==

[[File:GK111.png]]

This is a 3-pin parameterized Insulated Gate Bipolar Transistor (IGBT) device with three pins: Collector(C), Gate (G), and Emitter (E). It is primarily used as a fast electronic switch. The IGBT combines the simple gate-drive characteristics of MOSFETs with the high-current and low-saturation-voltage capability of bipolar transistors. The device's model consists of an isolated gate FET for the control input, and a PNP bipolar power transistor as a switch. To further modify the internal device models, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|cap||parasitic capacitance||F||1n||
|-
|rg||gate resistance||Ohms||5||
|-
|re||emitter resistance||Ohms||0.05||
|-
|bf||pnp transistor forward beta||-||1||
|-
|vto||MOSFET threshold voltage||V||5||
|-
|kt||MOSFET transconductance||-||2.99||
|-
|cgso||MOSFET voltage gate-source overlap capacitance||F||5u||
|-
|nd||diode emission coefficient||-||50||
|-
|cjo||diode junction capacitance||F||1n||
|-
|}

==Interactive Switch==

[[File:GK75.png]]

This device is an interactive switch that can be closed or opened either directly from the Schematic Editor by clicking on its symbol or from the Instrument Panel.

==Junction Field Effect Transistor (JFET)==

[[File:G12.png]]

The JFET is the simplest transistor device and has three pins: gate, drain and source. The JFET defaults are based on the Shichman and Hodges FET model. This is a square-law device because of the expression relating the drain current to the gate-to-source voltage:
Idrain=*(VGS-Vthreshold)2. In real JFETs, near the saturation point, the drain currents vary with the drain voltages. This can be modeled by the following formula: Idrain=*(VGS-VTO)2*(1+*VDS), which yields an increasing
drain current for increasing values of VDS.

The gate-to-source and gate-to-drain junctions each have a nonlinear capacitor. The zero-bias capacitance value is selected for each junction.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process model parameters are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||threshold voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||ohms||0||100
|-
|RS||source ohmic resistance||ohms||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|IS||gate junction saturation current||A||1.0e-14||1.0e-14
|-
|B||doping tail parameter|| ||1||1.1
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

== Light Emitting Diode (LED) ==

[[File:GK114.png]]

This is a two-pin parameterized diode device that emits light of a certain wavelength when it is forward-biased.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rs||ohmic resistance||Ohms||10||
|-
|vj||junction potential||V||0.6||
|-
|cjo||zero bias junction capacitance||F||10p||
|-
|tt||transit time||sec||0.1n||
|-
|}

==Linear Current-Controlled Current Source (CCCS)==

[[File:G2.png]]

The CCCS is a current source whose current is directly proportional to the current across a controlling Ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the current gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the current gain.

Model Identifier: cccs

Netlist Format:

F<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

F1 1 0 V1 1.0

==Linear Current-Controlled Voltage Source (CCVS)==

[[File:G4.png]]

The CCVS is a voltage source whose voltage is directly proportional to the current through a controlling ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the trans-resistance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the trans-resistance gain.

Model Identifier: ccvs

Netlist Format:

H<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

H1 1 0 V1 1.0

==Linear Voltage-Controlled Current Source (VCCS)==

[[File:G3.png]]

The VCCS is a current source whose current is directly proportional to the voltage across a controlling voltmeter or the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the trans-conductance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the trans-conductance gain.

Model Identifier: vccs

Netlist Format:

G<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

G1 1 0 2 0 1.0

==Linear Voltage-Controlled Voltage Source (VCVS)==

[[File:G1.png]]

The VCVS is a voltage source whose voltage is directly proportional to the voltage across a controlling voltmeter of the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the voltage gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the voltage gain.

Model Identifier: vcvs

Netlist Format:

E<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

E1 1 0 2 0 1.0

==Lossless Transmission Line==

[[File:G21.png]]

The lossless transmission line is a four-pin two-port device that models only one propagating mode of an ideal transmission line. When using this SPICE model, should all four nodes of the actual circuit be distinct, two modes may be activated, and this device would be insufficient for that purpose. To circumvent this potential problem, two transmission line devices would be required. Due to the implementation details, you may produce more accurate simulation results with a lossy transmission line device with zero loss.

Optional initial condition parameters are the voltage and current at each of the transmission line ports.

The standard device parameters are Z0, TD, F, NL, IC, described below:

{| class="wikitable"
|-
|Z0||characteristic impedance
|-
|TD||transmission delay
|-
|F||frequency
|-
|NL||normalized electrical length of the transmission line with respect to the wavelength in the line at frequency F. (If F is specified, but NL is not, the default is 0.25.)
|-
|IC||initial condition (Specifies the voltage and current at each of the transmission line ports.)
|-
|}

==Lossy Transmission Line==

[[File:G22.png]]

The lossy transmission line is a four-pin two-port convolution model for uniform constant-parameter distributed lines. MNAME is the process model name, which
includes a set of pre-specified options as described below.

The device model [[parameters]] are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|R||resistance /length||Ohm /m||0.0||0.2
|-
|L||inductance/length||henrys/m||0.0||9.13e-9
|-
|C||capacitance/length||farads/m||0.0||3.65e-12
|-
|LEN||length of line||m||none||1.0
|-
|LININTERP||use linear interpolation||flag||not set||set
|-
|QUADINTERP||use quadratic interpolation||flag||not set||set
|-
|MIXEDINTERP||use linear when quadratic seems bad||flag||not set||set
|-
|COMPACTREL||special reltol for straight line checking||flag||RETOL||1.0e-3
|-
|COMPACTABS||special abstol for straight line checking||flag||ABSTOL||1.0e-9
|-
|NOCONTROL||don't do complex time control||flag||not set||set
|-
|STEPLIMIT||always limit timestep to 0.8*(delay of line)|| || ||
|-
|NOSTEPLIMIT||don't always limit timestep to 0.8*(delay of line)||flag||not set||set
|-
|TRUNCNR||use Newton-Raphson method for timestep calculation in LTRAtrunc||flag||not set||set
|-
|TRUNCDONTCUT||don't limit timestep to keep impulse-response errors low||flag||not set||set
|-
|}

<P CLASS="Normal-1">
The RLC (uniform transmission line with series loss only), RC (uniform RC line), LC (lossless transmission
line), and RG (distributed series resistance and parallel conductance only) lines have been implemented.
The length (LEN) must be given. COMPACTREL and COMPACTABS control the compaction of past history values
used in convolution. Larger values for these lower accuracy but improve speed. These are used with the
TRYTOCOMPACT option. </P>

==Magnetic Core (XSPICE)==

[[File:G42.png]]

This device is used as a building block to create a wide variety of inductive and magnetic circuit models. It is almost always to be used in conjunction with the "lcouple" model to build up systems which simulate the behavior of linear and nonlinear magnetic components. There are two fundamental modes of operation for the core model. These are the "PWL" mode (which is the default and most
likely to be of use to you) and the "Hysteresis" mode.

<b>PWL Mode (mode = 1)</b>

In the PWL mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf) value. This value is divided by the total effective length of the core to produce a value for the Magnetic Field Intensity, H, which is then used to find the corresponding Flux Density, B, using the piecewise linear relationship described by you in the H_array / B_array coordinate pairs. B is then multiplied by the cross-sectional area of the core to find the Flux value, which is output as a current. The pertinent mathematical equations are:

H = mmf / L, where L = Length (in apmere-turns/meter)

B = f(H)

Φ = B * A, where A = Area

The B value is derived from a piecewise linear transfer function described to the model by the H_array and B_array coordinate pairs. This transfer function does not include hysteretic effects; for that, you would need to substitute a HYST model for the core. The magnetic flux value Φ in turn is used by the "lcouple"
code model to obtain a value for the voltage reflected back across its terminals to the driving electrical circuit.

<b>Hysteresis Mode (mode = 2)</b>

In the Hysteresis mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf)
value. This value is used as input to the equivalent of a hysteresis code model block. The parameters
defining the input low and high values, the output low and high values, and the amount of hysteresis are
as in that model. The output from this mode, as in PWL mode, is a current value which is seen across the magnetic core port.

One final note to be made about the two core models is that certain parameters are specific to one or the other. In particular, the in_low, in_high, out_lower_limit, out_upper_limit, and hysteresis parameters are not available in PWL mode. Likewise, the H_array, B_array, area, ad length values are unavailable
in Hysteresis mode. The input_domain and fraction parameters are common to both modes (though their behavior is somewhat different; for explanation of the input_domain and fraction values for the Hysteresis mode, please refer to the Hysteresis Block discussion.

Model Identifier: core

Netlist Format:

A<device_name> <mc1 _pin> <mc2_pin> <model_name>

.model <model_name> core area = <value> length = <value> H_array = [<value1> <value2>] B_array = [<value1> <value2>]
{<param1 = value> < param2 = value> ...}

Example:

A1 1 2 core

.model core core area = 1 length = 1 H_array = [0 1] B_array = [0 1]

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|H_array||magnetic field array||[0 1]||required
|-
|B_array||flux density array||[0 1]||required
|-
|Area||cross-sectional area||1||required
|-
|Length||core length||1||required
|-
|Input_domain||input smoothing domain||0.01||
|-
|Fraction||smoothing fraction/abs switch||True||
|-
|Mode||mode switch (1=pwl, 2=hyst)||1||
|-
|In_low||input low value||0.0||
|-
|In_high||input high value||1.0||
|-
|Hyst||hysteresis||0.1||
|-
|Out_lower_limit||output lower limit||0.0||
|-
|Out_upper_limit||output upper limit||1.0||
|-
|}

==Marker==

[[File:G16.png]]

The marker serves several purposes:

* It can appear as a default plot in simulations if the "Voltage Probe" box is checked.

* It can be used to set the initial voltage or voltage guess at the node it is connected to.

* It can be used as a port for a subcircuit when you choose the checkbox labeled "Use as Subcircuit Port" is checked.

* It can be used to explicitly set a node number in place of the arbitrarily assigned node number by the program. In this case, make sure the "Set Node Index" box is checked. Otherwise, it will act as just a voltage probe.

* It can be used to connect different parts of a circuit in place of wires. To use markers as virtual connectors, place them at points where wires would otherwise connect. Then set the Part Title of the two (or more) markers to the same name, and they will act as a single circuit node.

==MESFET==

[[File:G14.png]]

The MESFET is a Schottky-barrier gate FET with six times greater electron mobility than silicon. MESFETs are important devices for creating high frequency circuits. They function by creating a potential barrier between the gate and the channel when the metal gate
contacts the gallium-arsenide substrate. Electron velocity saturates for fields approximately ten times lower than with silicon. The Curtice model includes linear and saturated operation.

The standard parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

All the MESFET process model parameters are described in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||pinch-off voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|B||doping tail extending parameter||1/V||0.3||0.3
|-
|ALPHA||saturation voltage parameter||1/V||2||2
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||Ohm||0||100
|-
|RS||source ohmic resistance||Ohm||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula||-||0.5||
|-
|}

==MOSFET==

[[File:G13.png]]

The MOSFET is an active device that has up to 4 pins. The three standard pins are gate, drain, and source. These are given in the default symbol. The bulk node, which is grounded by default, is the fourth pin. The MOSFET with the bulk is named mos_n_lvl1_4 (the lvl1 is for level 1, the n for nmos, and the 4 for 4 pins.)

The standard [[parameters]] are L, W, AD, AS, PD, PS, NRD, NRS, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|L||channel length, in meters
|-
|W||channel width, in meters
|-
|AD,AS||areas of the drain and source diffusions, in meters2
|-
|PD,PS||perimeters of drain and source junctions, in meters(They default to 0.0.)
|-
|NRD,NRS||equivalent number of squares of the drain and source diffusions (These values multiply the sheet resistance for an accurate representation of parasitic series drain and source resistance of each transistor. The default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

There are five different default models: square-law I-V characteristic, analytical, semi-empirical, and BSIM and BSIM2 (Berkeley Short-channel IGFET Model), which include second-order effects such as channel-length
modulation, subthreshold conduction, scattering-limited velocity saturation, small-size effects, and charge-controlled capacitance. The process parameter LEVEL specifies which of the models is chosen as indicated below:

{| class="wikitable"
|-
|LEVEL 1||Schichman-Hodges
|-
|LEVEL 2||MOS2
|-
|LEVEL 3||MOS3
|-
|LEVEL 4||BSIM
|-
|LEVEL 5||BSIM2
|-
|LEVEL 6||MOS6
|-
|}

The process model [[parameters]] for levels 1,2,3, and 6 are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|LEVEL||model index|| ||1||
|-
|VTO||zero-bias threshold voltage||V||0.0||1.0
|-
|KP||transconductance parameter||A/V2||2e-5||3.1e-5
|-
|GAMMA||bulk threshold parameter||V1/2||0.0||0.37
|-
|PHI||surface potential||V||0.6||0.65
|-
|LAMBDA||channel-length modulation (level 1 & 2 only)||1/V||0.0||0.02
|-
|RD||drain ohmic resistance||ohms||0.0||1.0
|-
|RS||source ohmic resistance||ohms||0.0||1.0
|-
|CBD||zero-bias B-D junction capacitance||F||0.0||20fF
|-
|CBS||zero-bias B-S junction capacitance||F||0.0||20fF
|-
|IS||bulk junction saturation current||A||1.0e-14||1.0e-15
|-
|PB||bulk junction potential||V||0.8||0.87
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m||0.0||2e-10
|-
|RSH||drain & source diffusion sheet resistance||ohm/area||0.0||10.0
|-
|CJ||zero-bias bulk junction bottom capacitance per meter2 junction area||F/m2||0.0||2e-4
|-
|MJ||bulk junction bottom grading coefficient|| ||0.5||0.5
|-
|CJSW||zero-bias bulk junction sidewall capacitance per meter junction perimeter||F/m||0.0||1.0e-9
|-
|MJSW||bulk junction sidewall grading coefficient|| ||0.5, 0.33 (level1), (level2,3)||
|-
|JS||bulk junction saturation current per meter2 of junction area||A/m2|| ||1.0e-8
|-
|TOX||oxide thickness||meter||1.0e-7||1.0e-7
|-
|NSUB||substrate doping||1/cm3||0.0||4.0e15
|-
|NSS||surface state density||1/cm2||0.0||1.0e10
|-
|NFS||fast surface state density||1/cm2||0.0||1.0e10
|-
|TPG||type gate material(+1 if opp. substrate, 0 if A1 gate, -1 if same as substrate)|| ||1.0||
|-
|XJ||metallurgical junction depth||meter||0.0||1
|-
|LD||lateral diffusion||meter||0.0||0.8
|-
|UO||surface mobility||cm2/Vs||600||700
|-
|UCRIT||critical field for mobility degradation (level2 only)||V/cm||1.0e4||1.0e4
|-
|UEXP||critical field exponent in mobility degradation (level2 only)|| ||0.0||0.1
|-
|UTRA||transverse field coefficient (deleted for level2)|| ||0.0||0.3
|-
|VMAX||maximum drift velocity of carriers||m/s||0.0||5.0e4
|-
|NEFF||total channel-charge (fixed and mobile) coefficient (level2 only)|| ||1.0||5.0
|-
|KF||flicker noise coefficient|| ||0.0||1.0e-26
|-
|AF||flicker noise exponent|| ||1.0||1.2
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|DELTA||width effect on threshold voltage (level2,3)|| ||0.0||1.0
|-
|THETA||mobility modulation (level3 only)||1/V||0.0||0.1
|-
|ETA||static feedback (level3 only)|| ||0.0||1.0
|-
|KAPPA||saturation field factor (level3 only)|| ||0.2||0.5
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

The BSIM model has no default parameters, and leaving one out is considered an error. The additional process model parameters for level 4 and 5 models are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS
|-
|VFB||flat-band voltage||V
|-
|PHI||surface inversion potential||V
|-
|K1||body effect coefficient||V1/2
|-
|K2||drain/source depletion charge-sharing coefficient||
|-
|ETA||zero-bias drain-induced barrier-lowering coefficient||
|-
|MUZ||zero-bias mobility||cm2/V-s
|-
|DL||shortening of channel||m
|-
|DW||narrowing of channel||m
|-
|U0||zero-bias transverse-field mobility degradation coefficient||V-1
|-
|U1||zero-bias velocity saturation coefficient||m/V
|-
|X2MZ||sens. of mobility to substrate bias at Vds=0||cm2/V2-s
|-
|X2E||sens. of drain-induced barrier lowering effect to substrate bias||V-1
|-
|X3E||sens. of drain-induced barrier lowering effect to drain bias at Vds= Vdd||V-1
|-
|X2U0||sens. of transverse field mobility degradation to substrate bias||V-2
|-
|X2U1||sens. of velocity saturation effect to substrate bias||mV-2
|-
|MUS||mobility at zero substrate bias and at Vds= Vdd||cm2/V2-s
|-
|X2MS||sens. of mobility to substrate bias at Vds= Vdd||cm2/V2-s
|-
|X3MS||sens. of mobility to drain bias at Vds= Vdd||cm2/V2-s
|-
|X3U1||sens. of velocity saturation effect on drain bias at Vds= Vdd||mV-2
|-
|TOX||gate oxide thickness||m
|-
|TEMP||temperature at which [[parameters]] were measured||deg. C
|-
|VDD||measurement bias range||V
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m
|-
|XPART||gate-oxide capacitance-charge model flag||
|-
|N0||zero-bias subthreshold slope coefficient||
|-
|NB||sens. of subthreshold slope to substrate bias||
|-
|ND||sens. of subthreshold slope to drain bias||
|-
|RSH||drain and source diffusion sheet resistance||ohms/area
|-
|JS||source drain junction current density||A/m2
|-
|PB||built-in potential of source drain junction||V
|-
|MJ||grading coefficient of source drain junction||
|-
|PBSW||built-in potential of source drain junction sidewall||V
|-
|MJSW||grading coefficient of source drain junction sidewall||
|-
|CJ||source drain junction capacitance per unit area||F/ m2
|-
|CJSW||source drain junction sidewall capacitance per unit length||F/m
|-
|WDF||source drain junction default width||m
|-
|DELL||source drain junction length reduction||m
|-
|}

XPART=0 selects a 40/60 drain/source charge partition; XPART=1 selects a 0/100 partition.

==Mutual Inductors==

[[File:GK100.png]]

The mutual inductors device is a pair of inductors that are coupled to each other. L1 and L2 are the names of two inductors. You have to specify the inductance of inductor L1, the inductance of inductor L2, the initial current through each, and the coupling coefficient k, 0 ≤ k ≤ 1. The mutual inductance M expressed in units of H can be calculated using the following definition:

<math> k = \frac{M}{\sqrt{L_1 L_2}} </math>

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|inductance1||inductance of inductor 1||H||1||
|-
|inductance2||inductance of inductor 2||H||1||
|-
|ic1||initial current through inductor 1||A||0||
|-
|ic2||initial current through inductor 2||A||0||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Non-Ideal Current Transformer==

[[File:GK104.png]]

This 8-pin device models a non-ideal lossy current transformer. Its model consists of an ideal transformer with more secondary turns than primary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. on each side of the internal ideal transformer, there is a series leakage inductance LL<sub>k</sub>, followed by a shunt winding capacitance CW<sub>k</sub> and a series winding resistance RW<sub>k</sub>, which connects to the exterior positive pin on that side. The inter-winding resistance R<sub>12</sub> is connected across the negative pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||secondary-to-primary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary leakage inductance||H||1m||
|-
|ll2||secondary leakage inductance||H||1m||
|-
|cw1||primary winding capacitance||F||1p||
|-
|cw2||secondary winding capacitance||F||1p||
|-
|r12||inter-winding resistance||Ohms||10Meg||
|-
|}

==Non-Ideal Diode==

[[File:G9.png]]

This 2-pin device is a basic simplified model of a diode as a rectifier or switch. When forward-biased, it acts as a low-valued voltage source. When reverse-biased, it acts as an open circuit until the reverse voltage exceeds the specified breakdown voltage. Then it acts as a high-valued voltage source of the reverse polarity.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|vf||forward drop voltage||V||0.5||required
|-
|vr||reverse breakdown voltage||V||100||required
|-
|}

==Non-Ideal Voltage Transformer==

[[File:GK103.png]]

This 8-pin device models a non-ideal lossy voltage transformer. Its model consists of an ideal transformer with more primary turns than secondary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. There are series combinations of a winding resistance RW<sub>k</sub> and a leakage inductance LL<sub>k</sub> on the primary and secondary sides. These are connected between the positive interior and exterior pins on each side. There are also two shunt branches at the inputs of the primary and secondary sides (connected between the positive and negative exterior pins), each consisting of a distributed turn-to-turn winding resistance RDC<sub>k</sub> in series with a distributed turn-to-turn winding capacitance CW<sub>k</sub>. The inter-winding capacitance CWW<sub>12</sub> is connected across the positive pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||primary-to-secondary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary winding leakage inductance||H||1m||
|-
|ll2||secondary winding leakage inductance||H||1m||
|-
|rdc1||primary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw1||primary distributed turn-to-turn winding capacitance||F||1p||
|-
|rdc2||secondary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw2||secondary distributed turn-to-turn winding capacitance||F||1p||
|-
|cww12||inter-winding capacitance||F||1p||
|-
|}

==Nonlinear Capacitor==

[[File:GK89.png]]

The nonlinear capacitor model allows the capacitor to be described by an arbitrary relationship between the capacitor's charge Q and the voltage V across the capacitor. In other words, Q = f(V). The nonlinear capacitance is then defined as C(V) = dQ/dV. You need to define the charge Q by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ C_DEF } * v(pos,neg)

which implies a linear capacitor, where Q = C<sub>DEF</sub> V. Therefore, C = C(V) = dQ/dV = C<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|C_DEF||default capacitance||F||1||
|-
|}

==Nonlinear Conductor==

[[File:GK88.png]]

The nonlinear conductor model allows the conductor to be described by an arbitrary relationship between the conductor's current I and the voltage V across the conductor. In other words, I = f(V). The nonlinear conductance is then defined as G(V) = dI/dV. You need to define the current I by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ G_DEF } * v(pos,neg)

which implies a linear conductor, where I = G<sub>DEF</sub> V. Therefore, G = G(V) = dI/dV = G<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|G_DEF||default capacitance||S||1||
|-
|}

==Nonlinear Dependent Sources==

[[File:G18.png]]

Nonlinear dependent (arbitrary) sources use an equation or mathematical expression to describe their behavior. One and only one of the two forms: V=<expr> or I=<expr> must be given.

Netlist Format:

B<device_name> v = <expression>

B<device_name> i = <expression>

Examples:

v = I(v1) + 3* I(v2)

I = v(i1) + 3* v(2) + 5 * v(3) ^2

The first example is a current-controlled voltage source. The v on the left side of the equation
indicates that it is a voltage source. I(v1) and I(v2) are the currents through voltage sources named v1 and v2, respectively.

The second example is a voltage-controlled current source. v(2) and v(3) represents the voltages at nodes 2 and 3, respectively, and v(i1) represents the voltage across a current source named i1.

The following mathematical functions defined for real variables can be used in the expressions:

abs(x), acos(x), acosh(x), asin(x), asinh(x), atan(x), atanh(x), cos(x), cosh(x), exp(x), ln(x), log(x), max(x,y), min(x,y), pwr(x,y), pwrs(x,y), sgn(x), sin(x), sinh(x), sqrt(x), tan(x), tanh(x), u(x), uramp(x).

The function "sgn" is the signum function and its value is 1 if the argument is positive or zero and -1 if the argument is negative.
The function "u(x)" is the unit step and "uramp(x)" is the integral of the unit step. The
unit step is one if its argument is greater than zero and zero if its argument is less than zero. The
ramp function (uramp) is 0 for argument values less than zero and equal to the argument for argument values
greater than zero.

The following operators are permissible: +, -, *, /, and ^.

The power functions have equivalent expressions: pwr(x,y) = x^y and pwrs(x,y) = sgn(x)*abs(x)^y.

Two constants can also be used in expressions: pi = 3.1415926 and e = 2.7182818.

There is a conditional function with the syntax IF(Condition, Expression1, Expression2). If "Condition" is met, then the return value of the function is Expression1; otherwise, it is Expression2. An example of this type of function is IF(v(1)>=0,1,-1), which is equivalent to sgn(v(1)).

To get time into an expression, integrate the current from a constant current source with a capacitor
and use the voltage across the capacitor.

==Nonlinear Inductor==

[[File:GK90.png]]

The nonlinear inductor model allows the inductor to be described by an arbitrary relationship between the inductor's magnetic flux Φ and the current I flowing through the inductor . In other words, Φ = f(I). The nonlinear inductance is then defined as L(I) = dΦ/dI. You need to define the flux Φ by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ L_DEF } * i(vx)

which implies a linear inductor, where Φ = L<sub>DEF</sub> I. Therefore, L = L(I) = dΦ/dI = L<sub>DEF</sub>.

Another example is 1e-4*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|L_DEF||default inductance||H||1||
|-
|}

==Nonlinear Resistor==

[[File:GK87.png]]

The nonlinear resistor model allows the resistor to be described by an arbitrary relationship between the voltage V across the resistor and its current I. In other words, V = f(I). The nonlinear resistance is then defined as R(I) = dV/dI. You need to define the voltage V by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ R_DEF } * i(vx)

which implies a linear resistor, where V = R<sub>DEF</sub> I. Therefore, R = R(I) = dV/dI = R<sub>DEF</sub>.

Another example is 10*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R_DEF||default resistance||Ω||1||
|-
|}

==Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This three-pin device models a parameterized operational amplifier with a very high voltage gain, a very high input impedance and a very low output impedance. The behavioral model of the parameterized Op-Amp device is based on the algorithm found in the book <B>Macromodeling with Spice</B>,
authored by Connelly & Choi, published by Prentice Hall. The default parameters are those of the 741 Op-Amp. This device doesn't require external DC bias voltage sources. Its positive and negative DC bias voltages are specified as its parameters. Sometimes the simulation doesn't converge if there is no DC path from the output of the Op-Amp to the ground.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|r_in_dm||differential mode input resistance||Ohms||2Meg||
|-
|r_in_cm||common mode input resistance||Ohms||2G||
|-
|Avd0||differential mode DC gain||dB||106||
|-
|CMRR||common mode rejection ratio||dB||90||
|-
|r_out||output resistance||Ohms||75||
|-
|c_in||input capacitance||F||1.4p||
|-
|ios||input offset current||A||20n||
|-
|ib||input bias current||A||80n||
|-
|vio||input offset voltage||V||1m||
|-
|slew_pos||positive slew rate||V/s||0.5e6||
|-
|slew_neg||negative slew rate||V/s||0.5e6||
|-
|curr_src_max||maximum output source current||A||25m||
|-
|curr_sink_||maximum output sink current||A25m||
|-
|fp1||dominant pole frequency||Hz||5||
|-
|fp2||second pole frequency||Hz||2Meg||
|-
|fp3||third pole frequency||Hz||20Meg||
|-
|fp4||fourth pole frequency||Hz||100Meg||
|-
|fz||first zero frequency||Hz||5Meg||
|-
|vcc_pos||positive dc voltage source||V||12||
|-
|vcc_neg||negative dc voltage source||V||12||
|-
|}

== Optocoupler ==

[[File:GK115.png]]

This is a five-pin parameterized optocoupler device. Its model consists of an ideal diode device in series with an Ohmic resistance connected between the Anode (A) and Cathode (K) pins together with a bipolar junction transistor device with three accessible pins, Collector (C), Base (B) and Emitter (E). A current-controlled current source is connected between base and collector of the BJT, whose current is controlled by the current passing through the diode. The proportionality constant is twice the specified value of the current transfer ratio (ctr) parameter.

You can change or enhance the models of the diode and BJT by adding more parameters. To do so, you have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ctr||current transfer ratio||-||0.5||
|-
|rd||diode ohmic resistance||Ohms||0.1||
|-
|}

== Overtone Crystal ==

[[File:GK79.png]]

This is a 2-pin parameterized overtone crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|LM||fundamental motional inductance||H||250m||
|-
|CM1||fundamental motional capacitance||F||10f||
|-
|RM1||fundamental motional resistance||Ohms||20||
|-
|RM3||3rd overtone motional resistance||Ohms||50||
|-
|RM5||5th overtone motional resistance||Ohms||100||
|-
|RM7||7th overtone motional resistance||Ohms||150||
|-
|C0||shunt capacitance||F||3p||
|-
|}

== Photodiode ==

[[File:GK113.png]]

This is a 4-pin parameterized photodiode device. A pair of pins, Anode (A) and Cathode (K), represent the physical terminals of the photodiode. The photodiode model connected between the anode and cathode pins consists of the parallel connection of an ideal diode, a dark current source, a noise current source, a current-controlled current source, a diode capacitance, a shunt resistance altogether with a series resistance.

Another pair of pins IS+ and IS- act as an ammeter that must be inserted in a control circuit. The current passing through this ammeter controls the current of the photodiode. The default proportionality constant is unity. The controlling current is typically a function of light intensity incident on the surface of the photodiode.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|id||dark current||A||1n||
|-
|ir||noise current||A||1p||
|-
|cd||diode capacitance||F||10p||
|-
|rs||series resistance||Ohms||1m||
|-
|rp||parallel resistance||Ohms||1Meg||
|-
|}

==Piecewise Linear (PWL) Controlled Source==

[[File:GL49.png]]

The Piecewise Linear (PWL) Controlled Source is a single-input and single-output function generator whose output is not necessarily
linear for all input values. Instead, it follows an I/O relationship that is specified by the x_array and y_array coordinates. The x_array and y_array values represent vectors of coordinate points on the x and y axes, respectively. The x_array values are progressively increasing input coordinate points, and the associated y_array values represent the outputs at those points. There may be as few as two pairs specified, or as many as memory and simulation speed allow.

In order to fully specify outputs for values of Vin outside of the bounds of the PWL function, the PWL
controlled source model extends the slope found between the lowest two coordinate pairs and the highest
two coordinate pairs. This has the effect of making the transfer function completely linear for Vin
less than x_array[0] and Vin greater than x_array[n]. It also has the potentially subtle effect of unrealistically
causing an output to reach a very large or small value for large inputs. You should thus keep in mind
that the PWL Source does not inherently provide a limiting capability.

In order to diminish the potential for divergence of simulations when using the PWL block, a form
of smoothing around the x_array and y_array coordinate points is necessary. This is due to the iterative
nature of the simulator and its reliance on smooth first derivatives of transfer functions in order to
arrive at a matrix solution. Consequently, the two parameters "input_domain" and "fraction" are included
to allow you some control over the amount and nature o the smoothing performed.

Fraction is a switch that is either TRUE or FALSE. When TRUE (the default setting), the simulator assumes
that the specified input_domain value is to be interpreted as a fractional figure. Otherwise, it is interpreted
as an absolute value. Thus, if fraction = TRUE and input_domain = 0.10, the simulator assumes that the smoothing
radius about each coordinate point is to be set equal to 10% of the length of either the x_array segment
above each coordinate point, or the x_array segment below each coordinate point. The specific segment
length chosen will be the smallest of these two for each coordinate point.

If fraction = FALSE and input_domain = 0.10, then the simulator will begin smoothing the transfer function at 0.10
volts (or amperes) below each x_array coordinate and will continue the smoothing process for another 0.10
volts (or amperes) above each x_array coordinate point.

Model Identifier: pwl

Netlist Format:

A<device_name> %vd(<in_pin> <in_ref_pin>) %vd(<out_pin> <out_ref_pin>) <model_name>

.model <model_name> pwl x_array = [<value1> <value2> ...] y_array = [<value1>
<value2> ...] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(2 3) %vd(1 4) pwl
.model pwl pwl x_array = [0 1] y_array = [0 1]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|x_array||x-element array||V||[0 1]||required
|-
|y_array||y-element array||V||[0 1]||required
|-
|input_domain||input smoothing domain||-||0.01||
|-
|fraction||smoothing %/abs switch||-||True||
|-
|}

== PM Modulated Source ==

[[File:GL25.png]]

This is a voltage source with a single-tone phase modulated waveform. The PM modulation index MDI is defined as the ratio of maximum phase deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Potentiometer ==

[[File:GK77.png]]

This is a 3-pin device that models a potentiometer with options for either linear or logarithmic resistance. position = 0 corresponds to the wiper being at the extreme left and position = 1 corresponds to the wiper being at the extreme right. With the default position = 0.5 corresponding to the midpoint, this device functions as a one-half voltage divider.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|position||position of wiper connection||-||0.5||Must be between 0.0 and 1.0.
|-
|log||log-linear switch||-||False||Select False for linear and True for logarithmic.
|-
|r||total resistance||Ohms||0.1u||
|-
|log_multiplier||multiplier constant for log resistance||-||1.0||
|-
|}

== Programmable Unijunction Transistor (PUT)==

[[File:GK112.png]]

This is a 3-pin parameterized Programmable Unijunction Transistor (PUT) device with three pins: Base 1 (B1), Base 2 (B2) and Emitter (E). It is biased with a positive voltage between the two bases. This device has a unique characteristic that when it is triggered, its emitter current increases regeneratively until it is restricted by emitter power supply. It exhibits a negative resistance characteristic and so it can be employed as an oscillator. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To change these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|eta||-||-||0.6||
|-
|rbb||total base-to-base resistance||Ohms||40k||
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

==Random Resistor==

[[File:GK93.png]]

The random resistor device models a resistor whose resistance is a random number between 0 and a maximum specified value.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|max_val||maximum resistance value||Ω||1k||
|-
|}

==Real Capacitor==

[[File:GK117.png]]

This is primarily a non-ideal, temperature-dependent capacitor model. You can access it from the Parts Menu as '''User-Defined Capacitor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent capacitance is computed using the quadratic equation:

C(T) = C(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance and a series inductance together with the capacitor, all in parallel with a shunt resistance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Resr||series resistance||Ω||10||
|-
|Ls||inductance||H||1p||
|-
|C||capacitance||F||1n||
|-
|Rp||parallel resistance||Ω||1G||
|-
|ic||voltage initial condition||V||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||F/°C||0.1||
|-
|tc2||second-order temperature coefficient||F/°C<sup>2</sup>||0.01||
|-
|}

==Real Inductor==

[[File:GK118.png]]

This is primarily a non-ideal inductor model. You can access it from the Parts Menu as '''User-Defined Inductor'''. Its series resistor has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance together with the inductor, and the combination in parallel with a shunt capacitance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Rdc||series resistance||Ω||10||
|-
|L||inductance||H||1||
|-
|Cp||capacitance||F||1p||
|-
|ic||current initial condition||A||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Real Resistor==

[[File:GK116.png]]

This is primarily a non-ideal, temperature-dependent resistor model. You can access it from the Parts Menu as '''User-Defined Resistor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series inductance together with the resistor.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R||resistance||Ω||1k||
|-
|Ls||inductance||H||1n||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Resistor==

[[File:GK119.png]]

Resistors are passive devices that dissipate power. Their resistance value varies depending on how much power they can dissipate and is measured
in Ohms. The transient, DC and AC behaviors of a resistor are all described by the same equation:

v = R * i

where v is the voltage across the resistor, i is the current passing through the resistor, and R is the resistance. The value of R must be nonzero.

All resistor names must begin with R.

Netlist Format:

R<device_name> <N+> <N-> <value>

Example:

R1 1 2 1k

[[RF.Spice A/D]] provides three types of resistor: Simple, User-Defined (Real Resistor) and Semiconductor. The resistance of the simple resistor is a single value expressed in Ohms. You can also set the Monte Carlo tolerance for this resistor.

==Schottky Diode==

[[File:GK80.png]]

The Schottky diode has the same model as the generic diode with a nonzero transit time (tt), a nonzero junction capacitance (cjo) and a typically larger saturation current (is), a lower junction potential (vj) and a smaller grading coefficient (m).

==Semiconducting Capacitor==

[[File:GK83.png]]

This is the more general form of the Capacitor model and allows for the calculation of the actual capacitance value from strictly geometric information and the specifications of the process.

General Form:

CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>

If VALUE is specified, it defines the capacitance. If MNAME is specified, then the capacitance is calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. Either VALUE or MNAME, LENGTH, and WIDTH may be specified, but not both sets. The optional initial condition "IC" is the initial voltage across the capacitor for transient simulations.

The capacitance is computed as:

CAP = CJ * (LENGTH - NARROW) * (WIDTH - NARROW)+ 2 * CJSW * (LENGTH + WIDTH - 2NARROW) * CAP

To modify the model parameters, first double click on the capacitor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit CJ, CJSW, NARROW, DEFW, and CAP.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CJ||junction bottom capacitance||F/m<sup>2</sup>||-||
|-
|CJSW||junction sidewall capacitance||F/m ||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|CAP||nominal capacitance for Monte Carlo simulation||F||1||
|-
|}

== Semiconductor Resistor ==

[[File:GK82.png]]

This is the more general form of the resistor model and allows for the modeling of temperature effects and for the calculation of the actual resistance value from strictly geometric information and the specifications of the process.

General Form:

RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>

If VALUE is specified, it overrides the geometric information and defines the resistance. If MNAME is specified, then the resistance may be calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. The (optional) TEMP value is the temperature at which this device is to operate, and overrides the temperature specification in the SPICE Options Dialog.

The resistance is computed as:

R(T0) = (RSH) * [(L - NARROW) / (W - NARROW)] * RES

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

To modify the model parameters, first double click on the resistor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit TC1, TC2, RSH, RES, etc.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|TC1||first order temperature coefficient||Ω/°C||-||
|-
|TC2||second order temperature coefficient||Ω/°C<sup>2</sup>||-||
|-
|RSH||sheet resistance||Ω/sq||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|TNOM||the parameter measurement temperature||deg C ||27||
|-
|RES||resistance multiplier for Monte Carlo simulation||Ohms||1||
|-
|}

== Silicon-Controlled Rectifier (SCR)==

[[File:GK109.png]]

This is a 3-pin parameterized Silicon-Controlled Rectifier (SCR) device with three pins: Anode (A), Cathode (K) and Gate (G). It is a unidirectional device which can conduct current only in one direction. The SCR can be triggered only by a positive current going into its gate. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

== SPDT Switch ==

[[File:GK72.png]]

This is a 5-pin device that models a single-pole double-throw switch. The input voltage is transferred to the first output pin if the control voltage is at a high state. Otherwise, its is transferred to the second output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== SPST Switch ==

[[File:GK71.png]]

This is a 4-pin device that models a single-pole single-throw switch. It is virtually equivalent of the standard voltage-controlled switch.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Tabulated Conductor==

[[File:GK92.png]]

The tabulated conductor model allows the conductance to be described by a table relating the device's current i(t) to its terminal voltage v(t). In effect, the conductance is defined as G = di(t)/dv(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (v,i) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tabulated Resistor==

[[File:GK91.png]]

The tabulated resistor model allows the resistance to be described by a table relating the device's terminal voltage v(t) to its current i(t). In effect, the resistance is defined as R = dv(t)/di(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (i,v) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tapped Inductor==

[[File:GK101.png]]

This 3-pin device models a tapped inductor with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lt||total inductance||H||1m||
|-
|ratio||ratio of number of turns between positive terminal and tap to total number of turns||-||0.5||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

== Temperature-Dependent Current Source ==

[[File:GL14.png]]

This is a current source whose current is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

== Temperature-Dependent Voltage Source ==

[[File:GL13.png]]

This is a voltage source whose voltage is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

==Thermometer==
[[File:G115.png]]

The Thermometer is a two-pin device that measures the operating temperature of a circuit. The voltage across the device pins is equal to SPICE's operating temperature in degrees centigrade. The output voltage of the Thermometer can be used in conjunction with linear or nonlinear dependent sources to model temperature-dependent quantities.

Model Identifier: thermo

Parameters:

This device has no parameters.

== Triac Thyristor ==

[[File:GK110.png]]

This is a 3-pin bidirectional thyristor device that conducts current in either direction when triggered. A thyristor is analogous to a relay in that a small voltage and current can control a much larger voltage and current. The triac has two anode pins termed Main Terminal 1 (MT1) and Main Terminal 2 (MT2) and a Gate (G) pin. In order to create a triggering current for a triac, either a positive or negative voltage can be applied to the gate. Once triggered, the thyristor continues to conduct, even if the gate current ceases, until the main current drops below a certain level called the holding current. The device's model involves two NPN BJT transistors and two PNP BJT transistors. The forward beta parameters of the NPN and PNP transistors are set equal to 20 and 5, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|bvf||breakdown voltage of forward diodes||V||100||
|-
|rh||resistance controlling reverse holding current||Ohms||100||
|-
|rgp||resistance controlling forward holding current and trigger current||Ohms||50||
|-
|}

==Uniform RC Transmission Line==

[[File:G23.png]]

The standard parameters are L, and N. They are described below:

Two of the nodes are the element nodes connected by the RC line. The third is the node to which the capacitances
are connected. L is the length of the RC line in meters. N is the number of lumped segments to use in
modeling the RC line.

This device is derived from a model proposed by Gertzberrg. It expands the URC line into a network of
lumped RC segments with internally generated nodes. These segments increase toward the middle of the
URC line in a geometric progression with K as the proportionality constant.

The URC line is made up entirely of resistor and capacitor segments, unless the ISPERL parameter has a
non-zero value. In this case, capacitors are replaced by reverse biased diodes with an equivalent zero-bias
junction capacitance, a saturation current of ISPERL amps per meter of transmission line, and optional
series resistance of RSPERL ohms per meter.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|K||propagation constant||-||2||1.2
|-
|FMAX||maximum frequency of interest||Hz||1.0G||6.5Meg
|-
|RPERL||resistance per unit length||Ohm /m||1000||10
|-
|CPERL||capacitance per unit length||F/m||1.0e-15||1pF
|-
|ISPERL||saturation current per unit length||A/m||0||-
|-
|RSPERL||diode resistance per unit length||Ohm/m||0||-
|-
|}

==Varactor Diode==

[[File:GK81.png]]

A varactor diode is a combination of the generic diode with additional package inductance, package capacitance and a series resistance. This diode device has a typically large value of junction capacitance (cjo).

Parameters (in addition to standard diode parameters):

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|q||quality factor||-||5000||
|-
|f0||frequency of Q-factor specification||Hz||50Meg||
|-
|ls||package inductance||H||0.5n||
|-
|cp||package capacitance ||F||0.05p||
|-
|}

==Voltage-Controlled Capacitor==

[[File:GK85.png]]

This 3-pin device models a voltage-controlled two-terminal capacitor whose capacitance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in F/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_C||conversion factor||F/V||1.0||
|-
|}

==Voltage-Controlled Inductor==

[[File:GK86.png]]

This 3-pin device models a voltage-controlled two-terminal inductor whose inductance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in H/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_L||conversion factor||H/V||1.0||
|-
|}

==Voltage-Controlled Resistor==

[[File:GK84.png]]

This 3-pin device models a voltage-controlled two-terminal resistor whose resistance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in Ω/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_r||conversion factor||Ω/V||1.0||
|-
|}

==Voltage-Controlled Switch==

[[File:G19.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Voltage-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Voltmeter or controlling voltage nodes, as well as the turn-on and turn-off voltages in Volts and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the rest of [[parameters]]. When the voltage across the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the voltage across the switch or controlling device is less than or equal to the turn off current, the switch opens.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|V_ON||turn-on voltage||V||0.5||
|-
|V_OFF||turn-off voltage||V||0.0||
|-
|RON||on resistance||Ohms||1.0||
|-
|ROFF||off resistance||Ohms||1G||
|-
|}

==Voltage Noise Source==

[[File:GL15.png]]

This is a voltage noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the parameters of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise voltage||V/√Hz||1n||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Voltage Source==

[[File:G17A.png]]

A voltage source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a voltage source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset voltage. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==XSpice Devices and their models==

XSpice devices have the following form:
<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 4pt 0pt 1px 0pt ; font-family: 02070309020205020404,sans-serif; ">
A<device_name> <node1> <node2> ... <model_name></P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., A2 1 2 transfer_function

Note that XSpice devices must start with the "A" designation, much as a resistor starts with
an "R". Some devices will have grouped (or vector) pins and are designated by being placed
inside square brackets. In the example shown below, the 1 and 2 pins are grouped. Pin 3 is not. </P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 [1 2] 3 summer </P>

Some models will have voltage differential pairs of pins and will be denoted by a %vd( ). In the following
example pins 1 and 4 are differential pairs, as well as pins 2 and 3. Differential pairs must go between
parentheses ().

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 %vd(1 4) %vd(2 3) triangle </P>

Refer to individual devices for more information.

Each XSpice device will also have a model associated with it. Each model will have the following form:

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
.model <model_name> <model_identifier> {<pname1 = pval1>} {<pname2 = pval2>}
...</P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., .model transfer_function s_xfer in_offset = 0.0 gain = 1.0</P>

Model_name refers to the name given in the device line. Model_identifier is an internal designation and
must be of an existing designation Refer to each device's example for the correct designation.

Parameter values are optional. If they aren't specified, then the default will be used. Some devices
have parameters that require a value and must be specified. Refer to individual devices for any required parameters.

==Zener Diode==

[[File:G10.png]]

The Zener Diode models the DC characteristics of most zeners. Since most data sheets for zener diodes do
not give detailed characteristics in the forward region, only a single point defines the forward characteristicThe
saturation current refers to the relatively constant reverse current that is produced when the voltage
across the zener is negative, but breakdown has not been reached. The reverse leakage current determines
the slight increase in reverse current as the voltage across the zener becomes more negative. It is modeled
as a resistance parallel to the zener with value v_breakdown / i_rev.

Note that the limt_switch parameter engages an internal limiting function for the zener. This can, in
some cases, prevent the simulator from converging to an unrealistic solution if the voltage across or
current into the device is excessive. If use of this feature fails to yield acceptable results, the convlimit
option should be tried (add the following statement to the SPICE input deck: .options convlimit)

Model Identifier: zener

Netlist Format:

A<device_name> <z_pin> <z_out_pin> <model_name>

.model <model_name> zener v_breakdown = 1 {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 zener

.model zener zener v_breakdown = 1

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|v_breakdown||breakdown voltage||1||required
|-
|i_breakdown||breakdown current||2.0e-2||
|-
|i_sat||saturation current||1.0e-12||
|-
|N_forward||forward emission coefficient||1.0||
|-
|limit_switch||switch for on-board limiting (convergence aid)||False||
|-
|}

<p> </p>
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D | Back to RF.Spice A/D Wiki Gateway]]'''

Glossary of Generic Analog & Mixed-Mode Devices & Sources

2018-10-11T16:43:18Z

Kazem Sabet: /* Nonlinear Dependent Sources */

==4-Bit ADC Bridge==

[[File:GK44.png]]

This 8-pin device is simply a bundle of 4 1-bit ADC bridges. Each analog input pin has a corresponding digital output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|}

==4-Bit DAC Bridge==

[[File:GK45.png]]

This 8-pin device is simply a bundle of 4 1-bit DAC bridges. Each digital input pin has a corresponding analog output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|}

== AC/RF Current Source ==

[[File:GL11.png]]

This is a simplified version of the standard Current Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak current amplitude||A||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal current||A||0||
|-
|}

== AC/RF Voltage Source ==

[[File:GL10.png]]

This is a simplified version of the standard Voltage Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak voltage amplitude||V||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal voltage||V||0||
|-
|}

==Alternate Ferrite Core Transformer==

[[File:GK96.png]]

The alternate ferrite core transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ferrite_Core_Transformer | Ferrite Core Transformer]], except for the reversed polarity of its secondary port.

==Alternate Ideal Transformer==

[[File:XFMR2.png]]

The alternate ideal transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ideal_Transformer | Ideal Transformer]], except for the reversed polarity of its secondary port.

== AM Modulated Source ==

[[File:GL23.png]]

This is a voltage source with a single-tone amplitude modulated waveform. The AM modulation index MDI is defined as the ratio of maximum amplitude deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Analog Clock ==

[[File:GL30.png]]

This is a periodic pulse generator with a default 0V low output level and a default 5V high output level.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|delay||delay time||sec||0||
|-
|rise||rise time||sec||0.1n||
|-
|fall||fall time||sec||0.1n||
|-
|pulse_wid||clock pulse width||sec||1u||required
|-
|period||clock period||-||2u||required
|-
|out_low||low output voltage level||V||0||
|-|-
|out_high||high output voltage level||V||5||
|-
|}

==Analog-to-Digital Converter (ADC) Bridge==
[[File:GK42.png]]

The ADC Bridge takes an analog value from an analog node and may be in the form of a voltage or current.
If the input is less than or equal to "in_low", then a digital "0" is generated. If
the input is greater than or equal to "in_high", a digital "1" is generated. Otherwise,
a digital "UNKNOWN" is the output value. Unlike the DAC Bridge, ramping or delay is not applicable.
Rather, the continuous ramping of the input provides for any associated delays in the digitized signal.

This model also posts an input load value based on the parameter input_load.

Model Identifier: adc_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> adc_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] adc_bridge

.model adc_bridge adc_bridge in_low = .1 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|rise_delay||L-to-H delay time||sec||1n||
|-
|fall_delay||H-to-L delay time||sec||1n||
|-
|}

== Arbitrary Temporal Waveform Generator ==

[[File:GL17.png]]

This is a voltage source with an arbitrary waveform defined by a mathematical expression. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(t)" standing for time.

Examples:

* v(t) is equivalent to f(t) = t.
* 0.1*(v(t))^2 is equivalent to f(t) = 0.1t^2.
* sin(2*pi*v(t)) is equivalent to f(t) = sin(2πt).

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Tmax||maximum signal duration||sec||1e6||required
|-
|}

==Auto-Transformer==

[[File:GK102.png]]

This 3-pin device models an auto-transformer with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lp||primary inductance||H||1m||
|-
|Ls||secondary inductance||H||1m||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Bipolar Junction Transistor (BJT)==
[[File:G11.png]]

The BJT is an active device which has up to 4 pins. The three standard pins are base, emitter, and collector. These are given in the default symbol. The substrate, which is grounded by default, is the fourth pin. To use the BJT with the substrate, create a new 4-pin BJT using the Device Editor and Symbol Editor.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

Area factor scales the model parameters RE and RC. IC VBE is the initial voltage from base emitter. IC VCE is the initial voltage from collector to emitter. TEMP is the overriding temperature. These parameters are based on the Gummel and Poon integral-charge model. If these parameters are not specified, then it will reduce to the simpler Ebers-Moll model.

The process model is mandatory for the BJT. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|IS||transport saturation current||A||1.0e-16||1.0e-15
|-
|BF||ideal maximum forward beta|| ||100||100
|-
|NF||forward current emission coefficient|| ||1.0||1
|-
|VAF||forward Early voltage||V||infinite||200
|-
|IKF||corner forward beta high current roll-off||A||infinite||0.01
|-
|ISE||B-E leakage saturation current||A||0||1.0e-13
|-
|NE||B-E leakage emission coefficient|| ||1.5||2
|-
|BR||ideal maximum reverse beta|| ||1||0.1
|-
|NR||reverse current emission coefficient|| ||1||1
|-
|VAR||reverse Early voltage||V||infinite||200
|-
|IKR||corner reverse beta high current roll-off||A||infinite||0.01
|-
|ISC||B-C leakage saturation current||A||0||1.0e-13
|-
|NC||B-C leakage emission coefficient|| ||2||1.5
|-
|RB||zero bias base resistance||ohms||0||100
|-
|IRB||current where base resistance falls halfway to minimum value||A||infinite||0.1
|-
|RBM||minimum base resistance at high currents||ohms||RB||10
|-
|RE||emitter resistance||ohms||0||1
|-
|RC||collector resistance||ohms||0||10
|-
|CJE||B-E zero bias depletion capacitance||F||0||2pF
|-
|VJE||B-E built-in potential||V||0.75||0.6
|-
|MJE||B-E junction exponential factor|| ||0.33||0.33
|-
|TF||ideal forward transit time||sec||0||0.1ns
|-
|XTF||coefficient for bias dependence of TF|| ||0||
|-
|VTF||voltage describing VBC dependence of TF||V||infinite||
|-
|ITF||high-current parameter for effect on TF||A||0||
|-
|PTF||excess phase at freq=1.0/(TF*2PI)Hz||degree||0||
|-
|CJC||B-C zero bias depletion capacitance||F||0||2pF
|-
|VJC||B-C built-in potential||V||0.75||0.5
|-
|MJC||B-C junction exponential factor|| ||0.33||0.5
|-
|XCJC||fraction of B-C depletion capacitance connected to internal base node|| ||1||
|-
|TR||ideal reverse transit time||sec||0||10ns
|-
|CJS||zero bias collector-substrate capacitance||F||0||2pF
|-
|VJS||substrate junction built-in potential||V||0.75||
|-
|MJS||substrate junction exponential factor|| ||0||0.5
|-
|XTB||forward and reverse beta temp. exponent|| ||0||
|-
|EG||energy gap for temperature effect on IS||eV||1.11||
|-
|XTI||temperature exponent for effect on IS|| ||3||
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

==Capacitance Meter==
[[File:G37.png]]

The Capacitance Meter measures the total capacitance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total capacitance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense a capacitance value and alter their behavior based upon it.

Model Identifier: cmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> cmeter {<gain = value>}

Example:

A1 1 2 cap_meter

.model cap_meter cmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Capacitor==
[[File:GK120.png]]

Capacitors are used to store electrical energy. They can filter or remove AC signals or block DC current without disrupting AC signals. A capacitor's ability to store energy is termed capacitance and is measured in Farads, with values from pF to mF. The only time current flows through a capacitor is when the charge is collected on, or is removed from, its parallel plates. This means that the voltage across the capacitor is changing, which doesn't conform to DC analysis. In a physical circuit, there is a transition stage during which capacitors charge up to their final values. The result is the same as if these capacitors did not exist and the connections to them were left dangling. In other words, in a (steady-state) DC analysis, a capacitor behaves like an open circuit. Therefore, it is important that no section of the circuit is isolated from the capacitors. Every circuit node needs some path for DC current to the ground.

A capacitor's transient behavior is described by the equation:

i(t) = C * (dv(t)/dt)

Its initial voltage is only important when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An capacitor's AC behavior is described by the equation:

i = j ω * C * v

All capacitor names must begin with C.

Netlist Format:

C<device_name> <N+> <N-> <value>

Example:

C1 1 2 10p

[[RF.Spice A/D]] provides three types of capacitors: simple, user-defined (or real) and semiconductor. The standard capacitor parameters are N+, N-, VALUE, and IC. In a simple capacitor, VALUE must
be specified for the capacitance in Farads. IC is the (optional) initial condition for the capacitor voltage.

==Center-Tapped Ferrite Core Transformer==

[[File:GK97.png]]

This five-pin three-port device models a center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

==Controlled Sine Wave Oscillator==

[[File:G24.png]]

This is a four-terminal function generator with a sinusoidal wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.
This function has parameterizable values of low and high peak output voltage.

Model Identifier: sine

Netlist Form:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> sine cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) sine

.model sine sine cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[1 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|}

==Controlled Sources==

Circuits can contain linear dependent sources characterized by one of the following equations (where g,
e, f, and h are constants representing transconductance, voltage gain, current gain, and transresistance,
respectively):

<SPAN STYLE="font-size: 9pt ; ">i<sub>out</sub> = g v<sub>in</sub>
     v<sub>out</sub> = e v<sub>in</sub>
     i<sub>out</sub> = f i<sub>in</sub>
     v<sub>out</sub> = h i<sub>in</sub></SPAN>
<P CLASS="Bodytext" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; ">
For further information, refer to:</P>

Linear Current Controlled Current Source (CCCS)

Linear Voltage Controlled Current Source (VCCS)

Linear Current Controlled Voltage Source (CCVS)

Linear Voltage Controlled Voltage Source (VCVS)

==Controlled Square Wave Oscillator==

[[File:G25.png]]

This is a four-terminal function generator with a square wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: square

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> square cntl_array = [<value1> <value2>] freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) square

.model square square cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Duty_cycle||Duty cycle||-||0.5||
|-
|Rise_time||Output rise time||sec||1.0e-9||
|-
|Fall_time||Output fall time||sec||1.0e-9||
|-
|}

==Controlled Triangle Wave Oscillator==

[[File:G26.png]]

This is a four-terminal function generator with a triangle wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defined voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: triangle

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> tirangle cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>]{<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 4) %vd(2 3) triangle

.model triangle triangle cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Rise_duty||Rise time duty cycle||0.5||
|-
|}

== Crystal ==

[[File:GK78.png]]

This is a 2-pin parameterized crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CM||motional capacitance||F||10f||
|-
|C0||shunt capacitance||F||1p||
|-
|RM||motional resistance||Ohms||100||
|-
|LM||motional inductance||H||100m||
|-
|}

==Current Noise Source==

[[File:GL16.png]]

This is a current noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the [[parameters]] of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise current||A/√Hz||1p||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Current Source==

[[File:G17B.png]]

Current source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a current source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset current. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==Current-Controlled Switch==

[[File:G20.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Current-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the turn-on and turn-off currents in Amperes and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the rest of [[parameters]]. When the current through the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the current through the switch or controlling device is less than or equal to the turn off current, the switch opens.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|I_ON||turn-on current||A||0.0||
|-
|I_OFF||turn-off current||A||0.0||
|-
|RON||closed resistance||Ohms||1.0||
|-
|ROFF||open resistance||Ohms||1/GMIN||
|-
|}

==Darlington Pair==

[[File:GK108.png]]

A Darlington pair is a three-pin device that consists of two interconnected BJT transistors of the same type. The collectors of two transistors are connected together to provide the "Collector" pin of the pair. The base of the first BJT acts the "Base" pin of the pair. The emitter of the first BJT is internally connected to the base of the second BJT. The emitter of the second BJT acts as the "Emitter" pin of the pair. There are two types of Darlington pair: NPN and PNP. The parameterized generic Darlington pair also contains a diode connected between the collector and emitter pin as well as two base-emitter resistors, one across each BJT.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|is_bjt||bjt saturation current||A||1.0e-12||
|-
|bf_bjt||bjt forward beta||-||150||
|-
|nf_bjt||bjt forward emission coefficient||-||1||
|-
|ise_bjt||B-E leakage saturation current||A||0||
|-
|ne_bjt||B-E leakage emission coefficient||-||1||
|-
|br_bjt||ideal maximum reverse beta||-||1||
|-
|nr_bjt||reverse current emission coefficient||-||1||
|-
|isc_bjt||B-C leakage saturation current||A||0||
|-
|nc_bjt||B-C leakage emission coefficient||-||1||
|-
|rb_bjt||zero bias base resistance||Ohms||0||
|-
|irb_bjt||current where base resistance falls halfway to minimum value||A||inf||
|-
|rbm_bjt||minimum base resistance at high currents||ohms||0||
|-
|re_bjt||emitter resistance||Ohms||0||
|-
|rc_bjt||collector resistance||Ohms||0||
|-
|cje_bjt||B-E zero bias depletion capacitance||F||0||
|-
|vje_bjt||B-E built-in potential||V||0.75||
|-
|mje_bjt||B-E junction grading coefficient||-||0.33||
|-
|cjc_bjt||B-C zero bias depletion capacitance||F||0||
|-
|vjc_bjt||B-C built-in potential||V||0.75||
|-
|mjc_bjt||B-C junction exponential factor||-||0.33||
|-
|tf_bjt||ideal forward transit time||sec||0||
|-
|tr_bjt||ideal reverse transit time||sec||0||
|-
|is_d||diode saturation current||A||1.0e-12||
|-
|rs_d||diode resistance||Ohms||0||
|-
|n_d||diode emission coefficient||-||1||
|-
|cjo_d||diode junction capacitance||F||0||
|-
|vj_d||diode junction potential||V||1||
|-
|m_d||diode grading coefficient|| ||0.5||
|-
|tnom||parameter measurement temperature||deg C||27||
|-
|r1||first base-emitter resistance||Ohms||1k||
|-
|r2||second base-emitter resistance||Ohms||1k||
|-
|}

== DC Bias Sources Vcc, Vee, Vdd, Vss ==

[[File:GL12.png]]

These are simple 1-pin DC voltage sources. Vcc and Vdd provide a positive voltage, while Vee and Vss provide a negative voltage

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|vcc||bias voltage||V||+15||required
|-
|vee||bias voltage||V||-15||required
|-
|vdd||bias voltage||V||+15||required
|-
|vss||bias voltage||V||-15||required
|-
|}

==Digital-to-Analog Converter (DAC) Bridge==

[[File:GK43.png]]

The DAC Bridge takes a digital value from a digital node and can only be eiter "0", "1",
or "U". It then outputs the value "out_low", "out_high" or "out_udndef",
or ramps linearly toward one of these "final" values from its curent analog output level. This
ramping speed depends on the values of "t_rise" and "t_fall".

Model Identifier: dac_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> dac_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] dac_bridge

.model dac_bridge dac_bridge out_low = 0 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|out_undef||analog output for undefined digital input||V||0.5||required
|-
|input_load||capacitive input load||F||1p||
|-
|t_rise||L-to-H delay time||sec||1n||
|-
|t_fall||H-to-L delay time||sec||1n||
|-
|}

==Diode==

[[File:G9.png]]

Diodes allow current flow only in one direction, following their symbol's arrow, and thus can be used as simple solid
state switches in AC circuits.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process models can be either junction diodes or Schottky barrier diodes. Area factor scales the model parameters
IS, RS, CJO, and IBV. VD is the initial voltage, and TEMP is the overriding temperature. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||0||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|EG||activation energy||eV||1.11||
|-
|XTI||saturation current temp. exp.||-||3.0||
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||forward bias junction fit parameter||-||0.5||
|-
|BV||reverse breakdown voltage||V||inf||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|}

==Diode Bridge==

[[File:GK107.png]]

This four-pin device is a bridge configuration of four generic diodes.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||10p||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|BV||reverse breakdown voltage||V||1000||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|}

==Doubly Center-Tapped Ferrite Core Transformer==

[[File:GK98.png]]

This six-pin four-port device models a doubly center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of full-winding primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== DPDT Switch ==

[[File:GK74.png]]

This is an 8-pin device that models a double-pole double-throw switch. It has two input signals and four output pins. When the control voltage is at the high state, the first and second input voltages are transferred to the first and third output pins, respectively. When the control voltage is at the low state, the first and second input voltages are transferred to the second and fourth output pins, respectively.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== DPST Switch ==

[[File:GK73.png]]

This is a 6-pin device that models a double-pole single-throw switch. It has two input signals and two output signals. When the switch on, the first and second input voltages are transferred to the first and second output pins, respectively. When the switch is off, the output pin do not receive any input signals.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Ferrite Core Transformer==

[[File:GK95.png]]

This four-pin two-port device models a physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary turns||-||100||required
|-
|n_sec||number of secondary turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== FM Modulated Source ==

[[File:GL24.png]]

This is a voltage source with a single-tone frequency modulated waveform. The FM modulation index MDI is defined as the ratio of maximum frequency deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

==Frequency Meter==
[[File:G114.png]]

The Frequency Meter is a four-pin shunt device that is connected in parallel with an AC source just like a voltmeter and measures the operating frequency of the AC circuit. The input pins are connected across the AC source. The voltage across the output pins is equal to the frequency of the source in Hertz within a scale factor SF. Note that the Frequency Meter is designed to work with a single-tone AC source of unit amplitude. If the amplitude of the source is not one, multiply the SF parameter by the non-unit source amplitude value. The output voltage of the Frequency Meter can be used in conjunction with linear or nonlinear dependent sources to model frequency-dependent quantities.

Model Identifier: fmeter

Parameters:

The only parameter is the scale factor SF with a default value of 1.0. Set SF = 1e-6 to read out the frequency in MHz. Set SF = 1e-9 to read out the frequency in GHz. Set SF = 6.283185 (2*pi) to read out the angular frequency ω in radian/s.

== Fuse ==

[[File:GK76.png]]

This is a 2-pin interactive current-controlled switch. If the current passing through the fuse is less than a specified threshold current, the switch is closed. If the current exceeds the threshold level, the fuse breaks and remains open thereafter. The device's symbol changes to display its state.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|r||resistance when intact||Ohms||1.0||
|-
|i_thresh||threshold current||A||1.0||
|-
|}

==Ground==

[[File:G15.png]]

Ground has a voltage of zero (0) and is used as a reference to compute electrical values in the circuit.
All circuits <B>must</B> be grounded to be properly simulated. There is no limit on the number of grounds
you may use in a circuit. All components connected to ground are referenced to a common point and treated
as linked through ground.

==Hysteresis Block (XSPICE)==

[[File:G37.png]]

The Hysteresis block is a simple buffer stage that provides hysteresis of the output with respect to the
input. The in_low and in_high parameter values. The output values are limited to out_lower_limit and
out_upper_limit. The value of \93hyst\94 is added to the in_low and in_high points in order to specify the
points at which the slope of the hysteresis function would normally change abruptly as the input transitions
from a low to a high value. Likewise, the value of \93hyst\94 is subtracted from the in_high and in_low values
in order to specify the points at which the slope of the hysteresis function would normally change abruptly
as the input transitions from a high to a low value. In fact, the slope of the hysteresis function is
never allowed to change abruptly but is smoothly varied whenever the input_dowmain smoothing parameter
is set greater than zero.

Model Identifier: hyst

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> hyst {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 hysteresis_block

.model hysteresis_block hyst in_low = 0.0 in_high = 1.0

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default
|-
|In_low||input low value||0.0
|-
|in_high||input high value||1.0
|-
|hyst||hysteresis||0.1
|-
|out_lower_limit||output lower limit||0.0
|-
|out_upper_limit||output upper limit||1.0
|-
|input_domain||input smoothing domain||0.01
|-
|fraction||smoothing fraction/absolute value switch||true
|-
|}

==Ideal Center-Tapped Transformer with Push-Pull Input==

[[File:XFMR4.png]]

The ideal center-tapped transformer with push-pull input is a five-pin three-port device with two primary input ports and one secondary output port. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P1}{v_S} = \frac{v_P2}{v_S} = n </math>

where v<sub>S</sub> is the secondary voltage, v<sub>P1</sub> is measured between the top primary pin P1 and the center tap pin, and v<sub>P2</sub> is measured between the center tap pin and the bottom primary pin P2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P1</sub>/N<sub>S</sub> = N<sub>P2</sub>/N<sub>S</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Center-Tapped Transformer with Push-Pull Output==

[[File:XFMR3.png]]

The ideal center-tapped transformer with push-pull output is a five-pin three-port device with one primary input port and two secondary output ports. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P}{v_{S1}} = \frac{v_P}{v_{S2}} = n </math>

where v<sub>P</sub> is the primary voltage, v<sub>S1</sub> is measured between the top secondary pin S1 and the center tap pin, and v<sub>S2</sub> is measured between the center tap pin and the bottom secondary pin S2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S1</sub> = N<sub>P</sub>/N<sub>S2</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Diode==

[[File:GK106.png]]

This 2-pin device is a very basic and primitive model of a diode as a rectifier or switch. When the voltage across the device's terminals is positive, it acts as a short circuit. When the voltage across the device's terminals is negative, it acts as an open circuit.

Parameters:

None

==Ideal Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This is a very basic and primitive model of an operational amplifier. It has only one parameter, open loop gain with a default value of 50,000, which is adequate for most cases. The ideal Op-Amp device doesn't require any DC bias voltages.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|A||open loop gain||-||50,000||
|-
|}

==Ideal Transformer==

[[File:XFMR1.png]]

The ideal transformer is a four-pin two-port device with the following relationship between the voltages and currents at its primary and secondary ports:

<math> \frac{v_P}{v_S} = - \frac{i_S}{i_P} = \frac{N_P}{N_S} = n </math>

where v<sub>P</sub>, i<sub>P</sub>, N<sub>P</sub> are the primary voltage, current and number of turns, respectively, and v<sub>S</sub>, i<sub>S</sub>, N<sub>S</sub> are the secondary voltage, current and number of turns, respectively. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S</sub>, which represents the primary-to-secondary turns ratio. Note that the ideal transformer model is defined based on controlled sources and does not involve any magnetic physical parameters as opposed to mutual inductors or ferrite core transformer.

==Inductance Meter==

[[File:G37.png]]

The Inductance Meter measures the total inductance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total inductance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense an inductance value and alter their behavior based upon it. Care must be exercised when connecting an Inductance Meter to the inductors of a circuit. This is due to the fact that inductors are treated by SPICE as current sources. This can cause a problem when an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor.

Model Identifier: lmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> imeter {<gain = value>}

Example:

A1 1 2 inductance_meter

.model inductance_meter lmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Inductive Coupler Block==

[[File:GK99.png]]

The Inductive Coupler Block couples any two existing inductors. This block doesn't have any pins because it doesn't actually represent inductors, only the coupling between them. This is useful if you want to
couple two inductors that are in different parts of the circuit, or if you want to couple more than two inductors together. In the latter case, use more than one of these, with each one coupling a pair of inductors.

The standard parameters are Inductor1, Inductor2, and k. Inductor1 is the name of first inductor, Inductor2 is the name of the second inductor, and k is the coefficient of coupling, 0 < k ≤ 1.

==Inductive Coupling (XSPICE)==

[[File:G41.png]]

This function is a conceptual model which is used as a building block to create a wide variety of inductive and magnetic circuit models. This function is normally used in
conjunction with the “core” model, but it can also be used with resistors, hysteresis blocks, etc. to build up systems which mock the behavior of linear and nonlinear components.
The lcouple takes as an input (on the “l” port) a current. This current value is multiplied by the num_turns value, N, to produce an output value (a voltage value which appears on the
mmf_out port). The mmf_out acts similar to a magnetomotive force in a magnetic circuit;
when the lcouple is connected to the “core” model, or to some other resistive device, a current will flow. This current value (which is modulated by whatever the lcouple is
connected to) is then used by the lcouple to calculate a voltage “seen” at the “l” port. The voltage is a function of the derivative with respect to time of the current value seen at mmf_out.

The most common use for lcouple will be as a building block in the construction of transformer models. To create a transformer with a single input and a single output, you
would require two lcouple models plus one “core” model.

Example:

A1 (1 0) (2 3) lcouple1

.model lcouple1 lcouple ( num_turns = 10 )

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|num_turns||number of turns||-||1||required
|-
|}

==Inductor==

[[File:GK121.png]]

Inductors are used to store magnetic energy. An inductor's ability to counteract current changes passing through it is called its inductance (L), which is
measured in Henrys. In a (steady-state) DC analysis, the inductor acts like a short circuit. It is indeed treated as a current source, which can be problematic if an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor. The resistor may be of negligible value or one that accounts for the coil resistance of the inductor. In AC and transient analyses, the inductor develops a voltage across it in response to the changing magnetic
flux within its coil.

An inductor's transient behavior is described by the equation:

v(t) = L*(di(t)/dt)

The inductor's initial condition is optional. It is the initial value of the inductor current in Amperes that flows from node N+ through the inductor to node N-. The only time that the initial current matters is when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An inductor's AC behavior is described by the equation:

v = j ω * L * i

All inductor names must begin with L.

Netlist Format:

L<device_name> <N+> <N-> <value>

Example:

L1 1 2 10u

==Inductor with Ferrite Core==

[[File:GK94.png]]

This 2-pin device models a physical inductor with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. Unlike the standard inductor device, you do not specify an inductance value for the inductor with ferrite core. Rather, you specify physical parameters like cross sectional area, core length and number of turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_turns||number of turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== Insulated Gate Bipolar Transistor (IGBT)==

[[File:GK111.png]]

This is a 3-pin parameterized Insulated Gate Bipolar Transistor (IGBT) device with three pins: Collector(C), Gate (G), and Emitter (E). It is primarily used as a fast electronic switch. The IGBT combines the simple gate-drive characteristics of MOSFETs with the high-current and low-saturation-voltage capability of bipolar transistors. The device's model consists of an isolated gate FET for the control input, and a PNP bipolar power transistor as a switch. To further modify the internal device models, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|cap||parasitic capacitance||F||1n||
|-
|rg||gate resistance||Ohms||5||
|-
|re||emitter resistance||Ohms||0.05||
|-
|bf||pnp transistor forward beta||-||1||
|-
|vto||MOSFET threshold voltage||V||5||
|-
|kt||MOSFET transconductance||-||2.99||
|-
|cgso||MOSFET voltage gate-source overlap capacitance||F||5u||
|-
|nd||diode emission coefficient||-||50||
|-
|cjo||diode junction capacitance||F||1n||
|-
|}

==Interactive Switch==

[[File:GK75.png]]

This device is an interactive switch that can be closed or opened either directly from the Schematic Editor by clicking on its symbol or from the Instrument Panel.

==Junction Field Effect Transistor (JFET)==

[[File:G12.png]]

The JFET is the simplest transistor device and has three pins: gate, drain and source. The JFET defaults are based on the Shichman and Hodges FET model. This is a square-law device because of the expression relating the drain current to the gate-to-source voltage:
Idrain=*(VGS-Vthreshold)2. In real JFETs, near the saturation point, the drain currents vary with the drain voltages. This can be modeled by the following formula: Idrain=*(VGS-VTO)2*(1+*VDS), which yields an increasing
drain current for increasing values of VDS.

The gate-to-source and gate-to-drain junctions each have a nonlinear capacitor. The zero-bias capacitance value is selected for each junction.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process model parameters are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||threshold voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||ohms||0||100
|-
|RS||source ohmic resistance||ohms||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|IS||gate junction saturation current||A||1.0e-14||1.0e-14
|-
|B||doping tail parameter|| ||1||1.1
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

== Light Emitting Diode (LED) ==

[[File:GK114.png]]

This is a two-pin parameterized diode device that emits light of a certain wavelength when it is forward-biased.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rs||ohmic resistance||Ohms||10||
|-
|vj||junction potential||V||0.6||
|-
|cjo||zero bias junction capacitance||F||10p||
|-
|tt||transit time||sec||0.1n||
|-
|}

==Linear Current-Controlled Current Source (CCCS)==

[[File:G2.png]]

The CCCS is a current source whose current is directly proportional to the current across a controlling Ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the current gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the current gain.

Model Identifier: cccs

Netlist Format:

F<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

F1 1 0 V1 1.0

==Linear Current-Controlled Voltage Source (CCVS)==

[[File:G4.png]]

The CCVS is a voltage source whose voltage is directly proportional to the current through a controlling ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the trans-resistance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the trans-resistance gain.

Model Identifier: ccvs

Netlist Format:

H<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

H1 1 0 V1 1.0

==Linear Voltage-Controlled Current Source (VCCS)==

[[File:G3.png]]

The VCCS is a current source whose current is directly proportional to the voltage across a controlling voltmeter or the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the trans-conductance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the trans-conductance gain.

Model Identifier: vccs

Netlist Format:

G<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

G1 1 0 2 0 1.0

==Linear Voltage-Controlled Voltage Source (VCVS)==

[[File:G1.png]]

The VCVS is a voltage source whose voltage is directly proportional to the voltage across a controlling voltmeter of the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the voltage gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the voltage gain.

Model Identifier: vcvs

Netlist Format:

E<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

E1 1 0 2 0 1.0

==Lossless Transmission Line==

[[File:G21.png]]

The lossless transmission line is a four-pin two-port device that models only one propagating mode of an ideal transmission line. When using this SPICE model, should all four nodes of the actual circuit be distinct, two modes may be activated, and this device would be insufficient for that purpose. To circumvent this potential problem, two transmission line devices would be required. Due to the implementation details, you may produce more accurate simulation results with a lossy transmission line device with zero loss.

Optional initial condition parameters are the voltage and current at each of the transmission line ports.

The standard device parameters are Z0, TD, F, NL, IC, described below:

{| class="wikitable"
|-
|Z0||characteristic impedance
|-
|TD||transmission delay
|-
|F||frequency
|-
|NL||normalized electrical length of the transmission line with respect to the wavelength in the line at frequency F. (If F is specified, but NL is not, the default is 0.25.)
|-
|IC||initial condition (Specifies the voltage and current at each of the transmission line ports.)
|-
|}

==Lossy Transmission Line==

[[File:G22.png]]

The lossy transmission line is a four-pin two-port convolution model for uniform constant-parameter distributed lines. MNAME is the process model name, which
includes a set of pre-specified options as described below.

The device model [[parameters]] are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|R||resistance /length||Ohm /m||0.0||0.2
|-
|L||inductance/length||henrys/m||0.0||9.13e-9
|-
|C||capacitance/length||farads/m||0.0||3.65e-12
|-
|LEN||length of line||m||none||1.0
|-
|LININTERP||use linear interpolation||flag||not set||set
|-
|QUADINTERP||use quadratic interpolation||flag||not set||set
|-
|MIXEDINTERP||use linear when quadratic seems bad||flag||not set||set
|-
|COMPACTREL||special reltol for straight line checking||flag||RETOL||1.0e-3
|-
|COMPACTABS||special abstol for straight line checking||flag||ABSTOL||1.0e-9
|-
|NOCONTROL||don't do complex time control||flag||not set||set
|-
|STEPLIMIT||always limit timestep to 0.8*(delay of line)|| || ||
|-
|NOSTEPLIMIT||don't always limit timestep to 0.8*(delay of line)||flag||not set||set
|-
|TRUNCNR||use Newton-Raphson method for timestep calculation in LTRAtrunc||flag||not set||set
|-
|TRUNCDONTCUT||don't limit timestep to keep impulse-response errors low||flag||not set||set
|-
|}

<P CLASS="Normal-1">
The RLC (uniform transmission line with series loss only), RC (uniform RC line), LC (lossless transmission
line), and RG (distributed series resistance and parallel conductance only) lines have been implemented.
The length (LEN) must be given. COMPACTREL and COMPACTABS control the compaction of past history values
used in convolution. Larger values for these lower accuracy but improve speed. These are used with the
TRYTOCOMPACT option. </P>

==Magnetic Core (XSPICE)==

[[File:G42.png]]

This device is used as a building block to create a wide variety of inductive and magnetic circuit models. It is almost always to be used in conjunction with the "lcouple" model to build up systems which simulate the behavior of linear and nonlinear magnetic components. There are two fundamental modes of operation for the core model. These are the "PWL" mode (which is the default and most
likely to be of use to you) and the "Hysteresis" mode.

<b>PWL Mode (mode = 1)</b>

In the PWL mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf) value. This value is divided by the total effective length of the core to produce a value for the Magnetic Field Intensity, H, which is then used to find the corresponding Flux Density, B, using the piecewise linear relationship described by you in the H_array / B_array coordinate pairs. B is then multiplied by the cross-sectional area of the core to find the Flux value, which is output as a current. The pertinent mathematical equations are:

H = mmf / L, where L = Length (in apmere-turns/meter)

B = f(H)

Φ = B * A, where A = Area

The B value is derived from a piecewise linear transfer function described to the model by the H_array and B_array coordinate pairs. This transfer function does not include hysteretic effects; for that, you would need to substitute a HYST model for the core. The magnetic flux value Φ in turn is used by the "lcouple"
code model to obtain a value for the voltage reflected back across its terminals to the driving electrical circuit.

<b>Hysteresis Mode (mode = 2)</b>

In the Hysteresis mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf)
value. This value is used as input to the equivalent of a hysteresis code model block. The parameters
defining the input low and high values, the output low and high values, and the amount of hysteresis are
as in that model. The output from this mode, as in PWL mode, is a current value which is seen across the magnetic core port.

One final note to be made about the two core models is that certain parameters are specific to one or the other. In particular, the in_low, in_high, out_lower_limit, out_upper_limit, and hysteresis parameters are not available in PWL mode. Likewise, the H_array, B_array, area, ad length values are unavailable
in Hysteresis mode. The input_domain and fraction parameters are common to both modes (though their behavior is somewhat different; for explanation of the input_domain and fraction values for the Hysteresis mode, please refer to the Hysteresis Block discussion.

Model Identifier: core

Netlist Format:

A<device_name> <mc1 _pin> <mc2_pin> <model_name>

.model <model_name> core area = <value> length = <value> H_array = [<value1> <value2>] B_array = [<value1> <value2>]
{<param1 = value> < param2 = value> ...}

Example:

A1 1 2 core

.model core core area = 1 length = 1 H_array = [0 1] B_array = [0 1]

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|H_array||magnetic field array||[0 1]||required
|-
|B_array||flux density array||[0 1]||required
|-
|Area||cross-sectional area||1||required
|-
|Length||core length||1||required
|-
|Input_domain||input smoothing domain||0.01||
|-
|Fraction||smoothing fraction/abs switch||True||
|-
|Mode||mode switch (1=pwl, 2=hyst)||1||
|-
|In_low||input low value||0.0||
|-
|In_high||input high value||1.0||
|-
|Hyst||hysteresis||0.1||
|-
|Out_lower_limit||output lower limit||0.0||
|-
|Out_upper_limit||output upper limit||1.0||
|-
|}

==Marker==

[[File:G16.png]]

The marker serves several purposes:

* It can appear as a default plot in simulations if the "Voltage Probe" box is checked.

* It can be used to set the initial voltage or voltage guess at the node it is connected to.

* It can be used as a port for a subcircuit when you choose the checkbox labeled "Use as Subcircuit Port" is checked.

* It can be used to explicitly set a node number in place of the arbitrarily assigned node number by the program. In this case, make sure the "Set Node Index" box is checked. Otherwise, it will act as just a voltage probe.

* It can be used to connect different parts of a circuit in place of wires. To use markers as virtual connectors, place them at points where wires would otherwise connect. Then set the Part Title of the two (or more) markers to the same name, and they will act as a single circuit node.

==MESFET==

[[File:G14.png]]

The MESFET is a Schottky-barrier gate FET with six times greater electron mobility than silicon. MESFETs are important devices for creating high frequency circuits. They function by creating a potential barrier between the gate and the channel when the metal gate
contacts the gallium-arsenide substrate. Electron velocity saturates for fields approximately ten times lower than with silicon. The Curtice model includes linear and saturated operation.

The standard parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

All the MESFET process model parameters are described in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||pinch-off voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|B||doping tail extending parameter||1/V||0.3||0.3
|-
|ALPHA||saturation voltage parameter||1/V||2||2
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||Ohm||0||100
|-
|RS||source ohmic resistance||Ohm||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula||-||0.5||
|-
|}

==MOSFET==

[[File:G13.png]]

The MOSFET is an active device that has up to 4 pins. The three standard pins are gate, drain, and source. These are given in the default symbol. The bulk node, which is grounded by default, is the fourth pin. The MOSFET with the bulk is named mos_n_lvl1_4 (the lvl1 is for level 1, the n for nmos, and the 4 for 4 pins.)

The standard [[parameters]] are L, W, AD, AS, PD, PS, NRD, NRS, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|L||channel length, in meters
|-
|W||channel width, in meters
|-
|AD,AS||areas of the drain and source diffusions, in meters2
|-
|PD,PS||perimeters of drain and source junctions, in meters(They default to 0.0.)
|-
|NRD,NRS||equivalent number of squares of the drain and source diffusions (These values multiply the sheet resistance for an accurate representation of parasitic series drain and source resistance of each transistor. The default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

There are five different default models: square-law I-V characteristic, analytical, semi-empirical, and BSIM and BSIM2 (Berkeley Short-channel IGFET Model), which include second-order effects such as channel-length
modulation, subthreshold conduction, scattering-limited velocity saturation, small-size effects, and charge-controlled capacitance. The process parameter LEVEL specifies which of the models is chosen as indicated below:

{| class="wikitable"
|-
|LEVEL 1||Schichman-Hodges
|-
|LEVEL 2||MOS2
|-
|LEVEL 3||MOS3
|-
|LEVEL 4||BSIM
|-
|LEVEL 5||BSIM2
|-
|LEVEL 6||MOS6
|-
|}

The process model [[parameters]] for levels 1,2,3, and 6 are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|LEVEL||model index|| ||1||
|-
|VTO||zero-bias threshold voltage||V||0.0||1.0
|-
|KP||transconductance parameter||A/V2||2e-5||3.1e-5
|-
|GAMMA||bulk threshold parameter||V1/2||0.0||0.37
|-
|PHI||surface potential||V||0.6||0.65
|-
|LAMBDA||channel-length modulation (level 1 & 2 only)||1/V||0.0||0.02
|-
|RD||drain ohmic resistance||ohms||0.0||1.0
|-
|RS||source ohmic resistance||ohms||0.0||1.0
|-
|CBD||zero-bias B-D junction capacitance||F||0.0||20fF
|-
|CBS||zero-bias B-S junction capacitance||F||0.0||20fF
|-
|IS||bulk junction saturation current||A||1.0e-14||1.0e-15
|-
|PB||bulk junction potential||V||0.8||0.87
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m||0.0||2e-10
|-
|RSH||drain & source diffusion sheet resistance||ohm/area||0.0||10.0
|-
|CJ||zero-bias bulk junction bottom capacitance per meter2 junction area||F/m2||0.0||2e-4
|-
|MJ||bulk junction bottom grading coefficient|| ||0.5||0.5
|-
|CJSW||zero-bias bulk junction sidewall capacitance per meter junction perimeter||F/m||0.0||1.0e-9
|-
|MJSW||bulk junction sidewall grading coefficient|| ||0.5, 0.33 (level1), (level2,3)||
|-
|JS||bulk junction saturation current per meter2 of junction area||A/m2|| ||1.0e-8
|-
|TOX||oxide thickness||meter||1.0e-7||1.0e-7
|-
|NSUB||substrate doping||1/cm3||0.0||4.0e15
|-
|NSS||surface state density||1/cm2||0.0||1.0e10
|-
|NFS||fast surface state density||1/cm2||0.0||1.0e10
|-
|TPG||type gate material(+1 if opp. substrate, 0 if A1 gate, -1 if same as substrate)|| ||1.0||
|-
|XJ||metallurgical junction depth||meter||0.0||1
|-
|LD||lateral diffusion||meter||0.0||0.8
|-
|UO||surface mobility||cm2/Vs||600||700
|-
|UCRIT||critical field for mobility degradation (level2 only)||V/cm||1.0e4||1.0e4
|-
|UEXP||critical field exponent in mobility degradation (level2 only)|| ||0.0||0.1
|-
|UTRA||transverse field coefficient (deleted for level2)|| ||0.0||0.3
|-
|VMAX||maximum drift velocity of carriers||m/s||0.0||5.0e4
|-
|NEFF||total channel-charge (fixed and mobile) coefficient (level2 only)|| ||1.0||5.0
|-
|KF||flicker noise coefficient|| ||0.0||1.0e-26
|-
|AF||flicker noise exponent|| ||1.0||1.2
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|DELTA||width effect on threshold voltage (level2,3)|| ||0.0||1.0
|-
|THETA||mobility modulation (level3 only)||1/V||0.0||0.1
|-
|ETA||static feedback (level3 only)|| ||0.0||1.0
|-
|KAPPA||saturation field factor (level3 only)|| ||0.2||0.5
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

The BSIM model has no default parameters, and leaving one out is considered an error. The additional process model parameters for level 4 and 5 models are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS
|-
|VFB||flat-band voltage||V
|-
|PHI||surface inversion potential||V
|-
|K1||body effect coefficient||V1/2
|-
|K2||drain/source depletion charge-sharing coefficient||
|-
|ETA||zero-bias drain-induced barrier-lowering coefficient||
|-
|MUZ||zero-bias mobility||cm2/V-s
|-
|DL||shortening of channel||m
|-
|DW||narrowing of channel||m
|-
|U0||zero-bias transverse-field mobility degradation coefficient||V-1
|-
|U1||zero-bias velocity saturation coefficient||m/V
|-
|X2MZ||sens. of mobility to substrate bias at Vds=0||cm2/V2-s
|-
|X2E||sens. of drain-induced barrier lowering effect to substrate bias||V-1
|-
|X3E||sens. of drain-induced barrier lowering effect to drain bias at Vds= Vdd||V-1
|-
|X2U0||sens. of transverse field mobility degradation to substrate bias||V-2
|-
|X2U1||sens. of velocity saturation effect to substrate bias||mV-2
|-
|MUS||mobility at zero substrate bias and at Vds= Vdd||cm2/V2-s
|-
|X2MS||sens. of mobility to substrate bias at Vds= Vdd||cm2/V2-s
|-
|X3MS||sens. of mobility to drain bias at Vds= Vdd||cm2/V2-s
|-
|X3U1||sens. of velocity saturation effect on drain bias at Vds= Vdd||mV-2
|-
|TOX||gate oxide thickness||m
|-
|TEMP||temperature at which [[parameters]] were measured||deg. C
|-
|VDD||measurement bias range||V
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m
|-
|XPART||gate-oxide capacitance-charge model flag||
|-
|N0||zero-bias subthreshold slope coefficient||
|-
|NB||sens. of subthreshold slope to substrate bias||
|-
|ND||sens. of subthreshold slope to drain bias||
|-
|RSH||drain and source diffusion sheet resistance||ohms/area
|-
|JS||source drain junction current density||A/m2
|-
|PB||built-in potential of source drain junction||V
|-
|MJ||grading coefficient of source drain junction||
|-
|PBSW||built-in potential of source drain junction sidewall||V
|-
|MJSW||grading coefficient of source drain junction sidewall||
|-
|CJ||source drain junction capacitance per unit area||F/ m2
|-
|CJSW||source drain junction sidewall capacitance per unit length||F/m
|-
|WDF||source drain junction default width||m
|-
|DELL||source drain junction length reduction||m
|-
|}

XPART=0 selects a 40/60 drain/source charge partition; XPART=1 selects a 0/100 partition.

==Mutual Inductors==

[[File:GK100.png]]

The mutual inductors device is a pair of inductors that are coupled to each other. L1 and L2 are the names of two inductors. You have to specify the inductance of inductor L1, the inductance of inductor L2, the initial current through each, and the coupling coefficient k, 0 ≤ k ≤ 1. The mutual inductance M expressed in units of H can be calculated using the following definition:

<math> k = \frac{M}{\sqrt{L_1 L_2}} </math>

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|inductance1||inductance of inductor 1||H||1||
|-
|inductance2||inductance of inductor 2||H||1||
|-
|ic1||initial current through inductor 1||A||0||
|-
|ic2||initial current through inductor 2||A||0||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Non-Ideal Current Transformer==

[[File:GK104.png]]

This 8-pin device models a non-ideal lossy current transformer. Its model consists of an ideal transformer with more secondary turns than primary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. on each side of the internal ideal transformer, there is a series leakage inductance LL<sub>k</sub>, followed by a shunt winding capacitance CW<sub>k</sub> and a series winding resistance RW<sub>k</sub>, which connects to the exterior positive pin on that side. The inter-winding resistance R<sub>12</sub> is connected across the negative pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||secondary-to-primary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary leakage inductance||H||1m||
|-
|ll2||secondary leakage inductance||H||1m||
|-
|cw1||primary winding capacitance||F||1p||
|-
|cw2||secondary winding capacitance||F||1p||
|-
|r12||inter-winding resistance||Ohms||10Meg||
|-
|}

==Non-Ideal Diode==

[[File:G9.png]]

This 2-pin device is a basic simplified model of a diode as a rectifier or switch. When forward-biased, it acts as a low-valued voltage source. When reverse-biased, it acts as an open circuit until the reverse voltage exceeds the specified breakdown voltage. Then it acts as a high-valued voltage source of the reverse polarity.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|vf||forward drop voltage||V||0.5||required
|-
|vr||reverse breakdown voltage||V||100||required
|-
|}

==Non-Ideal Voltage Transformer==

[[File:GK103.png]]

This 8-pin device models a non-ideal lossy voltage transformer. Its model consists of an ideal transformer with more primary turns than secondary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. There are series combinations of a winding resistance RW<sub>k</sub> and a leakage inductance LL<sub>k</sub> on the primary and secondary sides. These are connected between the positive interior and exterior pins on each side. There are also two shunt branches at the inputs of the primary and secondary sides (connected between the positive and negative exterior pins), each consisting of a distributed turn-to-turn winding resistance RDC<sub>k</sub> in series with a distributed turn-to-turn winding capacitance CW<sub>k</sub>. The inter-winding capacitance CWW<sub>12</sub> is connected across the positive pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||primary-to-secondary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary winding leakage inductance||H||1m||
|-
|ll2||secondary winding leakage inductance||H||1m||
|-
|rdc1||primary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw1||primary distributed turn-to-turn winding capacitance||F||1p||
|-
|rdc2||secondary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw2||secondary distributed turn-to-turn winding capacitance||F||1p||
|-
|cww12||inter-winding capacitance||F||1p||
|-
|}

==Nonlinear Capacitor==

[[File:GK89.png]]

The nonlinear capacitor model allows the capacitor to be described by an arbitrary relationship between the capacitor's charge Q and the voltage V across the capacitor. In other words, Q = f(V). The nonlinear capacitance is then defined as C(V) = dQ/dV. You need to define the charge Q by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ C_DEF } * v(pos,neg)

which implies a linear capacitor, where Q = C<sub>DEF</sub> V. Therefore, C = C(V) = dQ/dV = C<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|C_DEF||default capacitance||F||1||
|-
|}

==Nonlinear Conductor==

[[File:GK88.png]]

The nonlinear conductor model allows the conductor to be described by an arbitrary relationship between the conductor's current I and the voltage V across the conductor. In other words, I = f(V). The nonlinear conductance is then defined as G(V) = dI/dV. You need to define the current I by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ G_DEF } * v(pos,neg)

which implies a linear conductor, where I = G<sub>DEF</sub> V. Therefore, G = G(V) = dI/dV = G<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|G_DEF||default capacitance||S||1||
|-
|}

==Nonlinear Dependent Sources==

[[File:G18.png]]

Nonlinear dependent (arbitrary) sources use an equation or mathematical expression to describe their behavior. One and only one of the two forms: V=<expr> or I=<expr> must be given.

Netlist Format:

B<device_name> v = <expression>

B<device_name> i = <expression>

Examples:

v = I(v1) + 3* I(v2)

I = v(i1) + 3* v(2) + 5 * v(3) ^2

The first example is a current-controlled voltage source. The v on the left side of the equation
indicates that it is a voltage source. I(v1) and I(v2) are the currents through voltage sources named v1 and v2, respectively.

The second example is a voltage-controlled current source. v(2) and v(3) represents the voltages at nodes 2 and 3, respectively, and v(i1) represents the voltage across a current source named i1.

The following mathematical functions defined for real variables can be used in the expressions:

abs(x), acos(x), acosh(x), asin(x), asinh(x), atan(x), atanh(x), cos(x), cosh(x), exp(x), ln(x), log(x), max(x,y), min(x,y), pwr(x,y), pwrs(x,y), sgn(x), sin(x), sinh(x), sqrt(x), tan(x), tanh(x), u(x), uramp(x).

The function "sgn" is the signum function and its value is 1 if the argument is positive or zero and -1 if the argument is negative.
The function "u(x)" is the unit step and "uramp(x)" is the integral of the unit step. The
unit step is one if its argument is greater than zero and zero if its argument is less than zero. The
ramp function (uramp) is 0 for argument values less than zero and equal to the argument for argument values
greater than zero.

The following operators are permissible: +, -, *, /, ^, and unary-.

To get time into an expression, integrate the current from a constant current source with a capacitor
and use the voltage across the capacitor.

==Nonlinear Inductor==

[[File:GK90.png]]

The nonlinear inductor model allows the inductor to be described by an arbitrary relationship between the inductor's magnetic flux Φ and the current I flowing through the inductor . In other words, Φ = f(I). The nonlinear inductance is then defined as L(I) = dΦ/dI. You need to define the flux Φ by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ L_DEF } * i(vx)

which implies a linear inductor, where Φ = L<sub>DEF</sub> I. Therefore, L = L(I) = dΦ/dI = L<sub>DEF</sub>.

Another example is 1e-4*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|L_DEF||default inductance||H||1||
|-
|}

==Nonlinear Resistor==

[[File:GK87.png]]

The nonlinear resistor model allows the resistor to be described by an arbitrary relationship between the voltage V across the resistor and its current I. In other words, V = f(I). The nonlinear resistance is then defined as R(I) = dV/dI. You need to define the voltage V by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ R_DEF } * i(vx)

which implies a linear resistor, where V = R<sub>DEF</sub> I. Therefore, R = R(I) = dV/dI = R<sub>DEF</sub>.

Another example is 10*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R_DEF||default resistance||Ω||1||
|-
|}

==Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This three-pin device models a parameterized operational amplifier with a very high voltage gain, a very high input impedance and a very low output impedance. The behavioral model of the parameterized Op-Amp device is based on the algorithm found in the book <B>Macromodeling with Spice</B>,
authored by Connelly & Choi, published by Prentice Hall. The default parameters are those of the 741 Op-Amp. This device doesn't require external DC bias voltage sources. Its positive and negative DC bias voltages are specified as its parameters. Sometimes the simulation doesn't converge if there is no DC path from the output of the Op-Amp to the ground.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|r_in_dm||differential mode input resistance||Ohms||2Meg||
|-
|r_in_cm||common mode input resistance||Ohms||2G||
|-
|Avd0||differential mode DC gain||dB||106||
|-
|CMRR||common mode rejection ratio||dB||90||
|-
|r_out||output resistance||Ohms||75||
|-
|c_in||input capacitance||F||1.4p||
|-
|ios||input offset current||A||20n||
|-
|ib||input bias current||A||80n||
|-
|vio||input offset voltage||V||1m||
|-
|slew_pos||positive slew rate||V/s||0.5e6||
|-
|slew_neg||negative slew rate||V/s||0.5e6||
|-
|curr_src_max||maximum output source current||A||25m||
|-
|curr_sink_||maximum output sink current||A25m||
|-
|fp1||dominant pole frequency||Hz||5||
|-
|fp2||second pole frequency||Hz||2Meg||
|-
|fp3||third pole frequency||Hz||20Meg||
|-
|fp4||fourth pole frequency||Hz||100Meg||
|-
|fz||first zero frequency||Hz||5Meg||
|-
|vcc_pos||positive dc voltage source||V||12||
|-
|vcc_neg||negative dc voltage source||V||12||
|-
|}

== Optocoupler ==

[[File:GK115.png]]

This is a five-pin parameterized optocoupler device. Its model consists of an ideal diode device in series with an Ohmic resistance connected between the Anode (A) and Cathode (K) pins together with a bipolar junction transistor device with three accessible pins, Collector (C), Base (B) and Emitter (E). A current-controlled current source is connected between base and collector of the BJT, whose current is controlled by the current passing through the diode. The proportionality constant is twice the specified value of the current transfer ratio (ctr) parameter.

You can change or enhance the models of the diode and BJT by adding more parameters. To do so, you have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ctr||current transfer ratio||-||0.5||
|-
|rd||diode ohmic resistance||Ohms||0.1||
|-
|}

== Overtone Crystal ==

[[File:GK79.png]]

This is a 2-pin parameterized overtone crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|LM||fundamental motional inductance||H||250m||
|-
|CM1||fundamental motional capacitance||F||10f||
|-
|RM1||fundamental motional resistance||Ohms||20||
|-
|RM3||3rd overtone motional resistance||Ohms||50||
|-
|RM5||5th overtone motional resistance||Ohms||100||
|-
|RM7||7th overtone motional resistance||Ohms||150||
|-
|C0||shunt capacitance||F||3p||
|-
|}

== Photodiode ==

[[File:GK113.png]]

This is a 4-pin parameterized photodiode device. A pair of pins, Anode (A) and Cathode (K), represent the physical terminals of the photodiode. The photodiode model connected between the anode and cathode pins consists of the parallel connection of an ideal diode, a dark current source, a noise current source, a current-controlled current source, a diode capacitance, a shunt resistance altogether with a series resistance.

Another pair of pins IS+ and IS- act as an ammeter that must be inserted in a control circuit. The current passing through this ammeter controls the current of the photodiode. The default proportionality constant is unity. The controlling current is typically a function of light intensity incident on the surface of the photodiode.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|id||dark current||A||1n||
|-
|ir||noise current||A||1p||
|-
|cd||diode capacitance||F||10p||
|-
|rs||series resistance||Ohms||1m||
|-
|rp||parallel resistance||Ohms||1Meg||
|-
|}

==Piecewise Linear (PWL) Controlled Source==

[[File:GL49.png]]

The Piecewise Linear (PWL) Controlled Source is a single-input and single-output function generator whose output is not necessarily
linear for all input values. Instead, it follows an I/O relationship that is specified by the x_array and y_array coordinates. The x_array and y_array values represent vectors of coordinate points on the x and y axes, respectively. The x_array values are progressively increasing input coordinate points, and the associated y_array values represent the outputs at those points. There may be as few as two pairs specified, or as many as memory and simulation speed allow.

In order to fully specify outputs for values of Vin outside of the bounds of the PWL function, the PWL
controlled source model extends the slope found between the lowest two coordinate pairs and the highest
two coordinate pairs. This has the effect of making the transfer function completely linear for Vin
less than x_array[0] and Vin greater than x_array[n]. It also has the potentially subtle effect of unrealistically
causing an output to reach a very large or small value for large inputs. You should thus keep in mind
that the PWL Source does not inherently provide a limiting capability.

In order to diminish the potential for divergence of simulations when using the PWL block, a form
of smoothing around the x_array and y_array coordinate points is necessary. This is due to the iterative
nature of the simulator and its reliance on smooth first derivatives of transfer functions in order to
arrive at a matrix solution. Consequently, the two parameters "input_domain" and "fraction" are included
to allow you some control over the amount and nature o the smoothing performed.

Fraction is a switch that is either TRUE or FALSE. When TRUE (the default setting), the simulator assumes
that the specified input_domain value is to be interpreted as a fractional figure. Otherwise, it is interpreted
as an absolute value. Thus, if fraction = TRUE and input_domain = 0.10, the simulator assumes that the smoothing
radius about each coordinate point is to be set equal to 10% of the length of either the x_array segment
above each coordinate point, or the x_array segment below each coordinate point. The specific segment
length chosen will be the smallest of these two for each coordinate point.

If fraction = FALSE and input_domain = 0.10, then the simulator will begin smoothing the transfer function at 0.10
volts (or amperes) below each x_array coordinate and will continue the smoothing process for another 0.10
volts (or amperes) above each x_array coordinate point.

Model Identifier: pwl

Netlist Format:

A<device_name> %vd(<in_pin> <in_ref_pin>) %vd(<out_pin> <out_ref_pin>) <model_name>

.model <model_name> pwl x_array = [<value1> <value2> ...] y_array = [<value1>
<value2> ...] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(2 3) %vd(1 4) pwl
.model pwl pwl x_array = [0 1] y_array = [0 1]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|x_array||x-element array||V||[0 1]||required
|-
|y_array||y-element array||V||[0 1]||required
|-
|input_domain||input smoothing domain||-||0.01||
|-
|fraction||smoothing %/abs switch||-||True||
|-
|}

== PM Modulated Source ==

[[File:GL25.png]]

This is a voltage source with a single-tone phase modulated waveform. The PM modulation index MDI is defined as the ratio of maximum phase deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Potentiometer ==

[[File:GK77.png]]

This is a 3-pin device that models a potentiometer with options for either linear or logarithmic resistance. position = 0 corresponds to the wiper being at the extreme left and position = 1 corresponds to the wiper being at the extreme right. With the default position = 0.5 corresponding to the midpoint, this device functions as a one-half voltage divider.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|position||position of wiper connection||-||0.5||Must be between 0.0 and 1.0.
|-
|log||log-linear switch||-||False||Select False for linear and True for logarithmic.
|-
|r||total resistance||Ohms||0.1u||
|-
|log_multiplier||multiplier constant for log resistance||-||1.0||
|-
|}

== Programmable Unijunction Transistor (PUT)==

[[File:GK112.png]]

This is a 3-pin parameterized Programmable Unijunction Transistor (PUT) device with three pins: Base 1 (B1), Base 2 (B2) and Emitter (E). It is biased with a positive voltage between the two bases. This device has a unique characteristic that when it is triggered, its emitter current increases regeneratively until it is restricted by emitter power supply. It exhibits a negative resistance characteristic and so it can be employed as an oscillator. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To change these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|eta||-||-||0.6||
|-
|rbb||total base-to-base resistance||Ohms||40k||
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

==Random Resistor==

[[File:GK93.png]]

The random resistor device models a resistor whose resistance is a random number between 0 and a maximum specified value.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|max_val||maximum resistance value||Ω||1k||
|-
|}

==Real Capacitor==

[[File:GK117.png]]

This is primarily a non-ideal, temperature-dependent capacitor model. You can access it from the Parts Menu as '''User-Defined Capacitor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent capacitance is computed using the quadratic equation:

C(T) = C(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance and a series inductance together with the capacitor, all in parallel with a shunt resistance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Resr||series resistance||Ω||10||
|-
|Ls||inductance||H||1p||
|-
|C||capacitance||F||1n||
|-
|Rp||parallel resistance||Ω||1G||
|-
|ic||voltage initial condition||V||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||F/°C||0.1||
|-
|tc2||second-order temperature coefficient||F/°C<sup>2</sup>||0.01||
|-
|}

==Real Inductor==

[[File:GK118.png]]

This is primarily a non-ideal inductor model. You can access it from the Parts Menu as '''User-Defined Inductor'''. Its series resistor has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance together with the inductor, and the combination in parallel with a shunt capacitance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Rdc||series resistance||Ω||10||
|-
|L||inductance||H||1||
|-
|Cp||capacitance||F||1p||
|-
|ic||current initial condition||A||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Real Resistor==

[[File:GK116.png]]

This is primarily a non-ideal, temperature-dependent resistor model. You can access it from the Parts Menu as '''User-Defined Resistor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series inductance together with the resistor.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R||resistance||Ω||1k||
|-
|Ls||inductance||H||1n||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Resistor==

[[File:GK119.png]]

Resistors are passive devices that dissipate power. Their resistance value varies depending on how much power they can dissipate and is measured
in Ohms. The transient, DC and AC behaviors of a resistor are all described by the same equation:

v = R * i

where v is the voltage across the resistor, i is the current passing through the resistor, and R is the resistance. The value of R must be nonzero.

All resistor names must begin with R.

Netlist Format:

R<device_name> <N+> <N-> <value>

Example:

R1 1 2 1k

[[RF.Spice A/D]] provides three types of resistor: Simple, User-Defined (Real Resistor) and Semiconductor. The resistance of the simple resistor is a single value expressed in Ohms. You can also set the Monte Carlo tolerance for this resistor.

==Schottky Diode==

[[File:GK80.png]]

The Schottky diode has the same model as the generic diode with a nonzero transit time (tt), a nonzero junction capacitance (cjo) and a typically larger saturation current (is), a lower junction potential (vj) and a smaller grading coefficient (m).

==Semiconducting Capacitor==

[[File:GK83.png]]

This is the more general form of the Capacitor model and allows for the calculation of the actual capacitance value from strictly geometric information and the specifications of the process.

General Form:

CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>

If VALUE is specified, it defines the capacitance. If MNAME is specified, then the capacitance is calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. Either VALUE or MNAME, LENGTH, and WIDTH may be specified, but not both sets. The optional initial condition "IC" is the initial voltage across the capacitor for transient simulations.

The capacitance is computed as:

CAP = CJ * (LENGTH - NARROW) * (WIDTH - NARROW)+ 2 * CJSW * (LENGTH + WIDTH - 2NARROW) * CAP

To modify the model parameters, first double click on the capacitor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit CJ, CJSW, NARROW, DEFW, and CAP.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CJ||junction bottom capacitance||F/m<sup>2</sup>||-||
|-
|CJSW||junction sidewall capacitance||F/m ||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|CAP||nominal capacitance for Monte Carlo simulation||F||1||
|-
|}

== Semiconductor Resistor ==

[[File:GK82.png]]

This is the more general form of the resistor model and allows for the modeling of temperature effects and for the calculation of the actual resistance value from strictly geometric information and the specifications of the process.

General Form:

RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>

If VALUE is specified, it overrides the geometric information and defines the resistance. If MNAME is specified, then the resistance may be calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. The (optional) TEMP value is the temperature at which this device is to operate, and overrides the temperature specification in the SPICE Options Dialog.

The resistance is computed as:

R(T0) = (RSH) * [(L - NARROW) / (W - NARROW)] * RES

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

To modify the model parameters, first double click on the resistor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit TC1, TC2, RSH, RES, etc.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|TC1||first order temperature coefficient||Ω/°C||-||
|-
|TC2||second order temperature coefficient||Ω/°C<sup>2</sup>||-||
|-
|RSH||sheet resistance||Ω/sq||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|TNOM||the parameter measurement temperature||deg C ||27||
|-
|RES||resistance multiplier for Monte Carlo simulation||Ohms||1||
|-
|}

== Silicon-Controlled Rectifier (SCR)==

[[File:GK109.png]]

This is a 3-pin parameterized Silicon-Controlled Rectifier (SCR) device with three pins: Anode (A), Cathode (K) and Gate (G). It is a unidirectional device which can conduct current only in one direction. The SCR can be triggered only by a positive current going into its gate. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

== SPDT Switch ==

[[File:GK72.png]]

This is a 5-pin device that models a single-pole double-throw switch. The input voltage is transferred to the first output pin if the control voltage is at a high state. Otherwise, its is transferred to the second output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== SPST Switch ==

[[File:GK71.png]]

This is a 4-pin device that models a single-pole single-throw switch. It is virtually equivalent of the standard voltage-controlled switch.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Tabulated Conductor==

[[File:GK92.png]]

The tabulated conductor model allows the conductance to be described by a table relating the device's current i(t) to its terminal voltage v(t). In effect, the conductance is defined as G = di(t)/dv(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (v,i) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tabulated Resistor==

[[File:GK91.png]]

The tabulated resistor model allows the resistance to be described by a table relating the device's terminal voltage v(t) to its current i(t). In effect, the resistance is defined as R = dv(t)/di(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (i,v) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tapped Inductor==

[[File:GK101.png]]

This 3-pin device models a tapped inductor with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lt||total inductance||H||1m||
|-
|ratio||ratio of number of turns between positive terminal and tap to total number of turns||-||0.5||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

== Temperature-Dependent Current Source ==

[[File:GL14.png]]

This is a current source whose current is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

== Temperature-Dependent Voltage Source ==

[[File:GL13.png]]

This is a voltage source whose voltage is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

==Thermometer==
[[File:G115.png]]

The Thermometer is a two-pin device that measures the operating temperature of a circuit. The voltage across the device pins is equal to SPICE's operating temperature in degrees centigrade. The output voltage of the Thermometer can be used in conjunction with linear or nonlinear dependent sources to model temperature-dependent quantities.

Model Identifier: thermo

Parameters:

This device has no parameters.

== Triac Thyristor ==

[[File:GK110.png]]

This is a 3-pin bidirectional thyristor device that conducts current in either direction when triggered. A thyristor is analogous to a relay in that a small voltage and current can control a much larger voltage and current. The triac has two anode pins termed Main Terminal 1 (MT1) and Main Terminal 2 (MT2) and a Gate (G) pin. In order to create a triggering current for a triac, either a positive or negative voltage can be applied to the gate. Once triggered, the thyristor continues to conduct, even if the gate current ceases, until the main current drops below a certain level called the holding current. The device's model involves two NPN BJT transistors and two PNP BJT transistors. The forward beta parameters of the NPN and PNP transistors are set equal to 20 and 5, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|bvf||breakdown voltage of forward diodes||V||100||
|-
|rh||resistance controlling reverse holding current||Ohms||100||
|-
|rgp||resistance controlling forward holding current and trigger current||Ohms||50||
|-
|}

==Uniform RC Transmission Line==

[[File:G23.png]]

The standard parameters are L, and N. They are described below:

Two of the nodes are the element nodes connected by the RC line. The third is the node to which the capacitances
are connected. L is the length of the RC line in meters. N is the number of lumped segments to use in
modeling the RC line.

This device is derived from a model proposed by Gertzberrg. It expands the URC line into a network of
lumped RC segments with internally generated nodes. These segments increase toward the middle of the
URC line in a geometric progression with K as the proportionality constant.

The URC line is made up entirely of resistor and capacitor segments, unless the ISPERL parameter has a
non-zero value. In this case, capacitors are replaced by reverse biased diodes with an equivalent zero-bias
junction capacitance, a saturation current of ISPERL amps per meter of transmission line, and optional
series resistance of RSPERL ohms per meter.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|K||propagation constant||-||2||1.2
|-
|FMAX||maximum frequency of interest||Hz||1.0G||6.5Meg
|-
|RPERL||resistance per unit length||Ohm /m||1000||10
|-
|CPERL||capacitance per unit length||F/m||1.0e-15||1pF
|-
|ISPERL||saturation current per unit length||A/m||0||-
|-
|RSPERL||diode resistance per unit length||Ohm/m||0||-
|-
|}

==Varactor Diode==

[[File:GK81.png]]

A varactor diode is a combination of the generic diode with additional package inductance, package capacitance and a series resistance. This diode device has a typically large value of junction capacitance (cjo).

Parameters (in addition to standard diode parameters):

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|q||quality factor||-||5000||
|-
|f0||frequency of Q-factor specification||Hz||50Meg||
|-
|ls||package inductance||H||0.5n||
|-
|cp||package capacitance ||F||0.05p||
|-
|}

==Voltage-Controlled Capacitor==

[[File:GK85.png]]

This 3-pin device models a voltage-controlled two-terminal capacitor whose capacitance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in F/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_C||conversion factor||F/V||1.0||
|-
|}

==Voltage-Controlled Inductor==

[[File:GK86.png]]

This 3-pin device models a voltage-controlled two-terminal inductor whose inductance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in H/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_L||conversion factor||H/V||1.0||
|-
|}

==Voltage-Controlled Resistor==

[[File:GK84.png]]

This 3-pin device models a voltage-controlled two-terminal resistor whose resistance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in Ω/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_r||conversion factor||Ω/V||1.0||
|-
|}

==Voltage-Controlled Switch==

[[File:G19.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Voltage-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Voltmeter or controlling voltage nodes, as well as the turn-on and turn-off voltages in Volts and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the rest of [[parameters]]. When the voltage across the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the voltage across the switch or controlling device is less than or equal to the turn off current, the switch opens.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|V_ON||turn-on voltage||V||0.5||
|-
|V_OFF||turn-off voltage||V||0.0||
|-
|RON||on resistance||Ohms||1.0||
|-
|ROFF||off resistance||Ohms||1G||
|-
|}

==Voltage Noise Source==

[[File:GL15.png]]

This is a voltage noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the parameters of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise voltage||V/√Hz||1n||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Voltage Source==

[[File:G17A.png]]

A voltage source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a voltage source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset voltage. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==XSpice Devices and their models==

XSpice devices have the following form:
<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 4pt 0pt 1px 0pt ; font-family: 02070309020205020404,sans-serif; ">
A<device_name> <node1> <node2> ... <model_name></P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., A2 1 2 transfer_function

Note that XSpice devices must start with the "A" designation, much as a resistor starts with
an "R". Some devices will have grouped (or vector) pins and are designated by being placed
inside square brackets. In the example shown below, the 1 and 2 pins are grouped. Pin 3 is not. </P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 [1 2] 3 summer </P>

Some models will have voltage differential pairs of pins and will be denoted by a %vd( ). In the following
example pins 1 and 4 are differential pairs, as well as pins 2 and 3. Differential pairs must go between
parentheses ().

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 %vd(1 4) %vd(2 3) triangle </P>

Refer to individual devices for more information.

Each XSpice device will also have a model associated with it. Each model will have the following form:

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
.model <model_name> <model_identifier> {<pname1 = pval1>} {<pname2 = pval2>}
...</P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., .model transfer_function s_xfer in_offset = 0.0 gain = 1.0</P>

Model_name refers to the name given in the device line. Model_identifier is an internal designation and
must be of an existing designation Refer to each device's example for the correct designation.

Parameter values are optional. If they aren't specified, then the default will be used. Some devices
have parameters that require a value and must be specified. Refer to individual devices for any required parameters.

==Zener Diode==

[[File:G10.png]]

The Zener Diode models the DC characteristics of most zeners. Since most data sheets for zener diodes do
not give detailed characteristics in the forward region, only a single point defines the forward characteristicThe
saturation current refers to the relatively constant reverse current that is produced when the voltage
across the zener is negative, but breakdown has not been reached. The reverse leakage current determines
the slight increase in reverse current as the voltage across the zener becomes more negative. It is modeled
as a resistance parallel to the zener with value v_breakdown / i_rev.

Note that the limt_switch parameter engages an internal limiting function for the zener. This can, in
some cases, prevent the simulator from converging to an unrealistic solution if the voltage across or
current into the device is excessive. If use of this feature fails to yield acceptable results, the convlimit
option should be tried (add the following statement to the SPICE input deck: .options convlimit)

Model Identifier: zener

Netlist Format:

A<device_name> <z_pin> <z_out_pin> <model_name>

.model <model_name> zener v_breakdown = 1 {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 zener

.model zener zener v_breakdown = 1

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|v_breakdown||breakdown voltage||1||required
|-
|i_breakdown||breakdown current||2.0e-2||
|-
|i_sat||saturation current||1.0e-12||
|-
|N_forward||forward emission coefficient||1.0||
|-
|limit_switch||switch for on-board limiting (convergence aid)||False||
|-
|}

<p> </p>
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D | Back to RF.Spice A/D Wiki Gateway]]'''

Glossary of Generic Analog & Mixed-Mode Devices & Sources

2018-10-11T16:28:55Z

Kazem Sabet: /* Nonlinear Dependent Sources */

==4-Bit ADC Bridge==

[[File:GK44.png]]

This 8-pin device is simply a bundle of 4 1-bit ADC bridges. Each analog input pin has a corresponding digital output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|}

==4-Bit DAC Bridge==

[[File:GK45.png]]

This 8-pin device is simply a bundle of 4 1-bit DAC bridges. Each digital input pin has a corresponding analog output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|}

== AC/RF Current Source ==

[[File:GL11.png]]

This is a simplified version of the standard Current Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak current amplitude||A||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal current||A||0||
|-
|}

== AC/RF Voltage Source ==

[[File:GL10.png]]

This is a simplified version of the standard Voltage Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak voltage amplitude||V||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal voltage||V||0||
|-
|}

==Alternate Ferrite Core Transformer==

[[File:GK96.png]]

The alternate ferrite core transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ferrite_Core_Transformer | Ferrite Core Transformer]], except for the reversed polarity of its secondary port.

==Alternate Ideal Transformer==

[[File:XFMR2.png]]

The alternate ideal transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ideal_Transformer | Ideal Transformer]], except for the reversed polarity of its secondary port.

== AM Modulated Source ==

[[File:GL23.png]]

This is a voltage source with a single-tone amplitude modulated waveform. The AM modulation index MDI is defined as the ratio of maximum amplitude deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Analog Clock ==

[[File:GL30.png]]

This is a periodic pulse generator with a default 0V low output level and a default 5V high output level.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|delay||delay time||sec||0||
|-
|rise||rise time||sec||0.1n||
|-
|fall||fall time||sec||0.1n||
|-
|pulse_wid||clock pulse width||sec||1u||required
|-
|period||clock period||-||2u||required
|-
|out_low||low output voltage level||V||0||
|-|-
|out_high||high output voltage level||V||5||
|-
|}

==Analog-to-Digital Converter (ADC) Bridge==
[[File:GK42.png]]

The ADC Bridge takes an analog value from an analog node and may be in the form of a voltage or current.
If the input is less than or equal to "in_low", then a digital "0" is generated. If
the input is greater than or equal to "in_high", a digital "1" is generated. Otherwise,
a digital "UNKNOWN" is the output value. Unlike the DAC Bridge, ramping or delay is not applicable.
Rather, the continuous ramping of the input provides for any associated delays in the digitized signal.

This model also posts an input load value based on the parameter input_load.

Model Identifier: adc_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> adc_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] adc_bridge

.model adc_bridge adc_bridge in_low = .1 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|rise_delay||L-to-H delay time||sec||1n||
|-
|fall_delay||H-to-L delay time||sec||1n||
|-
|}

== Arbitrary Temporal Waveform Generator ==

[[File:GL17.png]]

This is a voltage source with an arbitrary waveform defined by a mathematical expression. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(t)" standing for time.

Examples:

* v(t) is equivalent to f(t) = t.
* 0.1*(v(t))^2 is equivalent to f(t) = 0.1t^2.
* sin(2*pi*v(t)) is equivalent to f(t) = sin(2πt).

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Tmax||maximum signal duration||sec||1e6||required
|-
|}

==Auto-Transformer==

[[File:GK102.png]]

This 3-pin device models an auto-transformer with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lp||primary inductance||H||1m||
|-
|Ls||secondary inductance||H||1m||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Bipolar Junction Transistor (BJT)==
[[File:G11.png]]

The BJT is an active device which has up to 4 pins. The three standard pins are base, emitter, and collector. These are given in the default symbol. The substrate, which is grounded by default, is the fourth pin. To use the BJT with the substrate, create a new 4-pin BJT using the Device Editor and Symbol Editor.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

Area factor scales the model parameters RE and RC. IC VBE is the initial voltage from base emitter. IC VCE is the initial voltage from collector to emitter. TEMP is the overriding temperature. These parameters are based on the Gummel and Poon integral-charge model. If these parameters are not specified, then it will reduce to the simpler Ebers-Moll model.

The process model is mandatory for the BJT. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|IS||transport saturation current||A||1.0e-16||1.0e-15
|-
|BF||ideal maximum forward beta|| ||100||100
|-
|NF||forward current emission coefficient|| ||1.0||1
|-
|VAF||forward Early voltage||V||infinite||200
|-
|IKF||corner forward beta high current roll-off||A||infinite||0.01
|-
|ISE||B-E leakage saturation current||A||0||1.0e-13
|-
|NE||B-E leakage emission coefficient|| ||1.5||2
|-
|BR||ideal maximum reverse beta|| ||1||0.1
|-
|NR||reverse current emission coefficient|| ||1||1
|-
|VAR||reverse Early voltage||V||infinite||200
|-
|IKR||corner reverse beta high current roll-off||A||infinite||0.01
|-
|ISC||B-C leakage saturation current||A||0||1.0e-13
|-
|NC||B-C leakage emission coefficient|| ||2||1.5
|-
|RB||zero bias base resistance||ohms||0||100
|-
|IRB||current where base resistance falls halfway to minimum value||A||infinite||0.1
|-
|RBM||minimum base resistance at high currents||ohms||RB||10
|-
|RE||emitter resistance||ohms||0||1
|-
|RC||collector resistance||ohms||0||10
|-
|CJE||B-E zero bias depletion capacitance||F||0||2pF
|-
|VJE||B-E built-in potential||V||0.75||0.6
|-
|MJE||B-E junction exponential factor|| ||0.33||0.33
|-
|TF||ideal forward transit time||sec||0||0.1ns
|-
|XTF||coefficient for bias dependence of TF|| ||0||
|-
|VTF||voltage describing VBC dependence of TF||V||infinite||
|-
|ITF||high-current parameter for effect on TF||A||0||
|-
|PTF||excess phase at freq=1.0/(TF*2PI)Hz||degree||0||
|-
|CJC||B-C zero bias depletion capacitance||F||0||2pF
|-
|VJC||B-C built-in potential||V||0.75||0.5
|-
|MJC||B-C junction exponential factor|| ||0.33||0.5
|-
|XCJC||fraction of B-C depletion capacitance connected to internal base node|| ||1||
|-
|TR||ideal reverse transit time||sec||0||10ns
|-
|CJS||zero bias collector-substrate capacitance||F||0||2pF
|-
|VJS||substrate junction built-in potential||V||0.75||
|-
|MJS||substrate junction exponential factor|| ||0||0.5
|-
|XTB||forward and reverse beta temp. exponent|| ||0||
|-
|EG||energy gap for temperature effect on IS||eV||1.11||
|-
|XTI||temperature exponent for effect on IS|| ||3||
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

==Capacitance Meter==
[[File:G37.png]]

The Capacitance Meter measures the total capacitance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total capacitance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense a capacitance value and alter their behavior based upon it.

Model Identifier: cmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> cmeter {<gain = value>}

Example:

A1 1 2 cap_meter

.model cap_meter cmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Capacitor==
[[File:GK120.png]]

Capacitors are used to store electrical energy. They can filter or remove AC signals or block DC current without disrupting AC signals. A capacitor's ability to store energy is termed capacitance and is measured in Farads, with values from pF to mF. The only time current flows through a capacitor is when the charge is collected on, or is removed from, its parallel plates. This means that the voltage across the capacitor is changing, which doesn't conform to DC analysis. In a physical circuit, there is a transition stage during which capacitors charge up to their final values. The result is the same as if these capacitors did not exist and the connections to them were left dangling. In other words, in a (steady-state) DC analysis, a capacitor behaves like an open circuit. Therefore, it is important that no section of the circuit is isolated from the capacitors. Every circuit node needs some path for DC current to the ground.

A capacitor's transient behavior is described by the equation:

i(t) = C * (dv(t)/dt)

Its initial voltage is only important when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An capacitor's AC behavior is described by the equation:

i = j ω * C * v

All capacitor names must begin with C.

Netlist Format:

C<device_name> <N+> <N-> <value>

Example:

C1 1 2 10p

[[RF.Spice A/D]] provides three types of capacitors: simple, user-defined (or real) and semiconductor. The standard capacitor parameters are N+, N-, VALUE, and IC. In a simple capacitor, VALUE must
be specified for the capacitance in Farads. IC is the (optional) initial condition for the capacitor voltage.

==Center-Tapped Ferrite Core Transformer==

[[File:GK97.png]]

This five-pin three-port device models a center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

==Controlled Sine Wave Oscillator==

[[File:G24.png]]

This is a four-terminal function generator with a sinusoidal wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.
This function has parameterizable values of low and high peak output voltage.

Model Identifier: sine

Netlist Form:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> sine cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) sine

.model sine sine cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[1 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|}

==Controlled Sources==

Circuits can contain linear dependent sources characterized by one of the following equations (where g,
e, f, and h are constants representing transconductance, voltage gain, current gain, and transresistance,
respectively):

<SPAN STYLE="font-size: 9pt ; ">i<sub>out</sub> = g v<sub>in</sub>
     v<sub>out</sub> = e v<sub>in</sub>
     i<sub>out</sub> = f i<sub>in</sub>
     v<sub>out</sub> = h i<sub>in</sub></SPAN>
<P CLASS="Bodytext" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; ">
For further information, refer to:</P>

Linear Current Controlled Current Source (CCCS)

Linear Voltage Controlled Current Source (VCCS)

Linear Current Controlled Voltage Source (CCVS)

Linear Voltage Controlled Voltage Source (VCVS)

==Controlled Square Wave Oscillator==

[[File:G25.png]]

This is a four-terminal function generator with a square wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: square

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> square cntl_array = [<value1> <value2>] freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) square

.model square square cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Duty_cycle||Duty cycle||-||0.5||
|-
|Rise_time||Output rise time||sec||1.0e-9||
|-
|Fall_time||Output fall time||sec||1.0e-9||
|-
|}

==Controlled Triangle Wave Oscillator==

[[File:G26.png]]

This is a four-terminal function generator with a triangle wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defined voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: triangle

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> tirangle cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>]{<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 4) %vd(2 3) triangle

.model triangle triangle cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Rise_duty||Rise time duty cycle||0.5||
|-
|}

== Crystal ==

[[File:GK78.png]]

This is a 2-pin parameterized crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CM||motional capacitance||F||10f||
|-
|C0||shunt capacitance||F||1p||
|-
|RM||motional resistance||Ohms||100||
|-
|LM||motional inductance||H||100m||
|-
|}

==Current Noise Source==

[[File:GL16.png]]

This is a current noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the [[parameters]] of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise current||A/√Hz||1p||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Current Source==

[[File:G17B.png]]

Current source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a current source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset current. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==Current-Controlled Switch==

[[File:G20.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Current-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the turn-on and turn-off currents in Amperes and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the rest of [[parameters]]. When the current through the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the current through the switch or controlling device is less than or equal to the turn off current, the switch opens.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|I_ON||turn-on current||A||0.0||
|-
|I_OFF||turn-off current||A||0.0||
|-
|RON||closed resistance||Ohms||1.0||
|-
|ROFF||open resistance||Ohms||1/GMIN||
|-
|}

==Darlington Pair==

[[File:GK108.png]]

A Darlington pair is a three-pin device that consists of two interconnected BJT transistors of the same type. The collectors of two transistors are connected together to provide the "Collector" pin of the pair. The base of the first BJT acts the "Base" pin of the pair. The emitter of the first BJT is internally connected to the base of the second BJT. The emitter of the second BJT acts as the "Emitter" pin of the pair. There are two types of Darlington pair: NPN and PNP. The parameterized generic Darlington pair also contains a diode connected between the collector and emitter pin as well as two base-emitter resistors, one across each BJT.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|is_bjt||bjt saturation current||A||1.0e-12||
|-
|bf_bjt||bjt forward beta||-||150||
|-
|nf_bjt||bjt forward emission coefficient||-||1||
|-
|ise_bjt||B-E leakage saturation current||A||0||
|-
|ne_bjt||B-E leakage emission coefficient||-||1||
|-
|br_bjt||ideal maximum reverse beta||-||1||
|-
|nr_bjt||reverse current emission coefficient||-||1||
|-
|isc_bjt||B-C leakage saturation current||A||0||
|-
|nc_bjt||B-C leakage emission coefficient||-||1||
|-
|rb_bjt||zero bias base resistance||Ohms||0||
|-
|irb_bjt||current where base resistance falls halfway to minimum value||A||inf||
|-
|rbm_bjt||minimum base resistance at high currents||ohms||0||
|-
|re_bjt||emitter resistance||Ohms||0||
|-
|rc_bjt||collector resistance||Ohms||0||
|-
|cje_bjt||B-E zero bias depletion capacitance||F||0||
|-
|vje_bjt||B-E built-in potential||V||0.75||
|-
|mje_bjt||B-E junction grading coefficient||-||0.33||
|-
|cjc_bjt||B-C zero bias depletion capacitance||F||0||
|-
|vjc_bjt||B-C built-in potential||V||0.75||
|-
|mjc_bjt||B-C junction exponential factor||-||0.33||
|-
|tf_bjt||ideal forward transit time||sec||0||
|-
|tr_bjt||ideal reverse transit time||sec||0||
|-
|is_d||diode saturation current||A||1.0e-12||
|-
|rs_d||diode resistance||Ohms||0||
|-
|n_d||diode emission coefficient||-||1||
|-
|cjo_d||diode junction capacitance||F||0||
|-
|vj_d||diode junction potential||V||1||
|-
|m_d||diode grading coefficient|| ||0.5||
|-
|tnom||parameter measurement temperature||deg C||27||
|-
|r1||first base-emitter resistance||Ohms||1k||
|-
|r2||second base-emitter resistance||Ohms||1k||
|-
|}

== DC Bias Sources Vcc, Vee, Vdd, Vss ==

[[File:GL12.png]]

These are simple 1-pin DC voltage sources. Vcc and Vdd provide a positive voltage, while Vee and Vss provide a negative voltage

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|vcc||bias voltage||V||+15||required
|-
|vee||bias voltage||V||-15||required
|-
|vdd||bias voltage||V||+15||required
|-
|vss||bias voltage||V||-15||required
|-
|}

==Digital-to-Analog Converter (DAC) Bridge==

[[File:GK43.png]]

The DAC Bridge takes a digital value from a digital node and can only be eiter "0", "1",
or "U". It then outputs the value "out_low", "out_high" or "out_udndef",
or ramps linearly toward one of these "final" values from its curent analog output level. This
ramping speed depends on the values of "t_rise" and "t_fall".

Model Identifier: dac_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> dac_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] dac_bridge

.model dac_bridge dac_bridge out_low = 0 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|out_undef||analog output for undefined digital input||V||0.5||required
|-
|input_load||capacitive input load||F||1p||
|-
|t_rise||L-to-H delay time||sec||1n||
|-
|t_fall||H-to-L delay time||sec||1n||
|-
|}

==Diode==

[[File:G9.png]]

Diodes allow current flow only in one direction, following their symbol's arrow, and thus can be used as simple solid
state switches in AC circuits.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process models can be either junction diodes or Schottky barrier diodes. Area factor scales the model parameters
IS, RS, CJO, and IBV. VD is the initial voltage, and TEMP is the overriding temperature. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||0||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|EG||activation energy||eV||1.11||
|-
|XTI||saturation current temp. exp.||-||3.0||
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||forward bias junction fit parameter||-||0.5||
|-
|BV||reverse breakdown voltage||V||inf||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|}

==Diode Bridge==

[[File:GK107.png]]

This four-pin device is a bridge configuration of four generic diodes.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||10p||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|BV||reverse breakdown voltage||V||1000||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|}

==Doubly Center-Tapped Ferrite Core Transformer==

[[File:GK98.png]]

This six-pin four-port device models a doubly center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of full-winding primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== DPDT Switch ==

[[File:GK74.png]]

This is an 8-pin device that models a double-pole double-throw switch. It has two input signals and four output pins. When the control voltage is at the high state, the first and second input voltages are transferred to the first and third output pins, respectively. When the control voltage is at the low state, the first and second input voltages are transferred to the second and fourth output pins, respectively.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== DPST Switch ==

[[File:GK73.png]]

This is a 6-pin device that models a double-pole single-throw switch. It has two input signals and two output signals. When the switch on, the first and second input voltages are transferred to the first and second output pins, respectively. When the switch is off, the output pin do not receive any input signals.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Ferrite Core Transformer==

[[File:GK95.png]]

This four-pin two-port device models a physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary turns||-||100||required
|-
|n_sec||number of secondary turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== FM Modulated Source ==

[[File:GL24.png]]

This is a voltage source with a single-tone frequency modulated waveform. The FM modulation index MDI is defined as the ratio of maximum frequency deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

==Frequency Meter==
[[File:G114.png]]

The Frequency Meter is a four-pin shunt device that is connected in parallel with an AC source just like a voltmeter and measures the operating frequency of the AC circuit. The input pins are connected across the AC source. The voltage across the output pins is equal to the frequency of the source in Hertz within a scale factor SF. Note that the Frequency Meter is designed to work with a single-tone AC source of unit amplitude. If the amplitude of the source is not one, multiply the SF parameter by the non-unit source amplitude value. The output voltage of the Frequency Meter can be used in conjunction with linear or nonlinear dependent sources to model frequency-dependent quantities.

Model Identifier: fmeter

Parameters:

The only parameter is the scale factor SF with a default value of 1.0. Set SF = 1e-6 to read out the frequency in MHz. Set SF = 1e-9 to read out the frequency in GHz. Set SF = 6.283185 (2*pi) to read out the angular frequency ω in radian/s.

== Fuse ==

[[File:GK76.png]]

This is a 2-pin interactive current-controlled switch. If the current passing through the fuse is less than a specified threshold current, the switch is closed. If the current exceeds the threshold level, the fuse breaks and remains open thereafter. The device's symbol changes to display its state.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|r||resistance when intact||Ohms||1.0||
|-
|i_thresh||threshold current||A||1.0||
|-
|}

==Ground==

[[File:G15.png]]

Ground has a voltage of zero (0) and is used as a reference to compute electrical values in the circuit.
All circuits <B>must</B> be grounded to be properly simulated. There is no limit on the number of grounds
you may use in a circuit. All components connected to ground are referenced to a common point and treated
as linked through ground.

==Hysteresis Block (XSPICE)==

[[File:G37.png]]

The Hysteresis block is a simple buffer stage that provides hysteresis of the output with respect to the
input. The in_low and in_high parameter values. The output values are limited to out_lower_limit and
out_upper_limit. The value of \93hyst\94 is added to the in_low and in_high points in order to specify the
points at which the slope of the hysteresis function would normally change abruptly as the input transitions
from a low to a high value. Likewise, the value of \93hyst\94 is subtracted from the in_high and in_low values
in order to specify the points at which the slope of the hysteresis function would normally change abruptly
as the input transitions from a high to a low value. In fact, the slope of the hysteresis function is
never allowed to change abruptly but is smoothly varied whenever the input_dowmain smoothing parameter
is set greater than zero.

Model Identifier: hyst

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> hyst {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 hysteresis_block

.model hysteresis_block hyst in_low = 0.0 in_high = 1.0

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default
|-
|In_low||input low value||0.0
|-
|in_high||input high value||1.0
|-
|hyst||hysteresis||0.1
|-
|out_lower_limit||output lower limit||0.0
|-
|out_upper_limit||output upper limit||1.0
|-
|input_domain||input smoothing domain||0.01
|-
|fraction||smoothing fraction/absolute value switch||true
|-
|}

==Ideal Center-Tapped Transformer with Push-Pull Input==

[[File:XFMR4.png]]

The ideal center-tapped transformer with push-pull input is a five-pin three-port device with two primary input ports and one secondary output port. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P1}{v_S} = \frac{v_P2}{v_S} = n </math>

where v<sub>S</sub> is the secondary voltage, v<sub>P1</sub> is measured between the top primary pin P1 and the center tap pin, and v<sub>P2</sub> is measured between the center tap pin and the bottom primary pin P2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P1</sub>/N<sub>S</sub> = N<sub>P2</sub>/N<sub>S</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Center-Tapped Transformer with Push-Pull Output==

[[File:XFMR3.png]]

The ideal center-tapped transformer with push-pull output is a five-pin three-port device with one primary input port and two secondary output ports. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P}{v_{S1}} = \frac{v_P}{v_{S2}} = n </math>

where v<sub>P</sub> is the primary voltage, v<sub>S1</sub> is measured between the top secondary pin S1 and the center tap pin, and v<sub>S2</sub> is measured between the center tap pin and the bottom secondary pin S2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S1</sub> = N<sub>P</sub>/N<sub>S2</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Diode==

[[File:GK106.png]]

This 2-pin device is a very basic and primitive model of a diode as a rectifier or switch. When the voltage across the device's terminals is positive, it acts as a short circuit. When the voltage across the device's terminals is negative, it acts as an open circuit.

Parameters:

None

==Ideal Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This is a very basic and primitive model of an operational amplifier. It has only one parameter, open loop gain with a default value of 50,000, which is adequate for most cases. The ideal Op-Amp device doesn't require any DC bias voltages.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|A||open loop gain||-||50,000||
|-
|}

==Ideal Transformer==

[[File:XFMR1.png]]

The ideal transformer is a four-pin two-port device with the following relationship between the voltages and currents at its primary and secondary ports:

<math> \frac{v_P}{v_S} = - \frac{i_S}{i_P} = \frac{N_P}{N_S} = n </math>

where v<sub>P</sub>, i<sub>P</sub>, N<sub>P</sub> are the primary voltage, current and number of turns, respectively, and v<sub>S</sub>, i<sub>S</sub>, N<sub>S</sub> are the secondary voltage, current and number of turns, respectively. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S</sub>, which represents the primary-to-secondary turns ratio. Note that the ideal transformer model is defined based on controlled sources and does not involve any magnetic physical parameters as opposed to mutual inductors or ferrite core transformer.

==Inductance Meter==

[[File:G37.png]]

The Inductance Meter measures the total inductance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total inductance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense an inductance value and alter their behavior based upon it. Care must be exercised when connecting an Inductance Meter to the inductors of a circuit. This is due to the fact that inductors are treated by SPICE as current sources. This can cause a problem when an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor.

Model Identifier: lmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> imeter {<gain = value>}

Example:

A1 1 2 inductance_meter

.model inductance_meter lmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Inductive Coupler Block==

[[File:GK99.png]]

The Inductive Coupler Block couples any two existing inductors. This block doesn't have any pins because it doesn't actually represent inductors, only the coupling between them. This is useful if you want to
couple two inductors that are in different parts of the circuit, or if you want to couple more than two inductors together. In the latter case, use more than one of these, with each one coupling a pair of inductors.

The standard parameters are Inductor1, Inductor2, and k. Inductor1 is the name of first inductor, Inductor2 is the name of the second inductor, and k is the coefficient of coupling, 0 < k ≤ 1.

==Inductive Coupling (XSPICE)==

[[File:G41.png]]

This function is a conceptual model which is used as a building block to create a wide variety of inductive and magnetic circuit models. This function is normally used in
conjunction with the “core” model, but it can also be used with resistors, hysteresis blocks, etc. to build up systems which mock the behavior of linear and nonlinear components.
The lcouple takes as an input (on the “l” port) a current. This current value is multiplied by the num_turns value, N, to produce an output value (a voltage value which appears on the
mmf_out port). The mmf_out acts similar to a magnetomotive force in a magnetic circuit;
when the lcouple is connected to the “core” model, or to some other resistive device, a current will flow. This current value (which is modulated by whatever the lcouple is
connected to) is then used by the lcouple to calculate a voltage “seen” at the “l” port. The voltage is a function of the derivative with respect to time of the current value seen at mmf_out.

The most common use for lcouple will be as a building block in the construction of transformer models. To create a transformer with a single input and a single output, you
would require two lcouple models plus one “core” model.

Example:

A1 (1 0) (2 3) lcouple1

.model lcouple1 lcouple ( num_turns = 10 )

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|num_turns||number of turns||-||1||required
|-
|}

==Inductor==

[[File:GK121.png]]

Inductors are used to store magnetic energy. An inductor's ability to counteract current changes passing through it is called its inductance (L), which is
measured in Henrys. In a (steady-state) DC analysis, the inductor acts like a short circuit. It is indeed treated as a current source, which can be problematic if an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor. The resistor may be of negligible value or one that accounts for the coil resistance of the inductor. In AC and transient analyses, the inductor develops a voltage across it in response to the changing magnetic
flux within its coil.

An inductor's transient behavior is described by the equation:

v(t) = L*(di(t)/dt)

The inductor's initial condition is optional. It is the initial value of the inductor current in Amperes that flows from node N+ through the inductor to node N-. The only time that the initial current matters is when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An inductor's AC behavior is described by the equation:

v = j ω * L * i

All inductor names must begin with L.

Netlist Format:

L<device_name> <N+> <N-> <value>

Example:

L1 1 2 10u

==Inductor with Ferrite Core==

[[File:GK94.png]]

This 2-pin device models a physical inductor with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. Unlike the standard inductor device, you do not specify an inductance value for the inductor with ferrite core. Rather, you specify physical parameters like cross sectional area, core length and number of turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_turns||number of turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== Insulated Gate Bipolar Transistor (IGBT)==

[[File:GK111.png]]

This is a 3-pin parameterized Insulated Gate Bipolar Transistor (IGBT) device with three pins: Collector(C), Gate (G), and Emitter (E). It is primarily used as a fast electronic switch. The IGBT combines the simple gate-drive characteristics of MOSFETs with the high-current and low-saturation-voltage capability of bipolar transistors. The device's model consists of an isolated gate FET for the control input, and a PNP bipolar power transistor as a switch. To further modify the internal device models, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|cap||parasitic capacitance||F||1n||
|-
|rg||gate resistance||Ohms||5||
|-
|re||emitter resistance||Ohms||0.05||
|-
|bf||pnp transistor forward beta||-||1||
|-
|vto||MOSFET threshold voltage||V||5||
|-
|kt||MOSFET transconductance||-||2.99||
|-
|cgso||MOSFET voltage gate-source overlap capacitance||F||5u||
|-
|nd||diode emission coefficient||-||50||
|-
|cjo||diode junction capacitance||F||1n||
|-
|}

==Interactive Switch==

[[File:GK75.png]]

This device is an interactive switch that can be closed or opened either directly from the Schematic Editor by clicking on its symbol or from the Instrument Panel.

==Junction Field Effect Transistor (JFET)==

[[File:G12.png]]

The JFET is the simplest transistor device and has three pins: gate, drain and source. The JFET defaults are based on the Shichman and Hodges FET model. This is a square-law device because of the expression relating the drain current to the gate-to-source voltage:
Idrain=*(VGS-Vthreshold)2. In real JFETs, near the saturation point, the drain currents vary with the drain voltages. This can be modeled by the following formula: Idrain=*(VGS-VTO)2*(1+*VDS), which yields an increasing
drain current for increasing values of VDS.

The gate-to-source and gate-to-drain junctions each have a nonlinear capacitor. The zero-bias capacitance value is selected for each junction.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process model parameters are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||threshold voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||ohms||0||100
|-
|RS||source ohmic resistance||ohms||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|IS||gate junction saturation current||A||1.0e-14||1.0e-14
|-
|B||doping tail parameter|| ||1||1.1
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

== Light Emitting Diode (LED) ==

[[File:GK114.png]]

This is a two-pin parameterized diode device that emits light of a certain wavelength when it is forward-biased.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rs||ohmic resistance||Ohms||10||
|-
|vj||junction potential||V||0.6||
|-
|cjo||zero bias junction capacitance||F||10p||
|-
|tt||transit time||sec||0.1n||
|-
|}

==Linear Current-Controlled Current Source (CCCS)==

[[File:G2.png]]

The CCCS is a current source whose current is directly proportional to the current across a controlling Ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the current gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the current gain.

Model Identifier: cccs

Netlist Format:

F<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

F1 1 0 V1 1.0

==Linear Current-Controlled Voltage Source (CCVS)==

[[File:G4.png]]

The CCVS is a voltage source whose voltage is directly proportional to the current through a controlling ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the trans-resistance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the trans-resistance gain.

Model Identifier: ccvs

Netlist Format:

H<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

H1 1 0 V1 1.0

==Linear Voltage-Controlled Current Source (VCCS)==

[[File:G3.png]]

The VCCS is a current source whose current is directly proportional to the voltage across a controlling voltmeter or the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the trans-conductance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the trans-conductance gain.

Model Identifier: vccs

Netlist Format:

G<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

G1 1 0 2 0 1.0

==Linear Voltage-Controlled Voltage Source (VCVS)==

[[File:G1.png]]

The VCVS is a voltage source whose voltage is directly proportional to the voltage across a controlling voltmeter of the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the voltage gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the voltage gain.

Model Identifier: vcvs

Netlist Format:

E<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

E1 1 0 2 0 1.0

==Lossless Transmission Line==

[[File:G21.png]]

The lossless transmission line is a four-pin two-port device that models only one propagating mode of an ideal transmission line. When using this SPICE model, should all four nodes of the actual circuit be distinct, two modes may be activated, and this device would be insufficient for that purpose. To circumvent this potential problem, two transmission line devices would be required. Due to the implementation details, you may produce more accurate simulation results with a lossy transmission line device with zero loss.

Optional initial condition parameters are the voltage and current at each of the transmission line ports.

The standard device parameters are Z0, TD, F, NL, IC, described below:

{| class="wikitable"
|-
|Z0||characteristic impedance
|-
|TD||transmission delay
|-
|F||frequency
|-
|NL||normalized electrical length of the transmission line with respect to the wavelength in the line at frequency F. (If F is specified, but NL is not, the default is 0.25.)
|-
|IC||initial condition (Specifies the voltage and current at each of the transmission line ports.)
|-
|}

==Lossy Transmission Line==

[[File:G22.png]]

The lossy transmission line is a four-pin two-port convolution model for uniform constant-parameter distributed lines. MNAME is the process model name, which
includes a set of pre-specified options as described below.

The device model [[parameters]] are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|R||resistance /length||Ohm /m||0.0||0.2
|-
|L||inductance/length||henrys/m||0.0||9.13e-9
|-
|C||capacitance/length||farads/m||0.0||3.65e-12
|-
|LEN||length of line||m||none||1.0
|-
|LININTERP||use linear interpolation||flag||not set||set
|-
|QUADINTERP||use quadratic interpolation||flag||not set||set
|-
|MIXEDINTERP||use linear when quadratic seems bad||flag||not set||set
|-
|COMPACTREL||special reltol for straight line checking||flag||RETOL||1.0e-3
|-
|COMPACTABS||special abstol for straight line checking||flag||ABSTOL||1.0e-9
|-
|NOCONTROL||don't do complex time control||flag||not set||set
|-
|STEPLIMIT||always limit timestep to 0.8*(delay of line)|| || ||
|-
|NOSTEPLIMIT||don't always limit timestep to 0.8*(delay of line)||flag||not set||set
|-
|TRUNCNR||use Newton-Raphson method for timestep calculation in LTRAtrunc||flag||not set||set
|-
|TRUNCDONTCUT||don't limit timestep to keep impulse-response errors low||flag||not set||set
|-
|}

<P CLASS="Normal-1">
The RLC (uniform transmission line with series loss only), RC (uniform RC line), LC (lossless transmission
line), and RG (distributed series resistance and parallel conductance only) lines have been implemented.
The length (LEN) must be given. COMPACTREL and COMPACTABS control the compaction of past history values
used in convolution. Larger values for these lower accuracy but improve speed. These are used with the
TRYTOCOMPACT option. </P>

==Magnetic Core (XSPICE)==

[[File:G42.png]]

This device is used as a building block to create a wide variety of inductive and magnetic circuit models. It is almost always to be used in conjunction with the "lcouple" model to build up systems which simulate the behavior of linear and nonlinear magnetic components. There are two fundamental modes of operation for the core model. These are the "PWL" mode (which is the default and most
likely to be of use to you) and the "Hysteresis" mode.

<b>PWL Mode (mode = 1)</b>

In the PWL mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf) value. This value is divided by the total effective length of the core to produce a value for the Magnetic Field Intensity, H, which is then used to find the corresponding Flux Density, B, using the piecewise linear relationship described by you in the H_array / B_array coordinate pairs. B is then multiplied by the cross-sectional area of the core to find the Flux value, which is output as a current. The pertinent mathematical equations are:

H = mmf / L, where L = Length (in apmere-turns/meter)

B = f(H)

Φ = B * A, where A = Area

The B value is derived from a piecewise linear transfer function described to the model by the H_array and B_array coordinate pairs. This transfer function does not include hysteretic effects; for that, you would need to substitute a HYST model for the core. The magnetic flux value Φ in turn is used by the "lcouple"
code model to obtain a value for the voltage reflected back across its terminals to the driving electrical circuit.

<b>Hysteresis Mode (mode = 2)</b>

In the Hysteresis mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf)
value. This value is used as input to the equivalent of a hysteresis code model block. The parameters
defining the input low and high values, the output low and high values, and the amount of hysteresis are
as in that model. The output from this mode, as in PWL mode, is a current value which is seen across the magnetic core port.

One final note to be made about the two core models is that certain parameters are specific to one or the other. In particular, the in_low, in_high, out_lower_limit, out_upper_limit, and hysteresis parameters are not available in PWL mode. Likewise, the H_array, B_array, area, ad length values are unavailable
in Hysteresis mode. The input_domain and fraction parameters are common to both modes (though their behavior is somewhat different; for explanation of the input_domain and fraction values for the Hysteresis mode, please refer to the Hysteresis Block discussion.

Model Identifier: core

Netlist Format:

A<device_name> <mc1 _pin> <mc2_pin> <model_name>

.model <model_name> core area = <value> length = <value> H_array = [<value1> <value2>] B_array = [<value1> <value2>]
{<param1 = value> < param2 = value> ...}

Example:

A1 1 2 core

.model core core area = 1 length = 1 H_array = [0 1] B_array = [0 1]

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|H_array||magnetic field array||[0 1]||required
|-
|B_array||flux density array||[0 1]||required
|-
|Area||cross-sectional area||1||required
|-
|Length||core length||1||required
|-
|Input_domain||input smoothing domain||0.01||
|-
|Fraction||smoothing fraction/abs switch||True||
|-
|Mode||mode switch (1=pwl, 2=hyst)||1||
|-
|In_low||input low value||0.0||
|-
|In_high||input high value||1.0||
|-
|Hyst||hysteresis||0.1||
|-
|Out_lower_limit||output lower limit||0.0||
|-
|Out_upper_limit||output upper limit||1.0||
|-
|}

==Marker==

[[File:G16.png]]

The marker serves several purposes:

* It can appear as a default plot in simulations if the "Voltage Probe" box is checked.

* It can be used to set the initial voltage or voltage guess at the node it is connected to.

* It can be used as a port for a subcircuit when you choose the checkbox labeled "Use as Subcircuit Port" is checked.

* It can be used to explicitly set a node number in place of the arbitrarily assigned node number by the program. In this case, make sure the "Set Node Index" box is checked. Otherwise, it will act as just a voltage probe.

* It can be used to connect different parts of a circuit in place of wires. To use markers as virtual connectors, place them at points where wires would otherwise connect. Then set the Part Title of the two (or more) markers to the same name, and they will act as a single circuit node.

==MESFET==

[[File:G14.png]]

The MESFET is a Schottky-barrier gate FET with six times greater electron mobility than silicon. MESFETs are important devices for creating high frequency circuits. They function by creating a potential barrier between the gate and the channel when the metal gate
contacts the gallium-arsenide substrate. Electron velocity saturates for fields approximately ten times lower than with silicon. The Curtice model includes linear and saturated operation.

The standard parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

All the MESFET process model parameters are described in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||pinch-off voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|B||doping tail extending parameter||1/V||0.3||0.3
|-
|ALPHA||saturation voltage parameter||1/V||2||2
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||Ohm||0||100
|-
|RS||source ohmic resistance||Ohm||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula||-||0.5||
|-
|}

==MOSFET==

[[File:G13.png]]

The MOSFET is an active device that has up to 4 pins. The three standard pins are gate, drain, and source. These are given in the default symbol. The bulk node, which is grounded by default, is the fourth pin. The MOSFET with the bulk is named mos_n_lvl1_4 (the lvl1 is for level 1, the n for nmos, and the 4 for 4 pins.)

The standard [[parameters]] are L, W, AD, AS, PD, PS, NRD, NRS, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|L||channel length, in meters
|-
|W||channel width, in meters
|-
|AD,AS||areas of the drain and source diffusions, in meters2
|-
|PD,PS||perimeters of drain and source junctions, in meters(They default to 0.0.)
|-
|NRD,NRS||equivalent number of squares of the drain and source diffusions (These values multiply the sheet resistance for an accurate representation of parasitic series drain and source resistance of each transistor. The default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

There are five different default models: square-law I-V characteristic, analytical, semi-empirical, and BSIM and BSIM2 (Berkeley Short-channel IGFET Model), which include second-order effects such as channel-length
modulation, subthreshold conduction, scattering-limited velocity saturation, small-size effects, and charge-controlled capacitance. The process parameter LEVEL specifies which of the models is chosen as indicated below:

{| class="wikitable"
|-
|LEVEL 1||Schichman-Hodges
|-
|LEVEL 2||MOS2
|-
|LEVEL 3||MOS3
|-
|LEVEL 4||BSIM
|-
|LEVEL 5||BSIM2
|-
|LEVEL 6||MOS6
|-
|}

The process model [[parameters]] for levels 1,2,3, and 6 are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|LEVEL||model index|| ||1||
|-
|VTO||zero-bias threshold voltage||V||0.0||1.0
|-
|KP||transconductance parameter||A/V2||2e-5||3.1e-5
|-
|GAMMA||bulk threshold parameter||V1/2||0.0||0.37
|-
|PHI||surface potential||V||0.6||0.65
|-
|LAMBDA||channel-length modulation (level 1 & 2 only)||1/V||0.0||0.02
|-
|RD||drain ohmic resistance||ohms||0.0||1.0
|-
|RS||source ohmic resistance||ohms||0.0||1.0
|-
|CBD||zero-bias B-D junction capacitance||F||0.0||20fF
|-
|CBS||zero-bias B-S junction capacitance||F||0.0||20fF
|-
|IS||bulk junction saturation current||A||1.0e-14||1.0e-15
|-
|PB||bulk junction potential||V||0.8||0.87
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m||0.0||2e-10
|-
|RSH||drain & source diffusion sheet resistance||ohm/area||0.0||10.0
|-
|CJ||zero-bias bulk junction bottom capacitance per meter2 junction area||F/m2||0.0||2e-4
|-
|MJ||bulk junction bottom grading coefficient|| ||0.5||0.5
|-
|CJSW||zero-bias bulk junction sidewall capacitance per meter junction perimeter||F/m||0.0||1.0e-9
|-
|MJSW||bulk junction sidewall grading coefficient|| ||0.5, 0.33 (level1), (level2,3)||
|-
|JS||bulk junction saturation current per meter2 of junction area||A/m2|| ||1.0e-8
|-
|TOX||oxide thickness||meter||1.0e-7||1.0e-7
|-
|NSUB||substrate doping||1/cm3||0.0||4.0e15
|-
|NSS||surface state density||1/cm2||0.0||1.0e10
|-
|NFS||fast surface state density||1/cm2||0.0||1.0e10
|-
|TPG||type gate material(+1 if opp. substrate, 0 if A1 gate, -1 if same as substrate)|| ||1.0||
|-
|XJ||metallurgical junction depth||meter||0.0||1
|-
|LD||lateral diffusion||meter||0.0||0.8
|-
|UO||surface mobility||cm2/Vs||600||700
|-
|UCRIT||critical field for mobility degradation (level2 only)||V/cm||1.0e4||1.0e4
|-
|UEXP||critical field exponent in mobility degradation (level2 only)|| ||0.0||0.1
|-
|UTRA||transverse field coefficient (deleted for level2)|| ||0.0||0.3
|-
|VMAX||maximum drift velocity of carriers||m/s||0.0||5.0e4
|-
|NEFF||total channel-charge (fixed and mobile) coefficient (level2 only)|| ||1.0||5.0
|-
|KF||flicker noise coefficient|| ||0.0||1.0e-26
|-
|AF||flicker noise exponent|| ||1.0||1.2
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|DELTA||width effect on threshold voltage (level2,3)|| ||0.0||1.0
|-
|THETA||mobility modulation (level3 only)||1/V||0.0||0.1
|-
|ETA||static feedback (level3 only)|| ||0.0||1.0
|-
|KAPPA||saturation field factor (level3 only)|| ||0.2||0.5
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

The BSIM model has no default parameters, and leaving one out is considered an error. The additional process model parameters for level 4 and 5 models are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS
|-
|VFB||flat-band voltage||V
|-
|PHI||surface inversion potential||V
|-
|K1||body effect coefficient||V1/2
|-
|K2||drain/source depletion charge-sharing coefficient||
|-
|ETA||zero-bias drain-induced barrier-lowering coefficient||
|-
|MUZ||zero-bias mobility||cm2/V-s
|-
|DL||shortening of channel||m
|-
|DW||narrowing of channel||m
|-
|U0||zero-bias transverse-field mobility degradation coefficient||V-1
|-
|U1||zero-bias velocity saturation coefficient||m/V
|-
|X2MZ||sens. of mobility to substrate bias at Vds=0||cm2/V2-s
|-
|X2E||sens. of drain-induced barrier lowering effect to substrate bias||V-1
|-
|X3E||sens. of drain-induced barrier lowering effect to drain bias at Vds= Vdd||V-1
|-
|X2U0||sens. of transverse field mobility degradation to substrate bias||V-2
|-
|X2U1||sens. of velocity saturation effect to substrate bias||mV-2
|-
|MUS||mobility at zero substrate bias and at Vds= Vdd||cm2/V2-s
|-
|X2MS||sens. of mobility to substrate bias at Vds= Vdd||cm2/V2-s
|-
|X3MS||sens. of mobility to drain bias at Vds= Vdd||cm2/V2-s
|-
|X3U1||sens. of velocity saturation effect on drain bias at Vds= Vdd||mV-2
|-
|TOX||gate oxide thickness||m
|-
|TEMP||temperature at which [[parameters]] were measured||deg. C
|-
|VDD||measurement bias range||V
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m
|-
|XPART||gate-oxide capacitance-charge model flag||
|-
|N0||zero-bias subthreshold slope coefficient||
|-
|NB||sens. of subthreshold slope to substrate bias||
|-
|ND||sens. of subthreshold slope to drain bias||
|-
|RSH||drain and source diffusion sheet resistance||ohms/area
|-
|JS||source drain junction current density||A/m2
|-
|PB||built-in potential of source drain junction||V
|-
|MJ||grading coefficient of source drain junction||
|-
|PBSW||built-in potential of source drain junction sidewall||V
|-
|MJSW||grading coefficient of source drain junction sidewall||
|-
|CJ||source drain junction capacitance per unit area||F/ m2
|-
|CJSW||source drain junction sidewall capacitance per unit length||F/m
|-
|WDF||source drain junction default width||m
|-
|DELL||source drain junction length reduction||m
|-
|}

XPART=0 selects a 40/60 drain/source charge partition; XPART=1 selects a 0/100 partition.

==Mutual Inductors==

[[File:GK100.png]]

The mutual inductors device is a pair of inductors that are coupled to each other. L1 and L2 are the names of two inductors. You have to specify the inductance of inductor L1, the inductance of inductor L2, the initial current through each, and the coupling coefficient k, 0 ≤ k ≤ 1. The mutual inductance M expressed in units of H can be calculated using the following definition:

<math> k = \frac{M}{\sqrt{L_1 L_2}} </math>

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|inductance1||inductance of inductor 1||H||1||
|-
|inductance2||inductance of inductor 2||H||1||
|-
|ic1||initial current through inductor 1||A||0||
|-
|ic2||initial current through inductor 2||A||0||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Non-Ideal Current Transformer==

[[File:GK104.png]]

This 8-pin device models a non-ideal lossy current transformer. Its model consists of an ideal transformer with more secondary turns than primary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. on each side of the internal ideal transformer, there is a series leakage inductance LL<sub>k</sub>, followed by a shunt winding capacitance CW<sub>k</sub> and a series winding resistance RW<sub>k</sub>, which connects to the exterior positive pin on that side. The inter-winding resistance R<sub>12</sub> is connected across the negative pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||secondary-to-primary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary leakage inductance||H||1m||
|-
|ll2||secondary leakage inductance||H||1m||
|-
|cw1||primary winding capacitance||F||1p||
|-
|cw2||secondary winding capacitance||F||1p||
|-
|r12||inter-winding resistance||Ohms||10Meg||
|-
|}

==Non-Ideal Diode==

[[File:G9.png]]

This 2-pin device is a basic simplified model of a diode as a rectifier or switch. When forward-biased, it acts as a low-valued voltage source. When reverse-biased, it acts as an open circuit until the reverse voltage exceeds the specified breakdown voltage. Then it acts as a high-valued voltage source of the reverse polarity.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|vf||forward drop voltage||V||0.5||required
|-
|vr||reverse breakdown voltage||V||100||required
|-
|}

==Non-Ideal Voltage Transformer==

[[File:GK103.png]]

This 8-pin device models a non-ideal lossy voltage transformer. Its model consists of an ideal transformer with more primary turns than secondary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. There are series combinations of a winding resistance RW<sub>k</sub> and a leakage inductance LL<sub>k</sub> on the primary and secondary sides. These are connected between the positive interior and exterior pins on each side. There are also two shunt branches at the inputs of the primary and secondary sides (connected between the positive and negative exterior pins), each consisting of a distributed turn-to-turn winding resistance RDC<sub>k</sub> in series with a distributed turn-to-turn winding capacitance CW<sub>k</sub>. The inter-winding capacitance CWW<sub>12</sub> is connected across the positive pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||primary-to-secondary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary winding leakage inductance||H||1m||
|-
|ll2||secondary winding leakage inductance||H||1m||
|-
|rdc1||primary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw1||primary distributed turn-to-turn winding capacitance||F||1p||
|-
|rdc2||secondary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw2||secondary distributed turn-to-turn winding capacitance||F||1p||
|-
|cww12||inter-winding capacitance||F||1p||
|-
|}

==Nonlinear Capacitor==

[[File:GK89.png]]

The nonlinear capacitor model allows the capacitor to be described by an arbitrary relationship between the capacitor's charge Q and the voltage V across the capacitor. In other words, Q = f(V). The nonlinear capacitance is then defined as C(V) = dQ/dV. You need to define the charge Q by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ C_DEF } * v(pos,neg)

which implies a linear capacitor, where Q = C<sub>DEF</sub> V. Therefore, C = C(V) = dQ/dV = C<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|C_DEF||default capacitance||F||1||
|-
|}

==Nonlinear Conductor==

[[File:GK88.png]]

The nonlinear conductor model allows the conductor to be described by an arbitrary relationship between the conductor's current I and the voltage V across the conductor. In other words, I = f(V). The nonlinear conductance is then defined as G(V) = dI/dV. You need to define the current I by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ G_DEF } * v(pos,neg)

which implies a linear conductor, where I = G<sub>DEF</sub> V. Therefore, G = G(V) = dI/dV = G<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|G_DEF||default capacitance||S||1||
|-
|}

==Nonlinear Dependent Sources==

[[File:G18.png]]

Nonlinear dependent (arbitrary) sources use an equation or mathematical expression to describe their behavior. One and only one of the two forms: V=<expr> or I=<expr> must be given.

Netlist Format:

B<device_name> v = <expression>

B<device_name> i = <expression>

Examples:

v = I(v1) + 3* I(v2)

I = v(i1) + 3* v(2) + 5 * v(3) ^2

The first example is a current-controlled voltage source. The v on the left side of the equation
indicates that it is a voltage source. I(v1) and I(v2) are the currents through voltage sources named v1 and v2, respectively.

The second example is a voltage-controlled current source. v(2) and v(3) represents the voltages at nodes 2 and 3, respectively, and v(i1) represents the voltage across a current source named i1.

The following mathematical functions defined for real variables can be used in the expressions:

abs, acos, acosh, asin, asinh, atan, atanh, cos, cosh, exp, ln, log, sgn, sin, sinh, sqrt, tan, tanh.

The function "u" is the unit step and "uramp" is the integral of the unit step. The
unit step is one if its argument is greater than zero and zero if its argument is less than zero. The
ramp function (uramp) is 0 for argument values less than zero and equal to the argument for argument values
greater than zero.

The following operators are permissible: +, -, *, /, ^, and unary-.

To get time into an expression, integrate the current from a constant current source with a capacitor
and use the voltage across the capacitor.

==Nonlinear Inductor==

[[File:GK90.png]]

The nonlinear inductor model allows the inductor to be described by an arbitrary relationship between the inductor's magnetic flux Φ and the current I flowing through the inductor . In other words, Φ = f(I). The nonlinear inductance is then defined as L(I) = dΦ/dI. You need to define the flux Φ by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ L_DEF } * i(vx)

which implies a linear inductor, where Φ = L<sub>DEF</sub> I. Therefore, L = L(I) = dΦ/dI = L<sub>DEF</sub>.

Another example is 1e-4*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|L_DEF||default inductance||H||1||
|-
|}

==Nonlinear Resistor==

[[File:GK87.png]]

The nonlinear resistor model allows the resistor to be described by an arbitrary relationship between the voltage V across the resistor and its current I. In other words, V = f(I). The nonlinear resistance is then defined as R(I) = dV/dI. You need to define the voltage V by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ R_DEF } * i(vx)

which implies a linear resistor, where V = R<sub>DEF</sub> I. Therefore, R = R(I) = dV/dI = R<sub>DEF</sub>.

Another example is 10*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R_DEF||default resistance||Ω||1||
|-
|}

==Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This three-pin device models a parameterized operational amplifier with a very high voltage gain, a very high input impedance and a very low output impedance. The behavioral model of the parameterized Op-Amp device is based on the algorithm found in the book <B>Macromodeling with Spice</B>,
authored by Connelly & Choi, published by Prentice Hall. The default parameters are those of the 741 Op-Amp. This device doesn't require external DC bias voltage sources. Its positive and negative DC bias voltages are specified as its parameters. Sometimes the simulation doesn't converge if there is no DC path from the output of the Op-Amp to the ground.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|r_in_dm||differential mode input resistance||Ohms||2Meg||
|-
|r_in_cm||common mode input resistance||Ohms||2G||
|-
|Avd0||differential mode DC gain||dB||106||
|-
|CMRR||common mode rejection ratio||dB||90||
|-
|r_out||output resistance||Ohms||75||
|-
|c_in||input capacitance||F||1.4p||
|-
|ios||input offset current||A||20n||
|-
|ib||input bias current||A||80n||
|-
|vio||input offset voltage||V||1m||
|-
|slew_pos||positive slew rate||V/s||0.5e6||
|-
|slew_neg||negative slew rate||V/s||0.5e6||
|-
|curr_src_max||maximum output source current||A||25m||
|-
|curr_sink_||maximum output sink current||A25m||
|-
|fp1||dominant pole frequency||Hz||5||
|-
|fp2||second pole frequency||Hz||2Meg||
|-
|fp3||third pole frequency||Hz||20Meg||
|-
|fp4||fourth pole frequency||Hz||100Meg||
|-
|fz||first zero frequency||Hz||5Meg||
|-
|vcc_pos||positive dc voltage source||V||12||
|-
|vcc_neg||negative dc voltage source||V||12||
|-
|}

== Optocoupler ==

[[File:GK115.png]]

This is a five-pin parameterized optocoupler device. Its model consists of an ideal diode device in series with an Ohmic resistance connected between the Anode (A) and Cathode (K) pins together with a bipolar junction transistor device with three accessible pins, Collector (C), Base (B) and Emitter (E). A current-controlled current source is connected between base and collector of the BJT, whose current is controlled by the current passing through the diode. The proportionality constant is twice the specified value of the current transfer ratio (ctr) parameter.

You can change or enhance the models of the diode and BJT by adding more parameters. To do so, you have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ctr||current transfer ratio||-||0.5||
|-
|rd||diode ohmic resistance||Ohms||0.1||
|-
|}

== Overtone Crystal ==

[[File:GK79.png]]

This is a 2-pin parameterized overtone crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|LM||fundamental motional inductance||H||250m||
|-
|CM1||fundamental motional capacitance||F||10f||
|-
|RM1||fundamental motional resistance||Ohms||20||
|-
|RM3||3rd overtone motional resistance||Ohms||50||
|-
|RM5||5th overtone motional resistance||Ohms||100||
|-
|RM7||7th overtone motional resistance||Ohms||150||
|-
|C0||shunt capacitance||F||3p||
|-
|}

== Photodiode ==

[[File:GK113.png]]

This is a 4-pin parameterized photodiode device. A pair of pins, Anode (A) and Cathode (K), represent the physical terminals of the photodiode. The photodiode model connected between the anode and cathode pins consists of the parallel connection of an ideal diode, a dark current source, a noise current source, a current-controlled current source, a diode capacitance, a shunt resistance altogether with a series resistance.

Another pair of pins IS+ and IS- act as an ammeter that must be inserted in a control circuit. The current passing through this ammeter controls the current of the photodiode. The default proportionality constant is unity. The controlling current is typically a function of light intensity incident on the surface of the photodiode.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|id||dark current||A||1n||
|-
|ir||noise current||A||1p||
|-
|cd||diode capacitance||F||10p||
|-
|rs||series resistance||Ohms||1m||
|-
|rp||parallel resistance||Ohms||1Meg||
|-
|}

==Piecewise Linear (PWL) Controlled Source==

[[File:GL49.png]]

The Piecewise Linear (PWL) Controlled Source is a single-input and single-output function generator whose output is not necessarily
linear for all input values. Instead, it follows an I/O relationship that is specified by the x_array and y_array coordinates. The x_array and y_array values represent vectors of coordinate points on the x and y axes, respectively. The x_array values are progressively increasing input coordinate points, and the associated y_array values represent the outputs at those points. There may be as few as two pairs specified, or as many as memory and simulation speed allow.

In order to fully specify outputs for values of Vin outside of the bounds of the PWL function, the PWL
controlled source model extends the slope found between the lowest two coordinate pairs and the highest
two coordinate pairs. This has the effect of making the transfer function completely linear for Vin
less than x_array[0] and Vin greater than x_array[n]. It also has the potentially subtle effect of unrealistically
causing an output to reach a very large or small value for large inputs. You should thus keep in mind
that the PWL Source does not inherently provide a limiting capability.

In order to diminish the potential for divergence of simulations when using the PWL block, a form
of smoothing around the x_array and y_array coordinate points is necessary. This is due to the iterative
nature of the simulator and its reliance on smooth first derivatives of transfer functions in order to
arrive at a matrix solution. Consequently, the two parameters "input_domain" and "fraction" are included
to allow you some control over the amount and nature o the smoothing performed.

Fraction is a switch that is either TRUE or FALSE. When TRUE (the default setting), the simulator assumes
that the specified input_domain value is to be interpreted as a fractional figure. Otherwise, it is interpreted
as an absolute value. Thus, if fraction = TRUE and input_domain = 0.10, the simulator assumes that the smoothing
radius about each coordinate point is to be set equal to 10% of the length of either the x_array segment
above each coordinate point, or the x_array segment below each coordinate point. The specific segment
length chosen will be the smallest of these two for each coordinate point.

If fraction = FALSE and input_domain = 0.10, then the simulator will begin smoothing the transfer function at 0.10
volts (or amperes) below each x_array coordinate and will continue the smoothing process for another 0.10
volts (or amperes) above each x_array coordinate point.

Model Identifier: pwl

Netlist Format:

A<device_name> %vd(<in_pin> <in_ref_pin>) %vd(<out_pin> <out_ref_pin>) <model_name>

.model <model_name> pwl x_array = [<value1> <value2> ...] y_array = [<value1>
<value2> ...] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(2 3) %vd(1 4) pwl
.model pwl pwl x_array = [0 1] y_array = [0 1]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|x_array||x-element array||V||[0 1]||required
|-
|y_array||y-element array||V||[0 1]||required
|-
|input_domain||input smoothing domain||-||0.01||
|-
|fraction||smoothing %/abs switch||-||True||
|-
|}

== PM Modulated Source ==

[[File:GL25.png]]

This is a voltage source with a single-tone phase modulated waveform. The PM modulation index MDI is defined as the ratio of maximum phase deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Potentiometer ==

[[File:GK77.png]]

This is a 3-pin device that models a potentiometer with options for either linear or logarithmic resistance. position = 0 corresponds to the wiper being at the extreme left and position = 1 corresponds to the wiper being at the extreme right. With the default position = 0.5 corresponding to the midpoint, this device functions as a one-half voltage divider.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|position||position of wiper connection||-||0.5||Must be between 0.0 and 1.0.
|-
|log||log-linear switch||-||False||Select False for linear and True for logarithmic.
|-
|r||total resistance||Ohms||0.1u||
|-
|log_multiplier||multiplier constant for log resistance||-||1.0||
|-
|}

== Programmable Unijunction Transistor (PUT)==

[[File:GK112.png]]

This is a 3-pin parameterized Programmable Unijunction Transistor (PUT) device with three pins: Base 1 (B1), Base 2 (B2) and Emitter (E). It is biased with a positive voltage between the two bases. This device has a unique characteristic that when it is triggered, its emitter current increases regeneratively until it is restricted by emitter power supply. It exhibits a negative resistance characteristic and so it can be employed as an oscillator. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To change these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|eta||-||-||0.6||
|-
|rbb||total base-to-base resistance||Ohms||40k||
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

==Random Resistor==

[[File:GK93.png]]

The random resistor device models a resistor whose resistance is a random number between 0 and a maximum specified value.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|max_val||maximum resistance value||Ω||1k||
|-
|}

==Real Capacitor==

[[File:GK117.png]]

This is primarily a non-ideal, temperature-dependent capacitor model. You can access it from the Parts Menu as '''User-Defined Capacitor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent capacitance is computed using the quadratic equation:

C(T) = C(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance and a series inductance together with the capacitor, all in parallel with a shunt resistance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Resr||series resistance||Ω||10||
|-
|Ls||inductance||H||1p||
|-
|C||capacitance||F||1n||
|-
|Rp||parallel resistance||Ω||1G||
|-
|ic||voltage initial condition||V||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||F/°C||0.1||
|-
|tc2||second-order temperature coefficient||F/°C<sup>2</sup>||0.01||
|-
|}

==Real Inductor==

[[File:GK118.png]]

This is primarily a non-ideal inductor model. You can access it from the Parts Menu as '''User-Defined Inductor'''. Its series resistor has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance together with the inductor, and the combination in parallel with a shunt capacitance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Rdc||series resistance||Ω||10||
|-
|L||inductance||H||1||
|-
|Cp||capacitance||F||1p||
|-
|ic||current initial condition||A||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Real Resistor==

[[File:GK116.png]]

This is primarily a non-ideal, temperature-dependent resistor model. You can access it from the Parts Menu as '''User-Defined Resistor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series inductance together with the resistor.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R||resistance||Ω||1k||
|-
|Ls||inductance||H||1n||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Resistor==

[[File:GK119.png]]

Resistors are passive devices that dissipate power. Their resistance value varies depending on how much power they can dissipate and is measured
in Ohms. The transient, DC and AC behaviors of a resistor are all described by the same equation:

v = R * i

where v is the voltage across the resistor, i is the current passing through the resistor, and R is the resistance. The value of R must be nonzero.

All resistor names must begin with R.

Netlist Format:

R<device_name> <N+> <N-> <value>

Example:

R1 1 2 1k

[[RF.Spice A/D]] provides three types of resistor: Simple, User-Defined (Real Resistor) and Semiconductor. The resistance of the simple resistor is a single value expressed in Ohms. You can also set the Monte Carlo tolerance for this resistor.

==Schottky Diode==

[[File:GK80.png]]

The Schottky diode has the same model as the generic diode with a nonzero transit time (tt), a nonzero junction capacitance (cjo) and a typically larger saturation current (is), a lower junction potential (vj) and a smaller grading coefficient (m).

==Semiconducting Capacitor==

[[File:GK83.png]]

This is the more general form of the Capacitor model and allows for the calculation of the actual capacitance value from strictly geometric information and the specifications of the process.

General Form:

CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>

If VALUE is specified, it defines the capacitance. If MNAME is specified, then the capacitance is calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. Either VALUE or MNAME, LENGTH, and WIDTH may be specified, but not both sets. The optional initial condition "IC" is the initial voltage across the capacitor for transient simulations.

The capacitance is computed as:

CAP = CJ * (LENGTH - NARROW) * (WIDTH - NARROW)+ 2 * CJSW * (LENGTH + WIDTH - 2NARROW) * CAP

To modify the model parameters, first double click on the capacitor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit CJ, CJSW, NARROW, DEFW, and CAP.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CJ||junction bottom capacitance||F/m<sup>2</sup>||-||
|-
|CJSW||junction sidewall capacitance||F/m ||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|CAP||nominal capacitance for Monte Carlo simulation||F||1||
|-
|}

== Semiconductor Resistor ==

[[File:GK82.png]]

This is the more general form of the resistor model and allows for the modeling of temperature effects and for the calculation of the actual resistance value from strictly geometric information and the specifications of the process.

General Form:

RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>

If VALUE is specified, it overrides the geometric information and defines the resistance. If MNAME is specified, then the resistance may be calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. The (optional) TEMP value is the temperature at which this device is to operate, and overrides the temperature specification in the SPICE Options Dialog.

The resistance is computed as:

R(T0) = (RSH) * [(L - NARROW) / (W - NARROW)] * RES

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

To modify the model parameters, first double click on the resistor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit TC1, TC2, RSH, RES, etc.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|TC1||first order temperature coefficient||Ω/°C||-||
|-
|TC2||second order temperature coefficient||Ω/°C<sup>2</sup>||-||
|-
|RSH||sheet resistance||Ω/sq||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|TNOM||the parameter measurement temperature||deg C ||27||
|-
|RES||resistance multiplier for Monte Carlo simulation||Ohms||1||
|-
|}

== Silicon-Controlled Rectifier (SCR)==

[[File:GK109.png]]

This is a 3-pin parameterized Silicon-Controlled Rectifier (SCR) device with three pins: Anode (A), Cathode (K) and Gate (G). It is a unidirectional device which can conduct current only in one direction. The SCR can be triggered only by a positive current going into its gate. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

== SPDT Switch ==

[[File:GK72.png]]

This is a 5-pin device that models a single-pole double-throw switch. The input voltage is transferred to the first output pin if the control voltage is at a high state. Otherwise, its is transferred to the second output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== SPST Switch ==

[[File:GK71.png]]

This is a 4-pin device that models a single-pole single-throw switch. It is virtually equivalent of the standard voltage-controlled switch.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Tabulated Conductor==

[[File:GK92.png]]

The tabulated conductor model allows the conductance to be described by a table relating the device's current i(t) to its terminal voltage v(t). In effect, the conductance is defined as G = di(t)/dv(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (v,i) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tabulated Resistor==

[[File:GK91.png]]

The tabulated resistor model allows the resistance to be described by a table relating the device's terminal voltage v(t) to its current i(t). In effect, the resistance is defined as R = dv(t)/di(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (i,v) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tapped Inductor==

[[File:GK101.png]]

This 3-pin device models a tapped inductor with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lt||total inductance||H||1m||
|-
|ratio||ratio of number of turns between positive terminal and tap to total number of turns||-||0.5||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

== Temperature-Dependent Current Source ==

[[File:GL14.png]]

This is a current source whose current is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

== Temperature-Dependent Voltage Source ==

[[File:GL13.png]]

This is a voltage source whose voltage is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

==Thermometer==
[[File:G115.png]]

The Thermometer is a two-pin device that measures the operating temperature of a circuit. The voltage across the device pins is equal to SPICE's operating temperature in degrees centigrade. The output voltage of the Thermometer can be used in conjunction with linear or nonlinear dependent sources to model temperature-dependent quantities.

Model Identifier: thermo

Parameters:

This device has no parameters.

== Triac Thyristor ==

[[File:GK110.png]]

This is a 3-pin bidirectional thyristor device that conducts current in either direction when triggered. A thyristor is analogous to a relay in that a small voltage and current can control a much larger voltage and current. The triac has two anode pins termed Main Terminal 1 (MT1) and Main Terminal 2 (MT2) and a Gate (G) pin. In order to create a triggering current for a triac, either a positive or negative voltage can be applied to the gate. Once triggered, the thyristor continues to conduct, even if the gate current ceases, until the main current drops below a certain level called the holding current. The device's model involves two NPN BJT transistors and two PNP BJT transistors. The forward beta parameters of the NPN and PNP transistors are set equal to 20 and 5, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|bvf||breakdown voltage of forward diodes||V||100||
|-
|rh||resistance controlling reverse holding current||Ohms||100||
|-
|rgp||resistance controlling forward holding current and trigger current||Ohms||50||
|-
|}

==Uniform RC Transmission Line==

[[File:G23.png]]

The standard parameters are L, and N. They are described below:

Two of the nodes are the element nodes connected by the RC line. The third is the node to which the capacitances
are connected. L is the length of the RC line in meters. N is the number of lumped segments to use in
modeling the RC line.

This device is derived from a model proposed by Gertzberrg. It expands the URC line into a network of
lumped RC segments with internally generated nodes. These segments increase toward the middle of the
URC line in a geometric progression with K as the proportionality constant.

The URC line is made up entirely of resistor and capacitor segments, unless the ISPERL parameter has a
non-zero value. In this case, capacitors are replaced by reverse biased diodes with an equivalent zero-bias
junction capacitance, a saturation current of ISPERL amps per meter of transmission line, and optional
series resistance of RSPERL ohms per meter.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|K||propagation constant||-||2||1.2
|-
|FMAX||maximum frequency of interest||Hz||1.0G||6.5Meg
|-
|RPERL||resistance per unit length||Ohm /m||1000||10
|-
|CPERL||capacitance per unit length||F/m||1.0e-15||1pF
|-
|ISPERL||saturation current per unit length||A/m||0||-
|-
|RSPERL||diode resistance per unit length||Ohm/m||0||-
|-
|}

==Varactor Diode==

[[File:GK81.png]]

A varactor diode is a combination of the generic diode with additional package inductance, package capacitance and a series resistance. This diode device has a typically large value of junction capacitance (cjo).

Parameters (in addition to standard diode parameters):

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|q||quality factor||-||5000||
|-
|f0||frequency of Q-factor specification||Hz||50Meg||
|-
|ls||package inductance||H||0.5n||
|-
|cp||package capacitance ||F||0.05p||
|-
|}

==Voltage-Controlled Capacitor==

[[File:GK85.png]]

This 3-pin device models a voltage-controlled two-terminal capacitor whose capacitance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in F/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_C||conversion factor||F/V||1.0||
|-
|}

==Voltage-Controlled Inductor==

[[File:GK86.png]]

This 3-pin device models a voltage-controlled two-terminal inductor whose inductance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in H/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_L||conversion factor||H/V||1.0||
|-
|}

==Voltage-Controlled Resistor==

[[File:GK84.png]]

This 3-pin device models a voltage-controlled two-terminal resistor whose resistance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in Ω/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_r||conversion factor||Ω/V||1.0||
|-
|}

==Voltage-Controlled Switch==

[[File:G19.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Voltage-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Voltmeter or controlling voltage nodes, as well as the turn-on and turn-off voltages in Volts and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the rest of [[parameters]]. When the voltage across the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the voltage across the switch or controlling device is less than or equal to the turn off current, the switch opens.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|V_ON||turn-on voltage||V||0.5||
|-
|V_OFF||turn-off voltage||V||0.0||
|-
|RON||on resistance||Ohms||1.0||
|-
|ROFF||off resistance||Ohms||1G||
|-
|}

==Voltage Noise Source==

[[File:GL15.png]]

This is a voltage noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the parameters of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise voltage||V/√Hz||1n||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Voltage Source==

[[File:G17A.png]]

A voltage source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a voltage source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset voltage. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==XSpice Devices and their models==

XSpice devices have the following form:
<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 4pt 0pt 1px 0pt ; font-family: 02070309020205020404,sans-serif; ">
A<device_name> <node1> <node2> ... <model_name></P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., A2 1 2 transfer_function

Note that XSpice devices must start with the "A" designation, much as a resistor starts with
an "R". Some devices will have grouped (or vector) pins and are designated by being placed
inside square brackets. In the example shown below, the 1 and 2 pins are grouped. Pin 3 is not. </P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 [1 2] 3 summer </P>

Some models will have voltage differential pairs of pins and will be denoted by a %vd( ). In the following
example pins 1 and 4 are differential pairs, as well as pins 2 and 3. Differential pairs must go between
parentheses ().

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 %vd(1 4) %vd(2 3) triangle </P>

Refer to individual devices for more information.

Each XSpice device will also have a model associated with it. Each model will have the following form:

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
.model <model_name> <model_identifier> {<pname1 = pval1>} {<pname2 = pval2>}
...</P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., .model transfer_function s_xfer in_offset = 0.0 gain = 1.0</P>

Model_name refers to the name given in the device line. Model_identifier is an internal designation and
must be of an existing designation Refer to each device's example for the correct designation.

Parameter values are optional. If they aren't specified, then the default will be used. Some devices
have parameters that require a value and must be specified. Refer to individual devices for any required parameters.

==Zener Diode==

[[File:G10.png]]

The Zener Diode models the DC characteristics of most zeners. Since most data sheets for zener diodes do
not give detailed characteristics in the forward region, only a single point defines the forward characteristicThe
saturation current refers to the relatively constant reverse current that is produced when the voltage
across the zener is negative, but breakdown has not been reached. The reverse leakage current determines
the slight increase in reverse current as the voltage across the zener becomes more negative. It is modeled
as a resistance parallel to the zener with value v_breakdown / i_rev.

Note that the limt_switch parameter engages an internal limiting function for the zener. This can, in
some cases, prevent the simulator from converging to an unrealistic solution if the voltage across or
current into the device is excessive. If use of this feature fails to yield acceptable results, the convlimit
option should be tried (add the following statement to the SPICE input deck: .options convlimit)

Model Identifier: zener

Netlist Format:

A<device_name> <z_pin> <z_out_pin> <model_name>

.model <model_name> zener v_breakdown = 1 {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 zener

.model zener zener v_breakdown = 1

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|v_breakdown||breakdown voltage||1||required
|-
|i_breakdown||breakdown current||2.0e-2||
|-
|i_sat||saturation current||1.0e-12||
|-
|N_forward||forward emission coefficient||1.0||
|-
|limit_switch||switch for on-board limiting (convergence aid)||False||
|-
|}

<p> </p>
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D | Back to RF.Spice A/D Wiki Gateway]]'''

Glossary of Generic Analog & Mixed-Mode Devices & Sources

2018-10-11T15:58:36Z

Kazem Sabet: /* Nonlinear Dependent Sources */

==4-Bit ADC Bridge==

[[File:GK44.png]]

This 8-pin device is simply a bundle of 4 1-bit ADC bridges. Each analog input pin has a corresponding digital output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|}

==4-Bit DAC Bridge==

[[File:GK45.png]]

This 8-pin device is simply a bundle of 4 1-bit DAC bridges. Each digital input pin has a corresponding analog output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|}

== AC/RF Current Source ==

[[File:GL11.png]]

This is a simplified version of the standard Current Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak current amplitude||A||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal current||A||0||
|-
|}

== AC/RF Voltage Source ==

[[File:GL10.png]]

This is a simplified version of the standard Voltage Source, in which the AC "Use" box has been checked by default. Therefore, it is ready to be used for AC frequency sweep. Note that for AC frequency sweep, you do not need to specify the frequency.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|VA||peak voltage amplitude||V||1||required
|-
|Freq||frequency ||Hz||1||required
|-
|Phase||phase||deg||0||
|-
|offset||DC offset for small-signal voltage||V||0||
|-
|}

==Alternate Ferrite Core Transformer==

[[File:GK96.png]]

The alternate ferrite core transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ferrite_Core_Transformer | Ferrite Core Transformer]], except for the reversed polarity of its secondary port.

==Alternate Ideal Transformer==

[[File:XFMR2.png]]

The alternate ideal transformer is a four-pin two-port device, which has the same behavior as the [[Glossary of Generic Analog & Mixed-Mode Devices#Ideal_Transformer | Ideal Transformer]], except for the reversed polarity of its secondary port.

== AM Modulated Source ==

[[File:GL23.png]]

This is a voltage source with a single-tone amplitude modulated waveform. The AM modulation index MDI is defined as the ratio of maximum amplitude deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Analog Clock ==

[[File:GL30.png]]

This is a periodic pulse generator with a default 0V low output level and a default 5V high output level.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|delay||delay time||sec||0||
|-
|rise||rise time||sec||0.1n||
|-
|fall||fall time||sec||0.1n||
|-
|pulse_wid||clock pulse width||sec||1u||required
|-
|period||clock period||-||2u||required
|-
|out_low||low output voltage level||V||0||
|-|-
|out_high||high output voltage level||V||5||
|-
|}

==Analog-to-Digital Converter (ADC) Bridge==
[[File:GK42.png]]

The ADC Bridge takes an analog value from an analog node and may be in the form of a voltage or current.
If the input is less than or equal to "in_low", then a digital "0" is generated. If
the input is greater than or equal to "in_high", a digital "1" is generated. Otherwise,
a digital "UNKNOWN" is the output value. Unlike the DAC Bridge, ramping or delay is not applicable.
Rather, the continuous ramping of the input provides for any associated delays in the digitized signal.

This model also posts an input load value based on the parameter input_load.

Model Identifier: adc_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> adc_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] adc_bridge

.model adc_bridge adc_bridge in_low = .1 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|in_low||maximum 0-valued analog input||V||0.1||required
|-
|in_high||minimum 1-valued analog input||V||0.9||required
|-
|rise_delay||L-to-H delay time||sec||1n||
|-
|fall_delay||H-to-L delay time||sec||1n||
|-
|}

== Arbitrary Temporal Waveform Generator ==

[[File:GL17.png]]

This is a voltage source with an arbitrary waveform defined by a mathematical expression. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(t)" standing for time.

Examples:

* v(t) is equivalent to f(t) = t.
* 0.1*(v(t))^2 is equivalent to f(t) = 0.1t^2.
* sin(2*pi*v(t)) is equivalent to f(t) = sin(2πt).

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Tmax||maximum signal duration||sec||1e6||required
|-
|}

==Auto-Transformer==

[[File:GK102.png]]

This 3-pin device models an auto-transformer with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lp||primary inductance||H||1m||
|-
|Ls||secondary inductance||H||1m||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Bipolar Junction Transistor (BJT)==
[[File:G11.png]]

The BJT is an active device which has up to 4 pins. The three standard pins are base, emitter, and collector. These are given in the default symbol. The substrate, which is grounded by default, is the fourth pin. To use the BJT with the substrate, create a new 4-pin BJT using the Device Editor and Symbol Editor.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

Area factor scales the model parameters RE and RC. IC VBE is the initial voltage from base emitter. IC VCE is the initial voltage from collector to emitter. TEMP is the overriding temperature. These parameters are based on the Gummel and Poon integral-charge model. If these parameters are not specified, then it will reduce to the simpler Ebers-Moll model.

The process model is mandatory for the BJT. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|IS||transport saturation current||A||1.0e-16||1.0e-15
|-
|BF||ideal maximum forward beta|| ||100||100
|-
|NF||forward current emission coefficient|| ||1.0||1
|-
|VAF||forward Early voltage||V||infinite||200
|-
|IKF||corner forward beta high current roll-off||A||infinite||0.01
|-
|ISE||B-E leakage saturation current||A||0||1.0e-13
|-
|NE||B-E leakage emission coefficient|| ||1.5||2
|-
|BR||ideal maximum reverse beta|| ||1||0.1
|-
|NR||reverse current emission coefficient|| ||1||1
|-
|VAR||reverse Early voltage||V||infinite||200
|-
|IKR||corner reverse beta high current roll-off||A||infinite||0.01
|-
|ISC||B-C leakage saturation current||A||0||1.0e-13
|-
|NC||B-C leakage emission coefficient|| ||2||1.5
|-
|RB||zero bias base resistance||ohms||0||100
|-
|IRB||current where base resistance falls halfway to minimum value||A||infinite||0.1
|-
|RBM||minimum base resistance at high currents||ohms||RB||10
|-
|RE||emitter resistance||ohms||0||1
|-
|RC||collector resistance||ohms||0||10
|-
|CJE||B-E zero bias depletion capacitance||F||0||2pF
|-
|VJE||B-E built-in potential||V||0.75||0.6
|-
|MJE||B-E junction exponential factor|| ||0.33||0.33
|-
|TF||ideal forward transit time||sec||0||0.1ns
|-
|XTF||coefficient for bias dependence of TF|| ||0||
|-
|VTF||voltage describing VBC dependence of TF||V||infinite||
|-
|ITF||high-current parameter for effect on TF||A||0||
|-
|PTF||excess phase at freq=1.0/(TF*2PI)Hz||degree||0||
|-
|CJC||B-C zero bias depletion capacitance||F||0||2pF
|-
|VJC||B-C built-in potential||V||0.75||0.5
|-
|MJC||B-C junction exponential factor|| ||0.33||0.5
|-
|XCJC||fraction of B-C depletion capacitance connected to internal base node|| ||1||
|-
|TR||ideal reverse transit time||sec||0||10ns
|-
|CJS||zero bias collector-substrate capacitance||F||0||2pF
|-
|VJS||substrate junction built-in potential||V||0.75||
|-
|MJS||substrate junction exponential factor|| ||0||0.5
|-
|XTB||forward and reverse beta temp. exponent|| ||0||
|-
|EG||energy gap for temperature effect on IS||eV||1.11||
|-
|XTI||temperature exponent for effect on IS|| ||3||
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

==Capacitance Meter==
[[File:G37.png]]

The Capacitance Meter measures the total capacitance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total capacitance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense a capacitance value and alter their behavior based upon it.

Model Identifier: cmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> cmeter {<gain = value>}

Example:

A1 1 2 cap_meter

.model cap_meter cmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Capacitor==
[[File:GK120.png]]

Capacitors are used to store electrical energy. They can filter or remove AC signals or block DC current without disrupting AC signals. A capacitor's ability to store energy is termed capacitance and is measured in Farads, with values from pF to mF. The only time current flows through a capacitor is when the charge is collected on, or is removed from, its parallel plates. This means that the voltage across the capacitor is changing, which doesn't conform to DC analysis. In a physical circuit, there is a transition stage during which capacitors charge up to their final values. The result is the same as if these capacitors did not exist and the connections to them were left dangling. In other words, in a (steady-state) DC analysis, a capacitor behaves like an open circuit. Therefore, it is important that no section of the circuit is isolated from the capacitors. Every circuit node needs some path for DC current to the ground.

A capacitor's transient behavior is described by the equation:

i(t) = C * (dv(t)/dt)

Its initial voltage is only important when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An capacitor's AC behavior is described by the equation:

i = j ω * C * v

All capacitor names must begin with C.

Netlist Format:

C<device_name> <N+> <N-> <value>

Example:

C1 1 2 10p

[[RF.Spice A/D]] provides three types of capacitors: simple, user-defined (or real) and semiconductor. The standard capacitor parameters are N+, N-, VALUE, and IC. In a simple capacitor, VALUE must
be specified for the capacitance in Farads. IC is the (optional) initial condition for the capacitor voltage.

==Center-Tapped Ferrite Core Transformer==

[[File:GK97.png]]

This five-pin three-port device models a center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

==Controlled Sine Wave Oscillator==

[[File:G24.png]]

This is a four-terminal function generator with a sinusoidal wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.
This function has parameterizable values of low and high peak output voltage.

Model Identifier: sine

Netlist Form:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> sine cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) sine

.model sine sine cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[1 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|}

==Controlled Sources==

Circuits can contain linear dependent sources characterized by one of the following equations (where g,
e, f, and h are constants representing transconductance, voltage gain, current gain, and transresistance,
respectively):

<SPAN STYLE="font-size: 9pt ; ">i<sub>out</sub> = g v<sub>in</sub>
     v<sub>out</sub> = e v<sub>in</sub>
     i<sub>out</sub> = f i<sub>in</sub>
     v<sub>out</sub> = h i<sub>in</sub></SPAN>
<P CLASS="Bodytext" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; ">
For further information, refer to:</P>

Linear Current Controlled Current Source (CCCS)

Linear Voltage Controlled Current Source (VCCS)

Linear Current Controlled Voltage Source (CCVS)

Linear Voltage Controlled Voltage Source (VCVS)

==Controlled Square Wave Oscillator==

[[File:G25.png]]

This is a four-terminal function generator with a square wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defines voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: square

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> square cntl_array = [<value1> <value2>] freq_array = [<value1> <value2>] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 3) %vd(2 4) square

.model square square cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Duty_cycle||Duty cycle||-||0.5||
|-
|Rise_time||Output rise time||sec||1.0e-9||
|-
|Fall_time||Output fall time||sec||1.0e-9||
|-
|}

==Controlled Triangle Wave Oscillator==

[[File:G26.png]]

This is a four-terminal function generator with a triangle wave output, whose frequency is controlled by an input voltage. The functional dependency of the output frequency on the input voltage is piecewise linear and is defined as a two-dimensional table similar to a piecewise linear (PWL) controlled source. In the "frequency vs. voltage" curve, the array "cntl_array" defined voltage values in Volts and the array "freq_array" defines the corresponding frequencies in Hz.

Model Identifier: triangle

Netlist Format:

A<device_name> %vd(<cntl_in_pin> <cntl_in_ref_pin>) %vd(<out_pin>
<out_ref_pin>) <model_name>

.model <model_name> tirangle cntl_array = [<value1> <value2>]
freq_array = [<value1> <value2>]{<param1 = value> < param2 = value> ...}

Example:

A1 %vd(1 4) %vd(2 3) triangle

.model triangle triangle cntl_array = [0 1] freq_array = [1 1000]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Cntl_array||control array||V||[0 1]||required
|-
|Freq_array||frequency array||Hz||[0 1000]||required
|-
|Out_low||output peak low value||V||-1.0||
|-
|Out_high||output peak high value||V||1.0||
|-
|Rise_duty||Rise time duty cycle||0.5||
|-
|}

== Crystal ==

[[File:GK78.png]]

This is a 2-pin parameterized crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CM||motional capacitance||F||10f||
|-
|C0||shunt capacitance||F||1p||
|-
|RM||motional resistance||Ohms||100||
|-
|LM||motional inductance||H||100m||
|-
|}

==Current Noise Source==

[[File:GL16.png]]

This is a current noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the [[parameters]] of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise current||A/√Hz||1p||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Current Source==

[[File:G17B.png]]

Current source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a current source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset current. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==Current-Controlled Switch==

[[File:G20.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Current-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the turn-on and turn-off currents in Amperes and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the rest of [[parameters]]. When the current through the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the current through the switch or controlling device is less than or equal to the turn off current, the switch opens.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|I_ON||turn-on current||A||0.0||
|-
|I_OFF||turn-off current||A||0.0||
|-
|RON||closed resistance||Ohms||1.0||
|-
|ROFF||open resistance||Ohms||1/GMIN||
|-
|}

==Darlington Pair==

[[File:GK108.png]]

A Darlington pair is a three-pin device that consists of two interconnected BJT transistors of the same type. The collectors of two transistors are connected together to provide the "Collector" pin of the pair. The base of the first BJT acts the "Base" pin of the pair. The emitter of the first BJT is internally connected to the base of the second BJT. The emitter of the second BJT acts as the "Emitter" pin of the pair. There are two types of Darlington pair: NPN and PNP. The parameterized generic Darlington pair also contains a diode connected between the collector and emitter pin as well as two base-emitter resistors, one across each BJT.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|is_bjt||bjt saturation current||A||1.0e-12||
|-
|bf_bjt||bjt forward beta||-||150||
|-
|nf_bjt||bjt forward emission coefficient||-||1||
|-
|ise_bjt||B-E leakage saturation current||A||0||
|-
|ne_bjt||B-E leakage emission coefficient||-||1||
|-
|br_bjt||ideal maximum reverse beta||-||1||
|-
|nr_bjt||reverse current emission coefficient||-||1||
|-
|isc_bjt||B-C leakage saturation current||A||0||
|-
|nc_bjt||B-C leakage emission coefficient||-||1||
|-
|rb_bjt||zero bias base resistance||Ohms||0||
|-
|irb_bjt||current where base resistance falls halfway to minimum value||A||inf||
|-
|rbm_bjt||minimum base resistance at high currents||ohms||0||
|-
|re_bjt||emitter resistance||Ohms||0||
|-
|rc_bjt||collector resistance||Ohms||0||
|-
|cje_bjt||B-E zero bias depletion capacitance||F||0||
|-
|vje_bjt||B-E built-in potential||V||0.75||
|-
|mje_bjt||B-E junction grading coefficient||-||0.33||
|-
|cjc_bjt||B-C zero bias depletion capacitance||F||0||
|-
|vjc_bjt||B-C built-in potential||V||0.75||
|-
|mjc_bjt||B-C junction exponential factor||-||0.33||
|-
|tf_bjt||ideal forward transit time||sec||0||
|-
|tr_bjt||ideal reverse transit time||sec||0||
|-
|is_d||diode saturation current||A||1.0e-12||
|-
|rs_d||diode resistance||Ohms||0||
|-
|n_d||diode emission coefficient||-||1||
|-
|cjo_d||diode junction capacitance||F||0||
|-
|vj_d||diode junction potential||V||1||
|-
|m_d||diode grading coefficient|| ||0.5||
|-
|tnom||parameter measurement temperature||deg C||27||
|-
|r1||first base-emitter resistance||Ohms||1k||
|-
|r2||second base-emitter resistance||Ohms||1k||
|-
|}

== DC Bias Sources Vcc, Vee, Vdd, Vss ==

[[File:GL12.png]]

These are simple 1-pin DC voltage sources. Vcc and Vdd provide a positive voltage, while Vee and Vss provide a negative voltage

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|vcc||bias voltage||V||+15||required
|-
|vee||bias voltage||V||-15||required
|-
|vdd||bias voltage||V||+15||required
|-
|vss||bias voltage||V||-15||required
|-
|}

==Digital-to-Analog Converter (DAC) Bridge==

[[File:GK43.png]]

The DAC Bridge takes a digital value from a digital node and can only be eiter "0", "1",
or "U". It then outputs the value "out_low", "out_high" or "out_udndef",
or ramps linearly toward one of these "final" values from its curent analog output level. This
ramping speed depends on the values of "t_rise" and "t_fall".

Model Identifier: dac_bridge

Netlist Format:

A<device_name> [<in_pin> {<in2_pin>> ...}] [<out_pin> {<out2_pin> ...}] <model_name>

.model <model_name> dac_bridge {<param1 = value> < param2 = value> ...}

Example:

A [1] [2] dac_bridge

.model dac_bridge dac_bridge out_low = 0 fall_delay = 1n

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|out_low||analog output for 0 digital input||V||0||required
|-
|out_high||analog output for 1 digital input||V||1||required
|-
|out_undef||analog output for undefined digital input||V||0.5||required
|-
|input_load||capacitive input load||F||1p||
|-
|t_rise||L-to-H delay time||sec||1n||
|-
|t_fall||H-to-L delay time||sec||1n||
|-
|}

==Diode==

[[File:G9.png]]

Diodes allow current flow only in one direction, following their symbol's arrow, and thus can be used as simple solid
state switches in AC circuits.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process models can be either junction diodes or Schottky barrier diodes. Area factor scales the model parameters
IS, RS, CJO, and IBV. VD is the initial voltage, and TEMP is the overriding temperature. Descriptions of the process model parameters are given in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||0||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|EG||activation energy||eV||1.11||
|-
|XTI||saturation current temp. exp.||-||3.0||
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||forward bias junction fit parameter||-||0.5||
|-
|BV||reverse breakdown voltage||V||inf||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|}

==Diode Bridge==

[[File:GK107.png]]

This four-pin device is a bridge configuration of four generic diodes.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|IS||saturation current||A||1e-14||
|-
|RS||ohmic resistance||Ohms||0||
|-
|N||emission coefficient||-||1||
|-
|TT||transit-time||sec||0||
|-
|CJO||zero-bias junction capacitance||F||10p||
|-
|VJ||junction potential||V||1||
|-
|M||grading coefficient||-||0.5||
|-
|BV||reverse breakdown voltage||V||1000||
|-
|IBV||current at breakdown voltage||A||1e-3||
|-
|TNOM||parameter measurement temperature||deg C||27||
|-
|}

==Doubly Center-Tapped Ferrite Core Transformer==

[[File:GK98.png]]

This six-pin four-port device models a doubly center-tapped physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of full-winding primary inductor coupling turns||-||100||required
|-
|n_sec||number of full-winding secondary inductor coupling turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== DPDT Switch ==

[[File:GK74.png]]

This is an 8-pin device that models a double-pole double-throw switch. It has two input signals and four output pins. When the control voltage is at the high state, the first and second input voltages are transferred to the first and third output pins, respectively. When the control voltage is at the low state, the first and second input voltages are transferred to the second and fourth output pins, respectively.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== DPST Switch ==

[[File:GK73.png]]

This is a 6-pin device that models a double-pole single-throw switch. It has two input signals and two output signals. When the switch on, the first and second input voltages are transferred to the first and second output pins, respectively. When the switch is off, the output pin do not receive any input signals.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Ferrite Core Transformer==

[[File:GK95.png]]

This four-pin two-port device models a physical transformer with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. For this device you need to specify physical parameters like cross sectional area, core length and number of primary and secondary turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_prim||number of primary turns||-||100||required
|-
|n_sec||number of secondary turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== FM Modulated Source ==

[[File:GL24.png]]

This is a voltage source with a single-tone frequency modulated waveform. The FM modulation index MDI is defined as the ratio of maximum frequency deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

==Frequency Meter==
[[File:G114.png]]

The Frequency Meter is a four-pin shunt device that is connected in parallel with an AC source just like a voltmeter and measures the operating frequency of the AC circuit. The input pins are connected across the AC source. The voltage across the output pins is equal to the frequency of the source in Hertz within a scale factor SF. Note that the Frequency Meter is designed to work with a single-tone AC source of unit amplitude. If the amplitude of the source is not one, multiply the SF parameter by the non-unit source amplitude value. The output voltage of the Frequency Meter can be used in conjunction with linear or nonlinear dependent sources to model frequency-dependent quantities.

Model Identifier: fmeter

Parameters:

The only parameter is the scale factor SF with a default value of 1.0. Set SF = 1e-6 to read out the frequency in MHz. Set SF = 1e-9 to read out the frequency in GHz. Set SF = 6.283185 (2*pi) to read out the angular frequency ω in radian/s.

== Fuse ==

[[File:GK76.png]]

This is a 2-pin interactive current-controlled switch. If the current passing through the fuse is less than a specified threshold current, the switch is closed. If the current exceeds the threshold level, the fuse breaks and remains open thereafter. The device's symbol changes to display its state.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|r||resistance when intact||Ohms||1.0||
|-
|i_thresh||threshold current||A||1.0||
|-
|}

==Ground==

[[File:G15.png]]

Ground has a voltage of zero (0) and is used as a reference to compute electrical values in the circuit.
All circuits <B>must</B> be grounded to be properly simulated. There is no limit on the number of grounds
you may use in a circuit. All components connected to ground are referenced to a common point and treated
as linked through ground.

==Hysteresis Block (XSPICE)==

[[File:G37.png]]

The Hysteresis block is a simple buffer stage that provides hysteresis of the output with respect to the
input. The in_low and in_high parameter values. The output values are limited to out_lower_limit and
out_upper_limit. The value of \93hyst\94 is added to the in_low and in_high points in order to specify the
points at which the slope of the hysteresis function would normally change abruptly as the input transitions
from a low to a high value. Likewise, the value of \93hyst\94 is subtracted from the in_high and in_low values
in order to specify the points at which the slope of the hysteresis function would normally change abruptly
as the input transitions from a high to a low value. In fact, the slope of the hysteresis function is
never allowed to change abruptly but is smoothly varied whenever the input_dowmain smoothing parameter
is set greater than zero.

Model Identifier: hyst

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> hyst {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 hysteresis_block

.model hysteresis_block hyst in_low = 0.0 in_high = 1.0

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default
|-
|In_low||input low value||0.0
|-
|in_high||input high value||1.0
|-
|hyst||hysteresis||0.1
|-
|out_lower_limit||output lower limit||0.0
|-
|out_upper_limit||output upper limit||1.0
|-
|input_domain||input smoothing domain||0.01
|-
|fraction||smoothing fraction/absolute value switch||true
|-
|}

==Ideal Center-Tapped Transformer with Push-Pull Input==

[[File:XFMR4.png]]

The ideal center-tapped transformer with push-pull input is a five-pin three-port device with two primary input ports and one secondary output port. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P1}{v_S} = \frac{v_P2}{v_S} = n </math>

where v<sub>S</sub> is the secondary voltage, v<sub>P1</sub> is measured between the top primary pin P1 and the center tap pin, and v<sub>P2</sub> is measured between the center tap pin and the bottom primary pin P2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P1</sub>/N<sub>S</sub> = N<sub>P2</sub>/N<sub>S</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Center-Tapped Transformer with Push-Pull Output==

[[File:XFMR3.png]]

The ideal center-tapped transformer with push-pull output is a five-pin three-port device with one primary input port and two secondary output ports. Its model is based on the [[Glossary_of_Generic_Analog_Devices#Ideal_Transformer | Ideal Transformer]], and the relationship between its primary and secondary voltages is given by:

<math> \frac{v_P}{v_{S1}} = \frac{v_P}{v_{S2}} = n </math>

where v<sub>P</sub> is the primary voltage, v<sub>S1</sub> is measured between the top secondary pin S1 and the center tap pin, and v<sub>S2</sub> is measured between the center tap pin and the bottom secondary pin S2. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S1</sub> = N<sub>P</sub>/N<sub>S2</sub>, which represents the primary-to-secondary (half-winding) turns ratio.

==Ideal Diode==

[[File:GK106.png]]

This 2-pin device is a very basic and primitive model of a diode as a rectifier or switch. When the voltage across the device's terminals is positive, it acts as a short circuit. When the voltage across the device's terminals is negative, it acts as an open circuit.

Parameters:

None

==Ideal Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This is a very basic and primitive model of an operational amplifier. It has only one parameter, open loop gain with a default value of 50,000, which is adequate for most cases. The ideal Op-Amp device doesn't require any DC bias voltages.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|A||open loop gain||-||50,000||
|-
|}

==Ideal Transformer==

[[File:XFMR1.png]]

The ideal transformer is a four-pin two-port device with the following relationship between the voltages and currents at its primary and secondary ports:

<math> \frac{v_P}{v_S} = - \frac{i_S}{i_P} = \frac{N_P}{N_S} = n </math>

where v<sub>P</sub>, i<sub>P</sub>, N<sub>P</sub> are the primary voltage, current and number of turns, respectively, and v<sub>S</sub>, i<sub>S</sub>, N<sub>S</sub> are the secondary voltage, current and number of turns, respectively. The red dots show the polarity of the windings on each side. This model has one parameter: ratio = n = N<sub>P</sub>/N<sub>S</sub>, which represents the primary-to-secondary turns ratio. Note that the ideal transformer model is defined based on controlled sources and does not involve any magnetic physical parameters as opposed to mutual inductors or ferrite core transformer.

==Inductance Meter==

[[File:G37.png]]

The Inductance Meter measures the total inductance between a circuit node and the ground. The input pin of the device is connected to the measurement node. The output voltage of the device is then a scaled value equal to the total inductance seen on its input multiplied by the gain parameter. This model is primarily intended as a building block for other models which must sense an inductance value and alter their behavior based upon it. Care must be exercised when connecting an Inductance Meter to the inductors of a circuit. This is due to the fact that inductors are treated by SPICE as current sources. This can cause a problem when an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor.

Model Identifier: lmeter

Netlist Format:

A<device_name> <in_pin> <out_pin> <model_name>

.model <model_name> imeter {<gain = value>}

Example:

A1 1 2 inductance_meter

.model inductance_meter lmeter gain = 1

Parameters:

The only parameter is the gain with a default value of 1.0.

==Inductive Coupler Block==

[[File:GK99.png]]

The Inductive Coupler Block couples any two existing inductors. This block doesn't have any pins because it doesn't actually represent inductors, only the coupling between them. This is useful if you want to
couple two inductors that are in different parts of the circuit, or if you want to couple more than two inductors together. In the latter case, use more than one of these, with each one coupling a pair of inductors.

The standard parameters are Inductor1, Inductor2, and k. Inductor1 is the name of first inductor, Inductor2 is the name of the second inductor, and k is the coefficient of coupling, 0 < k ≤ 1.

==Inductive Coupling (XSPICE)==

[[File:G41.png]]

This function is a conceptual model which is used as a building block to create a wide variety of inductive and magnetic circuit models. This function is normally used in
conjunction with the “core” model, but it can also be used with resistors, hysteresis blocks, etc. to build up systems which mock the behavior of linear and nonlinear components.
The lcouple takes as an input (on the “l” port) a current. This current value is multiplied by the num_turns value, N, to produce an output value (a voltage value which appears on the
mmf_out port). The mmf_out acts similar to a magnetomotive force in a magnetic circuit;
when the lcouple is connected to the “core” model, or to some other resistive device, a current will flow. This current value (which is modulated by whatever the lcouple is
connected to) is then used by the lcouple to calculate a voltage “seen” at the “l” port. The voltage is a function of the derivative with respect to time of the current value seen at mmf_out.

The most common use for lcouple will be as a building block in the construction of transformer models. To create a transformer with a single input and a single output, you
would require two lcouple models plus one “core” model.

Example:

A1 (1 0) (2 3) lcouple1

.model lcouple1 lcouple ( num_turns = 10 )

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|num_turns||number of turns||-||1||required
|-
|}

==Inductor==

[[File:GK121.png]]

Inductors are used to store magnetic energy. An inductor's ability to counteract current changes passing through it is called its inductance (L), which is
measured in Henrys. In a (steady-state) DC analysis, the inductor acts like a short circuit. It is indeed treated as a current source, which can be problematic if an inductor is connected in series with a current source, or in series with a voltmeter, or in series with another inductor. The resistor may be of negligible value or one that accounts for the coil resistance of the inductor. In AC and transient analyses, the inductor develops a voltage across it in response to the changing magnetic
flux within its coil.

An inductor's transient behavior is described by the equation:

v(t) = L*(di(t)/dt)

The inductor's initial condition is optional. It is the initial value of the inductor current in Amperes that flows from node N+ through the inductor to node N-. The only time that the initial current matters is when the simulator performs a transient analysis, and the "Use Initial Conditions" checkbox is checked.

An inductor's AC behavior is described by the equation:

v = j ω * L * i

All inductor names must begin with L.

Netlist Format:

L<device_name> <N+> <N-> <value>

Example:

L1 1 2 10u

==Inductor with Ferrite Core==

[[File:GK94.png]]

This 2-pin device models a physical inductor with a magnetic ferrite core. Its model is based on XSPICE's magnetic core and inductive coupling models. Unlike the standard inductor device, you do not specify an inductance value for the inductor with ferrite core. Rather, you specify physical parameters like cross sectional area, core length and number of turns. The physical model of the magnetic device is defined by two vectors: magnetic field intensity H in A/m and magnetic flux density B (also known as magnetic induction) in Tesla. The default array values are:

H_array = [-250 -100 -50 -37.5 -25 -12.5 0 12.5 25 37.5 50 100 250]

B_array = [-0.375 -0.36 -0.32 -0.29 -0.24 -0.15 0 0.15 0.24 0.29 0.32 0.36 0.375]

To change the value of H/B arrays, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|n_turns||number of turns||-||100||required
|-
|area||cross-sectional area||m<sup>2</sup>||1e-5||
|-
|length||core length||m||0.01||
|-
|}

== Insulated Gate Bipolar Transistor (IGBT)==

[[File:GK111.png]]

This is a 3-pin parameterized Insulated Gate Bipolar Transistor (IGBT) device with three pins: Collector(C), Gate (G), and Emitter (E). It is primarily used as a fast electronic switch. The IGBT combines the simple gate-drive characteristics of MOSFETs with the high-current and low-saturation-voltage capability of bipolar transistors. The device's model consists of an isolated gate FET for the control input, and a PNP bipolar power transistor as a switch. To further modify the internal device models, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|cap||parasitic capacitance||F||1n||
|-
|rg||gate resistance||Ohms||5||
|-
|re||emitter resistance||Ohms||0.05||
|-
|bf||pnp transistor forward beta||-||1||
|-
|vto||MOSFET threshold voltage||V||5||
|-
|kt||MOSFET transconductance||-||2.99||
|-
|cgso||MOSFET voltage gate-source overlap capacitance||F||5u||
|-
|nd||diode emission coefficient||-||50||
|-
|cjo||diode junction capacitance||F||1n||
|-
|}

==Interactive Switch==

[[File:GK75.png]]

This device is an interactive switch that can be closed or opened either directly from the Schematic Editor by clicking on its symbol or from the Instrument Panel.

==Junction Field Effect Transistor (JFET)==

[[File:G12.png]]

The JFET is the simplest transistor device and has three pins: gate, drain and source. The JFET defaults are based on the Shichman and Hodges FET model. This is a square-law device because of the expression relating the drain current to the gate-to-source voltage:
Idrain=*(VGS-Vthreshold)2. In real JFETs, near the saturation point, the drain currents vary with the drain voltages. This can be modeled by the following formula: Idrain=*(VGS-VTO)2*(1+*VDS), which yields an increasing
drain current for increasing values of VDS.

The gate-to-source and gate-to-drain junctions each have a nonlinear capacitor. The zero-bias capacitance value is selected for each junction.

The standard device parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

The process model parameters are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||threshold voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||ohms||0||100
|-
|RS||source ohmic resistance||ohms||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|IS||gate junction saturation current||A||1.0e-14||1.0e-14
|-
|B||doping tail parameter|| ||1||1.1
|-
|KF||flicker-noise coefficient|| ||0||
|-
|AF||flicker-noise exponent|| ||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula|| ||0.5||
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

== Light Emitting Diode (LED) ==

[[File:GK114.png]]

This is a two-pin parameterized diode device that emits light of a certain wavelength when it is forward-biased.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rs||ohmic resistance||Ohms||10||
|-
|vj||junction potential||V||0.6||
|-
|cjo||zero bias junction capacitance||F||10p||
|-
|tt||transit time||sec||0.1n||
|-
|}

==Linear Current-Controlled Current Source (CCCS)==

[[File:G2.png]]

The CCCS is a current source whose current is directly proportional to the current across a controlling Ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the current gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the current gain.

Model Identifier: cccs

Netlist Format:

F<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

F1 1 0 V1 1.0

==Linear Current-Controlled Voltage Source (CCVS)==

[[File:G4.png]]

The CCVS is a voltage source whose voltage is directly proportional to the current through a controlling ammeter or a voltage source. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Ammeter or voltage source, as well as the trans-resistance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling ammeter, and you just specify the trans-resistance gain.

Model Identifier: ccvs

Netlist Format:

H<device_name> <N+> <N-> <controlling_device_name> <value>

Example:

H1 1 0 V1 1.0

==Linear Voltage-Controlled Current Source (VCCS)==

[[File:G3.png]]

The VCCS is a current source whose current is directly proportional to the voltage across a controlling voltmeter or the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the trans-conductance gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the trans-conductance gain.

Model Identifier: vccs

Netlist Format:

G<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

G1 1 0 2 0 1.0

==Linear Voltage-Controlled Voltage Source (VCVS)==

[[File:G1.png]]

The VCVS is a voltage source whose voltage is directly proportional to the voltage across a controlling voltmeter of the voltage between two circuit nodes. There are two versions: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling voltmeter or the two controlling nodes, as well as the voltage gain, which has a default value of one. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the voltage gain.

Model Identifier: vcvs

Netlist Format:

E<device_name> <N+> <N-> <NC+> <NC-> <value>

Example:

E1 1 0 2 0 1.0

==Lossless Transmission Line==

[[File:G21.png]]

The lossless transmission line is a four-pin two-port device that models only one propagating mode of an ideal transmission line. When using this SPICE model, should all four nodes of the actual circuit be distinct, two modes may be activated, and this device would be insufficient for that purpose. To circumvent this potential problem, two transmission line devices would be required. Due to the implementation details, you may produce more accurate simulation results with a lossy transmission line device with zero loss.

Optional initial condition parameters are the voltage and current at each of the transmission line ports.

The standard device parameters are Z0, TD, F, NL, IC, described below:

{| class="wikitable"
|-
|Z0||characteristic impedance
|-
|TD||transmission delay
|-
|F||frequency
|-
|NL||normalized electrical length of the transmission line with respect to the wavelength in the line at frequency F. (If F is specified, but NL is not, the default is 0.25.)
|-
|IC||initial condition (Specifies the voltage and current at each of the transmission line ports.)
|-
|}

==Lossy Transmission Line==

[[File:G22.png]]

The lossy transmission line is a four-pin two-port convolution model for uniform constant-parameter distributed lines. MNAME is the process model name, which
includes a set of pre-specified options as described below.

The device model [[parameters]] are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|R||resistance /length||Ohm /m||0.0||0.2
|-
|L||inductance/length||henrys/m||0.0||9.13e-9
|-
|C||capacitance/length||farads/m||0.0||3.65e-12
|-
|LEN||length of line||m||none||1.0
|-
|LININTERP||use linear interpolation||flag||not set||set
|-
|QUADINTERP||use quadratic interpolation||flag||not set||set
|-
|MIXEDINTERP||use linear when quadratic seems bad||flag||not set||set
|-
|COMPACTREL||special reltol for straight line checking||flag||RETOL||1.0e-3
|-
|COMPACTABS||special abstol for straight line checking||flag||ABSTOL||1.0e-9
|-
|NOCONTROL||don't do complex time control||flag||not set||set
|-
|STEPLIMIT||always limit timestep to 0.8*(delay of line)|| || ||
|-
|NOSTEPLIMIT||don't always limit timestep to 0.8*(delay of line)||flag||not set||set
|-
|TRUNCNR||use Newton-Raphson method for timestep calculation in LTRAtrunc||flag||not set||set
|-
|TRUNCDONTCUT||don't limit timestep to keep impulse-response errors low||flag||not set||set
|-
|}

<P CLASS="Normal-1">
The RLC (uniform transmission line with series loss only), RC (uniform RC line), LC (lossless transmission
line), and RG (distributed series resistance and parallel conductance only) lines have been implemented.
The length (LEN) must be given. COMPACTREL and COMPACTABS control the compaction of past history values
used in convolution. Larger values for these lower accuracy but improve speed. These are used with the
TRYTOCOMPACT option. </P>

==Magnetic Core (XSPICE)==

[[File:G42.png]]

This device is used as a building block to create a wide variety of inductive and magnetic circuit models. It is almost always to be used in conjunction with the "lcouple" model to build up systems which simulate the behavior of linear and nonlinear magnetic components. There are two fundamental modes of operation for the core model. These are the "PWL" mode (which is the default and most
likely to be of use to you) and the "Hysteresis" mode.

<b>PWL Mode (mode = 1)</b>

In the PWL mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf) value. This value is divided by the total effective length of the core to produce a value for the Magnetic Field Intensity, H, which is then used to find the corresponding Flux Density, B, using the piecewise linear relationship described by you in the H_array / B_array coordinate pairs. B is then multiplied by the cross-sectional area of the core to find the Flux value, which is output as a current. The pertinent mathematical equations are:

H = mmf / L, where L = Length (in apmere-turns/meter)

B = f(H)

Φ = B * A, where A = Area

The B value is derived from a piecewise linear transfer function described to the model by the H_array and B_array coordinate pairs. This transfer function does not include hysteretic effects; for that, you would need to substitute a HYST model for the core. The magnetic flux value Φ in turn is used by the "lcouple"
code model to obtain a value for the voltage reflected back across its terminals to the driving electrical circuit.

<b>Hysteresis Mode (mode = 2)</b>

In the Hysteresis mode, the model takes a voltage as input which it treats as a magnetomotive force (mmf)
value. This value is used as input to the equivalent of a hysteresis code model block. The parameters
defining the input low and high values, the output low and high values, and the amount of hysteresis are
as in that model. The output from this mode, as in PWL mode, is a current value which is seen across the magnetic core port.

One final note to be made about the two core models is that certain parameters are specific to one or the other. In particular, the in_low, in_high, out_lower_limit, out_upper_limit, and hysteresis parameters are not available in PWL mode. Likewise, the H_array, B_array, area, ad length values are unavailable
in Hysteresis mode. The input_domain and fraction parameters are common to both modes (though their behavior is somewhat different; for explanation of the input_domain and fraction values for the Hysteresis mode, please refer to the Hysteresis Block discussion.

Model Identifier: core

Netlist Format:

A<device_name> <mc1 _pin> <mc2_pin> <model_name>

.model <model_name> core area = <value> length = <value> H_array = [<value1> <value2>] B_array = [<value1> <value2>]
{<param1 = value> < param2 = value> ...}

Example:

A1 1 2 core

.model core core area = 1 length = 1 H_array = [0 1] B_array = [0 1]

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|H_array||magnetic field array||[0 1]||required
|-
|B_array||flux density array||[0 1]||required
|-
|Area||cross-sectional area||1||required
|-
|Length||core length||1||required
|-
|Input_domain||input smoothing domain||0.01||
|-
|Fraction||smoothing fraction/abs switch||True||
|-
|Mode||mode switch (1=pwl, 2=hyst)||1||
|-
|In_low||input low value||0.0||
|-
|In_high||input high value||1.0||
|-
|Hyst||hysteresis||0.1||
|-
|Out_lower_limit||output lower limit||0.0||
|-
|Out_upper_limit||output upper limit||1.0||
|-
|}

==Marker==

[[File:G16.png]]

The marker serves several purposes:

* It can appear as a default plot in simulations if the "Voltage Probe" box is checked.

* It can be used to set the initial voltage or voltage guess at the node it is connected to.

* It can be used as a port for a subcircuit when you choose the checkbox labeled "Use as Subcircuit Port" is checked.

* It can be used to explicitly set a node number in place of the arbitrarily assigned node number by the program. In this case, make sure the "Set Node Index" box is checked. Otherwise, it will act as just a voltage probe.

* It can be used to connect different parts of a circuit in place of wires. To use markers as virtual connectors, place them at points where wires would otherwise connect. Then set the Part Title of the two (or more) markers to the same name, and they will act as a single circuit node.

==MESFET==

[[File:G14.png]]

The MESFET is a Schottky-barrier gate FET with six times greater electron mobility than silicon. MESFETs are important devices for creating high frequency circuits. They function by creating a potential barrier between the gate and the channel when the metal gate
contacts the gallium-arsenide substrate. Electron velocity saturates for fields approximately ten times lower than with silicon. The Curtice model includes linear and saturated operation.

The standard parameters are AREA, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|AREA||area factor (optional) (If not specified, the default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

All the MESFET process model parameters are described in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|VTO||pinch-off voltage||V||-2||-2
|-
|BETA||transconductance parameter||A/V2||1.0e-4||1.0e-3
|-
|B||doping tail extending parameter||1/V||0.3||0.3
|-
|ALPHA||saturation voltage parameter||1/V||2||2
|-
|LAMBDA||channel-length modulation parameter||1/V||0||1.0e-4
|-
|RD||drain ohmic resistance||Ohm||0||100
|-
|RS||source ohmic resistance||Ohm||0||100
|-
|CGS||zero-bias G-S junction capacitance||F||0||5pF
|-
|CGD||zero-bias G-D junction capacitance||F||0||1pF
|-
|PB||gate junction potential||V||1||0.6
|-
|KF||flicker noise coefficient||-||0||
|-
|AF||flicker noise exponent||-||1||
|-
|FC||coefficient for forward-bias depletion capacitance formula||-||0.5||
|-
|}

==MOSFET==

[[File:G13.png]]

The MOSFET is an active device that has up to 4 pins. The three standard pins are gate, drain, and source. These are given in the default symbol. The bulk node, which is grounded by default, is the fourth pin. The MOSFET with the bulk is named mos_n_lvl1_4 (the lvl1 is for level 1, the n for nmos, and the 4 for 4 pins.)

The standard [[parameters]] are L, W, AD, AS, PD, PS, NRD, NRS, OFF, IC, and T. They are described below:

{| class="wikitable"
|-
|L||channel length, in meters
|-
|W||channel width, in meters
|-
|AD,AS||areas of the drain and source diffusions, in meters2
|-
|PD,PS||perimeters of drain and source junctions, in meters(They default to 0.0.)
|-
|NRD,NRS||equivalent number of squares of the drain and source diffusions (These values multiply the sheet resistance for an accurate representation of parasitic series drain and source resistance of each transistor. The default value is 1.0.)
|-
|OFF||initial condition for the DC analysis (optional)
|-
|IC||initial condition (optional) (Used when a transient analysis is desired, which starts from other than the quiescent operating point.)
|-
|T||operating temperature of the device (optional)
|-
|}

There are five different default models: square-law I-V characteristic, analytical, semi-empirical, and BSIM and BSIM2 (Berkeley Short-channel IGFET Model), which include second-order effects such as channel-length
modulation, subthreshold conduction, scattering-limited velocity saturation, small-size effects, and charge-controlled capacitance. The process parameter LEVEL specifies which of the models is chosen as indicated below:

{| class="wikitable"
|-
|LEVEL 1||Schichman-Hodges
|-
|LEVEL 2||MOS2
|-
|LEVEL 3||MOS3
|-
|LEVEL 4||BSIM
|-
|LEVEL 5||BSIM2
|-
|LEVEL 6||MOS6
|-
|}

The process model [[parameters]] for levels 1,2,3, and 6 are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|LEVEL||model index|| ||1||
|-
|VTO||zero-bias threshold voltage||V||0.0||1.0
|-
|KP||transconductance parameter||A/V2||2e-5||3.1e-5
|-
|GAMMA||bulk threshold parameter||V1/2||0.0||0.37
|-
|PHI||surface potential||V||0.6||0.65
|-
|LAMBDA||channel-length modulation (level 1 & 2 only)||1/V||0.0||0.02
|-
|RD||drain ohmic resistance||ohms||0.0||1.0
|-
|RS||source ohmic resistance||ohms||0.0||1.0
|-
|CBD||zero-bias B-D junction capacitance||F||0.0||20fF
|-
|CBS||zero-bias B-S junction capacitance||F||0.0||20fF
|-
|IS||bulk junction saturation current||A||1.0e-14||1.0e-15
|-
|PB||bulk junction potential||V||0.8||0.87
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m||0.0||4.0e-11
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m||0.0||2e-10
|-
|RSH||drain & source diffusion sheet resistance||ohm/area||0.0||10.0
|-
|CJ||zero-bias bulk junction bottom capacitance per meter2 junction area||F/m2||0.0||2e-4
|-
|MJ||bulk junction bottom grading coefficient|| ||0.5||0.5
|-
|CJSW||zero-bias bulk junction sidewall capacitance per meter junction perimeter||F/m||0.0||1.0e-9
|-
|MJSW||bulk junction sidewall grading coefficient|| ||0.5, 0.33 (level1), (level2,3)||
|-
|JS||bulk junction saturation current per meter2 of junction area||A/m2|| ||1.0e-8
|-
|TOX||oxide thickness||meter||1.0e-7||1.0e-7
|-
|NSUB||substrate doping||1/cm3||0.0||4.0e15
|-
|NSS||surface state density||1/cm2||0.0||1.0e10
|-
|NFS||fast surface state density||1/cm2||0.0||1.0e10
|-
|TPG||type gate material(+1 if opp. substrate, 0 if A1 gate, -1 if same as substrate)|| ||1.0||
|-
|XJ||metallurgical junction depth||meter||0.0||1
|-
|LD||lateral diffusion||meter||0.0||0.8
|-
|UO||surface mobility||cm2/Vs||600||700
|-
|UCRIT||critical field for mobility degradation (level2 only)||V/cm||1.0e4||1.0e4
|-
|UEXP||critical field exponent in mobility degradation (level2 only)|| ||0.0||0.1
|-
|UTRA||transverse field coefficient (deleted for level2)|| ||0.0||0.3
|-
|VMAX||maximum drift velocity of carriers||m/s||0.0||5.0e4
|-
|NEFF||total channel-charge (fixed and mobile) coefficient (level2 only)|| ||1.0||5.0
|-
|KF||flicker noise coefficient|| ||0.0||1.0e-26
|-
|AF||flicker noise exponent|| ||1.0||1.2
|-
|FC||coefficient for forward bias depletion capacitance formula|| ||0.5||
|-
|DELTA||width effect on threshold voltage (level2,3)|| ||0.0||1.0
|-
|THETA||mobility modulation (level3 only)||1/V||0.0||0.1
|-
|ETA||static feedback (level3 only)|| ||0.0||1.0
|-
|KAPPA||saturation field factor (level3 only)|| ||0.2||0.5
|-
|TNOM||parameter measurement temperature||deg. C||27||50
|-
|}

The BSIM model has no default parameters, and leaving one out is considered an error. The additional process model parameters for level 4 and 5 models are listed in the following table:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS
|-
|VFB||flat-band voltage||V
|-
|PHI||surface inversion potential||V
|-
|K1||body effect coefficient||V1/2
|-
|K2||drain/source depletion charge-sharing coefficient||
|-
|ETA||zero-bias drain-induced barrier-lowering coefficient||
|-
|MUZ||zero-bias mobility||cm2/V-s
|-
|DL||shortening of channel||m
|-
|DW||narrowing of channel||m
|-
|U0||zero-bias transverse-field mobility degradation coefficient||V-1
|-
|U1||zero-bias velocity saturation coefficient||m/V
|-
|X2MZ||sens. of mobility to substrate bias at Vds=0||cm2/V2-s
|-
|X2E||sens. of drain-induced barrier lowering effect to substrate bias||V-1
|-
|X3E||sens. of drain-induced barrier lowering effect to drain bias at Vds= Vdd||V-1
|-
|X2U0||sens. of transverse field mobility degradation to substrate bias||V-2
|-
|X2U1||sens. of velocity saturation effect to substrate bias||mV-2
|-
|MUS||mobility at zero substrate bias and at Vds= Vdd||cm2/V2-s
|-
|X2MS||sens. of mobility to substrate bias at Vds= Vdd||cm2/V2-s
|-
|X3MS||sens. of mobility to drain bias at Vds= Vdd||cm2/V2-s
|-
|X3U1||sens. of velocity saturation effect on drain bias at Vds= Vdd||mV-2
|-
|TOX||gate oxide thickness||m
|-
|TEMP||temperature at which [[parameters]] were measured||deg. C
|-
|VDD||measurement bias range||V
|-
|CGDO||gate-drain overlap capacitance per meter channel width||F/m
|-
|CGSO||gate-source overlap capacitance per meter channel width||F/m
|-
|CGBO||gate-bulk overlap capacitance per meter channel length||F/m
|-
|XPART||gate-oxide capacitance-charge model flag||
|-
|N0||zero-bias subthreshold slope coefficient||
|-
|NB||sens. of subthreshold slope to substrate bias||
|-
|ND||sens. of subthreshold slope to drain bias||
|-
|RSH||drain and source diffusion sheet resistance||ohms/area
|-
|JS||source drain junction current density||A/m2
|-
|PB||built-in potential of source drain junction||V
|-
|MJ||grading coefficient of source drain junction||
|-
|PBSW||built-in potential of source drain junction sidewall||V
|-
|MJSW||grading coefficient of source drain junction sidewall||
|-
|CJ||source drain junction capacitance per unit area||F/ m2
|-
|CJSW||source drain junction sidewall capacitance per unit length||F/m
|-
|WDF||source drain junction default width||m
|-
|DELL||source drain junction length reduction||m
|-
|}

XPART=0 selects a 40/60 drain/source charge partition; XPART=1 selects a 0/100 partition.

==Mutual Inductors==

[[File:GK100.png]]

The mutual inductors device is a pair of inductors that are coupled to each other. L1 and L2 are the names of two inductors. You have to specify the inductance of inductor L1, the inductance of inductor L2, the initial current through each, and the coupling coefficient k, 0 ≤ k ≤ 1. The mutual inductance M expressed in units of H can be calculated using the following definition:

<math> k = \frac{M}{\sqrt{L_1 L_2}} </math>

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|inductance1||inductance of inductor 1||H||1||
|-
|inductance2||inductance of inductor 2||H||1||
|-
|ic1||initial current through inductor 1||A||0||
|-
|ic2||initial current through inductor 2||A||0||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

==Non-Ideal Current Transformer==

[[File:GK104.png]]

This 8-pin device models a non-ideal lossy current transformer. Its model consists of an ideal transformer with more secondary turns than primary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. on each side of the internal ideal transformer, there is a series leakage inductance LL<sub>k</sub>, followed by a shunt winding capacitance CW<sub>k</sub> and a series winding resistance RW<sub>k</sub>, which connects to the exterior positive pin on that side. The inter-winding resistance R<sub>12</sub> is connected across the negative pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||secondary-to-primary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary leakage inductance||H||1m||
|-
|ll2||secondary leakage inductance||H||1m||
|-
|cw1||primary winding capacitance||F||1p||
|-
|cw2||secondary winding capacitance||F||1p||
|-
|r12||inter-winding resistance||Ohms||10Meg||
|-
|}

==Non-Ideal Diode==

[[File:G9.png]]

This 2-pin device is a basic simplified model of a diode as a rectifier or switch. When forward-biased, it acts as a low-valued voltage source. When reverse-biased, it acts as an open circuit until the reverse voltage exceeds the specified breakdown voltage. Then it acts as a high-valued voltage source of the reverse polarity.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|vf||forward drop voltage||V||0.5||required
|-
|vr||reverse breakdown voltage||V||100||required
|-
|}

==Non-Ideal Voltage Transformer==

[[File:GK103.png]]

This 8-pin device models a non-ideal lossy voltage transformer. Its model consists of an ideal transformer with more primary turns than secondary turns along with a number of parasitic elements. The interior pins with red wires give you direct access to the primary and secondary pins of the internal ideal transformer. There are series combinations of a winding resistance RW<sub>k</sub> and a leakage inductance LL<sub>k</sub> on the primary and secondary sides. These are connected between the positive interior and exterior pins on each side. There are also two shunt branches at the inputs of the primary and secondary sides (connected between the positive and negative exterior pins), each consisting of a distributed turn-to-turn winding resistance RDC<sub>k</sub> in series with a distributed turn-to-turn winding capacitance CW<sub>k</sub>. The inter-winding capacitance CWW<sub>12</sub> is connected across the positive pins of the primary and secondary of the ideal transformer model. In a more complete model, an external inductor LM can be connected between the positive and negative interior pins of either the primary or secondary to account for the effects of the magnetization inductance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ratio||primary-to-secondary turns ratio||-||2||required
|-
|rw1||primary winding resistance||Ohms||0.1||
|-
|rw2||secondary winding resistance||Ohms||0.1||
|-
|ll1||primary winding leakage inductance||H||1m||
|-
|ll2||secondary winding leakage inductance||H||1m||
|-
|rdc1||primary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw1||primary distributed turn-to-turn winding capacitance||F||1p||
|-
|rdc2||secondary distributed turn-to-turn winding resistance||Ohms||1u||
|-
|cw2||secondary distributed turn-to-turn winding capacitance||F||1p||
|-
|cww12||inter-winding capacitance||F||1p||
|-
|}

==Nonlinear Capacitor==

[[File:GK89.png]]

The nonlinear capacitor model allows the capacitor to be described by an arbitrary relationship between the capacitor's charge Q and the voltage V across the capacitor. In other words, Q = f(V). The nonlinear capacitance is then defined as C(V) = dQ/dV. You need to define the charge Q by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ C_DEF } * v(pos,neg)

which implies a linear capacitor, where Q = C<sub>DEF</sub> V. Therefore, C = C(V) = dQ/dV = C<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|C_DEF||default capacitance||F||1||
|-
|}

==Nonlinear Conductor==

[[File:GK88.png]]

The nonlinear conductor model allows the conductor to be described by an arbitrary relationship between the conductor's current I and the voltage V across the conductor. In other words, I = f(V). The nonlinear conductance is then defined as G(V) = dI/dV. You need to define the current I by a mathematical expression in the voltage V. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "v(pos,neg)" standing for the terminal voltage. The default expression is:

{ G_DEF } * v(pos,neg)

which implies a linear conductor, where I = G<sub>DEF</sub> V. Therefore, G = G(V) = dI/dV = G<sub>DEF</sub>.

Another example is 1e-4*(v(pos,neg))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|G_DEF||default capacitance||S||1||
|-
|}

==Nonlinear Dependent Sources==

[[File:G18.png]]

Nonlinear dependent (arbitrary) sources use an equation or mathematical expression to describe their behavior. One and only one of the two forms: V=<expr> or I=<expr> must be given.

Netlist Format:

B<device_name> v = <expression>

B<device_name> i = <expression>

Examples:

v = I(v1) + 3* I(v2)

I = v(i1) + 3* v(2) + 5 * v(3) ^2

The first example is a current-controlled voltage source. The v on the left side of the equation
indicates that it is a voltage source. I(v1) and I(v2) are the currents through voltage sources named v1 and v2, respectively.

The second example is a voltage-controlled current source. v(2) and v(3) represents the voltages at nodes 2 and 3, respectively, and v(i1) represents the voltage across a current source named i1.

The following mathematical functions defined for real variables can be used in the expressions:

abs, acos, acosh, asin, asinh, atan, atanh, cos, cosh, exp, ln, log, sin, sinh, sqrt, tan.

The function "u" is the unit step and "uramp" is the integral of the unit step. The
unit step is one if its argument is greater than zero and zero if its argument is less than zero. The
ramp function (uramp) is 0 for argument values less than zero and equal to the argument for argument values
greater than zero.

The following operators are permissible: +, -, *, /, ^, and unary-.

To get time into an expression, integrate the current from a constant current source with a capacitor
and use the voltage across the capacitor.

==Nonlinear Inductor==

[[File:GK90.png]]

The nonlinear inductor model allows the inductor to be described by an arbitrary relationship between the inductor's magnetic flux Φ and the current I flowing through the inductor . In other words, Φ = f(I). The nonlinear inductance is then defined as L(I) = dΦ/dI. You need to define the flux Φ by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ L_DEF } * i(vx)

which implies a linear inductor, where Φ = L<sub>DEF</sub> I. Therefore, L = L(I) = dΦ/dI = L<sub>DEF</sub>.

Another example is 1e-4*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|L_DEF||default inductance||H||1||
|-
|}

==Nonlinear Resistor==

[[File:GK87.png]]

The nonlinear resistor model allows the resistor to be described by an arbitrary relationship between the voltage V across the resistor and its current I. In other words, V = f(I). The nonlinear resistance is then defined as R(I) = dV/dI. You need to define the voltage V by a mathematical expression in the current I. You have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text. Enter any mathematical expression in the variable "i(vx)" standing for the device current. The default expression is:

{ R_DEF } * i(vx)

which implies a linear resistor, where V = R<sub>DEF</sub> I. Therefore, R = R(I) = dV/dI = R<sub>DEF</sub>.

Another example is 10*(i(vx))^2.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R_DEF||default resistance||Ω||1||
|-
|}

==Operational Amplifier (Op-Amp)==

[[File:GK105.png]]

This three-pin device models a parameterized operational amplifier with a very high voltage gain, a very high input impedance and a very low output impedance. The behavioral model of the parameterized Op-Amp device is based on the algorithm found in the book <B>Macromodeling with Spice</B>,
authored by Connelly & Choi, published by Prentice Hall. The default parameters are those of the 741 Op-Amp. This device doesn't require external DC bias voltage sources. Its positive and negative DC bias voltages are specified as its parameters. Sometimes the simulation doesn't converge if there is no DC path from the output of the Op-Amp to the ground.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|r_in_dm||differential mode input resistance||Ohms||2Meg||
|-
|r_in_cm||common mode input resistance||Ohms||2G||
|-
|Avd0||differential mode DC gain||dB||106||
|-
|CMRR||common mode rejection ratio||dB||90||
|-
|r_out||output resistance||Ohms||75||
|-
|c_in||input capacitance||F||1.4p||
|-
|ios||input offset current||A||20n||
|-
|ib||input bias current||A||80n||
|-
|vio||input offset voltage||V||1m||
|-
|slew_pos||positive slew rate||V/s||0.5e6||
|-
|slew_neg||negative slew rate||V/s||0.5e6||
|-
|curr_src_max||maximum output source current||A||25m||
|-
|curr_sink_||maximum output sink current||A25m||
|-
|fp1||dominant pole frequency||Hz||5||
|-
|fp2||second pole frequency||Hz||2Meg||
|-
|fp3||third pole frequency||Hz||20Meg||
|-
|fp4||fourth pole frequency||Hz||100Meg||
|-
|fz||first zero frequency||Hz||5Meg||
|-
|vcc_pos||positive dc voltage source||V||12||
|-
|vcc_neg||negative dc voltage source||V||12||
|-
|}

== Optocoupler ==

[[File:GK115.png]]

This is a five-pin parameterized optocoupler device. Its model consists of an ideal diode device in series with an Ohmic resistance connected between the Anode (A) and Cathode (K) pins together with a bipolar junction transistor device with three accessible pins, Collector (C), Base (B) and Emitter (E). A current-controlled current source is connected between base and collector of the BJT, whose current is controlled by the current passing through the diode. The proportionality constant is twice the specified value of the current transfer ratio (ctr) parameter.

You can change or enhance the models of the diode and BJT by adding more parameters. To do so, you have to open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|ctr||current transfer ratio||-||0.5||
|-
|rd||diode ohmic resistance||Ohms||0.1||
|-
|}

== Overtone Crystal ==

[[File:GK79.png]]

This is a 2-pin parameterized overtone crystal device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|LM||fundamental motional inductance||H||250m||
|-
|CM1||fundamental motional capacitance||F||10f||
|-
|RM1||fundamental motional resistance||Ohms||20||
|-
|RM3||3rd overtone motional resistance||Ohms||50||
|-
|RM5||5th overtone motional resistance||Ohms||100||
|-
|RM7||7th overtone motional resistance||Ohms||150||
|-
|C0||shunt capacitance||F||3p||
|-
|}

== Photodiode ==

[[File:GK113.png]]

This is a 4-pin parameterized photodiode device. A pair of pins, Anode (A) and Cathode (K), represent the physical terminals of the photodiode. The photodiode model connected between the anode and cathode pins consists of the parallel connection of an ideal diode, a dark current source, a noise current source, a current-controlled current source, a diode capacitance, a shunt resistance altogether with a series resistance.

Another pair of pins IS+ and IS- act as an ammeter that must be inserted in a control circuit. The current passing through this ammeter controls the current of the photodiode. The default proportionality constant is unity. The controlling current is typically a function of light intensity incident on the surface of the photodiode.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|id||dark current||A||1n||
|-
|ir||noise current||A||1p||
|-
|cd||diode capacitance||F||10p||
|-
|rs||series resistance||Ohms||1m||
|-
|rp||parallel resistance||Ohms||1Meg||
|-
|}

==Piecewise Linear (PWL) Controlled Source==

[[File:GL49.png]]

The Piecewise Linear (PWL) Controlled Source is a single-input and single-output function generator whose output is not necessarily
linear for all input values. Instead, it follows an I/O relationship that is specified by the x_array and y_array coordinates. The x_array and y_array values represent vectors of coordinate points on the x and y axes, respectively. The x_array values are progressively increasing input coordinate points, and the associated y_array values represent the outputs at those points. There may be as few as two pairs specified, or as many as memory and simulation speed allow.

In order to fully specify outputs for values of Vin outside of the bounds of the PWL function, the PWL
controlled source model extends the slope found between the lowest two coordinate pairs and the highest
two coordinate pairs. This has the effect of making the transfer function completely linear for Vin
less than x_array[0] and Vin greater than x_array[n]. It also has the potentially subtle effect of unrealistically
causing an output to reach a very large or small value for large inputs. You should thus keep in mind
that the PWL Source does not inherently provide a limiting capability.

In order to diminish the potential for divergence of simulations when using the PWL block, a form
of smoothing around the x_array and y_array coordinate points is necessary. This is due to the iterative
nature of the simulator and its reliance on smooth first derivatives of transfer functions in order to
arrive at a matrix solution. Consequently, the two parameters "input_domain" and "fraction" are included
to allow you some control over the amount and nature o the smoothing performed.

Fraction is a switch that is either TRUE or FALSE. When TRUE (the default setting), the simulator assumes
that the specified input_domain value is to be interpreted as a fractional figure. Otherwise, it is interpreted
as an absolute value. Thus, if fraction = TRUE and input_domain = 0.10, the simulator assumes that the smoothing
radius about each coordinate point is to be set equal to 10% of the length of either the x_array segment
above each coordinate point, or the x_array segment below each coordinate point. The specific segment
length chosen will be the smallest of these two for each coordinate point.

If fraction = FALSE and input_domain = 0.10, then the simulator will begin smoothing the transfer function at 0.10
volts (or amperes) below each x_array coordinate and will continue the smoothing process for another 0.10
volts (or amperes) above each x_array coordinate point.

Model Identifier: pwl

Netlist Format:

A<device_name> %vd(<in_pin> <in_ref_pin>) %vd(<out_pin> <out_ref_pin>) <model_name>

.model <model_name> pwl x_array = [<value1> <value2> ...] y_array = [<value1>
<value2> ...] {<param1 = value> < param2 = value> ...}

Example:

A1 %vd(2 3) %vd(1 4) pwl
.model pwl pwl x_array = [0 1] y_array = [0 1]

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|x_array||x-element array||V||[0 1]||required
|-
|y_array||y-element array||V||[0 1]||required
|-
|input_domain||input smoothing domain||-||0.01||
|-
|fraction||smoothing %/abs switch||-||True||
|-
|}

== PM Modulated Source ==

[[File:GL25.png]]

This is a voltage source with a single-tone phase modulated waveform. The PM modulation index MDI is defined as the ratio of maximum phase deviation to maximum signal amplitude.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|V0||offset||V||0||
|-
|VA||amplitude||V||1||
|-
|FC||carrier frequency ||Hz||1||required
|-
|MDI||modulation index||-||0||required
|-
|FS||signal frequency ||Hz||1||required
|-
|}

== Potentiometer ==

[[File:GK77.png]]

This is a 3-pin device that models a potentiometer with options for either linear or logarithmic resistance. position = 0 corresponds to the wiper being at the extreme left and position = 1 corresponds to the wiper being at the extreme right. With the default position = 0.5 corresponding to the midpoint, this device functions as a one-half voltage divider.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|position||position of wiper connection||-||0.5||Must be between 0.0 and 1.0.
|-
|log||log-linear switch||-||False||Select False for linear and True for logarithmic.
|-
|r||total resistance||Ohms||0.1u||
|-
|log_multiplier||multiplier constant for log resistance||-||1.0||
|-
|}

== Programmable Unijunction Transistor (PUT)==

[[File:GK112.png]]

This is a 3-pin parameterized Programmable Unijunction Transistor (PUT) device with three pins: Base 1 (B1), Base 2 (B2) and Emitter (E). It is biased with a positive voltage between the two bases. This device has a unique characteristic that when it is triggered, its emitter current increases regeneratively until it is restricted by emitter power supply. It exhibits a negative resistance characteristic and so it can be employed as an oscillator. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To change these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|eta||-||-||0.6||
|-
|rbb||total base-to-base resistance||Ohms||40k||
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

==Random Resistor==

[[File:GK93.png]]

The random resistor device models a resistor whose resistance is a random number between 0 and a maximum specified value.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|max_val||maximum resistance value||Ω||1k||
|-
|}

==Real Capacitor==

[[File:GK117.png]]

This is primarily a non-ideal, temperature-dependent capacitor model. You can access it from the Parts Menu as '''User-Defined Capacitor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent capacitance is computed using the quadratic equation:

C(T) = C(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance and a series inductance together with the capacitor, all in parallel with a shunt resistance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Resr||series resistance||Ω||10||
|-
|Ls||inductance||H||1p||
|-
|C||capacitance||F||1n||
|-
|Rp||parallel resistance||Ω||1G||
|-
|ic||voltage initial condition||V||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||F/°C||0.1||
|-
|tc2||second-order temperature coefficient||F/°C<sup>2</sup>||0.01||
|-
|}

==Real Inductor==

[[File:GK118.png]]

This is primarily a non-ideal inductor model. You can access it from the Parts Menu as '''User-Defined Inductor'''. Its series resistor has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series resistance together with the inductor, and the combination in parallel with a shunt capacitance.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Rdc||series resistance||Ω||10||
|-
|L||inductance||H||1||
|-
|Cp||capacitance||F||1p||
|-
|ic||current initial condition||A||0||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Real Resistor==

[[File:GK116.png]]

This is primarily a non-ideal, temperature-dependent resistor model. You can access it from the Parts Menu as '''User-Defined Resistor'''. It has two temperature coefficients: first-order TC1 temperature and second-order TC2. The value of the temperature-dependent resistance is computed using the quadratic equation:

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

The device's model includes a series inductance together with the resistor.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|R||resistance||Ω||1k||
|-
|Ls||inductance||H||1n||
|-
|temp||operating temperature||deg C||27||
|-
|tc1||first-order temperature coefficient||Ω/°C||0.1||
|-
|tc2||second-order temperature coefficient||Ω/°C<sup>2</sup>||0.01||
|-
|}

==Resistor==

[[File:GK119.png]]

Resistors are passive devices that dissipate power. Their resistance value varies depending on how much power they can dissipate and is measured
in Ohms. The transient, DC and AC behaviors of a resistor are all described by the same equation:

v = R * i

where v is the voltage across the resistor, i is the current passing through the resistor, and R is the resistance. The value of R must be nonzero.

All resistor names must begin with R.

Netlist Format:

R<device_name> <N+> <N-> <value>

Example:

R1 1 2 1k

[[RF.Spice A/D]] provides three types of resistor: Simple, User-Defined (Real Resistor) and Semiconductor. The resistance of the simple resistor is a single value expressed in Ohms. You can also set the Monte Carlo tolerance for this resistor.

==Schottky Diode==

[[File:GK80.png]]

The Schottky diode has the same model as the generic diode with a nonzero transit time (tt), a nonzero junction capacitance (cjo) and a typically larger saturation current (is), a lower junction potential (vj) and a smaller grading coefficient (m).

==Semiconducting Capacitor==

[[File:GK83.png]]

This is the more general form of the Capacitor model and allows for the calculation of the actual capacitance value from strictly geometric information and the specifications of the process.

General Form:

CXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <IC=VAL>

If VALUE is specified, it defines the capacitance. If MNAME is specified, then the capacitance is calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. Either VALUE or MNAME, LENGTH, and WIDTH may be specified, but not both sets. The optional initial condition "IC" is the initial voltage across the capacitor for transient simulations.

The capacitance is computed as:

CAP = CJ * (LENGTH - NARROW) * (WIDTH - NARROW)+ 2 * CJSW * (LENGTH + WIDTH - 2NARROW) * CAP

To modify the model parameters, first double click on the capacitor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit CJ, CJSW, NARROW, DEFW, and CAP.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|CJ||junction bottom capacitance||F/m<sup>2</sup>||-||
|-
|CJSW||junction sidewall capacitance||F/m ||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|CAP||nominal capacitance for Monte Carlo simulation||F||1||
|-
|}

== Semiconductor Resistor ==

[[File:GK82.png]]

This is the more general form of the resistor model and allows for the modeling of temperature effects and for the calculation of the actual resistance value from strictly geometric information and the specifications of the process.

General Form:

RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>

If VALUE is specified, it overrides the geometric information and defines the resistance. If MNAME is specified, then the resistance may be calculated from the process information in the model MNAME and the given LENGTH and WIDTH. If VALUE is not specified, then MNAME and LENGTH must be specified. If WIDTH is not specified, then it is taken from the default width given in the model. The (optional) TEMP value is the temperature at which this device is to operate, and overrides the temperature specification in the SPICE Options Dialog.

The resistance is computed as:

R(T0) = (RSH) * [(L - NARROW) / (W - NARROW)] * RES

R(T) = R(T0) * [ 1 + TC1 * (T - T0) + TC2 * (T-T0)^2 ]

To modify the model parameters, first double click on the resistor to edit its top-level model parameters. Then choose the button labeled {{key|Edit from Table}} in the process model section. This will open a window in which you can edit TC1, TC2, RSH, RES, etc.

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|TC1||first order temperature coefficient||Ω/°C||-||
|-
|TC2||second order temperature coefficient||Ω/°C<sup>2</sup>||-||
|-
|RSH||sheet resistance||Ω/sq||-||
|-
|DEFW||default device width||m||1u||
|-
|NARROW||narrowing due to side etching||m||0||
|-
|TNOM||the parameter measurement temperature||deg C ||27||
|-
|RES||resistance multiplier for Monte Carlo simulation||Ohms||1||
|-
|}

== Silicon-Controlled Rectifier (SCR)==

[[File:GK109.png]]

This is a 3-pin parameterized Silicon-Controlled Rectifier (SCR) device with three pins: Anode (A), Cathode (K) and Gate (G). It is a unidirectional device which can conduct current only in one direction. The SCR can be triggered only by a positive current going into its gate. The device's model involves an NPN BJT and a PNP BJT. The forward beta parameters of the two transistors are set equal to 100 and 1, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|rr||reverse resistance||Ohms||1Meg||
|-
|rgk||gate-to-cathode resistance||Ohms||100||
|-
|bvf||breakdown voltage of forward diode||V||100||
|-
|bvr||breakdown voltage of reverse diode||V||100||
|-
|bvgk||breakdown voltage of gate-to-cathode diode||V||5||
|-
|}

== SPDT Switch ==

[[File:GK72.png]]

This is a 5-pin device that models a single-pole double-throw switch. The input voltage is transferred to the first output pin if the control voltage is at a high state. Otherwise, its is transferred to the second output pin.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

== SPST Switch ==

[[File:GK71.png]]

This is a 4-pin device that models a single-pole single-throw switch. It is virtually equivalent of the standard voltage-controlled switch.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|von||turn-on voltage||V||3.3||
|-
|voff||turn-off voltage||V||0.3||
|-
|vt||threshold voltage||V||1.0||
|-
|ron||on resistance||Ohms||1.0||
|-
|roff||off resistance||Ohms||1Gig||
|-
|}

==Tabulated Conductor==

[[File:GK92.png]]

The tabulated conductor model allows the conductance to be described by a table relating the device's current i(t) to its terminal voltage v(t). In effect, the conductance is defined as G = di(t)/dv(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (v,i) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tabulated Resistor==

[[File:GK91.png]]

The tabulated resistor model allows the resistance to be described by a table relating the device's terminal voltage v(t) to its current i(t). In effect, the resistance is defined as R = dv(t)/di(t). The model provides two interpolation options: cubic spline and piecewise linear. You can enter the (i,v) data pairs in the text box provided in the property dialog. Or you can import the data from a text file.

==Tapped Inductor==

[[File:GK101.png]]

This 3-pin device models a tapped inductor with mutual coupling effect.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|Lt||total inductance||H||1m||
|-
|ratio||ratio of number of turns between positive terminal and tap to total number of turns||-||0.5||
|-
|k||coefficient of coupling||-||1.0||
|-
|}

== Temperature-Dependent Current Source ==

[[File:GL14.png]]

This is a current source whose current is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

== Temperature-Dependent Voltage Source ==

[[File:GL13.png]]

This is a voltage source whose voltage is an arbitrary function of the circuit temperature. You have to open the subcircuit model dialog by clicking the {{key|Edit Model...}} button and edit its text. Enter any mathematical expression in the variable "v(T)" standing for temperature. Note that the circuit temperature is set and controlled by the parameter "temp" in the Miscellaneous tab of the SPICE [[Simulation Options]] dialog.

Examples:

* v(T) is equivalent to f(T) = T.
* 1 + 0.1*(v(t))^2 is equivalent to f(T) = 1 + 0.1T.

Parameters:

None

==Thermometer==
[[File:G115.png]]

The Thermometer is a two-pin device that measures the operating temperature of a circuit. The voltage across the device pins is equal to SPICE's operating temperature in degrees centigrade. The output voltage of the Thermometer can be used in conjunction with linear or nonlinear dependent sources to model temperature-dependent quantities.

Model Identifier: thermo

Parameters:

This device has no parameters.

== Triac Thyristor ==

[[File:GK110.png]]

This is a 3-pin bidirectional thyristor device that conducts current in either direction when triggered. A thyristor is analogous to a relay in that a small voltage and current can control a much larger voltage and current. The triac has two anode pins termed Main Terminal 1 (MT1) and Main Terminal 2 (MT2) and a Gate (G) pin. In order to create a triggering current for a triac, either a positive or negative voltage can be applied to the gate. Once triggered, the thyristor continues to conduct, even if the gate current ceases, until the main current drops below a certain level called the holding current. The device's model involves two NPN BJT transistors and two PNP BJT transistors. The forward beta parameters of the NPN and PNP transistors are set equal to 20 and 5, respectively. To changes these values, open the subcircuit model dialog by clicking the {{key|View Subcircuit}} button and edit its text.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|rf||forward resistance||Ohms||1Meg||
|-
|bvf||breakdown voltage of forward diodes||V||100||
|-
|rh||resistance controlling reverse holding current||Ohms||100||
|-
|rgp||resistance controlling forward holding current and trigger current||Ohms||50||
|-
|}

==Uniform RC Transmission Line==

[[File:G23.png]]

The standard parameters are L, and N. They are described below:

Two of the nodes are the element nodes connected by the RC line. The third is the node to which the capacitances
are connected. L is the length of the RC line in meters. N is the number of lumped segments to use in
modeling the RC line.

This device is derived from a model proposed by Gertzberrg. It expands the URC line into a network of
lumped RC segments with internally generated nodes. These segments increase toward the middle of the
URC line in a geometric progression with K as the proportionality constant.

The URC line is made up entirely of resistor and capacitor segments, unless the ISPERL parameter has a
non-zero value. In this case, capacitors are replaced by reverse biased diodes with an equivalent zero-bias
junction capacitance, a saturation current of ISPERL amps per meter of transmission line, and optional
series resistance of RSPERL ohms per meter.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!EXAMPLE
|-
|K||propagation constant||-||2||1.2
|-
|FMAX||maximum frequency of interest||Hz||1.0G||6.5Meg
|-
|RPERL||resistance per unit length||Ohm /m||1000||10
|-
|CPERL||capacitance per unit length||F/m||1.0e-15||1pF
|-
|ISPERL||saturation current per unit length||A/m||0||-
|-
|RSPERL||diode resistance per unit length||Ohm/m||0||-
|-
|}

==Varactor Diode==

[[File:GK81.png]]

A varactor diode is a combination of the generic diode with additional package inductance, package capacitance and a series resistance. This diode device has a typically large value of junction capacitance (cjo).

Parameters (in addition to standard diode parameters):

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|q||quality factor||-||5000||
|-
|f0||frequency of Q-factor specification||Hz||50Meg||
|-
|ls||package inductance||H||0.5n||
|-
|cp||package capacitance ||F||0.05p||
|-
|}

==Voltage-Controlled Capacitor==

[[File:GK85.png]]

This 3-pin device models a voltage-controlled two-terminal capacitor whose capacitance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in F/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_C||conversion factor||F/V||1.0||
|-
|}

==Voltage-Controlled Inductor==

[[File:GK86.png]]

This 3-pin device models a voltage-controlled two-terminal inductor whose inductance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in H/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_L||conversion factor||H/V||1.0||
|-
|}

==Voltage-Controlled Resistor==

[[File:GK84.png]]

This 3-pin device models a voltage-controlled two-terminal resistor whose resistance is linearly proportional to a control voltage that is applied to a third (CTRL) pin. The proportionality constant is a conversion factor which you need to specify in Ω/V.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|K_r||conversion factor||Ω/V||1.0||
|-
|}

==Voltage-Controlled Switch==

[[File:G19.png]]

Switches are devices that exhibit high resistance when open (OFF state) and low resistance when closed (ON state). The switch model allows an almost ideal switch to be specified. With careful selection of the on and off resistances, they can effectively represent zero and infinite resistances in comparison to other circuit elements, while sustaining the model condition of a positive, finite value.

There are two versions of Voltage-Controlled Switch: two-terminal and four-terminal. For the two-terminal device, you must specify the name of the controlling Voltmeter or controlling voltage nodes, as well as the turn-on and turn-off voltages in Volts and on and off resistance values in Ohms. The four-terminal device already provides nodes for a controlling voltmeter, and you just specify the rest of [[parameters]]. When the voltage across the switch or controlling device is greater or equal to the turn-on current, the switch closes. When the voltage across the switch or controlling device is less than or equal to the turn off current, the switch opens.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNITS!!DEFAULT!!NOTES
|-
|V_ON||turn-on voltage||V||0.5||
|-
|V_OFF||turn-off voltage||V||0.0||
|-
|RON||on resistance||Ohms||1.0||
|-
|ROFF||off resistance||Ohms||1G||
|-
|}

==Voltage Noise Source==

[[File:GL15.png]]

This is a voltage noise generator characterized by a spectral density and corner frequency. You have to click the {{key|Edit Model...}} button to access the parameters of this device.

Parameters:

{| class="wikitable"
|-
!NAME!!PARAMETER!!UNIT!!DEFAULT!!NOTES
|-
|En||noise voltage||V/√Hz||1n||required
|-
|freq||noise corner frequency||Hz||100||required
|-
|}

==Voltage Source==

[[File:G17A.png]]

A voltage source has a DC value, a transient behavior, an AC behavior, and distortion parameters. The transient type, AC parameters, and distortion parameters are defined on the first tab of the source's property dialog. The transient expression can be a pulse, sinusoid, exponential, or piecewise linear. The DC value of a voltage source is its initial transient value. For a source with a sinusoidal transient behavior, for example, the DC value will be equal to its transient offset voltage. The AC parameters are magnitude and phase. These are used during the AC Frequency Sweep analysis. The distortion parameters, two sets of magnitude and phase, are used during the distortion analysis. The AC and distortion parameters are defined on the second tab of the source's property dialog.

==XSpice Devices and their models==

XSpice devices have the following form:
<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 4pt 0pt 1px 0pt ; font-family: 02070309020205020404,sans-serif; ">
A<device_name> <node1> <node2> ... <model_name></P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., A2 1 2 transfer_function

Note that XSpice devices must start with the "A" designation, much as a resistor starts with
an "R". Some devices will have grouped (or vector) pins and are designated by being placed
inside square brackets. In the example shown below, the 1 and 2 pins are grouped. Pin 3 is not. </P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 [1 2] 3 summer </P>

Some models will have voltage differential pairs of pins and will be denoted by a %vd( ). In the following
example pins 1 and 4 are differential pairs, as well as pins 2 and 3. Differential pairs must go between
parentheses ().

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 0pt ; text-indent: 36pt ; font-family: 02070309020205020404,sans-serif; ">
A1 %vd(1 4) %vd(2 3) triangle </P>

Refer to individual devices for more information.

Each XSpice device will also have a model associated with it. Each model will have the following form:

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
.model <model_name> <model_identifier> {<pname1 = pval1>} {<pname2 = pval2>}
...</P>

<P CLASS="syntaxstyle" STYLE="font-size: 9pt ; margin: 0pt 0pt 1px 36pt ; font-family: 02070309020205020404,sans-serif; ">
e.g., .model transfer_function s_xfer in_offset = 0.0 gain = 1.0</P>

Model_name refers to the name given in the device line. Model_identifier is an internal designation and
must be of an existing designation Refer to each device's example for the correct designation.

Parameter values are optional. If they aren't specified, then the default will be used. Some devices
have parameters that require a value and must be specified. Refer to individual devices for any required parameters.

==Zener Diode==

[[File:G10.png]]

The Zener Diode models the DC characteristics of most zeners. Since most data sheets for zener diodes do
not give detailed characteristics in the forward region, only a single point defines the forward characteristicThe
saturation current refers to the relatively constant reverse current that is produced when the voltage
across the zener is negative, but breakdown has not been reached. The reverse leakage current determines
the slight increase in reverse current as the voltage across the zener becomes more negative. It is modeled
as a resistance parallel to the zener with value v_breakdown / i_rev.

Note that the limt_switch parameter engages an internal limiting function for the zener. This can, in
some cases, prevent the simulator from converging to an unrealistic solution if the voltage across or
current into the device is excessive. If use of this feature fails to yield acceptable results, the convlimit
option should be tried (add the following statement to the SPICE input deck: .options convlimit)

Model Identifier: zener

Netlist Format:

A<device_name> <z_pin> <z_out_pin> <model_name>

.model <model_name> zener v_breakdown = 1 {<param1 = value> < param2 = value> ...}

Example:

A1 1 2 zener

.model zener zener v_breakdown = 1

Parameters:

{| class="wikitable"
|-
!Name!!Description!!Default!!Notes
|-
|v_breakdown||breakdown voltage||1||required
|-
|i_breakdown||breakdown current||2.0e-2||
|-
|i_sat||saturation current||1.0e-12||
|-
|N_forward||forward emission coefficient||1.0||
|-
|limit_switch||switch for on-board limiting (convergence aid)||False||
|-
|}

<p> </p>
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D | Back to RF.Spice A/D Wiki Gateway]]'''

EM.Illumina

2018-08-04T00:51:30Z

Kazem Sabet: /* Organizing Geometric Objects by Surface Type */

[[Image:Splash-po.jpg|right|720px]]
<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Illumina in a Nutshell ===

[[EM.Illumina]] is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use [[EM.Illumina]] to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

[[EM.Illumina]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in turn reradiate into the free space. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. Ray tracing from each source to the points on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, [[EM.Illumina]]'s simulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects.The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

[[Image:Info_icon.png|30px]] Click here to lean more about the '''[[Basic Principles of Physical Optics | Theory of Physical Optics]]'''.

<table>
<tr>
<td>
[[Image:Illumina L2 Fig title.png|thumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]]
</td>
</tr>
</table>

=== EM.Illumina as the Physical Optics Module of EM.Cube ===

[[EM.Illumina]] is the high-frequency, asymptotic '''Physical Optics Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Illumina]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[EM.Illumina]]'s simulator is seamlessly interfaced with [[EM.Cube|EM.CUBE]]'s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Illumina's PO Solver ===

[[EM.Illumina]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. For simple scatterer geometries, [[EM.Illumina]]'s GO-PO solver is fairly adequate. But for complex geometries that involve multiple shadowing effects, the IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the boundary conditions on one side of a surface only. PO analysis cannot handle the fields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

<table>
<tr>
<td>
[[Image:PO Ship Pattern.png|thumb|left|550px|Computed radiation pattern of a short dipole radiator over a large metallic battleship.]]
</td>
</tr>
</table>

== EM.Illumina Features at a Glance ==

=== Structure Definition ===

<ul>
<li>
Metal (PEC) solids and surfaces in free space</li>
<li>
PMC and impedance surfaces in free space</li>
<li>
Import STL CAD files as native polymesh structures</li>
<li>
Huygens blocks imported from full-wave modules</li>
</ul>

=== Sources ===

<ul>
<li>
Short dipoles</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Surface triangular mesh with control over tessellation parameters</li>
<li>
Local mesh editing of polymesh objects</li>
</ul>

=== Physical Optics Simulation ===

<ul>
<li>
Physical Optics solution of metal scatterers and impedance surfaces</li>
<li>
Conventional Geometrical Optics - Physical Optics (GOPO) solver</li>
<li>
Novel iterative PO solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li>
<li>
Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li>
<li>
Frequency and angular sweeps with data animation</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Multi-variable and multi-goal optimization of structure</li>
<li>
Remote simulation capability</li>
<li>
Both Windows and Linux versions of PO simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Electric and magnetic surface current distributions on metallic or impedance surfaces</li>
<li>
Near field intensity plots (vectorial - amplitude & phase)</li>
<li>
Huygens surface data generation for use in PO or other [[EM.Cube]] modules</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li>
<li>
Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Illumina ==

=== The Variety of Surface Types in EM.Illumina ===

[[EM.Illumina]] organizes physical objects by their surface type. Any object in [[EM.Illumina]] is assumed to be made of one of the three surface types:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]
| style="width:300px;" | Modeling perfect metal surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]
| style="width:300px;" | Modeling perfect magnetic surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance Surface]]
| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

[[EM.Illumina]] can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation.

=== Organizing Geometric Objects by Surface Type ===

You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under a group share the same color and other properties. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. There is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new EM.Illumina project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to CubeCAD. From CubeCAD, you can then move the imported objects to EM.Illumina.}}

<table>
<tr>
<td> [[File:PO MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td>
</tr>
</table>

== EM.Illumina's Excitation Sources ==

[[EM.Illumina]] provides three types of sources for the excitation of your physical optics simulation:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

A short Hertzian dipole is the simplest way of exciting a structure in [[EM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in its property dialog. Your physical structure in [[EM.Illumina]] can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

== EM.Illumina's Simulation Data & Observables ==

[[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO simulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

[[EM.Illumina]] currently provides the following observables:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Current distributions are visualized on the surface of PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.

<table>
<tr>
<td> [[Image:PO38.png|thumb|390px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]] </td>
</tr>
</table>

[[EM.Illumina]] allows you to visualize the near fields at a predefined field sensor plane of arbitrary dimensions. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> </td>
<td> [[Image:PO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.]] </td>
<td> [[Image:PO44.png|thumb|360px|Magnetic field distribution on a sensor plane above a metallic sphere.]] </td>
</tr>
</table>

You need to define a far field observable if you want to plot the radiation patterns of your physical structure. After a PO simulation is finished, three 3D radiation patterns plots are displayed in the project workspace and are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as well as the total far field.

{{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO46.png|thumb|360px|3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.]] </td>
</tr>
</table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>
</tr>
</table>

== Discretizing the Physical Structure in EM.Illumina ==

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density.

<table>
<tr>
<td>
[[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]
</td>
</tr>
</table>

Since EM.Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Illumina's Triangular Surface Mesh Generator ]]'''.

<table>
<tr>
<td> [[Image:POShip1.png|thumb|600px|Geometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td>
</tr>
<tr>
<td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the metallic battleship model.]] </td>
</tr>
</table>

== Running PO Simulations in EM.Illumina ==

=== EM.Illumina's Simulation Modes ===

Once you have set up your structure in [[EM.Illumina]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a Physical Optics simulation. [[EM.Illumina]] offers five simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the PO solver
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Illumina]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis ===

To open [[EM.Illumina]]'s Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|Run}} button of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, [[EM.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.

<table>
<tr>
<td> [[Image:Illumina L1 Fig10A.png|thumb|left|480px|EM.Illumina's Simulation Run dialog.]] </td>
</tr>
</table>

=== Setting The Numerical Parameters ===

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by η<sub>0</sub> in the residual error vector.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.Cube]]'s PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

<table>
<tr>
<td>
[[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]
</td>
</tr>
</table>

<br />

<hr>

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EM.Illumina

2018-08-04T00:50:38Z

Kazem Sabet: /* Organizing Geometric Objects by Surface Type */

[[Image:Splash-po.jpg|right|720px]]
<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td>
<tr>
</table>
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==Product Overview==

=== EM.Illumina in a Nutshell ===

[[EM.Illumina]] is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use [[EM.Illumina]] to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

[[EM.Illumina]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in turn reradiate into the free space. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. Ray tracing from each source to the points on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, [[EM.Illumina]]'s simulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects.The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

[[Image:Info_icon.png|30px]] Click here to lean more about the '''[[Basic Principles of Physical Optics | Theory of Physical Optics]]'''.

<table>
<tr>
<td>
[[Image:Illumina L2 Fig title.png|thumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]]
</td>
</tr>
</table>

=== EM.Illumina as the Physical Optics Module of EM.Cube ===

[[EM.Illumina]] is the high-frequency, asymptotic '''Physical Optics Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Illumina]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[EM.Illumina]]'s simulator is seamlessly interfaced with [[EM.Cube|EM.CUBE]]'s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Illumina's PO Solver ===

[[EM.Illumina]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. For simple scatterer geometries, [[EM.Illumina]]'s GO-PO solver is fairly adequate. But for complex geometries that involve multiple shadowing effects, the IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the boundary conditions on one side of a surface only. PO analysis cannot handle the fields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

<table>
<tr>
<td>
[[Image:PO Ship Pattern.png|thumb|left|550px|Computed radiation pattern of a short dipole radiator over a large metallic battleship.]]
</td>
</tr>
</table>

== EM.Illumina Features at a Glance ==

=== Structure Definition ===

<ul>
<li>
Metal (PEC) solids and surfaces in free space</li>
<li>
PMC and impedance surfaces in free space</li>
<li>
Import STL CAD files as native polymesh structures</li>
<li>
Huygens blocks imported from full-wave modules</li>
</ul>

=== Sources ===

<ul>
<li>
Short dipoles</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Surface triangular mesh with control over tessellation parameters</li>
<li>
Local mesh editing of polymesh objects</li>
</ul>

=== Physical Optics Simulation ===

<ul>
<li>
Physical Optics solution of metal scatterers and impedance surfaces</li>
<li>
Conventional Geometrical Optics - Physical Optics (GOPO) solver</li>
<li>
Novel iterative PO solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li>
<li>
Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li>
<li>
Frequency and angular sweeps with data animation</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Multi-variable and multi-goal optimization of structure</li>
<li>
Remote simulation capability</li>
<li>
Both Windows and Linux versions of PO simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Electric and magnetic surface current distributions on metallic or impedance surfaces</li>
<li>
Near field intensity plots (vectorial - amplitude & phase)</li>
<li>
Huygens surface data generation for use in PO or other [[EM.Cube]] modules</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li>
<li>
Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Illumina ==

=== The Variety of Surface Types in EM.Illumina ===

[[EM.Illumina]] organizes physical objects by their surface type. Any object in [[EM.Illumina]] is assumed to be made of one of the three surface types:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]
| style="width:300px;" | Modeling perfect metal surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]
| style="width:300px;" | Modeling perfect magnetic surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance Surface]]
| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

[[EM.Illumina]] can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation.

=== Organizing Geometric Objects by Surface Type ===

You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under a group share the same color and other properties. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. There is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new [[EM.Illumina]] project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to CubeCAD. From CubeCAD, you can then move the imported objects to [[EM.Illumina]].}}

<table>
<tr>
<td> [[File:PO MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td>
</tr>
</table>

== EM.Illumina's Excitation Sources ==

[[EM.Illumina]] provides three types of sources for the excitation of your physical optics simulation:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

A short Hertzian dipole is the simplest way of exciting a structure in [[EM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in its property dialog. Your physical structure in [[EM.Illumina]] can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

== EM.Illumina's Simulation Data & Observables ==

[[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO simulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

[[EM.Illumina]] currently provides the following observables:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Current distributions are visualized on the surface of PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.

<table>
<tr>
<td> [[Image:PO38.png|thumb|390px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]] </td>
</tr>
</table>

[[EM.Illumina]] allows you to visualize the near fields at a predefined field sensor plane of arbitrary dimensions. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> </td>
<td> [[Image:PO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.]] </td>
<td> [[Image:PO44.png|thumb|360px|Magnetic field distribution on a sensor plane above a metallic sphere.]] </td>
</tr>
</table>

You need to define a far field observable if you want to plot the radiation patterns of your physical structure. After a PO simulation is finished, three 3D radiation patterns plots are displayed in the project workspace and are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as well as the total far field.

{{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO46.png|thumb|360px|3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.]] </td>
</tr>
</table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>
</tr>
</table>

== Discretizing the Physical Structure in EM.Illumina ==

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density.

<table>
<tr>
<td>
[[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]
</td>
</tr>
</table>

Since EM.Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Illumina's Triangular Surface Mesh Generator ]]'''.

<table>
<tr>
<td> [[Image:POShip1.png|thumb|600px|Geometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td>
</tr>
<tr>
<td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the metallic battleship model.]] </td>
</tr>
</table>

== Running PO Simulations in EM.Illumina ==

=== EM.Illumina's Simulation Modes ===

Once you have set up your structure in [[EM.Illumina]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a Physical Optics simulation. [[EM.Illumina]] offers five simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the PO solver
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Illumina]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis ===

To open [[EM.Illumina]]'s Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|Run}} button of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, [[EM.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.

<table>
<tr>
<td> [[Image:Illumina L1 Fig10A.png|thumb|left|480px|EM.Illumina's Simulation Run dialog.]] </td>
</tr>
</table>

=== Setting The Numerical Parameters ===

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by η<sub>0</sub> in the residual error vector.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.Cube]]'s PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

<table>
<tr>
<td>
[[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Illumina#Product_Overview | Back to the Top of the Page]]'''

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EM.Illumina

2018-08-03T23:51:50Z

Kazem Sabet: /* The Variety of Surface Types in EM.Illumina */

[[Image:Splash-po.jpg|right|720px]]
<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Illumina in a Nutshell ===

[[EM.Illumina]] is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use [[EM.Illumina]] to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

[[EM.Illumina]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in turn reradiate into the free space. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. Ray tracing from each source to the points on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, [[EM.Illumina]]'s simulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects.The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

[[Image:Info_icon.png|30px]] Click here to lean more about the '''[[Basic Principles of Physical Optics | Theory of Physical Optics]]'''.

<table>
<tr>
<td>
[[Image:Illumina L2 Fig title.png|thumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]]
</td>
</tr>
</table>

=== EM.Illumina as the Physical Optics Module of EM.Cube ===

[[EM.Illumina]] is the high-frequency, asymptotic '''Physical Optics Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Illumina]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[EM.Illumina]]'s simulator is seamlessly interfaced with [[EM.Cube|EM.CUBE]]'s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Illumina's PO Solver ===

[[EM.Illumina]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. For simple scatterer geometries, [[EM.Illumina]]'s GO-PO solver is fairly adequate. But for complex geometries that involve multiple shadowing effects, the IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the boundary conditions on one side of a surface only. PO analysis cannot handle the fields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

<table>
<tr>
<td>
[[Image:PO Ship Pattern.png|thumb|left|550px|Computed radiation pattern of a short dipole radiator over a large metallic battleship.]]
</td>
</tr>
</table>

== EM.Illumina Features at a Glance ==

=== Structure Definition ===

<ul>
<li>
Metal (PEC) solids and surfaces in free space</li>
<li>
PMC and impedance surfaces in free space</li>
<li>
Import STL CAD files as native polymesh structures</li>
<li>
Huygens blocks imported from full-wave modules</li>
</ul>

=== Sources ===

<ul>
<li>
Short dipoles</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Surface triangular mesh with control over tessellation parameters</li>
<li>
Local mesh editing of polymesh objects</li>
</ul>

=== Physical Optics Simulation ===

<ul>
<li>
Physical Optics solution of metal scatterers and impedance surfaces</li>
<li>
Conventional Geometrical Optics - Physical Optics (GOPO) solver</li>
<li>
Novel iterative PO solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li>
<li>
Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li>
<li>
Frequency and angular sweeps with data animation</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Multi-variable and multi-goal optimization of structure</li>
<li>
Remote simulation capability</li>
<li>
Both Windows and Linux versions of PO simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Electric and magnetic surface current distributions on metallic or impedance surfaces</li>
<li>
Near field intensity plots (vectorial - amplitude & phase)</li>
<li>
Huygens surface data generation for use in PO or other [[EM.Cube]] modules</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li>
<li>
Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Illumina ==

=== The Variety of Surface Types in EM.Illumina ===

[[EM.Illumina]] organizes physical objects by their surface type. Any object in [[EM.Illumina]] is assumed to be made of one of the three surface types:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]
| style="width:300px;" | Modeling perfect metal surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]
| style="width:300px;" | Modeling perfect magnetic surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance Surface]]
| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

[[EM.Illumina]] can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation.

=== Organizing Geometric Objects by Surface Type ===

You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under a group share the same color and other properties. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. There is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new [[EM.Illumina]] project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]], you can then move the imported objects to [[EM.Illumina]].}}

<table>
<tr>
<td> [[File:PO MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td>
</tr>
</table>

== EM.Illumina's Excitation Sources ==

[[EM.Illumina]] provides three types of sources for the excitation of your physical optics simulation:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

A short Hertzian dipole is the simplest way of exciting a structure in [[EM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in its property dialog. Your physical structure in [[EM.Illumina]] can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

== EM.Illumina's Simulation Data & Observables ==

[[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO simulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

[[EM.Illumina]] currently provides the following observables:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Current distributions are visualized on the surface of PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.

<table>
<tr>
<td> [[Image:PO38.png|thumb|390px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]] </td>
</tr>
</table>

[[EM.Illumina]] allows you to visualize the near fields at a predefined field sensor plane of arbitrary dimensions. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> </td>
<td> [[Image:PO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.]] </td>
<td> [[Image:PO44.png|thumb|360px|Magnetic field distribution on a sensor plane above a metallic sphere.]] </td>
</tr>
</table>

You need to define a far field observable if you want to plot the radiation patterns of your physical structure. After a PO simulation is finished, three 3D radiation patterns plots are displayed in the project workspace and are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as well as the total far field.

{{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO46.png|thumb|360px|3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.]] </td>
</tr>
</table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>
</tr>
</table>

== Discretizing the Physical Structure in EM.Illumina ==

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density.

<table>
<tr>
<td>
[[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]
</td>
</tr>
</table>

Since EM.Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Illumina's Triangular Surface Mesh Generator ]]'''.

<table>
<tr>
<td> [[Image:POShip1.png|thumb|600px|Geometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td>
</tr>
<tr>
<td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the metallic battleship model.]] </td>
</tr>
</table>

== Running PO Simulations in EM.Illumina ==

=== EM.Illumina's Simulation Modes ===

Once you have set up your structure in [[EM.Illumina]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a Physical Optics simulation. [[EM.Illumina]] offers five simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the PO solver
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Illumina]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis ===

To open [[EM.Illumina]]'s Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|Run}} button of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, [[EM.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.

<table>
<tr>
<td> [[Image:Illumina L1 Fig10A.png|thumb|left|480px|EM.Illumina's Simulation Run dialog.]] </td>
</tr>
</table>

=== Setting The Numerical Parameters ===

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by η<sub>0</sub> in the residual error vector.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.Cube]]'s PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

<table>
<tr>
<td>
[[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Illumina#Product_Overview | Back to the Top of the Page]]'''

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EM.Picasso

2018-08-03T23:51:06Z

Kazem Sabet: /* Planar Object & Trace Types */

[[Image:Splash-planar new.jpg|right|720px]]
<strong><font color="#015865" size="4">Fast Full-Wave Simulator For Modeling Multilayer Planar Structures</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Picasso in a Nutshell ===

[[EM.Picasso]]<sup>®</sup> is a versatile planar structure simulator for modeling and design of printed antennas, planar microwave circuits, and layered periodic structures. [[EM.Picasso]]'s simulation engine is based on a 2.5-D full-wave Method of Moments (MoM) formulation that provides the ultimate modeling accuracy and computational speed for open-boundary multilayer structures. It can handle planar structures with arbitrary numbers of metal layouts, slot traces, vertical interconnects and lumped elements interspersed among different substrate layers.

Since its introduction in 2002, [[EM.Picasso]] has been successfully used by numerous users around the globe in industry, academia and government. It has also undergone several evolutionary cycles including a total reconstruction based on our integrated [[EM.Cube]] software foundation to expand its CAD and geometrical construction capabilities. [[EM.Picasso]]'s integration with [[EM.Cube]] facilitates import and export of many popular CAD formats (including DXF export of layered traces) and provides a seamless interface with [[EM.Cube]]'s other simulation tools.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Basic Principles of The Method of Moments | Theory of Planar Method of Moments]]'''.

<table>
<tr>
<td>
[[Image:ART PATCH Fig title.png|thumb|left|480px|3D radiation pattern of a slot-coupled patch antenna array with a corporate feed network.]]
</td>
</tr>
</table>

=== EM.Picasso as the Planar Module of EM.Cube ===

[[EM.Picasso]] is the frequency-domain, full-wave '''Planar Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Picasso]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Picasso's Planar MoM Simulator ===

[[EM.Picasso]] assumes that your planar structure has a substrate (background structure) of infinite lateral extents. In addition, the planar 2.5-D assumption restricts the 3D objects of your physical structure to embedded prismatic objects that can only support vertical currents. These assumptions limit the variety and scope of the applications of [[EM.Picasso]]. For example, you cannot use [[EM.Picasso]] to analyze a patch antenna with a finite-sized dielectric substrate. If the substrate edge effects are of concern in your modeling problem, you must use [[EM.Tempo]] instead. On the other hand, since [[EM.Picasso]]'s Planar MoM simulation engine incorporates the Green's functions of the background structure into the analysis, only the finite-sized traces like microstrips and slots are discretized by the mesh generator. As a result, the size of [[EM.Picasso]]'s computational problem is normally much smaller than that of [[EM.Tempo]]. In addition, [[EM.Picasso]] generates a hybrid rectangular-triangular mesh of your planar structure with a large number of equal-sized rectangular cells. Taking full advantage of all the symmetry and invariance properties of dyadic Green's functions often results in very fast computation times that easily make up for [[EM.Picasso]]'s limited applications. A particularly efficient application of [[EM.Picasso]] is the modeling of periodic multilayer structures at oblique incidence angles.

<table>
<tr>
<td>
[[Image:ART PATCH Fig12.png|thumb|left|480px|The hybrid planar mesh of the slot-coupled patch antenna array.]]
</td>
</tr>
</table>

== EM.Picasso Features at a Glance ==

=== Structure Definition ===

<ul>
<li>
Multilayer stack-up with unlimited number of substrate layers and trace planes</li>
<li>
PEC and conductive sheet traces for modeling ideal and non-ideal metallic layouts</li>
<li>
PMC traces for modeling slot layouts</li>
<li>
Vertical metal interconnects and embedded dielectric objects</li>
<li>
Full periodic structure capability with inter-connected unit cells</li>
<li>
Periodicity offset parameters to model triangular, hexagonal or other offset periodic lattice topologies</li>
</ul>

=== Sources, Loads & Ports ===

<ul>
<li>
Gap sources on lines</li>
<li>
De-embedded sources on lines for S parameter calculations</li>
<li>
Probe (coaxial feed) sources on vias</li>
<li>
Gap arrays with amplitude distribution and phase progression</li>
<li>
Periodic gaps with beam scanning</li>
<li>
Multi-port and coupled port definitions</li>
<li>
RLC lumped elements on strips with series-parallel combinations</li>
<li>
Short dipole sources</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from other [[EM.Cube]] modules</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Optimized hybrid mesh with rectangular and triangular cells</li>
<li>
Regular triangular surface mesh</li>
<li>
Local meshing of trace groups</li>
<li>
Local mesh editing of planar polymesh objects</li>
<li>
Fast mesh generation of array objects</li>
</ul>

=== Planar MoM Simulation ===

<ul>
<li>
2.5-D mixed potential integral equation (MPIE) formulation of planar layered structures</li>
<li>
2.5-D spectral domain integral equation formulation of periodic layered structures</li>
<li>
Accurate scattering parameter extraction and de-embedding using Prony's method</li>
<li>
Plane wave excitation with arbitrary angles of incidence</li>
<li>
A variety of matrix solvers including LU, BiCG and GMRES</li>
<li>
Uniform and fast adaptive frequency sweep</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Generation of reflection and transmission coefficient macromodels</li>
<li>
Multi-variable and multi-goal optimization of structure</li>
<li>
Remote simulation capability</li>
<li>
Both Windows and Linux versions of Planar MoM simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Current distribution intensity plots</li>
<li>
Near field intensity plots (vectorial - amplitude & phase)</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li>
<li>
Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li>
<li>
Radiation pattern of an arbitrary array configuration of the planar structure or periodic unit cell</li>
<li>
Reflection and Transmission Coefficients of Periodic Structures</li>
<li>
Monostatic and bi-static RCS </li>
<li>
Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li>
<li>
Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li>
<li>
Huygens surface generation</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building a Planar Structure in EM.Picasso ==

[[EM.Picasso]] is intended for construction and modeling of planar layered structures. By a planar structure we mean one that contains a background substrate of laterally infinite extents, made up of one or more material layers all stacked up vertically along the Z-axis. Planar objects of finite size are interspersed among these substrate layers. The background structure in [[EM.Picasso]] is called the "'''Layer Stack-up'''". The layer stack-up is always terminated from the top and bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material medium. Most planar structures used in RF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components are sandwiched between two grounds (PEC half-spaces) from both their top and bottom.

<table>
<tr>
<td>
[[Image:PMOM11.png|thumb|left|480px|EM.Picasso's navigation tree and trace types.]]
</td>
</tr>
</table>

=== Defining the Layer Stack-Up ===

When you start a new project in [[EM.Picasso]], there is always a default background structure that consists of a finite vacuum layer with a thickness of one project unit sandwiched between a vacuum top half-space and a PEC bottom half-space. Every time you open [[EM.Picasso]] or switched to it from [[EM.Cube]]'s other modules, the '''Stack-up Settings Dialog''' opens up. This is where you define the entire background structure. Once you close this dialog, you can open it again by right-clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Layer Stack-up Settings...''' from the contextual menu. Or alternatively, you can select the menu item '''Simulate > Computational Domain > Layer Stack-up Settings...'''

The Stack-up Settings dialog has two tabs: '''Layer Hierarchy''' and '''Embedded Sets'''. The Layer Hierarchy tab has a table that shows all the background layers in hierarchical order from the top half-space to the bottom half-space. It also lists the material composition of each layer, Z-coordinate of the bottom of each layer, its thickness (in project units) and material properties: permittivity (ε<sub>r</sub>), permeability (μ<sub>r</sub>), electric conductivity (σ) and magnetic conductivity (σ<sub>m</sub>). There is also a column that lists the names of embedded object sets inside each substrate layer, if any.

<table>
<tr>
<td> [[Image:PMOM8(1).png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog with the initial default values.]] </td>
</tr>
</table>

You can add new layers to your project's stack-up or delete its layers, or move layers up or down and thus change the layer hierarchy. To add a new background layer, click the arrow symbol on the {{key|Insert…}} button at the bottom of the dialog and select '''Substrate Layer''' from the button's dropdown list. A new dialog opens up where you can enter a label for the new layer and values for its material properties and thickness in project units. You can delete a layer by selecting its row in the table and clicking the '''Delete''' button. To move a layer up and down, click on its row to select and highlight it. Then click either the '''Move Up''' or '''Move Down''' buttons consecutively to move the selected layer to the desired location in the stack-up. Note that you cannot delete or move the top or bottom half-spaces. After creating a substrate layer, you can always edit its properties in the Layer Stack-up Settings dialog. Click on any layer's row in the table to select and highlight it and then click the {{key|Edit}} button. The substrate layer dialog opens up, where you can change the layer's label and assigned color as well as its constitutive parameters.

[[Image:Info_icon.png|30px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Assigning_Material_Properties_to_the_Physical_Structure | Materials in EM.Cube]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Using_EM.Cube.27s_Materials_List | Using EM.Cube's Materials Database]]'''.

For better visualization of your planar structure, [[EM.Picasso]] displays a virtual domain in a default orange color to represent part of the infinite background structure. The size of this virtual domain is a quarter wavelength offset from the largest bounding box that encompasses all the finite objects in the project workspace. You can change the size of the virtual domain or its display color from the Domain Settings dialog, which you can access either by clicking the '''Computational Domain''' [[File:domain_icon.png]] button of the '''Simulate Toolbar''', or using the keyboard shortcut {{key|Ctrl+A}}. Keep in mind that the virtual domain is only for visualization purposes and its size does not affect the MoM simulation. The virtual domain also shows the substrate layers in translucent colors. If you assign different colors to your substrate layers, you have get a better visualization of multilayer virtual domain box surrounding your project structure.

<table>
<tr>
<td> [[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:PMOM9.png|thumb|280px|EM.Picasso's Add Substrate Layer dialog.]] </td>
<td> [[Image:PMOM9A.png|thumb|440px|A microstrip-fed, slot-coupled patch antenna on a double-layer substrate with a PEC ground plane in the middle hosting the coupling slot.]] </td>
</tr>
</table>

=== Planar Object & Trace Types ===

[[EM.Picasso]] groups objects by their trace type and their hierarchical location in the substrate layer stack-up. A trace is a group of finite-sized planar objects that have the same material properties, same color and same Z-coordinate. All the planar objects belonging to the same metal or slot trace group are located on the same horizontal boundary plane in the layer stack-up. All the embedded objects belonging to the same embedded set lie inside the same substrate layer and have same material composition.

[[EM.Picasso]] provides the following types of objects for building a planar layered structure:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Trace]]
| style="width:300px;" | Modeling perfect metal traces on the interface between two substrate layers
| style="width:150px;" | Only surface objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Conductive Sheet Trace |Conductive Sheet Trace]]
| style="width:300px;" | Modeling lossy metal traces with finite conductivity and finite metallization thickness
| style="width:150px;" | Only surface objects
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Slot Trace |Slot Trace]]
| style="width:300px;" | Modeling cut-out slot traces and apertures on an infinite PEC ground plane
| style="width:150px;" | Only surface objects
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Embedded PEC Via Set |Embedded PEC Via Set]]
| style="width:300px;" | Modeling small and short vertical vias and plated-through holes inside substrate layers
| style="width:150px;" | Only surface objects
|-
| style="width:30px;" | [[File:diel_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Embedded Dielectric Object Set |Embedded Dielectric Object Set]]
| style="width:300px;" | Modeling small and short dielectric material inserts inside substrate layers
| style="width:150px;" | Only surface objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:150px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

You can define two types of metallic traces in [[EM.Picasso]]: '''PEC Traces''' and '''Conductive Sheet Traces'''. PEC traces represent infinitesimally thin (zero thickness) planar metal objects that are deposited or metallized on or between substrate layers. PEC objects are modeled by surface electric currents. Conductive sheet traces, on the other hand, represent imperfect metals. They have a finite conductivity and a very small thickness expressed in project units. A surface impedance boundary condition is enforced on the surface of conductive sheet objects.

'''Slot Traces''' are used to model cut-out slots and apertures in PEC ground planes. Planar slot objects are always assumed to lie on an infinite horizontal PEC ground plane with zero thickness, which is not explicitly displayed in the project workspace and its presence is implied. They are modeled by surface magnetic currents. When a slot is excited, tangential electric fields are formed on the aperture, which can be modeled as finite magnetic surface currents confined to the area of the slot. In other words, instead of modeling the electric surface currents on an infinite PEC ground around the slot, one can alternatively model the finite-extent magnetic surface currents on a perfect magnetic conductor (PMC) trace. Slot (PMC) objects provide the electromagnetic coupling between the two sides of an infinite PEC ground plane.

Besides planar metal and slot traces, [[EM.Picasso]] allows you to insert prismatic embedded objects inside the substrate layers. The height of such embedded objects is always the same as the height of their host substrate layer. Two types of embedded object sets are available: '''PEC Via Sets''' and '''Embedded Dielectric Sets'''. PEC via sets are metallic objects such as shorting pins, interconnect vias, plated-through holes, etc. all located and grouped together inside the same substrate layer. The embedded via objects are modeled as vertical volume conduction currents. Embedded dielectric sets are prismatic dielectric objects inserted inside a substrate layer. You can define a finite permittivity and conductivity for such objects. The embedded dielectric objects are modeled as vertical volume polarization currents.

{{Note|The height of an embedded object is always identical to the thickness of its host substrate layer.}}

=== Defining Traces & Embedded Object Sets ===

When you start a new project in [[EM.Picasso]], the project workspace looks empty, and there are no finite objects in it. However, a default background structure is always present. Finite objects are defined as part of traces or embedded sets. Once defined, you can see a list of project objects in the '''Physical Structure''' section of the navigation tree. Traces and object sets can be defined either from Layer Stack-up Settings dialog or from the navigation tree. In the '''Layer Stack-up Settings''' dialog, you can add a new trace to the stack-up by clicking the arrow symbol on the {{key|Insert}} button of the dialog. You have to choose from '''Metal (PEC)''', '''Slot (PMC)''' or '''Conductive Sheet''' options. A respective dialog opens up, where you can enter a label and assign a color. Once a new trace is defined, it is added, by default, to the top of the stack-up table underneath the top half-space. From here, you can move the trace down to the desired location on the layer hierarchy. Every time you define a new trace, it is also added under the respective category in the navigation tree. Alternatively, you can define a new trace from the navigation tree by right-clicking on one of the trace type names and selecting '''Insert New PEC Trace...'''or '''Insert New PMC Trace...'''or '''Insert New Conductive Sheet Trace...''' A respective dialog opens up for setting the trace properties. Once you close this dialog, it takes you directly to the Layer Stack-up Settings dialog so that you can set the right position of the trace on the stack-up.

Embedded object sets represent short material insertions inside substrate layers. They can be metal or dielectric. Metallic embedded objects can be used to model vias, plated-through holes, shorting pins and interconnects. These are called PEC via sets. Embedded dielectric objects can be used to model air voids, thin films and material inserts in metamaterial structures. Embedded objects can be defined either from the Layer Stack-up Settings dialog or directly from the navigation tree. Open the "Embedded Sets" tab of the stack-up dialog. This tab has a table that lists all the embedded object sets along with their material type, the host substrate layer, the host material and their height. To add a new object set, click the arrow symbol on the {{key|Insert}} button of the dialog and select one of the two options, '''PEC Via Set''' or '''Embedded Dielectric Set''', from the dropdown list. This opens up a new dialog where first you have to set the host layer of the new object set. A dropdown list labeled "'''Host Layer'''" gives a list of all the available finite substrate layers. You can also set the properties of the embedded object set, including its label, color and material properties. Keep in mind that you cannot control the height of embedded objects. Moreover, you cannot assign material properties to PEC via sets, while you can set values for the '''Permittivity'''(ε<sub>r</sub>) and '''Electric Conductivity'''(σ) of embedded dielectric sets. Vacuum is the default material choice. To define an embedded set from the navigation tree, right-click on the '''Embedded Object Sets''' item in the '''Physical Structure''' section of the navigation tree and select either '''Insert New PEC Via Set...''' or '''Insert New Embedded Dielectric Set...''' The respective New Embedded Object Set dialog opens up, where you can set the properties of the new object set. As soon as you close this dialog, it takes you to the Layer Stack-up Settings dialog, where you can verify the location of the new object set on the layer hierarchy.

<table>
<tr>
<td> [[Image:PMOM23.png|thumb|550px|EM.Picasso's Layer Stack-up dialog showing the Embedded Sets tab.]] </td>
</tr>
</table>

=== Drawing Planar Objects on Horizontal Work Planes ===

As soon as you start drawing geometrical objects in the project workspace, the '''Physical Structure''' section of the navigation tree gets populated. The names of traces are added under their respective trace type category, and the names of objects appear under their respective trace group. At any time, one and only one trace is active in the project workspace. The name of the active trace in the navigation tree is always displayed in bold letters. An active trace is where all the new objects you draw belong to. By default, the last defined trace or embedded object set is active. You can immediately start drawing new objects on the active trace. You can also set any trace or object set group active at any time by right-clicking on its name on the navigation tree and selecting '''Activate''' from the contextual menu.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

<table>
<tr>
<td> [[Image:PMOM23B.png|thumb|280px|EM.Picasso's Navigation Tree populated with planar objects.]] </td>
</tr>
</table>

[[EM.Picasso]] has a special feature that makes construction of planar structures very convenient and straightforward. <u>The horizontal Z-plane of the active trace or object set group is always set as the active work plane of the project workspace.</u> That means all new objects are drawn at the Z-coordinate of the currently active trace. As you change the active trace group or add a new one, the active work plane changes accordingly.

{{Note| In [[EM.Picasso]], you cannot modify the Z-coordinate of an object as it is set and controlled by its host trace.}}

[[EM.Picasso]] does not allow you to draw 3D or solid CAD objects. The solid object buttons in the '''Object Toolbar''' are disabled to prevent you from doing so. In order to create vias and embedded object, you simply have to draw their cross section geometry using planar surface CAD objects. [[EM.Picasso]] extrudes and extends these planar objects across their host layer automatically and displays them as 3D wireframe, prismatic objects. The automatic extrusion of embedded objects happens after mesh generation and before every planar MoM simulation. You can enforce this extrusion manually by right-clicking the '''Layer Stack-up''' item in the "Computational Domain" section of the navigation tree and selecting '''Update Planar Structure''' from the contextual menu.

{{Note| In [[EM.Picasso]], you can only draw horizontal planar surface CAD objects.}}

<table>
<tr>
<td> [[Image:PMOM23A.png|thumb|620px|A planar structure with a two-layer conductor-backed substrate, two PEC patches located at the tops of the lower and upper substrate layers, four PEC vias located inside the lower substrate layer between the lower patch and bottom ground and an embedded dielectric film located inside the top substrate layer sandwiched between the two patches.]] </td>
</tr>
</table>

=== EM.Picasso's Special Rules ===

# PEC ground planes at the top or bottom of a planar structure are regarded and modeled as PEC top or bottom half-spaces, respectively.
# A PEC ground plane placed in the middle of a substrate stack-up requires at least one slot object to provide electromagnetic coupling between its top and bottom sides. In this case, a slot trace is rather introduced at the given Z-plane, which also implies the presence of an infinite PEC ground.
# Metallic and slot traces cannot coexist on the same Z-plane. However, you can stack up multiple PEC and conductive sheet traces at the same Z-coordinate. Similarly, multiple slot traces can be placed at the same Z-coordinate.
# Metallic and slot traces are strictly defined at the interface planes between substrate layers. To define a suspended metallic trace inside a dielectric layer (as in the case of the center conductor of a stripline), you must split the dielectric layer into two thinner substrate layers and place your PEC trace at the interface between them.
# [[EM.Picasso]]'s simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and no circumferential components are allowed on embedded objects. The 2.5-D assumption holds very well in two cases: (a) when embedded objects are very thin with a very small cross section (with lateral dimensions less than 2-5% of the material wavelength) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the top and bottom.

== EM.Picasso's Excitation Sources ==

Your planar structure must be excited by some sort of signal source that induces electric surface currents on metal parts, magnetic surface currents on slot traces, and conduction or polarization volume currents on vertical vias and embedded objects. The excitation source you choose depends on the observables you seek in your project. [[EM.Picasso]] provides the following source types for exciting planar structures:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:gap_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]
| style="width:300px;" | General-purpose point voltage source (or filament current source on slot traces)
| style="width:300px;" | Associated with a PEC rectangle strip
|-
| style="width:30px;" | [[File:probe_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Probe Gap Circuit Source |Probe Gap Circuit Source]]
| style="width:300px;" | General-purpose voltage source for modeling coaxial feeds
| style="width:300px;" | Associated with an embedded PEC via set
|-
| style="width:30px;" | [[File:waveport_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Scattering Wave Port |Scattering Wave Port Source]]
| style="width:300px;" | Used for S-parameter computations
| style="width:300px;" | Associated with an open-ended PEC rectangle strip, extends long from the open end
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering & computation of reflection/transmission characteristics of periodic surfaces
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Picasso]] provides three types of lumped sources: gap source, probe source and de-embedded source. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal. Gap sources are placed across metal or slot traces. A rectangle strip object on a PEC or conductive sheet trace acts like a strip transmission line that carries electric currents along its length (local X direction). The characteristic impedance of the line is a function of its width (local Y direction). A gap source placed on a narrow metal strip creates a uniform electric field across the gap and pumps electric current into the line. A rectangle strip object on a slot trace acts like a slot transmission line on an infinite PEC ground plane that carries a magnetic current along its length (local X direction). The characteristic impedance of the slot line is a function of its width (local Y direction). A gap source placed on a narrow slot represents an ideal current source. A slot gap acts like an ideal current filament, which creates electric fields across the slot, equivalent to a magnetic current flowing into the slot line. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parameters]] can be calculated accurately.

{{Note| You can realize a coplanar waveguide (CPW) in [[EM.Picasso]] using two parallel slot lines with two aligned, collocated gap sources.}}

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays for Modeling Antenna Arrays]]'''.

A short dipole provides another way of exciting a planar structure in [[EM.Picasso]]. A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to excite your planar structure in [[EM.Picasso]]. In particular, you need a plane wave source to compute the radar cross section of a planar structure. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

<table>
<tr>
<td> [[Image:PMOM64A.png|thumb|550px|A multilayer planar structure containing a CPW line with a single coupled port and a lumped element on an overpassing metal strip.]] </td>
</tr>
</table>

=== Modeling Lumped Elements in EM.Picasso ===

Lumped elements are components, devices, or circuits whose overall dimensions are very small compared to the wavelength. As a result, they are considered to be dimensionless compared to the dimensions of a mesh cell. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of current flow, across which the device's governing equations are enforced. Using Kirkhoff's laws, these device equations normally establish a relationship between the currents and voltages across the device or circuit. Crossing the bridge to Maxwell's domain, the device equations must now be cast into a from o boundary conditions that relate the electric and magnetic currents and fields. [[EM.Picasso]] allows you to define passive circuit elements: '''Resistors''' (R), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations of them.

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

[[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.

{{Note|The impedance of the lumped circuit is calculated at the operating frequency of the project using the specified R, L and C values. As you change the frequency, the value of the impedance that is passed to the Planar MoM engine will change.}}

=== Calculating Scattering Parameters Using Prony's Method ===

The calculation of the scattering (S) parameters is usually an important objective of modeling planar structures especially for planar circuits like filters, couplers, etc. As you saw earlier, you can use lumped sources like gaps and probes and even active lumped elements to calculate the circuit characteristics of planar structures. The admittance / impedance calculations based on the gap voltages and currents are accurate at RF and lower microwave frequencies or when the port transmission lines are narrow. In such cases, the electric or magnetic current distributions across the width of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized. At higher frequencies, however, a more robust method is needed for calculating the port parameters.

One can calculate the scattering parameters of a planar structure directly by analyzing the current distribution patterns on the port transmission lines. The discontinuity at the end of a port line typically gives rise to a standing wave pattern that can clearly be discerned in the line's current distribution. From the location of the current minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, i.e. the S<sub>11</sub> parameter. A more robust technique is Prony’s method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following form:

:<math> f(x) \approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math>


where c<sub>i</sub> are complex coefficients and γ<sub>i</sub> are, in general, complex exponents. From the physics of transmission lines, we know that lossless lines may support one or more propagating modes with pure real propagation constants (real γ<sub>i</sub> exponents). Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary γ<sub>i</sub> exponents) that decay along the line as you move away from the location of such discontinuities.

In practical planar structures for which you want to calculate the scattering parameters, each port line normally supports one, and only one, dominant propagating mode. Multi-mode transmission lines are seldom used for practical RF and microwave applications. Nonetheless, each port line carries a superposition of incident and reflected dominant-mode propagating signals. An incident signal, by convention, is one that propagates along the line towards the discontinuity, where the phase reference plane is usually established. A reflected signal is one that propagates away from the port plane. Prony's method can be used to extract the incident and reflected propagating and evanescent exponential waves from the standing wave data. From a knowledge of the amplitudes (expansion coefficients) of the incident and reflected dominant propagating modes at all ports, the scattering matrix of the multi-port structure is then calculated. In Prony's method, the quality of the S parameter extraction results depends on the quality of the current samples and whether the port lines exhibit a dominant single-mode behavior. Clean current samples can be drawn in a region far from sources or discontinuities, typically a quarter wavelength away from the two ends of a feed line.

<table>
<tr>
<td> [[Image:PMOM71.png|thumb|600px|Minimum and maximum current locations of the standing wave pattern on a microstrip line feeding a patch antenna.]] </td>
</tr>
</table>

=== Defining Independent & Coupled Ports ===

Ports are used in a planar structure to order and index the sources for calculation of circuit parameters such as scattering (S), impedance (Z) and admittance (Y) parameters. In [[EM.Picasso]], you can use one or more of the following types of sources to define ports:

* Gap Sources
* Probe Sources
* Active Lumped Elements
* De-Embedded Sources

Ports are defined in the '''Observables''' section of the navigation tree. You can define any number of ports equal to or less than the total number of sources in your project. If you have N sources in your planar structure, then N default ports are defined, with one port assigned to each source according to their order on the navigation tree. Note that your project can have mixed gap and probes sources as well as active lumped element sources on PEC and slot traces or vias. You can also couple ports together to define coupled transmission lines such as coupled strips (CPS) or coplanar waveguides (CPW).

[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Ports]]'''.

== EM.Picasso's Simulation Data & Observables ==

Depending on the source type and the types of observables defined in a project, a number of output data are generated at the end of a planar MoM simulation. Some of these data are 2D by nature and some are 3D. The output simulation data generated by [[EM.Picasso]] can be categorized into the following groups:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on metal traces and magnetic surface current distribution on slot traces
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:port_icon.png]]
| style="width:150px;" | Port Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]]
| style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:period_icon.png]]
| style="width:150px;" | Periodic Characteristics
| style="width:150px;" | No observable required
| style="width:300px;" | Computing the reflection and transmission coefficients of a periodic surface
| style="width:250px;" | Requires a plane wave source and periodic boundary conditions
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

If your planar structure is excited by gap sources or probe sources or de-embedded sources, and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y) parameters of the designated ports. The scattering parameters are defined based on the port impedances specified in the project's Port Definition dialog. If more than one port has been defined in the project, the S/Z/Y matrices of the multiport network are calculated.

Electric and magnetic currents are the fundamental output data of a planar MoM simulation. After the numerical solution of the MoM linear system, they are found using the solution vector '''[I]''' and the definitions of the electric and magnetic vectorial basis functions:

:<math> \mathbf{[X]}_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math>

Note that currents are complex vector quantities. Each electric or magnetic current has three X, Y and Z components, and each complex component has a magnitude and phase. You can visualize the surface electric currents on metal (PEC) and conductive sheet traces, surface magnetic currents on slot (PMC) traces and vertical volume currents on the PEV vias and embedded dielectric objects. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the project workspace, superimposed on the surface of physical objects. In order to view the current distributions, you must first define them as observables before running the planar MoM simulation. At the top of the Current Distribution dialog and in the section titled '''Active Trace / Set''', you can select a trace or embedded object set where you want to observe the current distribution.

{{Note|You have to define a separate current distribution observable for each individual trace or embedded object set.}}

<table>
<tr>
<td> [[Image:PMOM85(1).png|thumb|left|600px|The current distribution map of a patch antenna.]] </td>
</tr>
</table>

[[EM.Picasso]] allows you to visualize the near fields at a specific field sensor plane. Note that unlike [[EM.Cube]]'s other computational modules, near field calculations in [[EM.Picasso]] usually takes a significant amount of time. This is due to the fact that at the end of a planar MoM simulation, the fields are not available anywhere (as opposed to [[EM.Tempo]]), and their computation requires integration of complex dyadic Green's functions of a multilayer background structure as opposed to the free space Green's functions.

{{Note|Keep in mind that since [[EM.Picasso]] uses a planar MoM solver, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> [[Image:PMOM116.png|thumb|left|600px|Near-zone electric field map above a microstrip-fed patch antenna.]] </td>
</tr>
<tr>
<td> [[Image:PMOM117.png|thumb|left|600px|Near-zone magnetic field map above a microstrip-fed patch antenna.]] </td>
</tr>
</table>

Even though [[EM.Picasso]]'s MoM engine does not need a radiation box, you still have to define a "Far Field" observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct [[EM.Cube]] to perform these calculations. Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in θ direction, the far field component in φ direction and the "Total" far field. The 2D radiation pattern graphs can be plotted from the '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.

<table>
<tr>
<td> [[Image:PMOM119.png|thumb|left|600px|3D polar radiation pattern plot of a microstrip-fed patch antenna.]] </td>
</tr>
</table>

When a planar structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields of that planar structure. [[EM.Picasso]] can also calculate the radar cross section (RCS) of a planar target. Note that in this case the RCS is defined for a finite-sized target in the presence of an infinite background structure. The scattered θ and φ components of the far-zone electric field are indeed what you see in the 3D far field visualization of radiation (scattering) patterns. Instead of radiation or scattering patterns, you can instruct [[EM.Picasso]] to plot 3D visualizations of σ<sub>θ</sub>, σ<sub>φ</sub> and the total RCS.

<table>
<tr>
<td> [[Image:PMOM125.png|thumb|left|600px|An example of the 3D monostatic radar cross section plot of a patch antenna.]] </td>
</tr>
</table>

== Discretizing a Planar Structure in EM.Picasso ==

The method of moments (MoM) discretizes all the finite-sized objects of a planar structure (excluding the background structure) into a set of elementary cells. Both the quality and resolution of the generated mesh greatly affect the accuracy of the MoM numerical solution. The mesh density gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the finite-sized geometrical objects. As a rule of thumb, a mesh density of about 20-30 cells per effective wavelength usually yields satisfactory results. But for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular output data that you seek in a simulation also influence your choice of mesh resolution. For example, far field characteristics like radiation patterns are less sensitive to the mesh density than field distributions on structures with a highly irregular shapes and boundaries.

<table>
<tr>
<td> [[Image:PMOM31.png|thumb|400px|The Planar Mesh Settings dialog.]] </td>
</tr>
</table>

EM.Picasso provides two types of mesh for a planar structure: a pure triangular surface mesh and a hybrid triangular-rectangular surface mesh. In both case, EM.Picasso attempts to create a highly regular mesh, in which most of the cells have almost equal areas. For planar structures with regular, mostly rectangular shapes, the hybrid mesh generator usually leads to faster computation times.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Picasso's Triangular Surface Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:PMOM48F.png|thumb|left|420px|Geometry of a multilayer slot-coupled patch array.]] </td>
</tr>
<tr>
<td> [[Image:PMOM48G.png|thumb|left|420px|Hybrid planar mesh of the slot-coupled patch array.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:PMOM48H.png|thumb|left|420px|Details of the hybrid planar mesh of the slot-coupled patch array around discontinuities.]] </td>
</tr>
</table>

=== The Hybrid Planar Mesh Generator ===

EM.Picasso's hybrid planar mesh generator tries to produce as many rectangular cells as possible especially in the case of objects with rectangular or linear boundaries. In connection or junction areas between adjacent objects or close to highly curved boundaries, triangular cells are used to fill the "irregular" regions in a conformal and consistent manner.

The mesh density gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e<sub>eff</sub> is the effective permittivity. By default, [[EM.Picasso]] generates a hybrid mesh with a mesh density of 20 cells per effective wavelength. The effective permittivity is defined differently for different types of traces and embedded object sets. This is to make sure that enough cells are placed in areas that might feature higher field concentration.

* For PEC and conductive sheet traces, the effective permittivity is defined as the larger of the permittivity of the two substrate layers just above and below the metallic trace.
* For slot traces, the effective permittivity is defined as the mean (average) of the permittivity of the two substrate layers just above and below the metallic trace.
* For embedded object sets, the effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets.

<table>
<tr>
<td> [[Image:PMOM32.png|thumb|360px|A comparison of triangular and planar hybrid meshes of a rectangular patch.]] </td>
<td> [[Image:PMOM30.png|thumb|360px|Mesh of two rectangular patches at two different substrate planes. The lower substrate layer has a higher permittivity.]] </td>
</tr>
</table>

=== General Rules of Planar Hybrid Mesh Generator ===

The integrity of the planar mesh and its continuity in the junction areas directly affects the quality and accuracy of the simulation results. EM.Picasso's hybrid planar mesh generator has some rules that are catered to 2.5-D MoM simulations:

* If two connected rectangular objects have the same side dimensions along their common linear edge with perfect alignment, a rectangular junction mesh is produced.
* If two connected rectangular objects have different side dimensions along their common linear edge or have edge offset, a set of triangular cells is generated along the edge of the object with the larger side.
* Rectangle strip objects that host a gap source or a lumped element always have a rectangular mesh around the gap area.
* If two objects reside on the same Z-plane, belong to the same trace group and have a common overlap area, they are first merged into a single object for the purpose of meshing using the "Boolean Union" operation.
* Embedded objects have prismatic meshes along the Z-axis.
* If an embedded object is located underneath or above a metallic trace object or connected from both top and bottom, it is meshed first and its mesh is then reflected on all of its attached horizontal trace objects.

<table>
<tr>
<td> [[File:PMOM36.png|250px]] [[File:PMOM38.png|250px]] [[File:PMOM37.png|250px]] </td>
</tr>
<tr>
<td> Two overlapping planar objects and a comparison of their triangular and hybrid planar meshes. </td>
</tr>
<tr>
<td> [[File:PMOM33.png|250px]] [[File:PMOM35.png|250px]] [[File:PMOM34.png|250px]] </td>
</tr>
<tr>
<td> Edge-connected rectangular planar objects and a comparison their triangular and hybrid planar meshes. </td>
</tr>
</table>

<table>
<tr>
<td> [[File:PMOM39.png|375px]] [[File:PMOM40.png|375px]] </td>
</tr>
<tr>
<td> Meshes of short and long vertical PEC vias connecting two horizontal metallic strips. </td>
</tr>
</table>

=== Refining the Planar Mesh Locally ===

It is very important to apply the right mesh density to capture all the geometrical details of your planar structure. This is especially true for "field discontinuity" regions such as junction areas between connected objects, where larger current concentrations are usually observed at sharp corners, or at the junction areas between metallic traces and PEC vias, as well as the areas around gap sources and lumped elements, which create voltage or current discontinuities.

The Planar Mesh Settings dialog gives a few options for customizing your planar mesh around geometrical and field discontinuities. The check box labeled "'''Refine Mesh at Junctions'''" increases the mesh resolution at the connection area between rectangular objects. The check box labeled "'''Refine Mesh at Gap Locations'''" might be particularly useful when gap sources or lumped elements are placed on a short transmission line connected from both ends. The check box labeled "'''Refine Mesh at Vias'''" increases the mesh resolution on the cross section of embedded object sets and at the connection regions of the metallic objects connected to them. EM.Picasso typically doubles the mesh resolution locally at the discontinuity areas when the respective boxes are checked. You should always visually inspect EM.Picasso's default generated mesh to see if the current mesh settings have produced an acceptable mesh.

Sometimes EM.Picasso's default mesh may contain very narrow triangular cells due to very small angles between two edges. In some rare cases, extremely small triangular cells may be generated, whose area is a small fraction of the average mesh cell. These cases typically happen at the junctions and other discontinuity regions or at the boundary of highly irregular geometries with extremely fine details. In such cases, increasing or decreasing the mesh density by one or few cells per effective wavelength often resolves that problem and eliminates those defective cells. Nonetheless, EM.Picasso's planar mesh generator offers an option to identify the defective triangular cells and either delete them or cure them. By curing we mean removing a narrow triangular cell and merging its two closely spaced nodes to fill the crack left behind. EM.Picasso by default deletes or cures all the triangular cells that have angles less than 10º. Sometimes removing defective cells may inadvertently cause worse problems in the mesh. You may choose to disable this feature and uncheck the box labeled "'''Remove Defective Triangular Cells'''" in the Planar Mesh Settings dialog. You can also change the value of the minimum allowable cell angle.

{{Note| Narrow, spiky triangular cells in a planar mesh are generally not desirable. You should get rid of the either by changing the mesh density or using the hybrid planar mesh generator's additional mesh refinement options.}}

<table>
<tr>
<td>
[[Image:PMOM44.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 1.]]
</td>
</tr>
<tr>
<td>
[[Image:PMOM42.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 2.]]
</td>
</tr>
</table>

== Running Planar MoM Simulations in EM.Picasso ==

=== EM.Picasso's Simulation Modes ===

[[EM.Picasso]] offers five Planar MoM simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Single-Frequency Planar MoM Analysis | Single-Frequency Analysis]]
| style="width:270px;" | Simulates the planar structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the planar MoM solver
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Picasso]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running a Single-Frequency Planar MoM Analysis ===

A single-frequency analysis is the simplest type of [[EM.Picasso]] simulation and involves the following steps:

* Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''.
* Define you background structure and its layer properties and trace types.
* Construct your planar structure using [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s drawing tools to create all the finite-sized metal and slot trace objects and possibly embedded metal or dielectric objects that are interspersed among the substrate layers.
* Define an excitation source and observables for your project.
* Examine the planar mesh, verify its integrity and change the mesh density if necessary.
* Run the Planar MoM simulation engine.
* Visualize the output simulation data.

To run a planar MoM analysis of your project structure, open the Run Simulation Dialog by clicking the '''Run''' [[File:run_icon.png]] button on the '''Simulate Toolbar''' or select '''Menu > Simulate > Run''' or use the keyboard shortcut {{key|Ctrl+R}}. The '''Single-Frequency Analysis''' option of the '''Simulation Mode''' dropdown list is selected by default. Once you click the {{key|Run}} button, the simulation starts. A new window called the "Output Window" opens up that reports the different stages of simulation and the percentage of the tasks completed at any time. After the simulation is successfully completed, a message pops up and reports the end of simulation. In certain cases like calculating scattering parameters of a circuit or reflection / transmission characteristics of a periodic surface, some results are also reported in the output window.

<table>
<tr>
<td> [[Image:Picasso L1 Fig18.png|thumb|left|480px|EM.Picasso's Simulation Run dialog.]] </td>
</tr>
</table>

=== Setting Numerical Parameters ===

A planar MoM simulation involves a number of numerical parameters that take preset default values unless you change them. You can access these parameters and change their values by clicking the '''Settings''' button next to the '''Select Engine''' drop-down list in [[EM.Picasso]]'s Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the default numerical parameter values intact. However, it is useful to familiarize yourself with these parameters, as they may affect the accuracy of your numerical results.

The Planar MoM Engine Settings Dialog is organized in a number of sections. Here we describe some of the numerical parameters. The "'''Matrix Fill'''" section of the dialog deals with the operations involving the dyadic Green's functions. You can set a value for the '''Convergence Rate for Integration''', which is 1E-5 by default. This is used for the convergence test of all the infinite integrals in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, the surface wave poles are captured in the complex integration plane using contour deformation. You can change the maximum number of iterations involved in this deformed contour integration, whose default value is 20. When the substrate is very thin with respect to the wavelength, the dyadic Green's functions exhibit numerical instability. Additional singularity extraction measures are taken to avoid numerical instability but at the expense of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01λ<sub>eff</sub>, where λ<sub>eff</sub> is the effective wavelength. You can modify the definition of "Thin Substrate" by entering a value for '''Thin Substrate Threshold''' different than the default 0.01. The parameter '''Max Coupling Range''' determines the distance threshold in wavelength between the observation and source points after which the Green's interactions are neglected. This distance by default is set to 1,000 wavelengths. For electrically small structures, the phase variation across the structure may be negligible. In such cases, a fast quasi-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''.

In the "Spectral Domain Integration" section of the dialog, you can set a value to '''Max Spectral Radius in k0''', which has a default value of 30. This means that the infinite spectral-domain integrals in the spectral variable k<sub>ρ</sub> are pre-calculated and tabulated up to a limit of 30k<sub>0</sub>, where k<sub>0</sub> is the free space propagation constant. These integrals may converge much faster based on the specified Convergence Rate for Integration described earlier. However, in certain cases involving highly oscillatory integrands, much larger integration limits like 100k<sub>0</sub> might be needed to warrant adequate convergence. For spectral-domain integration along the real k<sub>ρ</sub> axis, the interval [0, Nk<sub>0</sub>] is subdivided into a large number of sub-intervals, within each an 8-point Gauss-Legendre quadrature is applied. The next parameter, '''No. Radial Integration Divisions per k<sub>0</sub>''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k<sub>0</sub>]. In other words, the length of each integration sub-interval is k<sub>0</sub>/2. You can increase the resolution of integration by increasing this value above 2. Finally, instead of 2D Cartesian integration in the spectral domain, a polar integration is performed. You can set the '''No. of Angular Integration Points''', which has a default value of 100.

[[EM.Picasso]] provides a large selection of linear system solvers including both direct and iterative methods. [[EM.Picasso]], by default, provides a "'''Automatic'''" solver option that picks the best method based on the settings and size of the numerical problem. For linear systems with a size less than N = 3,000, the LU solver is used. For larger systems, BiCG is used when dealing with symmetric matrices, and GMRES is used for asymmetric matrices. You can instruct [[EM.Cube]] to write the MoM matrix and excitation and solution vectors into output data files for your examination. To do so, check the box labeled "'''Output MoM Matrix and Vectors'''" in the Matrix Fill section of the Planar MoM Engine Settings dialog. These are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectively.

<table>
<tr>
<td> [[Image:PMOM79.png|thumb|left|720px|EM.Picasso's Planar MoM Engine Settings dialog.]] </td>
</tr>
</table>

== Modeling Periodic Planar Structures in EM.Picasso ==

[[EM.Picasso]] allows you to simulate doubly periodic planar structures with periodicities along the X and Y directions. Once you designate your planar structure as periodic, [[EM.Picasso]]'s Planar MoM simulation engine uses a spectral domain solver to analyze it. In this case, the dyadic Green's functions of periodic planar structure take the form of doubly infinite summations rather than integrals.

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Method_of_Moments#Periodic_Planar_MoM_Simulation | Periodic Green's functions]]'''.

{{Note| [[EM.Picasso]] can handle both regular and skewed periodic lattices.}}

=== Defining a Periodic Structure in EM.Picasso ===

An infinite periodic structure in [[EM.Picasso]] is represented by a "'''Periodic Unit Cell'''". To define a periodic structure, you must open [[EM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''>''' '''Simulate > 'Computational Domain > Periodicity Settings...''' from the menu bar. In the Periodicity Settings Dialog, check the box labeled '''Periodic Structure'''. This will enable the section titled''"''Lattice Properties". You can define the periods along the X and Y axes using the boxes labeled '''Spacing'''. In a periodic structure, the virtual domain is replaced by a default blue periodic domain that is always centered around the origin of coordinates. Keep in mind that the periodic unit cell must always be centered at the origin of coordinates. The relative position of the structure within this centered unit cell will change the phase of the results.

<table>
<tr>
<td> [[Image:PMOM99.png|thumb|300px|EM.Picasso's Periodicity Settings dialog.]] </td>
</tr>
</table>

In many cases, your planar structure's traces or embedded objects are entirely enclosed inside the periodic unit cell and do not touch the boundary of the unit cell. [[EM.Picasso]] allows you to define periodic structures whose unit cells are interconnected. The interconnectivity applies only to PEC, PMC and conductive sheet traces, and embedded object sets are excluded. Your objects cannot cross the periodic domain. In other words, the neighboring unit cells cannot overlap one another. However, you can arrange objects with linear edges such that one or more flat edges line up with the domain's bounding box. In such cases, [[EM.Picasso]]'s planar MoM mesh generator will take into account the continuity of the currents across the adjacent connected unit cells and will create the connection basis functions at the right and top boundaries of the unit cell. It is clear that due to periodicity, the basis functions do not need to be extended at the left or bottom boundaries of the unit cell. As an example, consider a periodic metallic screen as shown in the figure on the right. The unit cell of this structure can be defined as a rectangular aperture in a PEC ground plane (marked as Unit Cell 1). In this case, the rectangle object is defined as a slot trace. Alternatively, you can define a unit cell in the form of a microstrip cross on a metal trace. In the latter case, however, the microstrip cross should extend across the unit cell and connect to the crosses in the neighboring cells in order to provide current continuity.

<table>
<tr>
<td> [[Image:image122.png|thumb|400px|Modeling a periodic screen using two different types of unit cell.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:pmom_per5_tn.png|thumb|300px|The PEC cross unit cell.]] </td>
<td> [[Image:pmom_per6_tn.png|thumb|300px|Planar mesh of the PEC cross unit cell. Note the cell extensions at the unit cell's boundaries.]] </td>
</tr>
</table>

=== Exciting Periodic Structures as Radiators in EM.Picasso ===

When a periodic planar structure is excited using a gap or probe source, it acts like an infinite periodic phased array. All the periodic replicas of the unit cell structure are excited. You can even impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the gap or probe source. At the bottom of the '''Planar Gap Circuit Source Dialog''' or '''Gap Source Dialog''', there is a button titled '''Periodic Scan...'''. You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the radiation patterns of a beam-steered antenna array, you have to define a finite-sized array factor in the Radiation Pattern dialog. You do this in the '''Impose Array Factor''' section of this dialog. The values of '''Element Spacing''' along the X and Y directions must be set equal to the value of '''Periodic Lattice Spacing''' along those directions.

<table>
<tr>
<td> [[Image:Period5.png|thumb|350px|Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] </td>
<td> [[Image:Period5_ang.png|thumb|350px|Setting the beam scan angles in Periodic Scan Angles dialog.]] </td>
</tr>
<tr>
<td> [[Image:Period6.png|thumb|350px|Setting the array factor in EM.Picasso's Radiation Pattern dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Period7.png|thumb|360px|Radiation pattern of an 8×8 finite-sized periodic printed dipole array with 0° phi and theta scan angles.]] </td>
<td> [[Image:Period8.png|thumb|360px|Radiation pattern of a beam-steered 8×8 finite-sized periodic printed dipole array with 45° phi and theta scan angles.]] </td>
</tr>
</table>

=== Exciting Periodic Structures Using Plane Waves in EM.Picasso ===

When a periodic planar structure is excited using a plane wave source, it acts as a periodic surface that reflects or transmits the incident wave. [[EM.Picasso ]] calculates the reflection and transmission coefficients of periodic planar structures. If you run a single-frequency plane wave simulation, the reflection and transmission coefficients are reported in the Output Window at the end of the simulation. Note that these periodic characteristics depend on the polarization of the incident plane wave. You set the polarization (TMz or TEz) in the '''Plane Wave Dialog''' when defining your excitation source. In this dialog you also set the values of the incident '''Theta''' and '''Phi''' angles. At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called "reflection.CPX" and "transmission.CPX".

{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[EM.Picasso]] computes the reflection and transmission coefficients of the layered background structure of your project.}}

<table>
<tr>
<td>
[[Image:PMOM102.png|thumb|580px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]]
</td>
</tr>
</table>

=== Running a Periodic MoM Analysis ===

You run a periodic MoM analysis just like an aperiodic MoM simulation from [[EM.Picasso]]'s Run Dialog. Here, too, you can run a single-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you can define several observables for your project. If you open the Planar MoM Engine Settings dialog, you will see a section titled "Infinite Periodic Simulation". In this section, you can set the number of Floquet modes that will be computed in the periodic Green's function summations. By default, the numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a total of 2500 Floquet terms will be computed for each periodic MoM simulation.

<table>
<tr>
<td>
[[Image:PMOM98.png|thumb|600px|Changing the number of Floquet modes from the Planar MoM Engine Settings dialog.]]
</td>
</tr>
</table>

You learned earlier how to use [[EM.Cube]]'s powerful, adaptive frequency sweep utility to study the frequency response of a planar structure. Adaptive frequency sweep uses rational function interpolation to generate smooth curves of the scattering parameters with a relatively small number of full-wave simulation runs in a progressive manner. Therefore, you need a port definition in your planar structure to be able to run an adaptive frequency sweep. This is clear in the case of an infinite periodic phased array, where your periodic unit cell structure must be excited using either a gap source or a probe source. You run an adaptive frequency sweep of an infinite periodic phased array in exactly the same way to do for regular, aperiodic, planar structures.

[[EM.Cube]]'s Planar Modules also allows you to run an adaptive frequency sweep of periodic surfaces excited by a plane wave source. In this case, the planar MoM engine calculates the reflection and transmission coefficients of the periodic surface. Note that you can conceptually consider a periodic surface as a two-port network, where Port 1 is the top half-space and Port 2 is the bottom half-space. In that case, the reflection coefficient R is equivalent to S<sub>11</sub> parameter, while the transmission coefficient T is equivalent to S<sub>21</sub> parameter. This is, of course, the case when the periodic surface is illuminated by the plane wave source from the top half-space, corresponding to 90°< θ = 180°. You can also illuminate the periodic surface by the plane wave source from the bottom half-space, corresponding to 0° = θ < 90°. In this case, the reflection coefficient R and transmission coefficient T are equivalent to S<sub>22</sub> and S<sub>12</sub> parameters, respectively. Having these interpretations in mind, [[EM.Cube]] enables the "'''Adaptive Frequency Sweep'''" option of the '''Frequency Settings Dialog''' when your planar structure has a periodic domain together with a plane wave source.



<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Picasso#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

EM.Libera

2018-08-03T23:49:37Z

Kazem Sabet: /* Building the Physical Structure in EM.Libera */

[[Image:Splash-mom.jpg|right|720px]]
<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space Structures</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Libera in a Nutshell ===

[[EM.Libera]] is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structures made up of metal and dielectric regions or a combination of them. It features two separate simulation engines, a Surface MoM solver and a Wire MoM solver, that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric objects in your physical structure. The Wire MoM solver can only handle metallic wireframe structures. [[EM.Libera]] selects the simulation engine automatically based on the types of objects present in your project workspace.

[[EM.Libera]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.

{{Note|In general, [[EM.Libera]] uses the surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, [[EM.Libera]] switches to the Wire MoM solver.}}

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of the '''[[Basic Principles of The Method of Moments | 3D Method of Moments]]'''.

<table>
<tr>
<td>
[[Image:Yagi Pattern.png|thumb|500px|3D far-field radiation pattern of the expanded Yagi-Uda antenna array with 13 directors.]]
</td>
</tr>
</table>

=== EM.Libera as the MoM3D Module of EM.Cube ===

You can use [[EM.Libera]] either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. [[EM.Libera]] also serves as the frequency-domain, full-wave '''MoM3D Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Libera]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===

The method of moments uses an open-boundary formulation of Maxwell's equations which does not require a discretization of the entire computational domain, but only the finite-sized objects within it. As a result, [[EM.Libera]]'s typical mesh size is typically much smaller that that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]'s triangular surface mesh provides a more accurate representation of your physical structure than [[EM.Tempo]]'s staircase brick volume mesh, which often requires a fairly high mesh density to capture the geometric details of curved surfaces. These can be serious advantages when deciding on which solver to use for analyzing highly resonant structures. In that respect, [[EM.Libera]] and [[EM.Picasso]] are similar as both utilize MoM solvers and surface mesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.

[[EM.Libera]]'s Wire MoM solver can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the current limitations of [[EM.Libera]], however, is its inability to mix wire structures with dielectric objects. If your physical structure contains one ore more wire objects, then all the PEC surface and solid CAD objects of the project workspace are reduced to wireframe models in order to perform a Wire MoM simulation. Also note that Surface MoM simulation of composite structures containing conjoined metal and dielectric parts may take long computation times due to the slow convergence of the iterative linear solver for such types of numerical problems. Since [[EM.Libera]] uses a surface integral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. For structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you use either [[EM.Tempo]] or [[EM.Picasso]] instead.

<table>
<tr>
<td>
[[Image:Hemi current.png|thumb|500px|The computed surface current distribution on a metallic dome structure excited by a plane wave source.]]
</td>
</tr>
</table>

== EM.Libera Features at a Glance ==

=== Physical Structure Definition ===

<ul>
<li>
Metal wires and curves in free space</li>
<li>
Metal surfaces and solids in free space</li>
<li>
Homogeneous dielectric solid objects in free space</li>
<li>
Import STL CAD files as native polymesh structures</li>
<li>
Export wireframe structures as STL CAD files</li>
</ul>

=== Sources, Loads & Ports ===

<ul>
<li>
Gap sources on wires (for Wire MoM) and gap sources on long, narrow, metal strips (for Surface MoM)</li>
<li>
Gap arrays with amplitude distribution and phase progression</li>
<li>
Multi-port port definition for gap sources</li>
<li>
Short dipole sources</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
RLC lumped elements on wires and narrow strips with series-parallel combinations</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-Ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Polygonized mesh of curves and wireframe mesh of surfaces and solids for Wire MoM simulation</li>
<li>
User defined wire radius</li>
<li>
Connection of wires/lines to wireframe surfaces and solids using polymesh objects</li>
<li>
Surface triangular mesh of surfaces and solids for Surface MoM simulation</li>
<li>
Local mesh editing of polymesh objects</li>
</ul>

=== 3D Wire MoM & Surface MoM Simulations ===

<ul>
<li>
3D Pocklington integral equation formulation of wire structures</li>
<li>
3D electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of PEC structures</li>
<li>
PMCHWT formulation of homogeneous dielectric objects</li>
<li>
AIM acceleration of Surface MoM solver</li>
<li>
Uniform and fast adaptive frequency sweep</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Multi-variable and multi-goal optimization of scene</li>
<li>
Fully parallelized Surface MoM solver using MPI</li>
<li>
Both Windows and Linux versions of Wire MoM simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Wireframe and electric and magnetic current distributions</li>
<li>
Near Field intensity plots (vectorial - amplitude & phase)</li>
<li>
Huygens surface data generation for use in MoM3D or other [[EM.Cube]] modules</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li>
<li>
Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li>
<li>
Radiation pattern of an arbitrary array configuraition of the wire structure</li>
<li>
Bi-static and mono-static radar cross section: 3D visualization and 2D graphs</li>
<li>
Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li>
<li>
Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Libera ==

All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of the navigation tree. In [[EM.Libera]], you can create three different types of objects:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]
| style="width:300px;" | Modeling perfect metals
| style="width:250px;" | Solid, surface and curve objects
| None
|-
| style="width:30px;" | [[File:thin_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]
| style="width:300px;" | Modeling wire radiators
| style="width:250px;" | Curve objects
| Wire MoM solver only
|-
| style="width:30px;" | [[File:diel_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric Material]]
| style="width:300px;" | Modeling any homogeneous material
| style="width:250px;" | Solid objects
| Surface MoM solver only
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
| None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

Both of [[EM.Libera]]'s two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and volumetric metal objects under '''PEC Objects'''. In other words, you can draw lines, polylines and other curve objects as thin wires, which have a radius parameters expressed in project units. All types of solid and surface CAD objects can be drawn in a PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.

<table>
<tr>
<td>
[[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]]
</td>
</tr>
</table>

Once a new object group node has been created on the navigation tree, it becomes the "Active" group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active group. There is only one object group that is active at any time. Any object type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create object groups, and then draw new CAD objects under the active object group. However, if you start a new [[EM.Libera]] project from scratch, and start drawing a new object without having previously defined any object groups, a new default PEC object group is created and added to the navigation tree to hold your new CAD object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. From [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you can then move the imported objects to [[EM.Libera]].}}

== EM.Libera's Excitation Sources ==

Your 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, electric surface currents on metal surface and both electric magnetic surface currents on the surface of dielectric objects. The excitation source you choose depends on the observables you seek in your project. [[EM.Libera]] provides the following source types for exciting your physical structure:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:gap_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]
| style="width:300px;" | General-purpose point voltage source
| style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver
|-
| style="width:30px;" | [[File:gap_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]
| style="width:300px;" | General-purpose point voltage source
| style="width:300px;" | Associated with an PEC or thin wire line or polyline, works only with WMOM solver
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current and is used to define an ideal voltage source. Wire gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected.
Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source.

{{Note|If you want to excite a curved wire antenna such as a circular loop or helix with a wire gap source, first you have to convert the curve object into a polyline using [[CubeCAD]]'s Polygonize Tool.}}

A short dipole provides another simple way of exciting a 3D structure in [[EM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''.

<table>
<tr>
<td> [[Image:wire_pic14_tn.png|thumb|left|640px|A wire gap source placed on one side of a polyline representing a polygonized circular loop.]] </td>
</tr>
<tr>
</table>

<table>
<tr>
<td> [[Image:po_phys16_tn.png|thumb|left|420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]] </td>
</tr>
</table>

=== Modeling Lumped Circuits ===

In [[EM.Libera]], you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. [[EM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

[[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.

=== Defining Ports ===

Ports are used to order and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the navigation tree. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. All port impedances are 50Ω by default.

[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.

<table>
<tr>
<td> [[Image:MOM7A.png|thumb|360px|Two metallic strips hosting a gap source and a lumped element.]] </td>
<td> [[Image:MOM7B.png|thumb|360px|The surface mesh of the two strips with a gap source and a lumped element.]] </td>
</tr>
</table>

== EM.Libera's Simulation Data & Observables ==

At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:port_icon.png]]
| style="width:150px;" | Port Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]]
| style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Depending on the types of objects present in your project workspace, [[EM.Libera]] performs either a Surface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted.

<table>
<tr>
<td> [[Image:wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a PEC plate.]] </td>
<td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.]] </td>
</tr>
</table>

{{Note|Keep in mind that since [[EM.Libera]] uses MoM solvers, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> [[Image:wire_pic32_tn.png|thumb|360px|Electric field plot of the circular loop antenna.]] </td>
<td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]] </td>
</tr>
</table>

You need to define a far field observable if you want to plot radiation patterns of your physical structure in [[EM.Libera]]. After a 3D MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.

<table>
<tr>
<td> [[Image:wire_pic38_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Theta component.]] </td>
<td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.]] </td>
<td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the circular loop antenna.]] </td>
</tr>
</table>

When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Libera]] calculates the radar cross section (RCS) of a target. Three RCS quantities are computed: the θ and φ components of the radar cross section as well as the total radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. In addition, [[EM.Libera]] calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree.

{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

{{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}}

<table>
<tr>
<td> [[Image:wire_pic51_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td>
<td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td>
<td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]] </td>
</tr>
</table>

== 3D Mesh Generation in EM.Libera ==

=== A Note on EM.Libera's Mesh Types ===

[[EM.Libera]] features two simulation engines, Wire MoM and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the connection points between two or more wires, junction basis functions are generated to ensure current continuity.

On the other hands, [[EM.Libera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera's Triangular Surface Mesh Generator ]]'''.

<table>
<tr>
<td> [[Image:Mesh5.png|thumb|400px|EM.Libera's Mesh Settings dialog showing the parameters of the linear wireframe mesh generator.]] </td>
</tr>
</table>

=== The Linear Wireframe Mesh Generator ===

You can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Libera]]'s Wire MoM simulator. When you structure contains at least one PEC line, polyline or any curve CAD object, [[EM.Libera]] will automatically invoke its linear wireframe mesh generator. This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the specified mesh density. It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are determined by the specified mesh density. Note that polygonizing operation is temporary and solely for he purpose of mesh generation. As for surface and solid CAD objects, a wireframe mesh of these objects is created which consists of a large number of interconnected linear (wire) elements.

{{Note| The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. It also discretizes surface and solid CAD objects temporarily using CubeCAD's Polymesh tool.}}

<table>
<tr>
<td> [[Image:Mesh6.png|thumb|200px|The geometry of an expanding helix with a circular ground.]] </td>
<td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the helix with the default mesh density of 10 cells/λ<sub>0</sub>.]] </td>
<td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 25 cells/λ<sub>0</sub>.]] </td>
<td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/λ<sub>0</sub>.]] </td>
</tr>
</table>

=== Mesh of Connected Objects ===

All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the surface objects belonging to the same PEC group are merged together and their internal edges are removed before meshing. Note that a solid and a surface object belonging to the same PEC group might not always be merged properly.

When two objects belonging to two different material groups overlap or intersect each other, [[EM.Libera]] has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top of a PEC plate. The two object share a circular area at the base of the cylinder. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, [[EM.Libera]] does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu > Simulate < discretization < Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the top of the table. You can select an group from the table and change its hierarch using the {{key|Move Up}} or {{key|Move Down}} buttons of the dialog. You can also change the color of junction cells that belong to each group.

<table>
<tr>
<td> [[Image:MOM3.png|thumb|300px|EM.Libera's Mesh Hierarchy dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:MOM1.png|thumb|360px|A dielectric cylinder attached to a PEC plate.]] </td>
<td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]] </td>
</tr>
</table>

=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===

If the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure. From the point of view of this mesh generator, all PEC surface objects and PEC solid objects are treated as wireframe objects. If you want to model a wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of the surface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s polymesh objects to accomplish this objective.

{{Note|In [[EM.Cube]], polymesh objects are regards as already-meshed objects and are not re-meshed again during a simulation.}}

You can convert any surface object or solid object to a polymesh using CubeCAD's '''Polymesh Tool'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool | Converting Object to Polymesh]]''' in [[EM.Cube]].

Once an object is converted to a polymesh, you can place your wire at any of its nodes. In that case, [[EM.Libera]]'s Wire MoM engine will sense the coincident nodes between line segments and will create a junction basis function to ensure current continuity.

<table>
<tr>
<td> [[Image:MOM4.png|thumb|360px|Geometry of a monopole wire connected to a PEC plate.]] </td>
<td> [[Image:MOM5.png|thumb|360px|Placing the wire on the polymesh version of the PEC plate.]] </td>
</tr>
</table>

== Running 3D MoM Simulations in EM.Libera ==

=== EM.Libera's Simulation Modes ===

Once you have set up your structure in [[EM.Libera]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a 3D MoM simulation. [[EM.Libera]] offers five simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]
| style="width:270px;" | Simulates the planar structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Libera]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running a Single-Frequency MoM Analysis ===

In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed by one of [[EM.Libera]]'s two MoM solvers. If your project contains at least one line or curve object, the Wire MoM solver is automatically selected. Otherwise, the Surface MoM solver will always be used to simulate your numerical problem. In either case, the engine type is set automatically.

To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D MoM simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the MoM simulation process. A prompt announces the completion of the MoM simulation.

<table>
<tr>
<td> [[Image:Libera L1 Fig13.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] </td>
</tr>
<tr>
<td> [[Image:MOM3D MAN10.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td>
</tr>
</table>

=== Setting MoM Numerical Parameters ===

MoM simulations involve a number of numerical parameters that normally take default values unless you change them. You can access these parameters and change their values by clicking on the '''Settings''' button next to the "Select Engine" dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.

First we discuss the Wire MoM Engine Settings dialog. In the '''Solver''' section of this dialog, you can choose the type of '''Linear Solver'''. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.

<table>
<tr>
<td>
[[Image:MOM9B.png|thumb|left|480px|EM.Libera's Wire MoM Engine Settings dialog.]]
</td>
</tr>
</table>

The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the dialog, you can choose among the three PEC formulations: EFIE, MFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is α = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[EM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.

For both Wire MoM and Surface MoM solvers, you can instruct [[EM.Libera]] to write the contents of the MoM matrix and excitation and solutions vectors into data files with '''.DAT1''' file extensions. These files can be accessed from the '''Input/Output Files''' tab of the Data Manager. In both case, you have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your structure is excited by a plane wave source. When checked, the field sensors plot the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualized.

<table>
<tr>
<td> [[Image:MOM9.png|thumb|left|640px|EM.Libera's Surface MoM Engine Settings dialog.]] </td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Libera#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

EM.Illumina

2018-08-03T23:48:35Z

Kazem Sabet: /* The Variety of Surface Types in EM.Illumina */

[[Image:Splash-po.jpg|right|720px]]
<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Illumina in a Nutshell ===

[[EM.Illumina]] is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use [[EM.Illumina]] to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

[[EM.Illumina]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in turn reradiate into the free space. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. Ray tracing from each source to the points on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, [[EM.Illumina]]'s simulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects.The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

[[Image:Info_icon.png|30px]] Click here to lean more about the '''[[Basic Principles of Physical Optics | Theory of Physical Optics]]'''.

<table>
<tr>
<td>
[[Image:Illumina L2 Fig title.png|thumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]]
</td>
</tr>
</table>

=== EM.Illumina as the Physical Optics Module of EM.Cube ===

[[EM.Illumina]] is the high-frequency, asymptotic '''Physical Optics Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Illumina]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[EM.Illumina]]'s simulator is seamlessly interfaced with [[EM.Cube|EM.CUBE]]'s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Illumina's PO Solver ===

[[EM.Illumina]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. For simple scatterer geometries, [[EM.Illumina]]'s GO-PO solver is fairly adequate. But for complex geometries that involve multiple shadowing effects, the IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the boundary conditions on one side of a surface only. PO analysis cannot handle the fields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

<table>
<tr>
<td>
[[Image:PO Ship Pattern.png|thumb|left|550px|Computed radiation pattern of a short dipole radiator over a large metallic battleship.]]
</td>
</tr>
</table>

== EM.Illumina Features at a Glance ==

=== Structure Definition ===

<ul>
<li>
Metal (PEC) solids and surfaces in free space</li>
<li>
PMC and impedance surfaces in free space</li>
<li>
Import STL CAD files as native polymesh structures</li>
<li>
Huygens blocks imported from full-wave modules</li>
</ul>

=== Sources ===

<ul>
<li>
Short dipoles</li>
<li>
Import previously generated wire mesh solution as collection of short dipoles</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Surface triangular mesh with control over tessellation parameters</li>
<li>
Local mesh editing of polymesh objects</li>
</ul>

=== Physical Optics Simulation ===

<ul>
<li>
Physical Optics solution of metal scatterers and impedance surfaces</li>
<li>
Conventional Geometrical Optics - Physical Optics (GOPO) solver</li>
<li>
Novel iterative PO solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li>
<li>
Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li>
<li>
Frequency and angular sweeps with data animation</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
<li>
Multi-variable and multi-goal optimization of structure</li>
<li>
Remote simulation capability</li>
<li>
Both Windows and Linux versions of PO simulation engine available</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Electric and magnetic surface current distributions on metallic or impedance surfaces</li>
<li>
Near field intensity plots (vectorial - amplitude & phase)</li>
<li>
Huygens surface data generation for use in PO or other [[EM.Cube]] modules</li>
<li>
Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li>
<li>
Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Illumina ==

=== The Variety of Surface Types in EM.Illumina ===

[[EM.Illumina]] organizes physical objects by their surface type. Any object in [[EM.Illumina]] is assumed to be made of one of the three surface types:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]
| style="width:300px;" | Modeling perfect metal surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]
| style="width:300px;" | Modeling perfect magnetic surfaces
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance Surface]]
| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects
| style="width:250px;" | Solid and surface objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

[[EM.Illumina]] can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation.

=== Organizing Geometric Objects by Surface Type ===

You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under a group share the same color and other properties. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. There is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new [[EM.Illumina]] project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

{{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]], you can then move the imported objects to [[EM.Illumina]].}}

<table>
<tr>
<td> [[File:PO MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td>
</tr>
</table>

== EM.Illumina's Excitation Sources ==

[[EM.Illumina]] provides three types of sources for the excitation of your physical optics simulation:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]
| style="width:300px;" | Almost omni-directional physical radiator
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]
| style="width:300px;" | Used for modeling scattering
| style="width:300px;" | None, stand-alone source
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

A short Hertzian dipole is the simplest way of exciting a structure in [[EM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in its property dialog. Your physical structure in [[EM.Illumina]] can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

== EM.Illumina's Simulation Data & Observables ==

[[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO simulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

[[EM.Illumina]] currently provides the following observables:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:currdistr_icon.png]]
| style="width:150px;" | Current Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]
| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]]
| style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Far-Field Scattering Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent electric and magnetic surface current data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Current distributions are visualized on the surface of PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.

<table>
<tr>
<td> [[Image:PO38.png|thumb|390px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]] </td>
</tr>
</table>

[[EM.Illumina]] allows you to visualize the near fields at a predefined field sensor plane of arbitrary dimensions. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}

<table>
<tr>
<td> </td>
<td> [[Image:PO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.]] </td>
<td> [[Image:PO44.png|thumb|360px|Magnetic field distribution on a sensor plane above a metallic sphere.]] </td>
</tr>
</table>

You need to define a far field observable if you want to plot the radiation patterns of your physical structure. After a PO simulation is finished, three 3D radiation patterns plots are displayed in the project workspace and are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as well as the total far field.

{{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO46.png|thumb|360px|3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.]] </td>
</tr>
</table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<table>
<tr>
<td> [[Image:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>
</tr>
</table>

== Discretizing the Physical Structure in EM.Illumina ==

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density.

<table>
<tr>
<td>
[[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]
</td>
</tr>
</table>

Since EM.Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Illumina's Triangular Surface Mesh Generator ]]'''.

<table>
<tr>
<td> [[Image:POShip1.png|thumb|600px|Geometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td>
</tr>
<tr>
<td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the metallic battleship model.]] </td>
</tr>
</table>

== Running PO Simulations in EM.Illumina ==

=== EM.Illumina's Simulation Modes ===

Once you have set up your structure in [[EM.Illumina]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a Physical Optics simulation. [[EM.Illumina]] offers five simulation modes:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:80px;" | Single run
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]
| style="width:270px;" | Varies the operating frequency of the PO solver
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at a specified set of frequency samples
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:80px;" | Multiple runs
| style="width:250px;" | Runs at the center frequency fc
| style="width:80px;" | None
|}

You can set the simulation mode from [[EM.Illumina]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis ===

To open [[EM.Illumina]]'s Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|Run}} button of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, [[EM.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.

<table>
<tr>
<td> [[Image:Illumina L1 Fig10A.png|thumb|left|480px|EM.Illumina's Simulation Run dialog.]] </td>
</tr>
</table>

=== Setting The Numerical Parameters ===

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by η<sub>0</sub> in the residual error vector.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.Cube]]'s PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

<table>
<tr>
<td>
[[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]
</td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Illumina#Product_Overview | Back to the Top of the Page]]'''

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''

EM.Ferma

2018-08-03T23:47:20Z

Kazem Sabet: /* Variety of Physical Objects in EM.Ferma */

[[Image:Splash-static.jpg|right|720px]]
<strong><font color="#2603c4" size="4">Electrostatic, Magnetostatic & Thermal Solvers For DC And Low Frequency Simulations</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Ferma in a Nutshell ===

EM.Ferma is a 3D static solver. It features two distinct electrostatic and magnetostatic simulation engines and a steady-state thermal simulation engine that can be used to solve a variety of static and low-frequency electromagnetic and thermal problems. The thermal solver includes both conduction and convection heat transfer mechanisms. All the three simulation engines are based on finite difference solutions of Poisson's equation for electric and magnetic potentials and temperature.

With EM.Ferma, you can explore the electric fields due to volume charge distributions or fixed-potential perfect conductors, and magnetic fields due to wire or volume current sources and permanent magnets. Your structure may include dielectric or magnetic (permeable) material blocks. Using the thermal simulator, you can solve for the steady-state temperature distribution of structures that include perfect thermal conductors, insulators and volume heat sources. You can also use EM.Ferma's 2D quasi-static mode to compute the characteristic impedance (Z0) and effective permittivity of transmission line structures with complex cross section profiles.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Electrostatic & Magnetostatic Field Analysis | Theory of Electrostatic and Magnetostatic Methods]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Steady-State_Thermal_Analysis | Theory of Steady-State Heat Transfer Methods]]'''.

<table>
<tr>
<td>
[[Image:Magnet lines1.png|thumb|left|400px| Vector plot of magnetic field distribution in a cylindrical permanent magnet.]]
</td>
</tr>
</table>

=== EM.Ferma as the Static Module of EM.Cube ===

EM.Ferma is the low-frequency '''Static Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Ferma shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== Advantages & Limitations of EM.Ferma's Static Simulator ===

EM.Ferma computes the electric and magnetic fields independent of each other based on electrostatic and magnetostatic approximations, respectively. As a result, any "electromagnetic" coupling effects or wave retardation effects are ignored in the simulation process. In exchange, static or quasi-static solutions are computationally much more efficient than the full-wave solutions of Maxwell's equations. Therefore, for low-frequency electromagnetic modeling problems or for simulation of sub-wavelength devices, EM.Ferma offers a faster alternative to [[EM.Cube]]'s full-wave modules like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]]. EM.Ferma currently provides a fixed-cell brick volume mesh generator. To model highly irregular geometries or curved objects, you may have to use very small cell sizes, which may lead to a large computational problem.

<table>
<tr>
<td>
[[Image:Ferma L8 Fig title.png|thumb|left|400px| Vector plot of electric field distribution in a coplanar waveguide (CPW) transmission line.]]
</td>
</tr>
</table>

== EM.Ferma Features at a Glance ==

=== Physical Structure Definition ===

<ul>
<li>
Perfect electric conductor(PEC) solids and surfaces (Electrostatics)</li>
<li>
Dielectric objects (Electrostatics)</li>
<li>
Magnetic (permeable) objects (Magnetostatics)</li>
<li>
Perfect thermal conductor (PTC) solids and surfaces (Thermal)</li>
<li>
Insulator objects (Thermal)</li>
</ul>

=== Sources ===

<ul>
<li>
Fixed-potential PEC for maintaining equi-potential metal objects (Electrostatics)</li>
<li>
Volume charge sources (Electrostatics)</li>
<li>
Volume current sources (Magnetostatics)</li>
<li>
Wire current sources (Magnetostatics)</li>
<li>
Permanent magnets (Magnetostatics)</li>
<li>
Fixed-temperature PTC for maintaining iso-thermal objects (Thermal)</li>
<li>
Volume heat sources (Thermal)</li>
</ul>

=== Mesh generation ===

<ul>
<li>
Fixed-size brick cells</li>
</ul>

=== 3D Electrostatic & Magnetostatic Simulation ===

<ul>
<li>
Finite difference solution of Laplace and Poisson equations for the electric scalar potential with Dirichlet and Neumann domain boundary conditions </li>
<li>
Finite difference solution of Laplace and Poisson equations for the magnetic vector potential with Dirichlet domain boundary conditions </li>
<li>
Calculation of electric scalar potential and electric field</li>
<li>
Calculation of magnetic vector potential and magnetic field</li>
<li>
Calculation of electric flux over user defined flux boxes and capacitance</li>
<li>
Calculation of magnetic flux over user defined flux surfaces and inductance</li>
<li>
Calculation of electric and magnetic energies, Ohmic power loss and resistance</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
</ul>

=== 2D Quasi-Static Simulation ===

<ul>
<li>
2D Finite difference solution of cross section of transmission line structures</li>
<li>
3D domain solution as well as 2D solution of a longitudinally infinite version of the structure defined on a 2D plane  </li>
<li>
Calculation of electric potential and electric field distribution</li>
<li>
Parametric sweep of transmission line's geometric and material parameters</li>
<li>
Optimization of transmission line's parameters for impedance design</li>
</ul>

=== Steady-State Thermal Simulation ===

<ul>
<li>
Finite difference solution of Laplace and Poisson equations for the temperature with Dirichlet and Neumann domain boundary conditions </li>
<li>
Calculation of temperature and heat flux density</li>
<li>
Calculation of thermal energy density on field sensor planes</li>
<li>
Calculation of thermal flux over user defined flux boxes</li>
<li>
Calculation of thermal energy</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Electric and magnetic field intensity and vector plots on planes</li>
<li>
Electric and magnetic potential intensity plots on planes</li>
<li>
Temperature and heat flux intensity and vector plots on planes</li>
<li>
Electric and magnetic energy density, dissipated power density and thermal energy density plots on planes</li>
<li>
Animation of field and potential plots after parametric sweeps</li>
<li>
Graphs of characteristic impedance and effective permittivity of transmission line structures vs. sweep variables</li>
<li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Ferma ==

=== Variety of Physical Objects in EM.Ferma ===

The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the boundary of the computational domain. As soon as you introduce a dielectric object next to a charge source or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson equation subject to the domain boundary conditions as well as material interface boundary conditions. The simplest thermal problem involves one or more thermal plates held at fixed temperatures. Once you introduce material blocks, you have to enforce conductive and convective boundary conditions at the interface between different materials and air. EM.Ferma uses the Finite Difference (FD) technique to find a numerical solution of your static boundary value problem.

[[EM.Ferma]] offers the following types of physical objects:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Physical Object Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
! scope="col"| Notes & Restrictions
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Fixed-Potential PEC |Fixed-Potential Perfect Electric Conductor (PEC)]]
| style="width:300px;" | Modeling perfect metals with a fixed voltage
| style="width:100px;" | Solid and surface objects
| style="width:250px;" | Can be considered an electric source if the fixed voltage is nonzero
|-
| style="width:30px;" | [[File:diel_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric/Magnetic Material]]
| style="width:300px;" | Modeling any homogeneous or inhomogeneous material
| style="width:100px;" | Solid objects
| style="width:250px;" | non-source material
|-
| style="width:30px;" | [[File:aniso_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Charge |Volume Charge]]
| style="width:300px;" | Modeling volume charge sources with a fixed charge density or an expression in the global coordinates (x,y,z)
| style="width:100px;" | Solid objects
| style="width:250px;" | Acts as an electric source
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Current |Volume Current]]
| style="width:300px;" | Modeling volume current sources with a fixed volume current density vector or expressions in the global coordinates (x,y,z)
| style="width:100px;" | Solid objects
| style="width:250px;" | Acts as a magnetic source
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Permanent Magnet |Permanent Magnet]]
| style="width:300px;" | Modeling permanent magnet sources with a fixed magnetization vector or expressions in the global coordinates (x,y,z)
| style="width:100px;" | Solid objects
| style="width:250px;" | Acts as a magnetic source
|-
| style="width:30px;" | [[File:thin_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Current |Wire Current]]
| style="width:300px;" | Modeling wire current sources
| style="width:100px;" | line and polyline objects
| style="width:250px;" | Acts as a magnetic source
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Fixed-Temperature PTC |Fixed-Temperature Perfect Thermal Conductor (PTC)]]
| style="width:300px;" | Modeling isothermal surfaces with a fixed temperature
| style="width:100px;" | Solid and surface objects
| style="width:250px;" | Can be considered a thermal source if the fixed temperature is different than the ambient temperature (shares the same navigation tree node as PEC object)
|-
| style="width:30px;" | [[File:diel_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Insulator Material]]
| style="width:300px;" | Modeling any homogeneous or inhomogeneous material
| style="width:100px;" | Solid objects
| style="width:250px;" | non-source material (shares the same navigation tree node as dielectric material)
|-
| style="width:30px;" | [[File:aniso_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Heat Source |Volume Heat Source]]
| style="width:300px;" | Modeling volume heat sources with a fixed heat density or an expression in the global coordinates (x,y,z)
| style="width:100px;" | Solid objects
| style="width:250px;" | Acts as a thermal source (shares the same navigation tree node as volume charge)
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:100px;" | All types of objects
| style="width:250px;" | None
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

=== Grouping Objects by Material or Source Type ===

Your physical structure in EM.Ferma is typically made up of some kind of source object either in the free space or in the presence of one or more material objects. EM.Ferma's electrostatic and magnetostatic or thermal simulation engines then discretize the entire computational domain including these source and material objects and solve the Laplace or Poisson equations to find the electric or magnetic fields or temperature everywhere in the computational domain.

All the geometric objects in the project workspace are organized together into object groups which share the same properties including color and electric or magnetic parameters. It is recommended that you first create object groups, and then draw new objects under the active group. To create a new object group, right-click on its category name in the "Physical Structure" section of the navigation tree and select one of the "Insert New Group..." items from the contextual menu. However, if you start a new EM.Ferma project from scratch, and start drawing a new object without having previously defined any object groups, a new default "Fixed-Potential PEC" object group with a zero voltage is created and added to the navigation tree to hold your new geometric object.

It is important to note that there is a one-to-one correspondence between electrostatic and thermal simulation entities:

{| class="wikitable"
|-
! scope="col"| Electrostatic Item
! scope="col"| Corresponding Thermal Item
|-
| style="width:200px;" | Electric Scalar Potential
| style="width:200px;" | Temperature
|-
| style="width:200px;" | Electric Field
| style="width:200px;" | Heat Flux Density
|-
| style="width:200px;" | Perfect Electric Conductor
| style="width:200px;" | Perfect Thermal Conductor
|-
| style="width:200px;" | Dielectric Material
| style="width:200px;" | Insulator Material
|-
| style="width:200px;" | Volume Charge
| style="width:200px;" | Volume Heat Source
|}

{{Note|Electrostatic and thermal solvers share the same material categories on the navigation tree. This means that PEC objects are treated as PTC objects, dielectric objects are treated as insulator objects and volume charges are treated as volume heat sources when the thermal solver is enabled.}}

Once a new object group node has been created in the navigation tree, it becomes and remains the "Active" object group, which is always listed in bold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active object group. There is only one object group that is active at any time. Any group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

<table>
<tr>
<td> [[Image:STAT MAN1.png|thumb|left|480px|EM.Ferma's navigation tree.]] </td>
</tr>
</table>

=== A Note on Material and Source Types in EM.Ferma ===

In [[EM.Cube]]'s other modules, material types are categorized under the "Physical Structure" section of the navigation tree, and sources are organized under a separate "Sources" section. In those modules, all the geometric objects you draw in your project workspace typically represent material bodies. All of [[EM.Cube]] modules except for EM.Ferma require at least one excitation source to be selected from the "Sources" section of the navigation tree before you can run a simulation.

In EM.Ferma, materials and sources are all lumped together and listed under the "Physical Structure" section of the navigation tree. In other words, there is no separate "Sources" section. For example, you can define default zero-potential perfect electric conductors (PEC) in your project to model metal objects. You can also define fixed-potential PEC objects with a nonzero voltage, which can effectively act as a voltage source for your boundary value problem. In this case, you will solve the Lapalce equation subject to the specified nonzero potential boundary values. Both types of PEC objects are defined from the same PEC node of the navigation tree by assigning different voltage values. Charge and current sources are also defined as geometric objects, and you have to draw them in the project workspace just like other material objects.

== EM.Ferma's Computational Domain ==

===The Domain Box===

In EM.Ferma, the Poisson or Laplace equations are solved subject to boundary conditions using the Finite Difference technique. As a result, you need to specify a finite computational domain and then specify the domain boundary conditions. EM.Ferma's computational domain defines where the domain boundary condition will be specified. A default domain box is always placed in the project workspace as soon as you draw your first object. The domain can be seen as a blue cubic wireframe that surrounds all of the CAD objects in the project workspace.

To modify the domain settings, click the Domain button of the Simulate Toolbar or right-click on "3D Static Domain" entry in the Navigation Tree and select "Domain Settings..." from the contextual menu. In the Domain Settings Dialog, the computational domain can be defined in two different ways: Default and Custom. The default type places an enclosing box with a specified offset from the largest bounding box of your project's CAD objects. The default offset value is 20 project units, but you can change this value arbitrarily. The custom type defines a fixed domain box by specifying the coordinates of its two opposite corners labeled Min and Max in the world coordinate system.

<table>
<tr>
<td> [[Image:Qsource5.png|thumb|left|480px|EM.Ferma's Domain Settings dialog.]] </td>
</tr>
</table>

===Domain Boundary Conditions===

*EM.Ferma allows you to specify the electric potential boundary conditions on the domain box. Two options are available. The Dirichlet boundary condition is the default option and is specified as a fixed potential value on the surface of the domain walls. By default, this value is 0 Volts. The Neumann boundary condition specifies the normal derivative of the electric scalar potential on the surface of the domain walls. This is equivalent to a constant normal electric field component on the domain walls and its value is specified in V/m.

*The magnetostatic simulation engine always assumes Dirichlet domain boundary conditions and sets the values of the magnetic vector potential to zero on all the domain walls.

*EM.Ferma provides two options for thermal boundary conditions on the domain box. The Dirichlet boundary condition is the default option and is specified as a fixed temperature value on the surface of the domain walls. By default, this value is 0°C. The Neumann boundary condition specifies the normal derivative of the temperature on the surface of the domain walls. This is equivalent to a constant heat flux passing through the domain walls and its value is specified in W/m<sup>2</sup>. A zero heat flux means a perfectly insulated domain box and is known as the adiabatic boundary condition.

To modify the boundary conditions, right-click on "Boundary Conditions" in the navigation tree, and select "Boundary Conditions..." from the contextual menu to open the Boundary Conditions Dialog. When you switch from the electrostatic-magnetostatic solver to the thermal solver in EM.Ferma's Run Simulation dialog, it automatically checks the box labeled '''Treat as a Thermal Structure''' in the Boundary Conditions dialog. Conversely, if you check this box in the Boundary Conditions dialog, the solver type is set to the thermal solver in the Simulation Run dialog. In the "Global Thermal Properties" section of the Boundary Conditions dialog, you can set the values of the ambient temperature in °C, thermal conductivity of the environment in W/(m.K) and the convective coefficient in W/(m<sup>2</sup>.K). You can also disable the enforcement of the convective boundary condition on the surface of solid insulator objects.

<table>
<tr>
<td> [[Image:fermbc.png|thumb|left|480px|EM.Ferma's Boundary Conditions dialog.]] </td>
</tr>
</table>

== EM.Ferma's Simulation Data & Observables ==

At the end of an electrostatic simulation, the electric field vector and electric scalar potential values are computed at all the mesh grid points of the entire computational domain. At the end of an magnetostatic simulation, the magnetic field vector and magnetic vector potential values are computed at all the grid nodes. At the end of a thermal simulation, the temperature and heat flux vector are computed at all the mesh grid points of the entire computational domain.

Besides the electric and magnetic fields and temperature, EM.Ferma can compute a number of field integral quantities such as voltage, current, flux, energy, etc. The field components, potential values and field integrals are written into output data files and can be visualized on the screen or graphed in Data Manager only if you define a field sensor or a field integral observable. In the absence of any observable defined in the navigation tree, the static simulation will be carried out and completed, but no output simulation data will be generated.

EM.Ferma offers the following types of output simulation data:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Observable Type
! scope="col"| Applications
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:450px;" | Computing electric and magnetic field components, electric scalar potential and magnitude of magnetic vector potential on a planar cross section of the computational domain
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Electric and Magnetic Energy and Dissipated Power Density Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:450px;" | Computing electric and magnetic energy densities and dissipated power density on a planar cross section of the computational domain
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Temperature and Heat Flux Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:450px;" | Computing temperature and heat flux components on a planar cross section of the computational domain
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Thermal Energy Density Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:450px;" | Computing thermal energy density on a planar cross section of the computational domain
|-
| style="width:30px;" | [[File:field_integ_icon.png]]
| style="width:150px;" | Field Integral Quantities
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Static_Field_Integral_Observable | Static Field Integral]]
| style="width:450px;" | Computing line, surface and volume integrals of the electric and magnetic fields and heat flux
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

<table>
<tr>
<td> [[Image:Ferma L1 Fig15.png|thumb|left|640px|Electric field distribution of a spherical charge on a horizontal field sensor plane.]] </td>
</tr>
<tr>
<td> [[Image:Ferma L1 Fig16.png|thumb|left|640px|Electric scalar potential distribution of a spherical charge on a horizontal field sensor plane.]] </td>
</tr>
</table>

The table below list the different types of field integrals and their definitions:

{| class="wikitable"
|-
! scope="col"| Field Integral
! scope="col"| Definition
! scope="col"| Output Data File
|-
! scope="row"| Voltage
| <math> V = - \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| voltage.DAT
|-
! scope="row"| Current
| <math> I = \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| current.DAT
|-
! scope="row"| Conduction Current
| <math> I_{cond} = \int\int_S \mathbf{J(r)} . \mathbf{ds} = \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| conduction_current.DAT
|-
! scope="row"| Electric Flux
| <math> \Phi_E = \int\int_{S_o} \mathbf{D(r)} . \mathbf{ds} = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} </math>
| flux_E.DAT
|-
! scope="row"| Magnetic Flux
| <math> \Phi_H = \int\int_S \mathbf{B(r)} . \mathbf{ds} = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} </math>
| flux_H.DAT
|-
! scope="row"| Electric Energy
| <math> W_E = \frac{1}{2} \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv </math>
| energy_E.DAT
|-
! scope="row"| Magnetic Energy
| <math> W_H = \frac{1}{2} \int\int\int_V \mu \vert \mathbf{H(r)} \vert ^2 dv </math>
| energy_H.DAT
|-
! scope="row"| Ohmic Power Loss
| <math> P_{ohmic} = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| ohmic.DAT
|-
! scope="row"| Capacitance
| <math> C = \Phi_E/V = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} / \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| capacitance.DAT
|-
! scope="row"| Capacitance (Alternative)
| <math> C = 2W_E/V^2 = 2 \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv / \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2</math>
| capacitance.DAT
|-
! scope="row"| Self-Inductance
| <math> L = \Phi_H/I = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| inductance.DAT
|-
! scope="row"| Self-Inductance (Alternative)
| <math> L = 2W_M/I^2 = 2 \int \int \int_V \mu \vert \mathbf{H(r)} \vert ^2 dv / \left( \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} \right)^2</math>
| inductance.DAT
|-
! scope="row"| Mutual Inductance
| <math> M = \Phi_H^{\prime}/I = \int\int_{S^{\prime}} \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| mutual_inductance.DAT
|-
! scope="row"| Resistance
| <math> R = V/I_{cond} = - \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| resistance.DAT
|-
! scope="row"| Resistance (Alternative 1)
| <math> R = V^2/P_{ohmic} = \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2 / \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| resistance.DAT
|-
! scope="row"| Resistance (Alternative 2)
| <math> R = P_{ohmic}/I_{cond}^2 = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv / \left( \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} \right)^2</math>
| resistance.DAT
|-
! scope="row"| Thermal Flux
| <math> \Phi_T = \int\int_{S_o} \mathbf{q(r)} . \mathbf{ds} </math>
| flux_T.DAT
|-
! scope="row"| Thermal Energy
| <math> W_T = Q = \int \int \int_V \rho_V c_p \left( T\mathbf{(r)} - T_{env} \right) dv </math>
| energy_T.DAT
|}

<table>
<tr>
<td>
[[Image:Qsource13.png|thumb|left|480px|Defining the capacitance observable in the field integral dialog.]]
</td>
</tr>
<tr>
<tr>
<td>
[[Image:Qsource11.png|thumb|left|480px|The electric flux box for calculation of charge around a capacitor.]]
</td>
</tr>
<tr>
<td>
[[Image:Qsource12.png|thumb|left|480px|A line defining the voltage path for calculation of voltage between capacitor plates.]]
</td>
</tr>
</table>

== Discretizing the Physical Structure in EM.Ferma ==

===The Static Mesh===

The Finite Difference technique discretizes the computational domain using a 3D rectangular grid. EM.Ferma generates a fixed-cell mesh. This means that the extents of the mesh cells along the principal axes are fixed: Δx, Δy, Δz. By default, the mesh cell size is set to one unit project along all the three directions (with Δx = Δy = Δz). To modify the cell size, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static Mesh" in the Navigation Tree, and select "Mesh Settings..." from the contextual menu to open the Mesh Settings Dialog.

{{Note|To obtain accurate results, it is highly recommended to use a square mesh as much as possible.}}

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's Fixed-Cell Brick Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Qsource2.png|thumb|360px|Geometry of a spherical charge source and the enclosing domain box.]] </td>
<td> [[Image:Qsource3.png|thumb|360px|Fixed-cel mesh of the spherical charge object.]] </td>
</tr>
</table>

== Running Static Simulations in EM.Ferma ==

=== EM.Ferma's Simulation Modes ===

[[EM.Ferma]] currently offers three different simulation modes as follows:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:100px;" | Single run
| style="width:200px;" | N/A
| style="width:150px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:100px;" | Multiple runs
| style="width:200px;" | N/A
| style="width:150px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:100px;" | Multiple runs
| style="width:200px;" | N/A
| style="width:150px;" | None
|}

=== Running an Electrostatic, Magnetostatic or Thermal Analysis ===

[[EM.Ferma]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Thermal. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in the presence of electric sources (volume charges and fixed-potential PEC blocks) and dielectric material media. The magnetostatic engine solves the magnetic form of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, in the presence of magnetic sources (wire and volume currents and permanent magnetic blocks) and magnetic material media. The thermal engine solves the thermal form of Poisson's equation for steady-state temperature subject to thermal boundary conditions, in the presence of heat sources (volume sources and fixed-temperature PTC blocks) and insulator material media.

To run a static simulation, first you have to open the Run Dialog. This is done by clicking the "Run" button of the Simulate Toolbar, or by selecting the "Run" item of the Simulate Menu, or simply using the keyboard shortcut "Ctrl+R". There are two available options for the simulation engine: '''Electrostatic-Magnetostatic Solver''' and '''Steady-State Thermal Solver'''. Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation.

<table>
<tr>
<td> [[Image:Ferma L1 Fig11.png|thumb|left|600px|EM.Ferma's Simulation Run dialog.]] </td>
</tr>
</table>

In EM.Ferma you don't have to choose between the electrostatic or magnetostatic simulation engines. The program looks at the types of sources and material objects present in your project workspace and then it determines whether an electrostatic analysis or a magnetostatic analysis or possibly both should be performed. When there are only electric sources present, you will get nonzero electric fields and zero magnetic fields. When there are only magnetic sources present, you will get nonzero magnetic fields and zero electric fields. On the other hand, since the electrostatic and thermal solvers share the same navigation resources, you can run only one of the two engines at a time. By default, the electrostatic solver is enabled.

An "Analysis" is the simplest simulation mode of EM.Ferma. It is a single-shot finite difference solution of your static problem. The physical structure of your project workspace is first discretized using a fixed-cell mesh and the Poisson equation is solved numerically everywhere in the computational domain. The field and potential values at each mesh node are computed, and the specified observables are written into data files. The other available simulation modes, parametric sweep and optimization, involve multiple runs of the static solvers.

===Static Simulation Engine Settings===

EM.Ferma offers two different types of linear system solver for solving the matrix equations that result from discretization of Poisson's equation: an iterative solver based on the stabilized Bi-Conjugate Gradient (BiCG) method and a Gauss-Seidel solver. The default solver type is BiCG. You can specify some numerical parameters related to the BiCG solver. To do that, you need to open the Simulation Engine Settings Dialog by clicking the "Settings" button located next to the "Select Engine" drop-down list. From this dialog you can set the maximum number of BiCG iterations, which has a default value of 10,000. You can also set a value for "Convergence Error". The default value for electrostatic analysis is 0.001. For magnetostatic analysis, the specified value of convergence error is reduced by a factor 1000 automatically. Therefore, the default convergence error in this case is 10<sup>-6</sup>.

{{Note|The value of convergence error affect the accuracy of your simulation results. For most practical scenarios, the default values are adequate. You can reduce the convergence error for better accuracy at the expense of longer computation time.}}

<table>
<tr>
<td>
[[Image:Qsource7.png|thumb|left|480px|EM.Ferma's Static Engine Settings dialog.]]
</td>
</tr>
</table>

== The 2D Quasi-Static Simulation Mode==

EM.Ferma's electrostatic simulation engine features a 2D solution mode where your physical model is treated as a longitudinally infinite structure in the direction normal to specified "2D Solution Plane". A 2D solution plane is defined based on a "Field Sensor" definition that already exists in your project. To explore EM.Ferma's 2D mode, right-click on '''2D Solution Planes''' in the "Computational Domain" section of the navigation tree and select '''2D Domain Settings...''' from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Reduce the 3D Domain to a 2D Solution Plane". The first field sensor observable in the navigation tree is used for the definition of the 2D solution plane.

At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the field sensor plane. It is assumed that your structure is invariant along the direction normal to the 2D solution plane. Therefore, your computed field and potential profiles must be valid at all the planes perpendicular to the specified longitudinal direction. A 2D structure of this type can be considered to represent a transmission line of infinite length. EM.Ferma also performs a quasi-static analysis of the transmission line structure, and usually provides good results at lower microwave frequencies (f < 10GHz). It computes the characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of the multi-conductor TEM or quasi-TEM transmission line. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively.

<table>
<tr>
<td> [[Image:Qsource14.png|thumb|left|450px|The 2D static domain dialog.]] </td>
</tr>
</table>

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Electrostatic_%26_Magnetostatic_Field_Analysis#2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures | 2D Quasi-Static Analysis of Transmission Lines]]'''.

<table>
<tr>
<td>
[[Image:Qsource16.png|thumb|left|480px|A field sensor and 2D solution plane defined for a microstrip line.]]
</td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Qsource17.png|thumb|left|480px|Electric field distribution of the microstrip line on the 2D solution plane.]] </td>
</tr>
<tr>
<td> [[Image:Qsource18.png|thumb|left|480px|Electric scalar potential distribution of the microstrip line on the 2D solution plane.]] </td>
</tr>
</table>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[EM.Ferma#Product_Overview | Back to the Top of the Page]]'''

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EM.Tempo

2018-08-03T23:44:43Z

Kazem Sabet: /* Building the Physical Structure in EM.Tempo */

[[Image:Splash-fdtd.jpg|right|720px]]
<strong><font color="#961717" size="4">Fast Multicore & GPU-Accelerated FDTD Solvers for Simulating the Most Complex Electromagnetic Modeling Problems</font></strong>
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td>
<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Tempo_Documentation | EM.Tempo Tutorial Gateway]]'''

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==

=== EM.Tempo in a Nutshell ===

EM.Tempo is a powerful electromagnetic simulator for full-wave modeling of 3D radiation, scattering and propagation problems. It features a highly efficient Finite Difference Time Domain (FDTD) simulation engine that has been optimized for speed and memory usage. EM.Tempo brings to your desktop the ultimate in computational power. Its FDTD solver has been parallelized to take full advantage of multi-core processor architectures. With a large variety of geometrical, material and excitation features including open-boundary and periodic structures, you can use EM.Tempo as a general purpose 3D field simulator for most of your electromagnetic modeling needs. EM.Tempo's new advanced simulation capabilities are the key to a thorough understanding of the interaction of electromagnetic waves with complex media such as anisotropic composites, metamaterials or biological environments or with passive and active devices and nonlinear circuits.

EM.Tempo has undergone several evolutionary development cycles since its inception in 2004. The original simulation engine utilized an FDTD formulation based on the uniaxial perfectly matched layer (UPML) boundary termination. Subsequently, a more advanced boundary termination based on the convolutional perfectly matched layer (CPML) was implemented with a far superior performance for all oblique wave incidences in different types of media. EM.Tempo now has the ability to model laterally infinite layered structures using CPML walls that touch material media. A novel formulation of periodic boundary conditions was implemented based on the constant transverse wavenumber method (or direct spectral FDTD). In 2013 we introduced an Open-MP optimized multi-core version of the FDTD engine as well as a hardware-accelerated solver that runs on CUDA-enabled graphical processing unit (GPU) platforms. Both of these fast solvers are now a standard part of the EM.Tempo Pro package.

[[Image:Info_icon.png|30px]] Click here for an overview of the '''[[Basic Principles of The Finite Difference Time Domain Method | Basic FDTD Theory]]'''.

<table>
<tr>
<td>
[[Image:ART GOLF Fig title.png|thumb|left|400px| The 3D far-field radiation pattern of a vehicle-mounted antenna structure simulated by EM.Tempo.]]
</td>
</tr>
</table>

=== EM.Tempo as the FDTD Module of EM.Cube ===

EM.Tempo is a general-purpose EM simulator than can solve most types of electromagnetic modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains. It has also been integrated within the [[EM.Cube]] simulation environment as its full-wave "FDTD Module". EM.Tempo shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== The Advantages & Limitations of EM.Tempo's FDTD Simulator ===

A time domain simulation like FDTD offers several advantages over frequency domain simulations. In certain applications, the time domain signature or behavior of a system, e.g. the transient response of a circuit or an antenna, is sought. In other applications, you may need to determine the wideband frequency response of a system. In such cases, using a frequency domain technique, you have to run the simulation engine many times to adequately sample the specified frequency range. In contrast, using the FDTD method requires a single-run simulation. The temporal field data are transformed into the Fourier domain to obtain the wideband frequency response of the simulated system. Among other advantages of the FDTD method are its versatility in handling complex material compositions as well as its superb numerical stability. It is worth noting that unlike most frequency domain methods, the FDTD technique does not involve numerical solution of large ill-conditioned matrix equations that are often very sensitive to the mesh quality.

Like every numerical technique, the FDTD method has disadvantages, too. Adding the fourth dimension, time, to the computations increases the size of the numerical problem significantly. Unfortunately, this translates to both larger memory usage and longer computation times. Note that the field data are generated in both the 3D space and time. EM.Tempo uses a staircase "Yee" mesh to discretize the physical structure. This works perfectly fine for rectangular objects that are oriented along the three principal axes. In the case of highly curved structures or slanted surfaces and lines, however, this may compromise the geometrical fidelity of your structure. EM.Tempo provides a default adaptive FDTD mesher that can capture the fine details of geometric contours, slanted thin layers, surfaces, etc. to arbitrary precision. However, with smaller mesh cells, the stability criterion leads to smaller time steps; hence, longer computation times. Another disadvantage of the FDTD technique compared to naturally open-boundary methods like the method of moments (MoM) is its finite-extent computational domain. This means that to model open boundary problems like radiation or scattering, absorbing boundary conditions are needed to dissipate the incident waves at the walls of the computational domain and prevent them from reflecting back into the domain. The accuracy of the FDTD simulation results depends on the quality of these absorbers and their distance from the actual physical structure. EM.Tempo provides high quality perfectly matched layer (PML) terminations at the boundaries, which can be placed fairly close to your physical structure to reduce the total size of the computational domain.

<table>
<tr>
<td>
[[Image:Airplane Mesh.png|thumb|left|480px|The Yee mesh of an imported aircraft CAD model.]]
</td>
</tr>
</table>

== EM.Tempo Features at a Glance ==

=== Physical Structure Definition ===

<ul>
<li>
PEC, PMC and dielectric materials and thin wires</li>
<li>
Uniaxial and fully anisotropic materials with four complete constitutive tensors</li>
<li>
Dispersive materials of Debye, Drude and Lorentz types with arbitrary number of poles</li>
<li>
Generalized uniaxial and doubly negative refractive index metamaterials with arbitrary numbers of both electric and magnetic poles</li>
<li>
Two types of gyrotropic materials: ferrites and magnetoplasmas</li>
<li>
PEC, PMC and convolutional perfectly match layer (CPML) boundary conditions</li>
<li>
Doubly periodic structures</li>
</ul>

=== Sources, Ports & Devices ===

<ul>
<li>
Lumped voltage sources with internal resistance placed on a PEC line or thin wire object with an arbitrary orientation</li>
<li>
Distributed sources with uniform, sinusoidal and edge-singular profiles</li>
<li>
Microstrip, coplanar Waveguide (CPW) and coaxial ports</li>
<li>
Waveguide sources with the dominant TE<sub>10</sub> modal profile</li>
<li>
Multi-port and coupled port definitions</li>
<li>
Two types of filamentary current sources: Hertzian short dipole radiators with arbitrary orientation and long wire current sources aligned along one of the principal axes with a uniform, triangular or sinusoidal current distribution profile</li>
<li>
Plane wave excitation with linear and circular polarizations</li>
<li>
Multi-ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li>
<li>
Gaussian beam excitation</li>
<li>
Huygens sources</li>
<li>
Source arrays with weight distribution & phase progression</li>
<li>
Periodic sources with user defined beam scan angles</li>
<li>
Standard excitation waveforms (Gaussian pulse, modulated Gaussian and sinusoidal) for optimal frequency domain computations </li>
<li>
Arbitrary user-defined temporal excitation waveforms using mathematical expressions and Python functions</li>
<li>
Passive lumped devices: R, L, C, series RL and parallel RC and nonlinear diode device</li>
<li>
Active lumped one-port and two-port devices placed on PEC lines aligned along one of the principal axes with arbitrary Netlist definitions</li>
<li>
Active distributed one-port and two-port devices placed under microstrip lines with arbitrary Netlist definitions</li>
</ul>

=== Mesh Generation ===

<ul>
<li>
Fast generation of Yee grid mesh of solids, surfaces and curves</li>
<li>
Geometry-aware and material-aware adaptive mesh generator with gradual grid transitions</li>
<li>
Fixed-cell uniform mesh generator with three unequal cell dimensions</li>
<li>
Mesh view with three principal grid profilers</li>
<li>
Manual control of mesh parameters and fixed grid points</li>
</ul>

=== 3D FDTD Simulation ===

<ul>
<li>
Wideband full-wave simulation of 3D structures</li>
<li>
Transient analysis with arbitrary user defined excitation waveforms</li>
<li>
Multi-frequency computation of frequency domain quantities in a single FDTD simulation run</li>
<li>
OpenMP-parallelized multi-core and multi-thread FDTD simulation engine</li>
<li>
GPU-accelerated FDTD simulation engine based on NVIDIA CUDA platforms</li>
<li>
Total-field-scattered-field analysis of plane wave and Gaussian beam excitation</li>
<li>
Full-wave analysis of periodic structures with arbitrary plane wave incidence angles using the Direct Spectral FDTD method</li>
<li>
Infinite material half-space Green's functions for calculation of far fields in presence of a lossy ground</li>
<li>
Accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation</li>
<li>
Parametric sweeps of variable object properties or source parameters including frequency and angular sweeps</li>
<li>
Multi-variable and multi-goal optimization of structures</li>
<li>
Automated generation of compact reduced order surrogate models from full-wave simulation data</li>
</ul>

=== Data Generation & Visualization ===

<ul>
<li>
Near-field intensity (colorgrid), contour and surface plots (vectorial - amplitude & phase)</li>
<li>
Near-field probes for monitoring field components in both time & frequency domains</li>
<li>
Far-field radiation patterns: 3D pattern visualization and 2D polar and Cartesian graphs</li>
<li>
Far-field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li>
<li>
Radiation pattern of arbitrary array configurations of the FDTD structure or periodic unit cell</li>
<li>
Bistatic and monostatic radar cross section</li>
<li>
Huygens surface data generation for use in other [[EM.Cube]] modules</li>
<li>
Periodic reflection/transmission coefficients and k-β diagrams</li>
<li>
Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li>
<li>
Time and frequency domain port voltages, currents and powers</li>
<li>
Touchstone-style S-parameter text files for direct export to [[RF.Spice A/D]]</li>
<li>
Interanl node voltages and currents of Netlist-based one-port and two-port networks</li>
<li>
Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes</li>
<li>
Animation of temporal evolution of fields</li>
<li>
Custom output parameters defined as mathematical expressions or Python functions of standard outputs</li>
</ul>

== Building the Physical Structure in EM.Tempo ==

=== Material Variety in EM.Tempo ===

Your physical structure in EM.Tempo can be made up of several geometric objects with different material compositions. In other words, the geometric objects you draw or import from external files are grouped together based on a common material composition. EM.Tempo's material types are divided into seven categories:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Material Type
! scope="col"| Applications
! scope="col"| Geometric Object Types Allowed
|-
| style="width:30px;" | [[File:pec_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]
| style="width:300px;" | Modeling perfect metals
| style="width:250px;" | Solid, surface and curve objects
|-
| style="width:30px;" | [[File:thin_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Thin Wire |Thin Wire]]
| style="width:300px;" | Modeling wire radiators
| style="width:250px;" | Lines parallel to one of the three principal axes
|-
| style="width:30px;" | [[File:pmc_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC)]]
| style="width:300px;" | Modeling perfect magnetic sheets
| style="width:250px;" | Rectangle strips parallel to one of the three principal planes
|-
| style="width:30px;" | [[File:diel_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dielectric Material |Dielectric Material]]
| style="width:300px;" | Modeling any homogeneous material
| style="width:250px;" | Solid objects
|-
| style="width:30px;" | [[File:aniso_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Anisotropic Material |Anisotropic Material]]
| style="width:300px;" | Modeling unaxial or generalized anisotriopic materials
| style="width:250px;" | Solid objects
|-
| style="width:30px;" | [[File:disp_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dispersive Material |Dispersive Material]]
| style="width:300px;" | Modeling Debye, Drude and Lorentz materials and generalized metamaterials
| style="width:250px;" | Solid objects
|-
| style="width:30px;" | [[File:voxel_group_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gyrotropic_Material |Gyrotropic Material]]
| style="width:300px;" | Modeling ferrites and magnetoplasmas
| style="width:250px;" | Solid objects
|-
| style="width:30px;" | [[File:Virt_group_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]
| style="width:300px;" | Used for representing non-physical items
| style="width:250px;" | All types of objects
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

=== Organizing the Physical Structure by Material Groups ===

EM.Tempo groups your geometric objects in the project workspace based on their material type. All the objects belonging to the same material group share the same color and same material properties. Under each material node in the navigation tree, you can create new material groups of the same type but with different properties such as color, texture, or electric and magnetic constitutive parameters.

Once a new material node has been created on the navigation tree, it becomes the "Active" material group of the project workspace, which is always listed in bold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active material type. There is only one material group that is active at any time. Any material can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create material groups, and then draw new objects under the active material group. However, if you start a new EM.Tempo project from scratch, and start drawing a new object without having previously defined any material groups, a new default PEC group is created and added to the navigation tree to hold your new object.

{{Note|You can import external objects only to CubeCAD. You can then move the imported objects form CubeCAD to EM.Tempo.}}

[[Image:Info_icon.png|30px]] Click here to access the '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.

<table>
<tr>
<td>
[[Image:Tempo NavTree.png|thumb|left|400px|EM.Tempo's navigation tree.]]
</td>
</tr>
</table>

=== Material Hierarchy in EM.Tempo ===

[[EM.Tempo]] allows overlapping objects although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same material type and group overlap, they are merged using the Boolean union operation during the mesh generation process. If two overlapping objects belong to two different material categories, then the material properties of the FDTD cells in the overlap region will follow the [[EM.Tempo]]'s material hierarchy rule. In that case, the overlap area cells will always be regarded as having the material type of the higher priority. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner:

# PEC
# PMC
# Dispersive
# Gyrotropic
# General Anisotropic
# Uniaxial Anisotropic
# Dielectric

If planned carefully, taking advantage of [[EM.Tempo]]'s material hierarchy rule would make the construction of complex objects easier. For example, a dielectric coated metallic cylinder can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in the illustration below. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinder.

<table>
<tr>
<td>
[[Image:FDTD_MAN2.png|thumb|left|360px|The geometric construction of a dielectric-coated metallic cylinder with a conformal foil.]]
</td>
</tr>
</table>

=== Moving Objects Among Different Material Groups or EM.Cube Modules ===

You can move any geometric object or a selection of objects from one material group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models from CubeCAD to [[EM.Tempo]]. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a material group called "Dielectric_1" in [[EM.Tempo]], then you have to select the menu item '''Move To → [[EM.Tempo]] → Dielectric_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.

<table>
<tr>
<td>
[[Image:Tempo_L11_Fig2.png|thumb|left|720px|Moving an imported object from CubeCAD to EM.Tempo.]]
</td>
</tr>
</table>

== EM.Tempo's Computational Domain & Boundary Conditions ==

===The FDTD Solution Domain===

The FDTD method requires a finite-extent solution domain. This is rather straightforward for shielded structures, where a typical PEC enclosure box defines the computational domain. For open-boundary structures like antennas and scatterers, the computational domain must be truncated using appropriate termination boundary conditions. The objective of termination boundary conditions is to eliminate the reflections from the walls of the domain box back to the computational domain.

In [[EM.Tempo]], you can define two types of domain box. A '''Default'''-type domain is a box that is placed at a specified offset distance from the largest extents of your physical structure (global bounding box). The offset is specified in free-space wavelengths. A '''Custom'''-type domain, on the other hand, is defined as a fixed-size and fixed-location box in the World Coordinate System (WCS). In this case, you have to specify the coordinates of the lower left front corner (Corner 1) and upper right back corner (Corner 2) of the domain box.

When you start a new project in [[EM.Tempo]], a default-type domain is automatically created with a default offset value set equal to a quarter free-space wavelength (0.25λ<sub>0</sub>). As soon as you draw your first object, a blue domain box shows up in the project workspace and encloses your object. As you add more objects and increase the overall size of your structure, the domain box grows accordingly to encompass your entire physical structure. When you delete objects from the project workspace, the domain box also shrinks accordingly.

===Changing the Domain Settings===

To set the solution domain of your FDTD project, follow these steps:

* Click the '''Domain''' [[Image:domain_icon.png]] button of the '''Simulate ''' Toolbar or select the menu item '''Simulate → Computational Domain → Domain Settings...''' or right click on the '''FDTD Domain''' item of the Navigation Tree and select '''Domain Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+A'''. The Domain Settings Dialog opens up, showing the current domain type selection.
* Select one of the two options for '''Domain Type'''<nowiki>: </nowiki>'''Default''' or '''Custom'''.
* If you select the "Default" domain type, the domain box is defined in terms of the offsets along the X, Y and Z directions from the largest extents of your physical structure. Select one of the two options for '''Offset Units: Grid''' and '''Wavelength'''. In the section titled '''"Domain Size"''', enter the amount of domain extension beyond the largest extents of the structure along the ±X, ±Y and ±Z directions. Note that in the case of a default-type domain box, the offset values based on your current project settings (frequency and units).
* When the '''Wavelength''' option is selected for '''Offset Units''', additional free space is added around the structure by the specified ±X, ±Y and ±Z offsets in free space wavelengths. Note that the free space wavelength for this purpose is calculated at the center frequency of the project. The default value of the offset in this case is a quarter free space wavelength. Note that with this option, the number of the additional cells and their cell size is not fixed; they vary from structure to structure.
* When the '''Grid''' option is selected for '''Offset Units''', the six offset values represent the number of additional free-space mesh cells that are placed in each direction beyond the largest bounding box around the physical structure. The default value of the offset in this case is eight grid cells along the ±X, ±Y and ±Z directions.
* If you select the "Custom" domain type instead, you need to enter values for the coordinates of the lower-left-front corner,''' Corner 1''', and the upper-right-back corner, '''Corner 2''', of the domain box.
* After you change values or settings, click the '''Apply''' button to make the changes effective. To recover the default values, click the '''Defaults''' button of the dialog. Click '''OK''' to save the settings and close the dialog.

By default, the domain box is shown as a wireframe box with blue lines. You can change the color of the domain box or hide it.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Domain_Settings | Domain Settings]]'''.

<table>
<tr>
<td>
[[Image:FDTD14.png|thumb|left|480px|EM.Tempo's domain settings dialog.]]
</td>
</tr>
</table>

===Settings the Domain Boundary Conditions===

[[EM.Tempo]] supports four types of domain boundary conditions: PEC, PMC, Convolutional Perfectly Matched Layers (CPML) and Periodic Boundary Conditions (PBC). By default, all the six sides of the computational domain box are set to CPML, representing a completely open-boundary structure. Different boundary conditions can be assigned to each of the six walls of the domain box. The periodic boundary conditions are special ones that are assigned through [[EM.Tempo]]'s Periodicity Dialog and will be discussed later under modeling of periodic structures. The current release of [[EM.Cube]] allows periodic boundary conditions only on the side walls of the computational domain, and not on the top or bottom walls.

To define the boundary conditions of the solution domain, follow these steps:

* Select the menu item '''Simulate → Computational Domain → Boundary Conditions''' or right click on the '''Boundary Conditions''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Boundary Conditions...''' from the contextual menu. The Boundary Conditions Dialog opens.
* You need to assign the type of boundary condition on each of the six domain boundaries: ±X, ±Y and ±Z. For each face, choose one of the three options available: '''PEC''', '''PMC '''or '''PML'''.

The PEC and PMC boundary conditions are the most straightforward to set up and use. Assigning the PEC boundary to one of the bounding walls of the solution domain simply forces the tangential component of the electric field to vanish at all points along that wall. Similarly, assigning the PMC boundary to one of the bounding walls of the solution domain forces the tangential component of the magnetic field to vanish at all points along that wall. For planar structures with a conductor-backed substrate, you can use the PEC boundary condition to designate the bottom of the substrate (the -Z Domain Wall) as a PEC ground. For shielded waveguide structures, you can designate all the lateral walls as PEC. Similarly to model shielded cavity resonators, you designate all the six walls as PEC.

<table>
<tr>
<td>
[[Image:FDTD13.png|thumb|left|480px|EM.Tempo's boundary conditions dialog.]]
</td>
</tr>
</table>

=== Advanced CPML Setup ===

In open-boundary electromagnetic modeling problems, you need a boundary condition that simply absorbs all the incoming radiation. For problems of this nature, an absorbing boundary condition (ABC) is often chosen that effectively minimizes wave reflections at the boundary. [[EM.Tempo]] uses Convolutional Perfectly Matched Layers (CPML) for absorbing boundary conditions. Usually two or more ABC layers must be placed at the boundaries of the physical structure to maximize wave absorption. The boundary CPML cells in the project workspace are not visible to the user. But, in effect, multiple rows of CPML cells are placed on the exterior side of each face of the visible domain box.

You can set the number of CPML layers as well as their order. This is done through the CPML Settings Dialog, which can be accessed by right clicking on the '''CPML''' item in the '''Computational Domain''' section of the navigation tree and selecting '''CPML Settings...''' from the contextual menu. By default, eight CPML layers of the third order are placed outside the FDTD problem domain. It is recommended that you always try a four-layer CPML first to assess the computational efficiency. The number of CPML layers may be increased if a very low reflection is required (<-40dB).

{{Note|[[EM.Tempo]]'s default quarter wavelength offset for the domain box and its 8-layer CPML walls are very conservative choices and can be relaxed in many cases. An offset equal to eight free-space grid cells beyond the largest bounding box usually gives a more compact, but still valid, domain box.}}

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#CPML_vs._PML | Perfectly Matched Layer Termination]]'''.

<table>
<tr>
<td> [[Image:FDTD MAN10.png|thumb|left|360px|The boundary CPML cells placed outside the visible domain box.]] </td>
<td> [[Image:FDTD15.png|thumb|left|400px|CPML Settings dialog.]] </td>
</tr>
</table>

=== Using CPML to Model Structures of Infinite Extents ===

You can use EM.Tempo to model planar structures of infinite extents. A planar substrate usually consists of one or more dielectric layers, possibly with a PEC ground plane at its bottom. To model a laterally infinite dielectric substrate, you must assign a PML boundary condition to the four lateral sides of the domain box and set the lateral domain offset values along the ±X and ±Y directions all equal to zero. If the planar structure ends in an infinite dielectric half-space from the bottom, you must assign a PML boundary condition to the bottom side of the domain box and set the -Z offset equal to zero. This leaves only the +Z offset with a nonzero value.

When a domain boundary wall is designated as CPML and its has a zero domain offset, meaning it touches a material block, the CPML cells outside the domain wall are reflected back inside the computational domain. In other words, the effective number of CPML layers will be twice the one specified in the CPML Settings dialog. This will effectively extend the material block infinitely beyond the boundary wall and will create an open boundary effect in the specified direction. It goes without saying that only "substrate" objects are supposed to touch the boundary walls in such a scenario. Because of the rolled-back CPML cells inside the domain, it is very important to make sure that other finite-sized parts and objects stay clear from the domain walls as well as from the invisible "interior" CPML cells.

{{Note|The current release of EM.Tempo does not support full-anisotropic or dispersive or gyrotropic layers of laterally infinite extents. In other words, your anisotropic or dispersive or gyrotropic material objects must not touch the CPML domain boundaries.}}

<table>
<tr>
<td> [[Image:FDTD MAN8.png|thumb|left|360px|The domain box of a patch antenna with a finite-sized substrate and ground.]] </td>
<td> [[Image:FDTD MAN9.png|thumb|left|360px|The domain box of a laterally infinite patch antenna with zero ±X, ±Y and -Z domain offsets. Note that the bottom PEC plate can be replaced with a PEC boundary condition at the -Z domain wall.]] </td>
</tr>
</table>

== EM.Tempo's Excitation Sources ==

=== Source Variety in EM.Tempo ===

Before you can run an FDTD simulation, you have to define a source to excite your project’s physical structure. EM.Tempo offers a variety of excitation mechanisms for your physical structure depending on your particular type of modeling problem or application:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Host Object
! scope="col"| Spatial Domain
! scope="col"| Restrictions / Additional Requirements
|-
| style="width:30px;" | [[File:lumped_src_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Lumped Source |Lumped Source]]
| style="width:250px;" | General-purpose point voltage source
| style="width:200px;" | PEC or thin wire line parallel to a principal axis
| style="width:200px;" | A single point
| style="width:200px;" | None
|-
| style="width:30px;" | [[File:distrb_src_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Distributed Source |Distributed Source]]
| style="width:250px;" | General-purpose distributed planar source with a uniform, edge-singular or sinusoidal impressed field profile
| style="width:200px;" | Virtual rectangle strip parallel to a principal plane
| style="width:200px;" | A rectangular area
| style="width:200px;" | None
|-
| style="width:30px;" | [[File:mstrip_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Microstrip Port |Microstrip Port Source]]
| style="width:250px;" | Used for S-parameter computations in microstrip-type structures
| style="width:200px;" | PEC rectangle strip parallel to a principal plane
| style="width:200px;" | A vertical rectangular area underneath the host strip
| style="width:200px;" | Requires a PEC ground plane strip underneath the host strip
|-
| style="width:30px;" | [[File:cpw_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Coplanar Waveguide (CPW) Port |Coplanar Waveguide (CPW) Port Source]]
| style="width:250px;" | Used for S-parameter computations in CPW-type structures
| style="width:200px;" | PEC rectangle strip parallel to a principal plane
| style="width:200px;" | Two parallel horizontal rectangular areas attached to the opposite lateral edges the host center strip
| style="width:200px;" | Requires two parallel PEC ground strips on the two sides of the host center strip
|-
| style="width:30px;" | [[File:coax_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Coaxial Port |Coaxial Port Source]]
| style="width:250px;" | Used for S-parameter computations in coaxial-type structures
| style="width:200px;" | PEC Cylinder oriented along a principal axis
| style="width:200px;" | A circular ring area enveloping the host inner conductor cylinder
| style="width:200px;" | Requires a concentric hollow outer conductor cylinder
|-
| style="width:30px;" | [[File:wg_src_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Waveguide Port |Waveguide Port Source]]
| style="width:250px;" | Used for S-parameter computations in waveguide structures
| style="width:200px;" | Hollow PEC box oriented along a principal axis
| style="width:200px;" | A rectangular area at the cross section of the host hollow box
| style="width:200px;" | The host box object can have one capped end at most.
|-
| style="width:30px;" | [[File:hertz_src_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Filamentary_Current_Source |Filamentary Current Source]]
| style="width:250px;" | General-purpose wire current source of two types: Hertzian short dipole radiator and long wire current source with a uniform, triangular or sinusoidal current distribution profile
| style="width:200px;" | None (stand-alone source)
| style="width:200px;" | A line
| style="width:200px;" | Hertzian short dipole radiators can have an arbitrary orientation, but long wire current sources must be aligned along one of the principal axes
|-
| style="width:30px;" | [[File:plane_wave_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Plane Wave |Plane Wave Source]]
| style="width:250px;" | Used for modeling electromagnetic scattering & computation of reflection/transmission characteristics of periodic surfaces
| style="width:200px;" | None (stand-alone source)
| style="width:200px;" | Surface of a cube enclosing the physical structure
| style="width:200px;" | None
|-
| style="width:30px;" | [[File:gauss_icon.png]]
| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gaussian Beam |Gaussian Beam Source]]
| style="width:250px;" | Used for modeling focused beams
| style="width:200px;" | None (stand-alone source)
| style="width:200px;" | Surface of a cube enclosing the physical structure
| style="width:200px;" | None
|-
| style="width:30px;" | [[File:huyg_src_icon.png]]
| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]
| style="width:250px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules
| style="width:200px;" | None (stand-alone source)
| style="width:200px;" | Surface of a cube
| style="width:200px;" | Imported from a Huygens surface data file
|}

Click on each category to learn more details about each source type and how to define one.

[[Image:Info_icon.png|30px]] More information about all the source types can be found in the '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.

In the most general sense, one can consider two fundamental types of excitation sources for an FDTD simulation: a lumped source and a distributed source. A lumped sources is localized at a single mesh point in the computational domain, while a distributed source is spread over several mesh cells. Among the source types of the above list, the microstrip port, CPW port, coaxial port, waveguide port, plane wave and Gaussian beam sources are indeed special cases of a distributed source for specific applications.

A lumped source is the most commonly used way of exciting a structure in EM.Tempo. A lumped source is a voltage source with a series internal resistor that must be placed on a PEC or thin wire line object that is parallel to one of the three principal axes. A lumped source is displayed as a small red arrow on the host line. Lumped sources are typically used to define ports and compute the port characteristics like S/Y/Z parameters. Using simple lumped sources, you can simulate a variety of transmission line structures including filters, couplers or antenna feeds. This approach may become less accurate at higher frequencies when the details of the feed structure become important and can no longer be modeled with highly localized lumped ports. In such cases, it is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the ports for calculation of the incident and reflected waves. Waveguide source is used to excite the dominant TE<sub>10</sub> mode of a hollow rectangular waveguide. Other special types of distributed sources are microstrip port, CPW port and coaxial ports that can be used effectively to excite their respective transmission line structures.

When you create an array of an object type that can host one of the above source types, you can also associate a source array with that array object.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Modeling Finite-Sized Source Arrays]]'''.

A plane wave source is a popular excitation method that is used for calculation of the radar cross section of targets or reflection and transmission characteristics of periodic surfaces. A Gaussian beam source is another source type that is highly localized as opposed to the uniform plane wave. For both plane wave and Gaussian beam sources,[EM.Tempo requires a finite incidence surface to calculate the excitation. When you create either of these sources, a plane wave box or a Gaussian beam box is created as part of their definition. A trident symbol on the box shows the propagation vector as well as the E-field and H-field polarization vectors. The time domain plane wave or Gaussian beam excitation is calculated on the surface of this box and injected into the computational domain. The plane wave box is displayed in the project workspace as a purple wireframe box enclosing the structure, while the Gaussian beam box appears as a green wireframe box. Both boxes have an initial default size with an offset of 0.2λ<sub>0</sub> from the largest bounding box enclosing your entire physical structure. In both source dialogs, the radio button '''Size: Default''' is selected by default. The radio button '''Size: Custom''' allows you to set the excitation box manually. The values for the coordinates of '''Corner 1''' and '''Corner 2''' can now be changed. Corner 1 is the front lower left corner and Corner 2 is the rear upper right corner of the box. The corner coordinates are defined in the world coordinate system (WCS).

<table>
<tr>
<td> [[Image:FDTD MAN11.png|thumb|360px|A plane wave box enclosing a PEC cylinder at oblique incidence: θ = 105° and φ = 315°.]] </td>
<td> [[Image:FDTD MAN12.png|thumb|360px|A Gaussian beam box enclosing a PEC cylinder at oblique incidence: θ = 105° and φ = 315°. The concentric circles represent the beam's focus point and radius.]] </td>
</tr>
</table>

=== Simulating a Multiport Structure in EM.Tempo ===

Ports are used to order and index sources for circuit parameter calculations like S/Y/Z parameters. In EM.Tempo, you can define ports at the location of the following types of sources:

*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Lumped Source |Lumped sources]]
*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Distributed Source |Distributed sources]]
*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Microstrip Port |Microstrip port sources]]
*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Coplanar Waveguide (CPW) Port |CPW port sources]]
*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Coaxial Port |Coaxial port sources]]
*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Waveguide Port |Waveguide port sources]]

Every time you create a new source with one of the above types, the program asks if you want to initiate a new port and associate it with the newly created source. If the physical structure of your project workspace has N sources, then N default ports are defined, with one port assigned to each source according to their order in the navigation tree. You can define any number of ports equal to or less than the total number of sources in your project.

If your physical structure has two or more sources, but you have not defined any ports, all the sources will excite the structure simultaneously during the simulation. However, when you assign N ports to the sources, then you have a multiport structure that is characterized by an N×N scattering matrix, an N×N impedance matrix, and an N×N admittance matrix. To calculate these matrices, EM.Tempo uses a binary excitation scheme in conjunction with the principle of linear superposition. In this binary scheme, the structure is analyzed a total of N times. Each time one of the N port-assigned sources is excited, and all the other port-assigned sources are turned off. In other words, the FDTD solver runs a "port sweep" internally. When the ''j''th port is excited, all the S<sub>ij</sub> parameters are calculated together based on the following definition:

:<math> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math>

where V<sub>i</sub> is the voltage across Port i, I<sub>i</sub> is the current flowing into Port i and Z<sub>i</sub> is the characteristic impedance of Port i. The sweep loop then moves to the next port until all ports have been excited.

In summary, to analyze an N-port structure, EM.Tempo runs N separate FDTD time marching loops. The S/Z/Y parameters are frequency-domain quantities. The port voltages and currents are Fourier-transformed to the frequency domain over the frequency range [fc-bw/2, fc+bw/2], where fc is the center frequency and bw is the bandwidth of your project. You can reduce the frequency range of the Fourier transform by settings new values for '''Start''' and '''End''' frequencies in the "Port Definition" dialog as long as these are within the range [fc-bw/2, fc+bw/2]. By default, 200 frequency samples are taken over the specified frequency range. This number can be modified from the FDTD simulation engine settings dialog.

{{Note|In order to obtain correct results, the port impedance must equal the characteristic impedance of the transmission line on which the port is established. This is not automatically taken care of by EM.Tempo.}}

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Sources & Ports]]'''.

<table>
<tr>
<td> [[Image:FDTD MAN15.png|thumb|left|640px|A two-port CWP transmission line segment.]] </td>
</tr>
<tr>
<td> [[Image:FDTD MAN16.png|thumb|left|480px|EM.Tempo's port definition dialog.]] </td>
</tr>
</table>

=== Excitation Waveform & Frequency Domain Computations ===

When an FDTD simulation starts, your project's source starts pumping energy into the computational domain at t > 0. Maxwell's equations are solved in all cells at every time step until the solution converges, or the maximum number of time steps is reached. A physical source has a zero value at t = 0, but it rises from zero at t > 0 according to a specified waveform. EM.Tempo currently offers four types of temporal waveform:

# Sinusoidal
# Gaussian Pulse
# Modulated Gaussian Pulse
# Arbitrary User-Defined Function

A sinusoidal waveform is single-tone and periodic. Its spectrum is concentrated around a single frequency, which is equal to your project's center frequency. A Gaussian pulse decays exponentially as t → ∞, but it has a lowpass frequency spectrum which is concentrated around f = 0. A modulated Gaussian pulse decays exponentially as t → ∞, and it has a bandpass frequency spectrum concentrated around your project's center frequency. For most practical problems, a modulated Gaussian pulse waveform with EM.Tempo's default parameters provides an adequate performance.

The accuracy of the FDTD simulation results depends on the right choice of temporal waveform. EM.Tempo's default waveform choice is a modulated Gaussian pulse. At the end of an FDTD simulation, the time domain field data are transformed into the frequency domain at your specified frequency or bandwidth to produce the desired observables.

{{Note|All of EM.Tempo's excitation sources have a default modulated Gaussian pulse waveform unless you change them.}}

[[Image:Info_icon.png|30px]] Click here to learn more about EM.Tempo's '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#The_Relationship_Between_Excitation_Waveform_and_Frequency-Domain_Characteristics | Standard & Custom Waveforms and Discrete Fourier Transforms]]'''.

=== Defining Custom Waveforms in EM.Tempo ===

In some time-domain applications, you may want to simulate the propagation of a certain kind of waveform in a circuit or structure. In addition to the default waveforms, EM.Tempo allows you to define custom waveforms by either time or frequency specifications for each individual source in your project. If you open up the property dialog of any source type in EM.Tempo, you will see an {{key|Excitation Waveform...}} button located in the "Source Properties" section of the dialog. Clicking this button opens up EM.Tempo's Excitation Waveform dialog. From this dialog, you can override EM.Tempo's default waveform and customize your own temporal waveform. The Excitation Waveform dialog offers three different options for defining the waveform:

* Automatically Generate Optimal Waveform
* Use Custom Frequency Domain Specifications
* Use Custom Time Domain Specifications

The first option, which is also the default option, constructs an optimal modulated Gaussian pulse waveform based on your project's specified center frequency and bandwidth. This optimal waveform guarantees the most accurate frequency domain computations for your simulation. The second option gives you a choice of the three standard waveforms and lets you define their waveform parameters in terms of frequency domain characteristics like center frequency and bandwidth and spectral contents. The third option lets you define a completely arbitrary temporal waveform for your source.

Select the third option of waveform definition and then choose the '''Custom''' option from the '''Waveform Type''' dropdown list. Enter a mathematical expression for your custom waveform a function of the time variable "T" or "t" in the box labeled '''Expression'''. You can use arithmetic operations, standard and library functions as well as user-defined Python functions.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Using Python to Create Functions, Models & Scripts#Creating Custom Python Functions | Creating Custom Python Functions]]'''.

<table>
<tr>
<td>
[[Image:FDTD MAN13.png|thumb|left|720px|EM.Tempo's excitation waveform dialog showing the default standard modulated Gaussian pulse temporal waveform.]]
</td>
</tr>
</table>

When you define a custom waveform in the Excitation Waveform dialog, make sure to click the {{key|Accept}} button of the dialog to make your changes effective. A graph of your custom waveform is plotted in the right panel of the dialog for your review. It is important to keep in mind that typical time scales in the FDTD simulation of RF structures are on the order of nanosecond or smaller. Using the variable "fc" in the expression of your waveform definition usually takes care of this required scaling. Otherwise, you need to use scaling factors like 1e-9 explicitly in your expression.
For example, in the figure below, we have defined a modulated Bessel waveform in the form of "sp.j0(t/2e-9)*sin(2*pi*fc*t)", where sp.j0(x) denotes the zeroth-order Bessel function of the first kind burrowed from Python's special functions module.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary of EM.Cube's Python Functions#Standard Python Functions | Python's Standard & Advanced Mathematical Functions]]'''.

{{Note| If you define a custom excitation waveform for your source, none of the standard frequency domain output data and parameters will be computed at the end of your FDTD simulation.}}

<table>
<tr>
<td>
[[Image:FDTD MAN14.png|thumb|left|720px|EM.Tempo's excitation waveform dialog showing a custom modulated Bessel temporal waveform defined using the Python function sp.j0(x).]]
</td>
</tr>
</table>

== EM.Tempo's Active & Passive Devices ==

=== Defining Lumped Devices ===

In [[EM.Tempo]], you can define eigth types of lumped devices:

# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Resistor | Resistor]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Inductor | Inductor]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Capacitor | Capacitor]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Series_RL_Device | Series RL Device]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Parallel_RC_Device | Parallel RC Device]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Diode | Nonlinear Diode]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_One-Port_Device | Active Lumped One-Port Device]]'''
# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_Two-Port_Device | Active Lumped Two-Port Device]]'''

Lumped devices are connected between two adjacent FDTD mesh nodes. Although lumped devices are not sources and the passive types do not excite a structure, their properties are similar to lumped sources. That is why they are listed under the '''Sources''' section of the navigation tree. A lumped device has to be associated with a PEC line object that is parallel to one of the three principal axes. Similar to lumped sources, lumped devices have an '''Offset''' parameter that is equal to the distance between their location on the host line and its start point.

A lumped device is characterized by a v-i equation of the form:

:<math>i(t) = L \{ v(t) \} </math>

where V(t) is the voltage across the device, i(t) is the current flowing through it and ''L'' is an operator function, which may involve differential or integral operators. Lumped devices are incorporated into the FDTD grid across two adjacent nodes in a similar manner to lumped sources. At the location of a lumped device, the FDTD solver enforces the device's governing equation by relating the device voltage and current to the electric and magnetic field components and updating the fields accordingly at every time step.

[[Image:Info_icon.png|30px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear & Nonlinear Passive & Active Devices]]'''.

{{Note|Small values of inductance may result in the divergence of the FDTD numerical scheme. To avoid this problem, you need to increase the mesh resolution and adopt a higher mesh density. This, of course, may lead to a much longer computation time.}}

<table>
<tr>
<td> [[Image:FDTD MAN17.png|thumb|left|480px|EM.Tempo's lumped device dialog for nonlinear diode.]] </td>
</tr>
<tr>
<td> [[Image:FDTD MAN17A.png|thumb|left|480px|EM.Tempo's lumped device dialog for active lumped two-port device.]] </td>
</tr>
</table>

=== Defining Active Distributed Multiport Networks ===

EM.Tempo also provides two types of active distributed multiport network devices:

# '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_One-Port_Device | Active Distributed One-Port Device/Circuit]]'''
# '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_Two-Port_Device | Active Distributed Two-Port Device/Circuit]]'''

Unlike the active lumped devices, these devices are rather distributed and their behavior is similar to a microstrip port source. In other words, the active distributed one-port device requires a rectangle strip object as a host, while the active distributed two-port device requires two rectangle strip objects for its definition. You can choose one of the edges of the strip object for establishing the circuit port. In the case of a two-port device, you need two parallel and end-to-end aligned strip objects.

The circuit behavior of these devices is defined by a Netlist file. Their property dialog provides a text editor for simply writing the Netlist description of the device. You can also import an existing external Netlist file with a ".CIR" or ".TXT" file extension using the button labeled {{key|Load Netlist}}..

{{Note|[[RF.Spice A/D]] can generate a Netlist file corresponding to an existing circuit project, which can then be saved to a text file with a ".TXT" file extension. }}

<table>
<tr>
<td> [[Image:ActiveOnePort.png|thumb|left|480px|EM.Tempo's active one-port device/circuit dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:ActiveTwoPort.png|thumb|left|720px|EM.Tempo's active two-port device/circuit dialog.]] </td>
</tr>
</table>

=== A Note on Using Active Devices ===

When your physical structure contains an active device, EM.Tempo performs an EM-circuit co-simulation that involves both the full-wave FDTD EM solver and the SPICE circuit solver. In a global self-consistent co-simulation, at each time step of the FDTD time marching loop, the electric and magnetic fields at the location of the device ports are used to compute the port voltages and currents. These quantities are then used in the SPCIE circuit solver to update all the voltages and currents at the internal nodes of the active device. The updated port voltages and currents are finally used to update the electric and magnetic fields in the physical mesh cells and the time marching loop proceeds to the next time step.

EM.Tempo can handle several active one-ports and two-ports simultaneously. In that case, all the devices are automatically compiled into a single Netlist that serves as the input of the SPICE solver. The individual internal nodes of each device need to be renamed for the global Netlist. Besides the main circuit, the Netlist of each device may contain several "subcircuits". Note that the subcircuit nodes are not re-indexed for the global Netlist as is expected.

{{Note|If you want to use a B-type nonlinear dependent source in the Netlist definition of an active one-port or two-port, it must be contained in a subcircuit definition rather than in the main circuit.}}

The figure below shows the geometry of a two-port amplifier device with microstrip input and output transmission lines. The Netlist of the two-port device is given below:

----

C1 1 0 1p

R1 1 0 50

E1 2 0 1 0 20

RS 2 3 10

R2 3 0 50

C2 3 0 1p

----

In this case, a linear voltage-controlled voltage source (E1) with a voltage gain of 20 has been used. The input and output nodes are 1 and 3, respectively.

<table>
<tr>
<td> [[Image:Amp circ.png|thumb|left|420px|The schematic of the amplifier circuit in RF.Spice A/D.]] </td>
</tr>
</table>

The same Netlist can be written using a B-type nonlinear dependent source as follows:

----

C1 1 0 1p

X1 1 0 2 0 amp_dev

.subckt amp_dev 1 2 3 4

R1 1 2 50

B1 3 4 v = 20*v(1,2)

.ends

RS 2 3 10

R2 3 0 50

C2 3 0 1p

----

{{Note|You can use active one-ports to define custom voltage or current sources for your entire physical structure rather than using one of the physical excitation source types of the navigation tree.}}

<table>
<tr>
<td> [[Image:Amp ex.png|thumb|left|550px|The geometry of a microstrip-based amplifier with an active two-port device.]] </td>
</tr>
</table>

== EM.Tempo's Observables & Simulation Data Types==

=== Understanding the FDTD Observable Types ===

EM.Tempo's FDTD simulation engine calculates all the six electric and magnetic field components (E<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub>, H<sub>x</sub>, H<sub>y</sub> and H<sub>z</sub>) at every mesh grid node at all time steps from t = 0 until the end of the time marching loop. However, in order to save memory usage, the engine discards the temporal field data from each time step to the next. Storage, manipulation and visualization of 3D data can become overwhelming for complex structures and larger computational domains. Furthermore, calculation of some field characteristics such as radiation patterns or radar cross section (RCS) can be sizable, time-consuming, post-processing tasks. That is why EM.Tempo asks you to define project observables to instruct what types of output data you want in each simulation process.

EM.Tempo offers the following types of output simulation data:

{| class="wikitable"
|-
! scope="col"| Icon
! scope="col"| Simulation Data Type
! scope="col"| Associated Observable Type
! scope="col"| Applications
! scope="col"| Restrictions
|-
| style="width:30px;" | [[File:fieldprobe_icon.png]]
| style="width:150px;" | Temporal Waveforms
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]
| style="width:300px;" | Computing electric and magnetic field components at a fixed location in the time domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldprobe_icon.png]]
| style="width:150px;" | Point Fields
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]
| style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components at a fixed location in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Near-Field Distribution Maps
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components on a planar cross section of the computational domain in the frequency domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:fieldsensor_icon.png]]
| style="width:150px;" | Time-Domain Near-Field Animation
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]
| style="width:300px;" | Computing either total electric or total magnetic field distribution on a planar cross section of the computational domain in the time domain
| style="width:250px;" | The field maps are generated at certain specified time intervals
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Patterns
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the 3D radiation pattern in spherical coordinates
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Radiation Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:farfield_icon.png]]
| style="width:150px;" | Far-Field Scattering Patterns
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]
| style="width:300px;" | Computing the 3D scattering pattern in spherical coordinates
| style="width:250px;" | Requires a plane wave or Gaussian beam source
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Radar Cross Section
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS)_Observable | RCS]]
| style="width:300px;" | Computing the bistatic and monostatic RCS of a target
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:rcs_icon.png]]
| style="width:150px;" | Polarimetric Scattering Matrix Data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS)_Observable | RCS]]
| style="width:300px;" | Computing the scattering matrix of a target for various plane wave source incident angles
| style="width:250px;" | Requires a plane wave source
|-
| style="width:30px;" | [[File:port_icon.png]]
| style="width:150px;" | Port Characteristics
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]]
| style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:port_icon.png]]
| style="width:150px;" | Port Voltages, Currents & Powers
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]]
| style="width:300px;" | Computing the port voltages, port currents and total port powers in both time and frequency domains
| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port
|-
| style="width:30px;" | [[File:period_icon.png]]
| style="width:150px;" | Periodic Reflection & Transmission Coefficients
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Periodic Characteristics |Periodic Characteristics]] (No observable definition required)
| style="width:300px;" | Computing the reflection and transmission coefficients of a periodic surface
| style="width:250px;" | Requires a plane wave source and periodic boundary conditions
|-
| style="width:30px;" | [[File:energy_icon.png]]
| style="width:150px;" | Electric and Magnetic Energy
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]
| style="width:300px;" | Computing the electric, magnetic and total energy inside the entire computational domain in the time domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:energy_icon.png]]
| style="width:150px;" | Dissipated Power
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]
| style="width:300px;" | Computing the total dissipated power inside the entire computational domain in the time domain
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:energy_icon.png]]
| style="width:150px;" | Electric and Magnetic Energy Density
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]
| style="width:300px;" | Computing the electric, magnetic and total energy density on a field sensor plane in the frequency domain
| style="width:250px;" | Requires at least one field sensor observable
|-
| style="width:30px;" | [[File:energy_icon.png]]
| style="width:150px;" | Dissipated Power (Ohmic Loss) Density and Specific Absorption Rate (SAR) Density
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]
| style="width:300px;" | Computing the dissipated power density and SAR density on a field sensor plane in the frequency domain
| style="width:250px;" | Requires at least one field sensor observable
|-
| style="width:30px;" | [[File:energy_icon.png]]
| style="width:150px;" | Poynting Vector
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]
| style="width:300px;" | Computing the complex Poynting vector on a field sensor plane in the frequency domain
| style="width:250px;" | Requires at least one field sensor observable
|-
| style="width:30px;" | [[File:huyg_surf_icon.png]]
| style="width:150px;" | Equivalent Electric and Magnetic Surface Currents
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens_Surface_Observable |Huygens Surface]]
| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules
| style="width:250px;" | None
|-
| style="width:30px;" | [[File:CartData_icon.png]]
| style="width:150px;" | Generic 3D Cartesian Spatial Data
| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#3D_Cartesian_Data_Observable | 3D Cartesian Data]]
| style="width:300px;" | Visualizing the contents of generic 3D Cartesian spatial data files overlaid on the project workspace
| style="width:250px;" | Requires import of an existing ".CAR" data file
|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].

Of EM.Tempo's frequency domain observables, the near fields, far fields and all of their associated parameters like directivity, RCS, etc., are calculated at a certain single frequency that is specified as part of the definition of the observable. To compute those frequency domain data at several frequencies, you need to define multiple observables, one for each frequency. On the other hand, port characteristics like S/Y/Z parameters and VSWR are calculated over the entire specified bandwidth of your project. Of EM.Tempo's source types, lumped sources, waveguide sources and distributed sources let you define one or more ports for your physical structure and compute its port characteristics. One of EM.Tempo's real advantages over frequency-domain solvers is its ability of generate wideband S/Z/Y parameter data in a single simulation run.

=== Examining the Near Fields in Time and Frequency Domains ===

EM.Tempo's FDTD time marching loop computes all the six electric and magnetic field components at every Yee cell of your structure's mesh at every time step. This amounts to a formidable amount of data that is computationally very inefficient to store. Instead, you can instruct EM.Tempo to save a small potion of these data for visualization and plotting purposes. Using a '''Field Probe''' at a specified point, you can record the a time-domain field component over the entire FDTD loop. The time-domain results are also transformed to the frequency domain within the specified bandwidth using a discrete Fourier transform (DFT).

<table>
<tr>
<td>
[[Image:FDTD77.png|thumb|left|480px|Time-domain evolution of the electric field at a given point.]]</td>
</tr>
</table>

In EM.Tempo, you can visualize the near fields at a specific frequency in a specific plane of the computational domain. To do so, you need to define a '''Field Sensor''' observable. EM.Tempo's field sensor defines a plane across the entire computational domain parallel to one of the three principal planes. The magnitude and phase of all the six components of the electric and magnetic fields on the mesh grid points on the sensor plane are computed and displayed.

<table>
<tr>
<td> [[Image:FDTD_FS2.png|thumb|left|420px|EM.Tempo's Field Sensor dialog.]] </td>
</tr>
<tr>
<td> [[Image:FDTD_FS1_new.png|thumb|left|480px|Three field sensor planes defined around a PEC ellipsoid illuminated by a plane wave source.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[Image:FDTD_FS3_new.png|thumb|left|360px|Electric field distribution above the PEC plate.]] </td>
<td> [[Image:FDTD_FS4_new.png|thumb|left|360px|Magnetic field distribution above the PEC plate.]] </td>
</tr>
</table>

=== Computing Far-Field Characteristics in FDTD ===

Far fields are the asymptotic form the fields when r → ∞ or k<sub>0</sub>r >> 1. Under these assumptions, the fields propagate outward as transverse electromagnetic (TEM) waves:

<math> \mathbf{H^{ff}(r)} = \frac{1}{\eta_0} \mathbf{ \hat{k} \times E^{ff}(r)} </math>

Far fields are typically computed in the spherical coordinate system as functions of the elevation and azimuth observation angles θ and φ. Only far-zone electric fields are normally considered. When your physical structure is excited using a lumped source, a waveguide source, a distributed source, a short dipole source, or an array of such sources, the far fields represent the radiation pattern of your source(s) in the far zone. In that case, you need to define a '''Radiation Pattern - Far Field Observable''' for your project. When your physical structure is illuminated by a plane wave source or a Gaussian beam source, the far fields represent the scattered fields. In the case of a plane source, you can compute the radar cross section (RCS) of your target structure. In that case, you need to define an '''RCS - Far Field Observable''' for your project.

In the FDTD method, the far fields are calculated using a near-field-to-far-field transformation of the field quantities on a given closed surface. EM.Tempo uses rectangular boxes to define these closed surfaces. You can use EM.Tempo's default radiation box or define your own custom box. Normally, the radiation box must enclose the entire FDTD structure. In this case, the calculated radiation pattern corresponds to the entire radiating structure. Alternatively, you can define a custom radiation box that may contain only parts of a structure, which results in a partial radiation pattern.

<table>
<tr>
<td> [[Image:FDTD_FF1.png|thumb|left|770px|EM.Tempo's Radiation Pattern dialog.]] </td>
</tr>
<tr>
<td> [[Image:FDTD_FF3.png|thumb|left|480px|EM.Tempo's Radar Cross Section dialog.]] </td>
</tr>
</table>

The default radiation box is placed at an offset of 0.1λ<sub>0</sub> from the largest bounding box of your physical structure. You can change the offset value from the "Far Field Acceleration" dialog, which can be accessed by clicking the {{key|Acceleration...}} button of EM.Tempo's Radiation Pattern dialog. Calculation of far-field characteristics at high angular resolutions can be a very time consuming computational task. You can accelerate this process by setting a lower '''Max. Far Field Sampling Rate''' from the same dialog. The default sampling rate is 30 samples per wavelength. A low sampling rate will under-sample the mesh grid points on the radiation box.

<table>
<tr>
<td> [[Image:FDTD_FF2.png|thumb|left|480px|EM.Tempo's far field acceleration dialog.]] </td>
</tr>
</table>

=== Radiation Pattern Above a Half-Space Medium ===

In EM.Tempo, you can use CPML boundary conditions with zero offsets to model a structure with infinite lateral extents. The calculation of the far fields using the near-field-to-far-field transformation requires the dyadic Green's function of the background structure. By default, the FDTD engine uses the free space dyadic Green's function for the far field calculation. In general, the EM.Tempo provides the dyadic Green's functions for four scenarios:

# Free space background
# Free space background terminated in an infinite PEC ground plane at the bottom
# Free space background terminated in an infinite PMC ground plane at the bottom
# Free space background terminated in an infinite dielectric half-space medium

<table>
<tr>
<td> [[Image:FDTD133.png|thumb|left|480px|EM.Tempo's far field background medium dialog.]] </td>
</tr>
</table>

In other words, EM.Tempo lets you calculate the far field radiation pattern of a structure in the presence of any of the above four background structure types. You can set these choices in EM.Tempo's "Far Field Background Medium" dialog. To access this dialog, open the Radiation Pattern dialog and click the button labeled {{key|Background...}}. From this dialog, you can also set the Z-coordinate of the top of the terminating half-space medium. If you set the -Z boundary condition of your computational domain to PEC or PMC types, the cases of infinite PEC or PMC ground planes from the above list are automatically selected, respectively, and the Z-coordinates of the ground plane and the bottom face of the computational domain will be identical.

The fourth case applies when your computational domain ends from the bottom in a dielectric layer with a CPML -Z boundary along with a -Z domain offset equal to zero. If you set the lateral domain offset values along the ±X and ±Y directions equal to zero, too, , then your structure is, in effect, terminated at an infinite half-space dielectric medium. In that case, you have to specify the permittivity ε<sub>r</sub> and electric conductivity σ of the terminating medium in the Background Medium dialog. You may additionally want to set the Z-coordinate of the top of that dielectric layer as the position of the interface between the free space and the lower dielectric half-space. Note that the current version of EM.Tempo does not calculate the far-field Green's function of a conductor-backed, dielectric substrate with a finite layer thickness. To use the background medium feature of EM.Tempo, your structure can have either an infinite PEC/PMC ground or a dielectric half-space termination.

<table>
<tr>
<td> [[Image:fdtd_out36_tn.png|thumb|left|360px|Radiation pattern of a vertical dipole above PEC ground.]] </td>
<td> [[Image:fdtd_out37_tn.png|thumb|left|360px|Radiation pattern of a vertical dipole above PMC ground.]] </td>
</tr>
<tr>
<td> [[Image:fdtd_out38_tn.png|thumb|left|360px|Radiation pattern of a horizontal dipole above PEC ground.]] </td>
<td> [[Image:fdtd_out39_tn.png|thumb|left|360px|Radiation pattern of a horizontal dipole above PMC ground.]] </td>
</tr>
</table>

=== Generating and Working with Multi-Frequency Simulation Data ===

One of the primary advantages of the FDTD method is its ability to run wideband EM simulations. The frequency domain data are computed by transforming the time-domain data to the Fourier domain. This is done automatically when EM.Tempo computes the port characteristics such as S/Z/Y parameters. The following frequency-domain observables are defined at a single frequency:

* Near-Field Sensor
* Far-field Radiation Pattern
* RCS
* Huygens Surface

The default computation frequency of the above observables is the project's center frequency (fc). You can change the observable frequency from the observable's property dialog and enter any frequency in Hz. The reason these types of simulation data are computed at a single frequency is their typically very large size. However, you can define as many instances of these observables and set different frequency values for each one. In the case of radiation pattern and RCS, there are two dialogs that can be accessed from the navigation tree. Right-click on the "Fer-Field Radiation Patterns" or "Radar Cross Sections" items of the navigation tree and select '''Insert Multi-Frequency Radiation Pattern...''' or '''Insert Multi-Frequency RCS...''' from the contextual menu.

<table>
<tr>
<td> [[Image:RadPattern multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radiation Pattern dialog.]] </td>
<td> [[Image:RCS multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radar Cross Section dialog.]] </td>
</tr>
</table>

Using the multi-frequency dialogs, you can set the value of Start Frequency, Stop Frequency and Step Frequency in Hz. You can also set the values of Theta Angle Increment and Phi Angle Increment in degrees. The default values of both quantities are 5°. In the case of RCS, you have choose one of the two options: '''Bistatic RCS''' or '''Monostatic RCS'''.

To facilitate the process of all the defining multi-frequency observables in EM.Tempo, you can also use the following Python functions at the command line:

----

emag_field_sensor_multi_freq(f1,f2,df,dir_coordinate,x0,y0,z0)

emag_farfield_multi_freq(f1,f2,df,theta_incr,phi_incr)

emag_rcs_bistatic_multi_freq(f1,f2,df,theta_incr,phi_incr)

emag_rcs_monostatic_multi_freq(f1,f2,df,theta_incr,phi_incr)

emag_huygens_surface_multi_freq(f1,f2,df,x1,y1,z1,x2,y2,z2)

----

In the above Python functions, f1 and f2 are the start and stop frequencies, respectively, and df is the frequency increment, all expressed in Hz. Note that the above commands simply create and insert the specified observables in the navigation tree. They do not run perform a simulation. The created observables have the same "base name" with ordered numeric indices. For example, far-field radiation patterns are names as Multi_FF_1, Multi_FF_2, ...

EM.Tempo also provides some additional Python functions for the far-field radiation patterns and RCS observables.

----

emag_farfield_consolidate(x1,x2,dx,base_name)

emag_rcs_consolidate(x1,x2,dx,base_name)

emag_farfield_explode(base_name)

emag_rcs_explode(base_name)

emag_farfield_average(n,base_name)

emag_rcs_average(n,base_name)

----

The two "consolidate" Python functions take the results of multi-frequency simulation observables and merge them into a single data file. The base name in the case of far-field radiation patterns is "Multi_FF" as pointed out earlier. The name of the resulting consolidated data file is the same as the base name with a "_All" suffix and a ".DAT" file extension. In the case of far-field radiation patterns, it is "Multi_FF_All.DAT". The two "explode" Python functions take a consolidated data file names as "base_name_All.DAT" and break it up into several single-frequency ".RAD" or ".RCS" data files. Finally, the two "average" Python functions take several radiation pattern or RCS files with a common base name in the current project folder, compute their average and save the results to a new data file named "base_name_ave" with a ".RAD" or ".RCS" file extensions, respectively.

== Generating the FDTD Mesh in EM.Tempo ==

=== EM.Tempo's Mesh Types ===

EM.Tempo generates a brick volume mesh for FDTD simulation. The FDTD mesh is a rectangular Yee mesh that extends to the entire computational domain. It is primarily constructed from three mesh grid profiles in the XY, YZ and ZX principal planes. These projections together create a 3D mesh space consisting of a large number of cubic volume cells (voxels) carefully assembled in a way that approximates the shape of the original structure.

In EM.Tempo, you can choose one of the three FDTD mesh types:

* Adaptive Mesh
* Regular Mesh
* Fixed-Cell Mesh

EM.Tempo's default mesh generator produces an adaptive brick mesh of your physical structure, whose mesh resolution varies with the frequency. As the operating frequency of your project increases, the default '''Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. The adaptive mesh is optimized in such a way as to capture all the geometric details, curvatures and thin slanted plates or sheets, which often pose a challenge to staircase meshing. It usually provides a reasonably accurate discretization of most complex structures.

Occasionally, you may opt for a more regularized FDTD mesh with almost equal grid line spacings everywhere, but still with a frequency-dependent cell size. In that case, you can use EM.Tempo's '''Regular''' FDTD mesh generator, which is indeed a simplified version of its adaptive mesh generator. The regular FDTD mesh enforces only two criteria: minimum mesh density and absolute minimum grid spacing. The grid cell sizes in this mesh are almost uniform in objects of the same material composition or in free-space regions.

EM.Tempo also offers a uniform, frequency-independent, '''Fixed-Cell''' FDTD mesh generator. The fixed-cell mesh consists of three uniform grids in the XY, YZ and ZX principal planes. However, the uniform mesh cell dimensions along the three direction, i.e. Δx, Δy and Δz do not have to be equal. The fixed-cell mesh generator tries to fit your physical structure to the mesh grid rather than adapting the mesh to your physical structure.

{{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed and independent of your project's frequency settings.}}

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Adaptive_Yee_Mesh | EM.Tempo's Adaptive Brick Mesh Generator]]'''.

[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Tempo's Fixed-Cell Brick Mesh Generator]]'''.

<table>
<tr>
<td> [[Image:Tempo L11 Fig5.png|thumb|left|550px|A human head model and a cellular phone handset on its side.]] </td>
</tr>
<tr>
<td> [[Image:Tempo L11 Fig7.png|thumb|left|550px|The FDTD mesh of the human head model and the cellular phone handset.]] </td>
</tr>
<tr>
<td> [[Image:Tempo L11 Fig8.png|thumb|left|550px|Another view of the FDTD mesh of the human head model and the cellular phone handset.]] </td>
</tr>
</table>

=== Discretizing the Physical Structure Using the Adaptive Yee Mesh ===

EM.Tempo's default mesh generator creates an adaptive brick volume mesh that uses a variable staircase profile, where the grid line spacings vary with the curvature (derivative) of the object edges or faces. As a result, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed in cells per effective wavelength. Since FDTD is a time-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency of the project: f<sub>max</sub> = f<sub>0</sub> + Δf/2, where f<sub>0</sub> (or fc) is your project's center frequency and Δf (or bw) is its specified bandwidth. In other words, the effective wavelength in the free space is λ<sub>0,eff</sub> = c / f<sub>max</sub>, c being the speed of light in the free space. The effective wavelength in a dielectric material with relative permittivity ε<sub>r</sub> and permeability μ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>.

The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. Therefore, the average ratio of the cell size in a dielectric region to the cell size in the free space is 1/√(ε<sub>r</sub>μ<sub>r</sub>). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is more visible in the case of curved solids, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using a staircase profile. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best way. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regions. For example, this often happens around the interface between the free space and high permittivity dielectric objects. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structures.

A carefully calculated, "<u>'''Adaptive'''</u>" mesh of your physical structure is generated in order to satisfy the following criteria:

* Optimize the number of mesh cells in each dimension. The product of the number of cells in all the three dimension determines the total mesh size. The larger the mesh size, the longer the simulation time, especially with the CPU version of the FDTD engine. Also, a very large mesh size requires more RAM, which may exceed your GPU memory capacity. Set the '''Minimum Mesh Density''' to a moderately low value to keep the mesh size manageable, but be careful not to set it too low (see the next item below).
* Ensure simulation accuracy by requiring an acceptable minimum number of cells per wavelength through each object and in the empty (free) space between them and the computational domain boundaries. An effective wavelength is defined for each material at the highest frequency of the project's specified spectrum. We recommend a '''Minimum Mesh Density '''of at least 15-20 cells/ wavelength. But for some resonant structures, 25 or even 30 cells per wavelength may be required to achieve acceptable accuracy. As you reduce the mesh density, the simulation accuracy decreases.
* Accurately represent and approximate the boundaries of edges or surfaces that are not grid-aligned by closely adhering to their geometric contours. This is controlled by the '''Minimum Grid Spacing Over Geometric Contours''', which can be specified either as a fraction of the free space grid spacing or as an absolute length value in project units.
* Maximize the minimum grid spacing in any dimension inside the computational domain and thus maximize the simulation time step. The time step size is dictated by the CFL stability criterion and is driven by the smallest grid spacing in each dimension. The smaller the time step, the larger the number of time steps required for convergence. This is controlled using the '''Absolute Minimum Grid Spacing''', which can be specified either as a fraction of the free space grid spacing or as an absolute value. It is critical to accurately represent and precisely maintain the object edge/surface boundaries in certain structures like resonant antennas and filters, as the phase of the reflected fields/waves is affected by the object boundary positions. When object boundaries are very close to each other, the mesh needs to represent them by two separate, but very closely spaced, grid lines. To control the minimum allowed grid spacing, use the '''Absolute Minimum Grid Spacing '''settings,
* Maintain a smooth grid with no abrupt jumps from low-density to high-density regions. This feature is enabled with the '''Create Gradual Grid Transitions '''check box (always checked by default).

When [[EM.Cube]] generates an FDTD mesh, a large number of geometrical considerations are taken into account. These include the bounding box of each object and its corners, the ends of a line, the apex of a cone or pyramid, or the locations of lumped sources, field probes and sensors, vertices of plane wave or far field boxes, to name a few examples. These points are “locked” as fixed grid nodes in the FDTD mesh. [[EM.Cube]] determines these points internally to generate a mesh that best approximates the original structure. As you saw earlier, you can use the FDTD mesh settings to control the shape and resolution of the mesh, for example, around the curved portions of your structure, or on slanted lines or faces, etc. These settings are global and apply to all the objects making up your physical structure.

You can control the global mesh more selectively using the Advanced FDTD Mesh Settings Dialog. To open this dialog, click the '''Advanced '''button at the bottom of the FDTD Mesh Settings dialog. For example, you can control the quality of the gradual grid transitions by setting the value of '''Max Adjacent Cell Size Ratio'''. The default value of this parameter is 1.3, which maintains a smooth grid line spacing scheme with no more than 1:1.3 ratio for adjacent cells. By default, grid lines are enforced at all source and observable locations. You have the option to disable this feature and round up source locations to their closest grid lines. You may also uncheck the box labeled "Adapt mesh resolution to material properties". In that case, the same effective wavelength will be used to determine the mesh resolution inside all materials as well as the free-space regions.

<table>
<tr>
<td>
[[Image:FDTD80.png|thumb|left|720px|EM.Tempo's mesh settings dialog.]]
</td>
</tr>
</table>

The figures below compare the three types of the FDTD mesh for a dielectric ellipsoid with ε<sub>r</sub> = 4. Note that the cell size inside the dielectric region is half the cell size in the air region.

<table>
<tr>
<td>
[[Image:FDTD MAN21.png|thumb|left|360px|The geometry of a dielectric ellipsoid with ε<sub>r</sub> = 4.]]
</td>
<td>
[[Image:FDTD MAN22.png|thumb|left|360px|The adaptive mesh of the dielectric ellipsoid.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:FDTD MAN18.png|thumb|left|360px|The top view of the adaptive FDTD mesh of the dielectric ellipsoid.]]
</td>
<td>
[[Image:FDTD MAN19.png|thumb|left|360px|The top view of the regular FDTD mesh of the dielectric ellipsoid with the same mesh density.]]
</td>
</tr>
<tr>
<td>
[[Image:FDTD MAN20A.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the larger cell size inside the air region.]]
</td>
<td>
[[Image:FDTD MAN20.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the smaller cell size inside the dielectric region.]]
</td>
</tr>
</table>

The figures below compare the low resolution and high resolution adaptive FDTD meshes of a PEC parabolic reflector. This structure involves both a curved surface and a very thin surface.

<table>
<tr>
<td>
[[Image:FDTD MAN23.png|thumb|left|450px|The geometry of a PEC parabolic reflector.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:FDTD MAN24.png|thumb|left|360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]]
</td>
<td>
[[Image:FDTD MAN27.png|thumb|left|360px|The high-resolution adaptive mesh of the PEC parabolic reflector.]]
</td>
</tr>
<tr>
<td>
[[Image:FDTD MAN26.png|thumb|left|360px|The top (XY) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]
</td>
<td>
[[Image:FDTD MAN25.png|thumb|left|360px|The right (YZ) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]
</td>
</tr>
</table>

=== Adding Fixed Grid Points to the Adaptive Yee Mesh ===

Adding fixed grid points to an FDTD mesh increases its resolution locally. Each fixed grid point adds three grid lines along the three principal axes passing through that point. You can add as many fixed grid points as you desire and create dense meshes at certain regions. Fixed grid points appear as grey points in the project workspace. To insert a new fixed grid point, follow these steps:

* Open the Fixed Grid Points Dialog by selecting '''Menu > Simulate > Discretization > Fixed Grid Points...''' or by right-clicking on the '''FDTD''' '''Mesh''' item of the navigation tree and selecting '''Fixed Grid Points Settings...'''
* Click the {{key|Add/Edit}} button to open the "Add Fixed Grid Point" dialog.
* Enter the (X, Y, Z) coordinates of the new fixed point in the coordinate boxes and click the {{key|OK}} button.
* To modify the coordinates of an existing fixed grid point, select it from the table and click the {{key|Add/Edit}} button.
* You can also remove a fix grid point from the FDTD mesh using the {{key|Delete}} button.

<table>
<tr>
<td> [[Image:FDTD36.png|thumb|left|480px|A user-defined fixed grid point in an FDTD mesh.]] </td>
</tr>
<tr>
<td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.Tempo's fixed grid points settings dialog.]] </td>
</tr>
<tr>
<td> [[Image:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]] </td>
</tr>
</table>

According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, EM.Tempo's adaptive mesh generator may create extremely tiny grid cells that would result in extremely small time steps. This would then translate into a very long computation time. [[EM.Cube]] offers the "Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. In a regular FDTD mesh, the grid cell sizes stay rather the same in objects of the same material composition. The mesh resolution increases in materials of higher permittivity and/or permeability based on the effective wavelength in exactly the same way as the adaptive mesh.

=== Profiling the Brick Mesh ===

A volumetric brick mesh is overwhelming for visualization in the 3D space. For this reason, [[EM.Cube]]'s mesh view shows only the outline of the cells on exterior surface of the (staircased) meshed objects. The mesh grid planes provide a 2D profile of the mesh cells along the principal coordinate planes. To display a mesh grid plane, select '''Menu > Simulate > Discretization > Grid Planes >''' and pick one of the three options: '''XY Plane''', '''YZ Plane''' or '''ZX Plane'''. You may also right click on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and select '''Show''' from the contextual menu.

While a mesh grid plane is visible, you can move it back and forth between the two boundary planes at the two opposite sides of the computational domain. You can do this in one of the following four ways:

* Using the keyboard's Page Up {{key|PgUp}} key and Page Down {{key|PgDn}} key.
* By selecting '''Menu > Simulate > Discretization > Grid Planes > Increment Grid''' or ''' Decrement Grid'''.
* By right clicking on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and selecting '''Increment Grid''' or ''' Decrement Grid''' from the contextual menu.
* Using the keyboard shortcut {{key|>}} or {{key|<}}.

As you “step through” or profile the mesh grid, you can see how the structure is discretized along internal planes of the computational domain.

<table>
<tr>
<td> [[Image:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]] </td>
<td> [[Image:Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td>
</tr>
</table>

=== The FDTD Grid Coordinate System (GCS) ===

When your physical structure is discretized using the brick mesh generator, a second coordinate system becomes available to you. The mesh grid coordinate system allows you to specify any location in the computational domain in terms of node indices on the mesh grid. [[EM.Cube]] displays the total number of mesh grid lines of the simulation domain (N<sub>x</sub> × N<sub>y</sub> × N<sub>z</sub>) along the three principal axes on the '''Status Bar'''. Therefore, the number of cells in each direction is one less than the number of grid lines, i.e. (N<sub>x</sub>-1)× (N<sub>y</sub>-1) × (N<sub>z</sub>-1). The lower left front corner of the domain box (Xmin, Ymin, Zmin) becomes the origin of the mesh grid coordinate system (I = 0, J = 0, K = 0). The upper right back corner of the domain box (Xmax, Ymax, Zmax) therefore becomes (I = N<sub>x</sub>-1, J = N<sub>y</sub>-1, K = N<sub>z</sub>-1).

[[EM.Cube]] allows you to navigate through the mesh grid and evaluate the grid points individually. Every time you display one of the three mesh grid planes, the "'''Grid Coordinate System (GCS)'''" is automatically activated. On the Status Bar, you will see [[Image:statusgrid.png]] instead of the default [[Image:statusworld.png]]. This means that the current coordinates reported on Status Bar are now expressed in grid coordinate system. The current grid point is displayed by a small white circle on the current mesh grid plane, and it always starts from (I = 0, J = 0, K = 0). Using the keyboard's '''Arrow Keys''', you can move the white circle through the mesh grid plane and read the current node's (I, J, K) indices on the status bar. You can switch back to the "'''World Coordinate System (WCS)'''" or change to the "'''Domain Coordinate System'''" by double-clicking the status bar box that shows the current coordinate system and cycling through the three options. The domain coordinate system is one that establishes its origin at the lower left front corner of the computational domain and measure distances in project unit just like the WCS.

<table>
<tr>
<td>
[[Image:FDTD35(1).png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.]]
</td>
</tr>
</table>

== Running FDTD Simulations in EM.Tempo ==

=== EM.Tempo's Simulation Modes ===

Once you build your physical structure in the project workspace and define an excitation source, you are ready to run an FDTD simulation. The simulation engine will run even if you have not defined any observables. Obviously, no simulation data will be generated in that case. [[EM.Tempo]] currently offers several different simulation modes as follows:

{| class="wikitable"
|-
! scope="col"| Simulation Mode
! scope="col"| Usage
! scope="col"| Number of Engine Runs
! scope="col"| Frequency
! scope="col"| Restrictions
|-
| style="width:120px;" | [[#Running a Wideband FDTD Analysis | Wideband Analysis]]
| style="width:270px;" | Simulates the physical structure "As Is"
| style="width:100px;" | Single run
| style="width:200px;" | Generates data for many frequency samples
| style="width:150px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables
| style="width:100px;" | Multiple runs
| style="width:200px;" | Runs at the center frequency fc
| style="width:150px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:100px;" | Multiple runs
| style="width:200px;" | Runs at the center frequency fc
| style="width:150px;" | None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]
| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model
| style="width:100px;" | Multiple runs
| style="width:200px;" | Runs at the center frequency fc
| style="width:150px;" | None
|-
| style="width:120px;" | [[#Running a Dispersion Sweep in EM.Tempo | Dispersion Sweep]]
| style="width:270px;" | Varies the value of wavenumber in a periodic structure
| style="width:100px;" | Multiple runs
| style="width:200px;" | Runs at multiple frequency points corresponding to constant wavenumber values
| style="width:150px;" | Only for periodic structures excited by a plane wave source
|}

=== Running a Wideband FDTD Analysis ===

The FDTD method is one of the most versatile numerical techniques for solving electromagnetic modeling problems. Choosing the right settings and optimal values for certain numerical parameters will have a significant impact on both accuracy and computational efficiency of an FDTD simulation. Below are a number of steps that you should typically follow by order when planning your FDTD simulation:

* Identify material types and proper domain boundary conditions.
* Identify the source type and excitation mechanism.
* Define the project observables.
* Mesh the physical structure and examine the quality of the generated mesh and it geometric fidelity.
* Determine the proper temporal waveform.
* Select the simulation mode and run the FDTD engine.

Wideband analysis is [[EM.Tempo]]'s simplest and most straightforward simulation mode. It runs the FDTD time marching loop once. At the end of the simulation, the time-domain field data are transformed into the frequency domain using a discrete Fourier transform (DFT). As a result, you can generate wideband frequency data from a single time-domain simulation run. The other simulation modes will be explained later in this manual.

To open the Simulation Run Dialog, click the '''Run''' [[Image:run_icon.png]] button of the '''Simulate Toolbar''' or select the menu item '''Simulate → Run...''' from the menu bar or use the keyboard shortcut {{key|Ctrl+R}}. To start the FDTD simulation, click the {{key|Run}} button at the bottom of this dialog. Once the simulation starts, the "Output Message Window" pops up and reports messages during the different stages of the FDTD simulation. During the FDTD time marching loop, after every 10th time step, the output window updates the values of the time step, elapsed time, the engine performance in Mega-cells per seconds, and the value of the convergence ratio U<sub>n</sub>/U<sub>max</sub> in dB. An [[EM.Tempo]] simulation is terminated when the ratio U<sub>n</sub>/U<sub>max</sub> falls below the specified power threshold or when the maximum number of time steps is reached. You can, however, terminate the FDTD engine earlier by clicking the '''Abort Simulation''' button.

<table>
<tr>
<td>
[[Image:Tempo L1 Fig13.png|thumb|left|480px|EM.Tempo's simulation run dialog.]]
</td>
</tr>
<tr>
<td>
[[Image:Tempo L1 Fig15.png|thumb|left|550px|EM.Tempo's output message window.]]
</td>
</tr>
</table>

=== The FDTD Simulation Engine Settings ===

An FDTD simulation involves a number of numerical parameters that can be accessed and modified from the FDTD Engine Settings Dialog. To open this dialog, select '''Menu > Simulate > Simulation Engine Settings... '''or open the '''Run Dialog''', and click the {{key|Settings}} button next to the engine dropdown list.

In the " '''Convergence''' " section of the dialog, you can set the '''Termination Criterion''' for the FDTD time loop. The time loop must stop after a certain point in time. If you use a decaying waveform like a Gaussian pulse or a Modulated Gaussian pulse, after certain number of time steps, the total energy of the computational domain drops to very negligible values, and continuing the time loop thereafter would not generate any new information about your physical structure. By contrast, a sinusoidal waveform will keep pumping energy into the computational domain forever, and you have to force the simulation engine to exit the time loop. [[EM.Tempo]] provides two mechanism to terminated the time loop. In the first approach, an energy-like quantity defined as U<sub>n</sub> = Σ [ ε<sub>0</sub>|'''E<sub>i,n</sub>'''|<sup>2</sup> + μ<sub>0</sub>|'''H<sub>i,n</sub>'''|<sup>2</sup> ].ΔV<sub>i</sub> is calculated and recorded at a large random set of points in the computational domain. Here i is the space index and n is the time index. The quantity U<sub>n</sub> has a zero value at t = 0 (i.e. n = 0), and its value starts to build up over time. With a Gaussian or Modulated Gaussian pulse waveform, U<sub>n</sub> reach a maximum value U<sub>max</sub> at some time step and starts to decline thereafter. The ratio 10.log( U<sub>n</sub>/ U<sub>max</sub>) expressed in dB is used as the convergence criterion. When its value drops below certain '''Power Threshold''', the time loop is exited. The default value of Power Threshold is -30dB, meaning that the FDTD engine will exit the time loop if the quantity U<sub>n</sub> drops to 1/1000 of its maximum value ever. The second termination criterion is simply reaching a '''Maximum Number of Time Steps''' , whose default value set to 10,000. A third option, which is [[EM.Tempo]]'s default setting (labeled "'''Both'''"), terminates the simulation as soon as either of the first two criteria is met first.

{{Note|Keep in mind that for highly resonant structures, you may have to increase the maximum number of time steps to very large values above 20,000.}}

The "'''Acceleration'''" section of the FDTD Simulation Engine Settings dialog give three options for the FDTD kernel:

# Serial CPU Solver
# Multi-Core CPU Solver
# GPU Solver

The serial CPU solver is [[EM.Tempo]]'s basic FDTD kernel that run the time marching loop on a single central processing unit (CPU) of your computer. The default option is the multi-core CPU solver. This is a highly parallelized version of the FDTD kernel based on the Open-MP framework. It takes full advantage of a multi-core, multi-CPU architecture, if your computer does have one. The GPU solver is a hardware-accelerated FDTD kernel optimized for CUDA-enabled graphical processing unit (GPU) cards. If your computer has a fast NVIDIA GPU card with enough onboard RAM, the GPU kernel can speed up your FDTD simulations up to 50 times or more over the single CPU solver.

For structures excited with a plane wave source, there are two standard FDTD formulations: '''Scattered Field '''(SF) formulation and '''Total Field - Scattered Field''' (TF-SF) formulation. [[EM.Tempo]] offers both formulations. The TF-SF solver is the default choice and is typically much faster than the SF solver for most problems. In two cases, when the structure has periodic boundary conditions or infinite CPML boundary conditions (zero domain offsets), only the SF solver is available.

<table>
<tr>
<td>
[[Image:FDTD58.png|thumb|left|720px|EM.Tempo's simulation engine settings dialog.]]
</td>
</tr>
</table>

==Modeling 3D Periodic Structures in EM.Tempo==

[[EM.Tempo]] allows you to simulate doubly periodic structures with periodicities along the X and Y directions. In the FDTD method, this is accomplished by applying periodic boundary conditions (PBC) at the side walls of the computational domain.

{{Note| [[EM.Tempo]] can only handle regular, non-skewed periodic lattices with no secondary offsets.}}

[[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]]'''.

===Defining a Periodic Structure in EM.Tempo===

By default, your physical structure in the project workspace is not periodic, and you have to instruct [[EM.Tempo]] to turn it into a periodic structure using its Periodicity Dialog. By designating a structure as periodic, you enforce periodic boundary conditions (PBC) on the side walls of its computational domain. Your structure in the project workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines.

To define a periodic structure, follow these steps:

* Select '''Menu > Simulate > Computational Domain > Periodicity Settings...''' or right click on the '''Periodicity''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Periodicity Settings...''' from the contextual menu. This open up the Periodicity Settings Dialog.
* Check the box labeled '''Periodic Structure''' and click the '''Apply''' button of this dialog. The default domain box initially shrinks to the edges of the physical structure in the project workspace. The default periods along the X and Y axes appear in the dialog, which are equal to the dimensions of the structure's bounding box.
* Enter new values for '''X Spacing''' and '''Y Spacing '''in project units and close the dialog.
* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC.

<table>
<tr>
<td>
[[Image:FDTD134.png|thumb|360px|EM.Tempo's periodicity settings dialog.]]
</td>
</tr>
</table>

===Exciting Periodic Structures as Radiators in EM.Tempo===

In [[EM.Tempo]], a periodic structure can be excited using various source types. Exciting the unit cell structure using a lumped source, a waveguide source, or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types, you excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S<sub>11</sub> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data.

[[EM.Tempo]]'s periodic FDTD simulator uses periodic boundary conditions (PBC) to model an infinite periodic array. All the periodic replicas of the unit cell structure are excited. In this case, you can impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the lumped source or waveguide source. At the bottom of the '''Lumped Source Dialog''' or '''Waveguide Source Dialog''', there is a section titled '''Periodic Beam Scan Angles'''. This section is grayed out when the project structure is not periodic. You can enter desired beam scan angle values for both '''Theta''' and '''Phi''' in degrees. To visualize the radiation pattern of the beam-steered array, you have to define a finite-sized array factor. You do this in the "Impose Array Factor" section of the '''Radiation Pattern Dialog'''.

{{Note|For large θ scan angles, the periodic FDTD time marching loop may take far more time steps to converge.}}

<table>
<tr>
<td> [[Image:Period1.png|thumb|350px|Setting periodic scan angles in EM.Tempo's Lumped Source dialog.]] </td>
<td> [[Image:Period2.png|thumb|350px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td>
</tr>
</table>

<table>
<tr>
<td> [[Image:Period3.png|thumb|360px|Radiation pattern of an 8×8 finite-sized periodic wire dipole array with 0° phi and theta scan angles.]] </td>
<td> [[Image:Period4.png|thumb|360px|Radiation pattern of a beam-steered 8×8 finite-sized periodic wire dipole array with 45° phi and theta scan angles.]] </td>
</tr>
</table>

===Exciting Periodic Structures Using Plane Waves in EM.Tempo===

Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. At the end of the FDTD simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into ASCII data files.

<table>
<tr>
<td> [[Image:Period11.png|thumb|380px|Geometry of a periodic printed strip FSS in EM.Tempo.]] </td>
<td> [[Image:Period12.png|thumb|340px|Define a custom periodic plane wave box in EM.Tempo.]] </td>
</tr>
</table>

Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. If the plane wave source illuminates the periodic unit cell from the top (90° < θ < 180°), the excitation surface is placed above the structure's bounding box. If the plane wave source illuminates the periodic unit cell from the bottom up (0° < θ < 90°), the excitation surface is placed below the structure's bounding box. In either case, the plane wave must intercept the excitation surface before hitting the unit cell's physical structure. It is highly recommended that you accept [[EM.Tempo]]'s default settings for the plane wave box of periodic structures. Nevertheless, you can change the location of the excitation surface if you wish. To do so, you have to open the '''Plane Wave Dialog'''. In the Excitation Box section of the dialog, select the '''Size: Custom''' option. Only the '''Z Coordinate''' of '''Corner 1''' is available for editing. The rest of the coordinates are enforced by the periodic domain. You can enter the incidence angles '''Theta''' and '''Phi''' in degrees. For periodic structures, only the '''TM<sub>z</sub>''' and '''TE<sub>z</sub>''' polarization options are available.

One of the pitfalls of the direct spectral FDTD method is the possibility of horizontal resonances, which may lead to indefinite oscillation or even divergence of field values during the time marching loop. This happens in the case of oblique plane wave incidence when θ > 0°. [[EM.Cube]]'s FDTD engine automatically detects such cases and avoids those resonances by shifting the modulation frequency of the modulated Gaussian pulse waveform away from the resonant frequency. However, in some cases, the size of oscillations may still remain large after a large number of time steps. Occasionally, a late-time diverging behavior may appear. To avoid situations like these, it is highly recommended that you place a time-domain field probe above your structure and monitor the temporal field behavior during the time marching loop as shown in the figure below.

{{Note|It is very important to keep in mind that only in the case of normal incidence does [[EM.Cube]] compute the reflection and transmission coefficients over the entire specified bandwidth of the project. At oblique incidences when θ > 0, the computed R/T coefficients after the discrete Fourier transformation are valid only at the center frequency of the project for the given value of the incident θ<sub>0</sub> angle. In other words, the computed R/T coefficients at all the other frequencies away from the center frequency correspond to different values of the incident θ angle. As a result, [[EM.Cube]] only saves the reflection and transmission coefficients at the center frequency into the output data files "reflection_coefficient.CPX" and "transmission_coefficient.CPX".}}

=== Running a Dispersion Sweep in EM.Tempo ===

The '''Dispersion Sweep '''option of the Simulation Mode drop-down list performs a sweep of constant k<sub>l</sub> wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.Tempo]] uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k<sub>li</sub>, you can find the reflection and transmission coefficients for all combinations of frequency f<sub>j</sub> and incident angle θ<sub>j</sub> such that (2π/c) . f<sub>j</sub>. sin θ<sub>j</sub> = k<sub>li</sub>. This provides a complete picture of the dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the eigenvalues of the periodic structure. The horizontal axis represents the constant transverse wavenumber k<sub>l</sub> (or beta). The vertical axis represents frequency. Sometimes, the free space wave number k<sub>0</sub> = (2π/c).f is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] plots frequency vs. wavenumber. Both the horizontal and vertical axes start from 0 and extend to f<sub>max</sub> and k<sub>l,max</sub>, respectively, where f<sub>max</sub> = f<sub>0</sub> + Δf/2, and Δf is the specified bandwidth of the project. For this sweep option you have to specify the number of wavenumber samples. Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle φ as specified in [[EM.Tempo]]'s Plane Wave Dialog.

<table>
<tr>
<td>
[[Image:KBT Settings.png|thumb|360px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:KBT R.png|thumb|360px|A typical reflection coefficient dispersion diagram of a periodic structure.]]
</td>
<td>
[[Image:KBT T.png|thumb|360px|A typical transmission coefficient dispersion diagram of a periodic structure.]]
</td>
</tr>
</table>

<br />

<hr>

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Basic Principles of Physical Optics

2018-07-27T15:53:29Z

Kazem Sabet: /* General Huygens Sources */

[[Image:Maxwell1.png|right|720px]]
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]'''

== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1, R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1, R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like [[EM.Tempo]] (FDTD), [[EM.Picasso]] (Planar MOM) or [[EM.Libera]] (3D MOM). Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

<br />

<hr>

[[Image:Top_icon.png|30px]] '''[[#Physical_Optics_as_an_Asymptotic_Technique | Back to the Top of the Page]]'''

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Basic Principles of Physical Optics

2018-07-27T15:53:10Z

Kazem Sabet: /* General Huygens Sources */

[[Image:Maxwell1.png|right|720px]]
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]'''

== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1, R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1, R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like [[EM.Tempo]] (FDTD), [[EM.Picasso]] (Planar MOM) or EM.Libers (3D MOM). Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

<br />

<hr>

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Basic Principles of Physical Optics

2018-07-27T15:51:39Z

Kazem Sabet: /* General Huygens Sources */

[[Image:Maxwell1.png|right|720px]]
<table>
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<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
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== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1, R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1, R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

<br />

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Basic Principles of Physical Optics

2018-07-27T15:51:12Z

Kazem Sabet: /* Calculating Near & Far Fields In PO */

[[Image:Maxwell1.png|right|720px]]
<table>
<tr>
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== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1, R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1, R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ -jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

<br />

<hr>

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Basic Principles of Physical Optics

2018-07-27T15:50:25Z

Kazem Sabet: /* Conventional Physical Optics (GO-PO) */

[[Image:Maxwell1.png|right|720px]]
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]'''

== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1, R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1, R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{-jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{-jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ -jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

<br />

<hr>

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Basic Principles of Physical Optics

2018-07-27T15:49:27Z

Kazem Sabet: /* Conventional Physical Optics (GO-PO) */

[[Image:Maxwell1.png|right|720px]]
<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>

[[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]'''

== Physical Optics as an Asymptotic Technique ==

Asymptotic methods are usually valid at high frequencies as k<sub>0</sub> R = 2π R/λ<sub>0</sub> >> 1, where R is the distance between the source and observation points, k<sub>0 </sub> is the free-space propagation constant and λ<sub>0 </sub>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].

In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given closed surface, respectively. A simple PO analysis involves only perfect electric conductors, and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina]] assumes that a source like a short dipole radiator or an incident plane wave induces currents on the surface of the metallic structure. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scatterer.

A challenging step in establishing the PO currents is the determination of the lit and shadow points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task as the size of the computational problem grows. Besides GO-PO, [[EM.Illumina]] also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.

== Conventional Physical Optics (GO-PO) ==

The following analysis assumes a general impedance surface. The general impedance boundary condition relates the tangential components of the electric and magnetic fields on the surface:

:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>

where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface, '''n''' is the local outward normal unit vector as shown in the figure below, and Z<sub>s</sub> is the surface impedance having units of Ohms.

To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and R<sub>||</sub> and R<sub>&perp;</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:

:<math> R_{\perp} = \frac{ \eta_s \cos\theta - 1} {\eta_s \cos\theta + 1} </math>

:<math> R_{\|} = \frac{\cos\theta - \eta_s } {\cos\theta + \eta_s } </math>

where θ is the incident angle between the propagation vector of the incident field and the normal to the surface, <math>\eta_s = Z_s/\eta_0</math> and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.

From the surface impedance boundary condition, it can easily be shown that

:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>

In the case of an impedance-matched surface, Z<sub>s</sub> = η<sub>0</sub>, η<sub>s</sub> = 1, and one can write:

:<math> R_{\|} = R_{\perp} = \frac{\cos\theta - 1} {\cos\theta + 1} </math>

<table>
<tr>
<td> [[Image:po_manual_1.png|thumb|500px|A diagram showing a scatterer lit by a source.]] </td>
</tr>
</table>

Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, η<sub>s</sub> = 0, R<sub>||</sub> = 1 and R<sub>&perp;</sub> = -1, and one can write:

:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>

:<math> \mathbf{M(r)} = 0 </math>

while for a PMC surface, Z<sub>s</sub> = ∞, η<sub>s</sub> = ∞, R<sub>||</sub> = -1 and R<sub>&perp;</sub> = 1, and one can write:

:<math> \mathbf{J(r)} = 0 </math>

:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>

A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.

== Calculating Near & Far Fields In PO ==

Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:

:<math> \mathbf{ E^{tot}(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds' </math>

:<math> \mathbf{ H^{tot}(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M(r') } ds' </math>


where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In [[EM.Illumina]], the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:

:<math> \begin{align} \mathbf{ E^{tot}(r) = E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>

:<math> \begin{align} \mathbf{ H^{tot}(r) = H^{inc}(r) } & - jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\} \frac{e^{-jk_0 R}}{4\pi R} ds' \\ & - jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds' \end{align} </math>


where <math>k_0 = \frac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y_0 = \eta_0 </math>, '''R''' ='''r''' - '''r'''', R = |'''R'''|, and

:<math>\mathbf{ \hat{R} = \frac{R}{|R|} = \frac{r-r'}{|r-r'|} }</math>

When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{-jk_0 \mathbf{\hat{r}\cdot r'}} ds' + \mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{-jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\} </math>

:<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>


== Iterative Physical Optics (IPO) ==

The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):

:<math> \mathbf{J(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{tot}(r)} \\ \mathbf{H_{\perp}^{tot}(r)} \end{bmatrix} </math>

:<math> \mathbf{M(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{tot}(r)} \\ \mathbf{E_{\perp}^{tot}(r)} \end{bmatrix} </math>

The shadowing phenomenon can be attributed to near-field interaction of surface currents. The current on the lit region produces a scattered field in the forward direction that is almost equal and out of phase with the incident wave. Hence, the sum of the scattered field and incident field over the shadowed region almost cancel each other, giving rise to a very small field there. This suggests that keeping track of multiple scattering can take care of shadowing problems automatically. In addition, the effects of multiple scattering can be readily accounted for by an iterative PO approach to be formulated next.

The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write

:<math> \mathbf{J^{(0)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{inc}(r)} \\ \mathbf{H_{\perp}^{inc}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(0)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{inc}(r)} \\ \mathbf{E_{\perp}^{inc}(r)} \end{bmatrix} </math>

which are the conventional PO currents. However, this approximation does not formally recognize the lit and shadowed areas. Instead of identifying the exact boundaries of the lit and shadowed areas over a complex target, a simple condition is used first to find the primary shadowed areas. Then, through PO iterations all shadowed areas are determined automatically. When calculating the field on the scatterer for every source point, a primary shadowing condition given by '''n.k'''< 0 is examined. In complex scatterer geometries, there are shadowed points in concave regions where '''n.k'''> 0, but the correct shadowing is eventually achieved through the iteration of the PO currents. Therefore, in computation of the above equations, only the contribution of the points that satisfy the following condition are considered:

:<math>\mathbf{ \hat{n} \cdot \hat{R}} < 0 \quad \text{or} \quad \mathbf{\hat{n} \cdot (r-r')} < 0</math>


At the subsequent iterations, the higher order PO currents are given by:

:<math> \mathbf{J^{(n)}(r)} = \mathbf{\hat{n}\times} \begin{bmatrix} 1-R_{||} & 0 \\ 0 & 1-R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{H_{||}^{(n-1)}(r)} \\ \mathbf{H_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

:<math> \mathbf{M^{(n)}(r)} = -\mathbf{\hat{n}\times} \begin{bmatrix} 1+R_{||} & 0 \\ 0 & 1+R_{\perp} \end{bmatrix} \cdot \begin{bmatrix} \mathbf{E_{||}^{(n-1)}(r)} \\ \mathbf{E_{\perp}^{(n-1)}(r)} \end{bmatrix} </math>

For most practical applications, iterations up to the second order is sufficient. The iterative solution will not only account for double-bounce scattering over the lit regions but it also removes the lower order currents erroneously placed over concave shadowed areas.

== General Huygens Sources ==

According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:

:<math> \begin{align} & \mathbf{ J(r) = \hat{n} \times H(r) } \\ & \mathbf{ M(r) = -\hat{n} \times E(r) } \end{align} </math>

In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:

:<math> \mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\ & -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\ & - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) } \end{align} \right\rbrace </math>

:<math> \mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R} \left\lbrace \begin{align} & Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\ & -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\ & + \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) } \end{align} \right\rbrace </math>

where the summation over index ''j'' is carried out for all the elementary cells Δ<sub>j</sub> that make up the Huygens box. In [[EM.Cube]] Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, Δ<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[EM.Illumina]] project. The Huygens source data are normally generated in one of [[EM.Cube]]'s full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.

The far fields of the Huygens surface currents are calculated from the following relations:

:<math> \mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r} \sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ -jk_0 \mathbf{\hat{r} \cdot r'} } \, ds' </math>

:<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math>

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