[[Image:Splash-mom.jpg|right|750px720px]]<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= An 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 Primer 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 metallic structures made up of metal and dielectric structuresregions or a combination of them. It features two full-wave Method of Moments (MoM) separate simulation engines, one based on a Wire Surface MoM formulation solver and the other based on a Surface Wire MoM formulation. In generalsolver, the surface that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver is used to simulate your physical structure, which can be made utilizes a surface integration equation formulation of metallic the metal and dielectric objects of arbitrary shapes as well as composite structures that contain conjoined metal and dielectric regions. If in your project workspace contains at least one line or curve object, EMphysical structure.Libera then invokes its The Wire MoM solver. In that case, can only handle metallic wireframe structures can be modeled, and all . [[EM.Libera]] selects the surface and solid PEC simulation engine automatically based on the types of objects are meshed as wireframespresent in your project workspace.
{{Note|You can use [[EM.Libera either for modeling metallic wire objects and wireframe structures or for simulating arbitrary ]] offers two distinct 3D metallic, dielectric and composite surfaces and volumetric structuresMoM simulation engines. EMThe Wire MoM solver is based on Pocklington's integral equation.Libera also serves as the frequency-domain, full-wave '''[[MoM3D Module]]''' The Surface MoM solver uses a number of surface integral equation formulations of Maxwell'''[[EMs equations.Cube]]'''In particular, a comprehensiveit uses an electric field integral equation (EFIE), integratedmagnetic field integral equation (MFIE), modular electromagnetic or combined field integral equation (CFIE) for modeling environmentPEC regions. EM.Libera shares On the visual interface, 3D parametric CAD modeler, data visualization toolsother hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and many more utilities magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and features collectively known as '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modulesexterior 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|40px30px]] Click here to learn more about the theory of the '''[[Getting_Started_with_EM.CUBE Basic Principles of The Method of Moments | EM.Cube Modeling Environment3D Method of Moments]]'''.
<table><tr><td>[[Image:Info_iconYagi Pattern.png|40px]] Click here to learn more about thumb|500px|3D far-field radiation pattern of the basic functionality of '''[[CubeCADexpanded Yagi-Uda antenna array with 13 directors.]]'''.</td></tr></table>
=== An Overview EM.Libera as the MoM3D Module of 3D Method Of Moments EM.Cube ===
The Method of Moments (MoM) is a rigorousYou 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]]''', numerical technique for solving open boundary a comprehensive, integrated, modular electromagnetic problemsmodeling environment. Using this technique[[EM.Libera]] shares the visual interface, you can analyze electromagnetic radiation3D parametric CAD modeler, data visualization tools, scattering and wave propagation problems with relatively short computation times many more utilities and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwell’s equations features collectively known as opposed to their differential forms used [[Building Geometrical Constructions in the finite element or finite difference time domain methodsCubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.
In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem. The given structure is immersed in the free space. The unknown currents or fields are discretized as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields are called basis functions. They obviously have a vectorial nature and must satisfy [[Maxwell's EquationsImage:Info_icon.png|Maxwell's equations30px]] and relevant boundary conditions individuallyClick here to learn more about '''[[Getting_Started_with_EM. The actual currents or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudesCube | EM. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structureCube Modeling Environment]]'''.
=== Advantages & Limitations of EM.Libera offers two distinct 3D MoM simulation engines. The first one is a Wire MoM solver, which is based on Pocklington's integral equation. This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wire-type antennas and arrays. The second engine features a powerful Surface MoM solver. It can model metallic surfaces and solids as well as solid dielectric objects. The Surface & Wire MoM solver uses a surface integral equation formulation of [[Maxwell's Equations|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. For modeling dielectric regions of the physical structure , the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problems.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, [[Image:Info_iconEM.png|40pxLibera]] Click here to learn more about the theory of ''s typical mesh size is typically much smaller that that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[3D Method EM.Libera]]'s triangular surface mesh provides a more accurate representation of Momentsyour 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.
== Constructing [[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 Physical Structure ==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.
=== Defining Groups Of PEC Objects === <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>
[[Image:wire_pic1.png|thumb|350px|== EM.Libera's Navigation Tree.]] EM.Libera features two different simulation engines: Wire MoM and Surface MoM. Both simulation engines can handle metallic structures. The Wire MoM engine models metallic objects as perfect electric conductor (PEC) wireframe structures, while the Surface MoM engine treats them as PEC surfaces. The PEC objects can be lines, curves, surfaces or solids. All the PEC objects are created under the '''PEC''' node in the '''Physical Structure''' section of the Navigation Tree. Objects are grouped together by their color. You can insert different PEC groups with different colors. A new PEC group can be defined by simply right clicking on the '''PEC''' item in the Navigation Tree and selecting '''Insert New PEC...''' from the contextual menu. A dialog for setting up the PEC properties opens up. From this dialog you can change the name of the group or its color. In EM.Libera, PEC objects have an additional property, which is '''Wire Radius''' expressed in project units. This parameter is used in conjunction with Pocklington's integral equation for wire objects only. The line and [[Curve Objects|curve objects]] you draw in the project workspace are not displayed as cylinders with the specified radius.Features at a Glance ==
=== Defining Dielectric Objects Physical Structure Definition ===
Of EM.Libera's two simulation engines, only the Surface MoM solver can handle dielectric objects. Dielectric objects are created under the '''Dielectric''' node <ul> <li> Metal wires and curves in the '''Physical Structure''' section of the Navigation Tree. They are grouped together by their color free space</li> <li> Metal surfaces and material properties. You can insert different solids in free space</li> <li> Homogeneous dielectric groups with different colors and different permittivity esolid objects in free space<sub/li>r <li> Import STL CAD files as native polymesh structures</subli> <li> Export wireframe structures as STL CAD files</li></ul> and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when σ → ∞.
To define a new Dielectric group=== Sources, follow these steps:Loads & Ports ===
* Right click <ul> <li> Gap sources on the '''Dielectric''' item of the Navigation Tree wires (for Wire MoM) and select '''Insert New Dielectric...''' from the contextual menu.* Specify a '''Label'''gap sources on long, '''Color''' narrow, metal strips (and optional Texturefor Surface MoM) </li> <li> Gap arrays with amplitude distribution and the electromagnetic properties 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 the dielectric material to be created: '''Relative Permittivity''' (eshort dipoles<sub/li>r <li> RLC lumped elements on wires and narrow strips with series-parallel combinations</subli>) <li> Plane wave excitation with linear and '''Electric Conductivity''' (s).circular polarizations</li>* You may also choose <li> Multi-Ray excitation capability (ray data imported from a list of preloaded material types. Click the button labeled '''Material''' to open [[EM.CubeTerrano]]'s Materials dialog. Select the desired material from the list or type the first letter of a material to find it. For example, typing '''V''' selects '''Vacuum''' in the list. Once you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automatically.external files)</li>* Click the '''OK''' button of the dielectric material dialog to accept the changes <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and close it.array configuration</li></ul>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining Materials in EM.Cube]]'''.=== Mesh Generation ===
{{Note|Under dielectric material groups, you cannot draw surface or curve CAD <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>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Material Group]]'''.=== 3D Wire MoM & Surface MoM Simulations ===
Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group <ul> <li> 3D Pocklington integral equation formulation of the project workspacewire structures</li> <li> 3D electric field integral equation (EFIE), 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 magnetic field integral equation (MFIE) and selecting the '''Activate''' item combined field integral equation (CFIE) formulation of the contextual menu. It is recommended that you first create surface groups, and then draw new PEC structures</li> <li> PMCHWT formulation of homogeneous dielectric objects under the active surface group. However, if you start a new [[EM.Illumina]] project from scratch, </li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and start drawing a new fast adaptive frequency sweep</li> <li> Parametric sweep with variable object without having previously defined any surface groups, a new default PEC surface group is created properties or source parameters</li> <li> Multi-variable and added to the navigation tree to hold your new CAD object.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>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Material Groups]]'''.=== Data Generation & Visualization ===
{{Note|In <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]], you can import external CAD models (modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as STEPdirectivity, IGESbeam width, STL modelsaxial ratio, side lobe levels and null parameters, etc.) only to [[CubeCAD]]. From [[CubeCAD]]</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, you can then move the imported objects VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to EMRF.Libera.}}Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
[[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Defining Materials == Building the Physical Structure in EM.Cube]]'''.Libera ==
== 3D Mesh Generation ==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= A Note on "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.LiberaCube's Mesh 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.Libera features two simulation enginesCube's Materials, Wire MoM and Surface MoMSources, 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 continuityDevices & Other Physical Object Types]].
On the other hands, Both of [[EM.Libera]]'s two simulation engines, Wire MoM and Surface MoM solver requires a triangular surface mesh of , can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and [[Solid Objects|solid volumetric metal objects]]under '''PEC Objects'''.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You In other words, you can control the cell size using the "Mesh Density" parameter. By defaultdraw lines, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfacespolylines and other curve objects as thin wires, which have 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" 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'''.
=== Creating & Viewing the Mesh ===
The mesh generation process in EM.Libera involves three steps:
# Setting the mesh properties.
# Generating the mesh.
# Verifying the mesh.
The objects of your physical structure are meshed based on a specified mesh density expressed in cells/λ<sub>0</sub>. The default mesh density is 10 cells/λ<sub>0</sub>. To view the PO mesh, click on the [[File:mesh_tool_tn.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the PO mesh is displayed in the project workspace, [[EM.Cube]]'s mesh view mode is enabled. In this mode, you can perform view operations like rotate view, pan, zoom, etc. However, you cannot select or move or edit objects. While the mesh view is enabled, the '''Show Mesh''' [[File:mesh_tool.png]] button remains depressed. To get back to the normal view or select mode, click this button one more time, or deselect '''Menu > Simulate > Discretization > Show Mesh''' to remove its check mark or simply click the '''Esc Key''' of the keyboard.
"Show Mesh" generates a new mesh and displays it if there is none in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating a PO mesh may take a long time depending on the complexity and size of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory and force [[EM.Cube]] to generate a mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.
To set the PO mesh properties, click on the [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Mesh Settings... '''or right click on the '''3-D Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the value of '''Mesh Density''' to generate a triangular mesh with a higher or lower resolutions. Some additional mesh [[parameters]] can be access by clicking the {{key|Tessellation Options}} button of the dialog. In the Tessellation Options dialog, you can change '''Curvature Angle Tolerance''' expressed in degrees, which as a default value of 15°. This parameter can affect the shape of the mesh especially in the case of solid CAD objects. It determines the apex angle of the triangular cells of the primary tessellation mesh which is generated initially before cell regularization. Lower values of the angle tolerance result in a less smooth and more pointed mesh of curved surface like a sphere.
<table>
<tr>
<td> [[Image:PO2wire_pic1.png|thumb|450px350px|Two ellipsoids of different (PEC and dielectric) compositionsEM.Libera's Navigation Tree.]] </td> <td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoids.]] </td>
</tr>
</table>
=== Mesh Once a new object group node has been created on the navigation tree, it becomes the "Active" group of Connected Objects === 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:MOM3Info_icon.png|thumb|320px|EM.Libera's Mesh Hierarchy dialog.30px]] All the objects belonging Click here 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 learn more about '''[[Solid Building Geometrical Constructions in CubeCAD#Transferring ObjectsAmong Different Groups or Modules |solid objects]], their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the [[Surface Moving Objects|surface objectsamong Different Groups]] 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, |In [[EM.Libera does provide a "Material Hierarchy" tableCube]], which you can modify. To access this tableimport external CAD models (such as STEP, IGES, STL models, select '''Menu > Simulate < discretization < Mesh Hierarchyetc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]..'''. 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 {{keyFrom [[Building_Geometrical_Constructions_in_CubeCAD |Move Up}} or {{key|Move Down}} buttons of the dialog. You CubeCAD]], you can also change then move the color of junction cells that belong imported objects to each group[[EM. Libera]].}}
<table><tr><td> [[Image:MOM1== EM.png|thumb|450px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM2.png|thumb|450px|The surface mesh of the dielectric cylinder and PEC plate.]] </td></tr></table>Libera's Excitation Sources ==
=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces === 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:
If the project workspace contains a line object, the wireframe mesh generator is used to discretize 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. From the point png]]| [[Glossary of view of this mesh generatorEM.Cube's Materials, all 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;" | [[Surface Objects|surface objectsFile:gap_src_icon.png]] and PEC | [[Solid ObjectsGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |solid objectsWire Gap Circuit Source]] are treated as wireframe objects. If you want to model a | style="width:300px;" | General-purpose point voltage source| style="width:300px;" | Associated with an PEC or thin wire radiator connected to a metal surfaceline or polyline, 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 wireworks only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon. This is not guaranteed automaticallypng]]| [[Glossary of EM. HoweverCube's Materials, you can use 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 polymesh objects to accomplish this objectiveMaterials, 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|}
{{Note|In Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]], polymesh objects are regards as already-meshed objects and are not re-meshed again during a simulation.}}
You can convert any surface object For antennas and planar circuits, where you typically define one or solid object to a polymesh using more ports, you usually use lumped sources. [[CubeCADEM.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 's ''Thin Wire Line'Polymesh Tool''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.
[[Image:Info_icon.png{{Note|40px]] Click here If you want to learn more about '''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 [[Discretizing_Objects#Converting_Objects_to_Polymesh | Converting Object to PolymeshCubeCAD]]''' in [[EM.Cube]]s Polygonize Tool.}}
Once an object is converted to A short dipole provides another simple way of exciting a polymesh, you 3D structure in [[EM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. You can place also use an incident plane wave to excite your wire at any of its nodesphysical structure in [[EM.Libera]]. In that caseparticular, EMyou need a plane wave source to compute the radar cross section of a target.Libera's Wire MoM engine will sense The direction of incidence is defined by the coincident nodes between line segments θ and will create 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 junction basis function 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 ensure current continuitylearn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''.
<table>
<tr>
<td> [[Image:MOM4wire_pic14_tn.png|thumb|450pxleft|Geometry of a monopole wire connected to a PEC plate.]] </td><td> [[Image:MOM5.png640px|thumb|450px|Placing the A wire gap source placed on the polymesh version one side of the PEC platea polyline representing a polygonized circular loop.]] </td>
</tr>
<tr>
</table>
== Excitation Sources ==
=== Gaps Sources on PEC Wires and Strips ===
A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current. In EM.Libera, a gap is used to define an excitation source in the form of an ideal voltage source. Gap sources can be placed on PEC '''Line''' and '''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.
{{Note|If you want to excite a curved wire antenna such as a circular loop or helix with a gap source, first you have to convert the curve object into a polyline using [[CubeCAD]]'s Polygonize Tool.}}
Gap sources can also 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.
To define a new gap source, follow these steps:
* Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.
* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A gap symbol is immediately placed on the selected object.
* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.
* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.
* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.
* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.
<table>
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<td> [[Image:MOM6po_phys16_tn.png|thumb|360pxleft|EM.Libera's Wire Gap Source dialog.]] </td><td> [[Image:MOM6B.png420px|thumb|360px|EM.Libera's Strip Gap Source dialogIlluminating a metallic sphere with an obliquely incident plane wave source.]] </td>
</tr>
<tr>
</table>
[[File:wire_pic14_tn.png]]=== Modeling Lumped Circuits ===
A In [[EM.Libera]], you can define simple lumped elements in a similar manner as gap source sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed on one side in the path of the current, across which Ohm's law is enforced as a polyline representing boundary condition. You can define passive RLC lumped elements or active lumped elements containing a polygonized circular loopvoltage 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 '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Defining_Finite-Sized_Source_Arrays Modeling_Lumped_Elements_in_the_MoM_Solvers | Using Source Arrays in Antenna ArraysDefining Lumped Elements]]'''.
=== Modeling Lumped Circuits === [[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]]'''.
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:=== Defining Ports ===
[[File:image106Ports 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.png]]
[[FileImage:wire_pic16_tnInfo_icon.png|thumb|200px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wire40px]] To define a new lumped element, follow these steps: * Right click on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the two options: '''Passive RLC''' or '''Active with Gap Source'''. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option Click here to select either learn more about the positive or negative direction for the source.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line[[Glossary_of_EM. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Load Properties''' section, the series and shunt resistance values Rs and Rp are specified in Ohms, the series and shunt inductance values Ls and Lp are specified in nH (nanohenry), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad). The impedance of the circuit is calculated at the operating frequency of the project. Only the elements that have been checked are taken into account. By default, only the series resistor has a value of 50Σ and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the '''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees.* If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical direction, offset, resistance, inductance and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase ProgressionCube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]''' in degrees along all three principal axes.
<table>
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<td> [[Image:MOM6AMOM7A.png|thumb|480px360px|EM.Libera's Wire Lumped Element dialogTwo metallic strips hosting a gap source and a lumped element.]] </td><td> [[Image:MOM6CMOM7B.png|thumb|480px360px|EM.Libera's Strip Lumped Element dialogThe surface mesh of the two strips with a gap source and a lumped element.]] </td>
</tr>
</table>
[[Image:port-definition.png|thumb|450px|== EM.Libera's Port Definition dialog.]]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= Defining Ports "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|}
Ports are used Click on each category to order and index gap sources for S parameter calculation. They are defined learn more details about it in the '''Observables''' section [[Glossary of the Navigation TreeEM. Right click on the Cube'''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the total number of existing sources in the workspace. 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. This includes both gap sources and active lumped elements (which contain gap sources). In the '''Port Association''' section of this dialog, you can go over each one of the sources and associate them with a desired port. Note that you can associate more than one source with same given port. In this case, you will have a coupled port. All the coupled sources are listed as associated with a single port. However, you cannot associate the same source with more than one port. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50s Simulation Observables Ω. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedancesGraph Types]].
Depending on the types of objects present in your project workspace, [[Image:MOM7.png|thumb|360px|EM.Libera's short dipole source dialog.]]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.
=== Hertzian Dipole Sources === <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>
A short dipole provides a simple way of exciting a structure {{Note|Keep in mind that since [[EM.Libera. A short dipole source acts like an infinitesimally small ideal current ]] uses MoM solvers, the calculated field value at the sourcepoint is infinite. To define As a short dipole sourceresult, follow these steps:the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}
* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Short Dipole dialog opens up.<table><tr>* In the '''Source Location''' section of the dialog, you can set the coordinate of the center of the short dipole<td> [[Image:wire_pic32_tn. By default, the source is placed at the origin png|thumb|360px|Electric field plot of the world coordinate system at (0,0,0)circular loop antenna.You can type in new coordinates or use the spin buttons to move the dipole around]] </td><td> [[Image:wire_pic33_tn.* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' png|thumb|360px|Magnetic field plot of the dipole in project unitscircular loop antenna.]] </td>* In the '''Direction Unit Vector''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitude.</tr></table>
You need to define a far field observable if you want to plot radiation patterns of your physical structure in [[Image:MOM8.png|thumb|360px|EM.Libera's Plane Wave dialog.]]=== Plane Wave Sources === . 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.
The wire-frame structure in the [[MoM3D ModuleImage:Info_icon.png|30px]] can be excited by an incident plane wave. In particular, a plane wave source can be used Click here to compute learn more about the radar cross section theory of a metallic target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. '''[[EM.CubeDefining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays |EM.CUBEUsing Array Factors to Model Antenna Arrays ]]'s [[MoM3D Module]] provides the following polarization options:''.
* TMz<table>* TEz<tr>* Custom Linear<td> [[Image:wire_pic38_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Theta component.]] </td>* LCPz<td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.]] </td>* RCPz<td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the circular loop antenna.]] </td></tr></table>
The direction of incidence When the physical structure is defined through 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 angles components of the unit propagation vector in radar cross section as well as the spherical coordinate systemtotal radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. The values In addition, [[EM.Libera]] calculates two types of these angles are set in degrees in the boxes labeled RCS for each structure: '''ThetaBi-Static RCS''' and '''PhiMono-Static RCS'''. The default values are In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ = 180° <sub>0</sub> and φ = 0° representing a normally incident plane wave propagating along <sub>0</sub>, and the -Z direction with a +X-polarized E-vectorRCS is measured and plotted at all θ and φ angles. In mono-static RCS, the TMstructure is illuminated by a plane wave at incidence angles θ<sub>z0</sub> and TEφ<sub>z0</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector RCS is measured and normalized Eplotted at the echo angles 180°- θ<sub>0</sub>; and H-field vectors are displayed φ<sub>0</sub>. It is clear that in the dialog. In the more general case of custom linear polarizationmono-static RCS, besides the incidence anglesPO simulation engine runs an internal angular sweep, you have to enter whereby the components values of the unit electric '''Field Vector'''. However, two requirements must be satisfied: '''ê . ê''' = 1 and '''ê × k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (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 plane wave source follow these steps: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.
* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' {{Note| The Plane wave Dialog opens up.* In 3D RCS plot is always displayed at the Field Definition section origin of the dialogspherical coordinate system, (0,0,0), you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of respect to which the Plane Wave far radiation zone is determined by the incident '''Theta''' and '''Phi''' angles in degreesdefined. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selectedOftentimes, you also need to enter this might not be the X, Y, Z components scattering center of the '''E-Field Vector'''your physical structure.}}
{{Note|In Computing the spherical coordinate system, normal plane wave incidence from the top of the domain downward corresponds to θ 3D mono-static RCS may take an enormous amount of 180°computation time. }}
<table><tr><td> [[FileImage:po_phys16_tnwire_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>
Figure: Illuminating a metallic sphere with an obliquely incident plane wave source== 3D Mesh Generation in EM.Libera ==
== Running 3D MoM Simulations = A Note on EM.Libera's Mesh Types ===
Once you have set up your structure in [[EM.Libera]] features two simulation engines, have defined sources and observables Wire MoM and have examined the quality of the structure's meshSurface MoM, you which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are ready discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to run a MoM simulationmesh density criterion. EMCurved wires are first converted to multi-segment polylines and then subdivided further if necessary.Libera offers four types of simulation:At the connection points between two or more wires, junction basis functions are generated to ensure current continuity.
* Single-Frequency Analysis* Frequency Sweep* Parametric Sweep* On the other hands, [[OptimizationEM.Libera]]* HDMR Sweep'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|40px30px]] Click here to learn more about '''[[Parametric_Modeling,_Sweep_%26_OptimizationPreparing_Physical_Structures_for_Electromagnetic_Simulation#Running_Parametric_Sweep_Simulations_in_EMWorking_with_EM.Cube .27s_Mesh_Generators | Running Parametric Sweep Simulations in EM.CubeWorking with Mesh Generator]]'''.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Parametric_Modeling,_Sweep_%26_OptimizationPreparing_Physical_Structures_for_Electromagnetic_Simulation#Optimization The_Triangular_Surface_Mesh_Generator | Running Optimization Simulations in EM.CubeLibera's Triangular Surface Mesh Generator ]]'''.
<table><tr><td> [[Image:Info_iconMesh5.png|40px]] Click here to learn more about '''[[Running_HDMR_Simulations_in_EM.Cube thumb|400px| Running HDMR Simulations in EM.CubeLibera's Mesh Settings dialog showing the parameters of the linear wireframe mesh generator.]]'''.</td></tr></table>
=== Running a Single-Frequency MoM Analysis The Linear Wireframe Mesh Generator ===
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 You can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Libera]]'s two Wire MoM solverssimulator. If your project When you structure contains at lease least one PEC line , polyline or any curve CAD object, the Wire MoM solver is automatically selected[[EM. Otherwise, the Surface MoM solver Libera]] will always be used 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 simulate your problemthe specified mesh density. In either case, It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are determined by the engine type specified mesh density. Note that polygonizing operation is set automaticallytemporary 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.
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 {{keyNote|Ctrl+R}}The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. By default, the Surface MoM solver is selected as your simulation engineIt also discretizes surface and solid CAD objects temporarily using CubeCAD's Polymesh tool. 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>
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<td> [[Image:MOM9CMesh6.png|thumb|450px200px|EMThe geometry of an expanding helix with a circular ground.Libera's Simulation Run dialog showing Wire MoM engine as ]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the solverhelix with the default mesh density of 10 cells/λ<sub>0</sub>.]] </td><td> [[Image:MOM9AMesh8.png|thumb|450px200px|EMWireframe mesh of the helix with a mesh density of 25 cells/λ<sub>0</sub>.Libera's Simulation Run dialog showing Surface MoM engine as ]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the solverhelix with a mesh density of 50 cells/λ<sub>0</sub>.]] </td>
</tr>
</table>
=== Setting MoM Numerical Parameters Mesh of Connected Objects ===
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 All the '''Settings''' button next objects belonging to the "Select Engine" dropdown list in same PEC or dielectric group are merged together using the '''Run Dialog'''Boolean union operation before meshing. Depending on which MoM solver has been chosen for solving If your problemstructure 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 corresponding Engine Settings dialog opens upsame PEC group might not always be merged properly.
First we discuss When two objects belonging to two different material groups overlap or intersect each other, [[EM.Libera]] has to determine how to designate the Wire MoM Engine Settings dialogoverlap or common volume or surface. In As an example, the '''Solver''' section 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 dialogcircle 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 choose the type of '''Linear Solvermodify. To access this table, select '''Menu > Simulate > discretization > Mesh Hierarchy... The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver PEC groups by default have the highest priority and is reside at the default option top of the Wire MoM solvertable. The BiCG solver is iterative. If BiCG is selected, you have to set a '''Tolerance''' for You can select an group from the table and change its convergencehierarchy using the {{key|Move Up}} or {{key|Move Down}} buttons of the dialog. You can also change the maximum number color of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''junction cells that belong to each group.
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<subtable>0</subtr><td> [[Image:MOM3. png|thumb|300px|EM.Libera's Surface MoM solver has been highly parallelized using MPI framework. When you install [[EMMesh Hierarchy dialog.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. </td></tr>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>
<table>
<tr>
<td> [[Image:MOM9BMOM1.png|thumb|420px360px|EM.Libera's Wire MoM Engine Settings dialogA dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM9MOM2.png|thumb|480px360px|EM.Libera's Surface MoM Engine Settings dialogThe surface mesh of the dielectric cylinder and PEC plate.]] </td>
</tr>
</table>
=== Running Frequency Sweep Simulations in EM.Libera Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===
[[Image:wire_pic24.png|thumb|450px| EM.Libera's Frequency Settings dialog.]]In If the project workspace contains a frequency sweep simulationline object, the operating frequency of the project wireframe mesh generator is varied during the simulation, and the frequency response of used to discretize your physical structure is computed at each frequency sample. EM.Libera offers two types of frequency sweep: uniform and adaptive. In a uniform sweep, equally spaced frequency samples are generated between From the start and end frequencies. In the case point of an adaptive sweep, you must specify the '''Maximum Number view of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samplesthis mesh generator, where the Wire MoM engine is initially run. Then, the intermediate frequency samples all PEC surface objects and PEC solid objects are calculated and inserted in a progressive mannertreated as wireframe objects. At each iteration, the frequency samples are used If you want to calculate model a rational approximation of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a mean-square sense. The adaptive sweep simulation results are always continuous and smooth. This is due wire radiator connected to the fact that a rational function curve is fitted through the discrete frequency data points. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. Howevermetal surface, you have to make sure that the process converges. Otherwise, you might get an entirely wrong, but still perfectly smooth, curve at the end resulting wireframe mesh of the simulation. To run surface has a 3D MoM frequency sweep, open node exactly at the '''Run Simulation Dialog''' and select '''Frequency Sweep''' from the '''Simulation Mode''' dropdown list in this dialog. The '''Settings''' button located next to the simulation mode dropdown list becomes enabled. If location where you click this button, the Frequency Settings Dialog opens up. First you have want to choose the '''Sweep Type''' with two options: '''Uniforms''' or '''Adaptive'''connect your wire. The default option This is a uniform sweepnot guaranteed automatically. In the frequency settings dialogHowever, you can set the start and end frequencies as well as the number of frequency samplesuse [[EM.Cube]]'s polymesh objects to accomplish this objective.
During a frequency sweep{{Note|In [[EM.Cube]], polymesh objects are regarded as the project's frequency changes, so does the wavelength. As already-meshed objects and are not re-meshed again during a result, the mesh of the structure also changes at each frequency samplesimulation. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:}}
* Fix mesh at the highest frequency.* Fix mesh at the center frequency.* Re-mesh at each frequencyYou can convert any surface object or solid object to a polymesh using CubeCAD's '''Polymesh Tool'''.
== Working with 3D MoM Simulation Data ==[[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 Output Simulation Data ===Wire MoM engine will sense the coincident nodes between line segments and will create a junction basis function to ensure current continuity.
At the end <table><tr><td> [[Image:MOM4.png|thumb|360px|Geometry of a 3D MoM simualtion, EM.Libera generates monopole wire connected to a number of output data files that contain all the computed simulation dataPEC plate. The primary solution of ]] </td><td> [[Image:MOM5.png|thumb|360px|Placing the Wire MoM simulation engine consists of the linear electric currents wire on the wires and wireframe structures. The primary solution polymesh version of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objectsplate. EM.Libera currently offers the following types of observables: * '''Port Characteristics''': S, Z and Y [[Parameters]] and Voltage Standing Wave Ratio (VSWR)</td>* '''Radiation Characteristics''': Radiation Patterns, Directivity, Total Radiated Power, Axial Ratio, Main Beam Theta and Phi, Radiation Efficiency, Half Power Beam Width (HPBW), Maximum Side Lobe Level (SLL), First Null Level (FNL), Front-to-Back Ratio (FBR), etc.</tr>* '''Scattering Characteristics''': Bi-static and Mono-static Radar Cross Section (RCS)* '''Current Distributions''': Electric and magnetic surface current amplitude and phase on all metal and dielectric surfaces and electric current amplitude and phase on all wires * '''Near-Field Distributions''': Electric and magnetic field amplitude and phase on specified planes and their central axes</table>
=== Scattering Parameters and Port Characteristics =Running 3D MoM Simulations in EM.Libera ==
If the project structure is excited by gap sources, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) [[parameters]] of the selected ports, all based on the port impedances specified in the project=== EM.Libera's "Port Definition". If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. The S [[parameters]] are written into output ASCII data files. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with "#". The admittance (Y) and impedance (Z) [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of the structure at the first port is also computed and saved to a real data '''.DAT''' file.Simulation Modes ===
You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item Once you have set up your structure in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[ParametersEM.Libera]]''', have defined sources and observables and have examined the quality of the structure'''Plot Y [[Parameters]]'''s mesh, '''Plot Z you are ready to run a 3D MoM simulation. [[ParametersEM.Libera]]''', or '''Plot VSWR'''. 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;" | [[Image#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:Info_icon270px;" | 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.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube |40pxFrequency Sweep]] Click here to learn | 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 about '''frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Data_Visualization_and_ProcessingParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Graphing_Port_Characteristics Running_Parametric_Sweep_Simulations_in_EM.Cube | Graphing Port CharacteristicsParametric 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 [[Image:Info_iconEM.png|40pxLibera]] Click here to learn more about '''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Scattering_Parameters | Rational Interpolation 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 Scattering Parameters]]'''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.
=== Visualizing Current Distributions 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 [[Image:MOM10.png|thumb|350px|EM.Libera]]'s Current Distribution dialogtwo 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.]]
At To open the end of a MoM3D simulation, [[EM.Cube|EM.CUBE]]'s Wire MoM engine generates a number of output data files that contain all the computed simulation data. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currents, you must first define current sensors before running the Wire MoM simulation. To do thisRun Simulation Dialog, right click on the '''Current DistributionsRun''' item in [[File:run_icon.png]] button of the '''ObservablesSimulate Toolbar''' section of the Navigation Tree and or select '''Insert New ObservableMenu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. The Current Distribution Dialog opens up. Accept the By default settings and close , the dialog. A new current distribution node Surface MoM solver is added to the Navigation Treeselected as your simulation engine. Unlike To start the [[Planar Module]]simulation, in click the [[MoM3D Module]] you can define only one current distribution node in {{key|Run}} button of this dialog. Once the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire 3D MoM simulation is completedstarts, a new plots are added under dialog called '''Output Window''' opens up that reports the current distribution node various stages of MoM simulation, displays the Navigation Tree. Separate plots are produced for the magnitude running time and phase shows the percentage of completion for certain tasks during the linear wire currentsMoM simulation process. The magnitude maps are plotted on a normalized scale with A prompt announces the minimum and maximum values displayed in completion of the legend box. The phase maps are plotted in radians between -π and πMoM simulation.
<table><tr><td> [[Image:Info_iconLibera L1 Fig13.png|40pxthumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] Click here to learn more about '''</td></tr><tr><td> [[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps Image:MOM3D MAN10.png| Visualizing 3D Current Distribution Maps]]''thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td></tr></table>
[[File:wire_pic26_tn.png|400px]] [[File:wire_pic27_tn.png|400px]]=== Setting MoM Numerical Parameters ===
Figure: A monopole antenna connected above MoM simulations involve a PEC plate number of numerical parameters that normally take default values unless you change them. You can access these parameters and its current distribution with change their values by clicking on the default plot settings'''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.
[[File:wire_pic28.png|360px]] [[File:wire_pic29_tn.png|440px]] Figure: The output plot settings dialog, and First we discuss the current distribution of the monopole-plate structure with a user defined upper limit. === Near Field Visualization === [[Image:MOM11.png|thumb|350px|EM.Libera's Field Sensor Wire MoM Engine Settings dialog.]] [[EM.Cube|EM.CUBE]] allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps: * Right click on In the '''Field Sensors''' item in the '''ObservablesSolver''' section of the Navigation Tree and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensor’s name. this dialog, you can also change choose the color type of the field sensor plane using the '''ColorLinear Solver''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available current options are '''X''', '''YLU''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBE]] creates a field sensor plane passing through the origin of coordinates Bi-Conjugate Gradient (0,0,0BiCG) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane LU solver is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree direct solver and can be right clicked for additional editing. Once a Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase default option of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse buttonWire MoM solver. The values of the magnitude plots are normalized between 0 and 1BiCG solver is iterative. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which If BiCG is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change the view of the field plot with the available view operations such as rotatingselected, panning, zooming, etc. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field Maps]]'''. [[File:wire_pic31_tn.png]] Figure: A circular loop antenna fed by a gap source. [[File:wire_pic32_tn.png|400px]] [[File:wire_pic33_tn.png|400px]] Electric and magnetic field plots of the circular loop antenna. === Visualizing 3D Radiation Patterns === [[Image:MOM12.png|thumb|380px|EM.Libera's Radiation Pattern dialog.]] Unlike the FDTD method, the method of moments does not need a far field box to perform near-to-far-field transformations. But you still need have to define set a far field observable if you want to plot radiation patterns in EM.Libera. A far field can be defined by right clicking on the '''Far FieldsTolerance''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens upfor its convergence. You can accept most of the default settings in this dialog. The Output Settings section allows you to also change the '''Angle Increment''' for both Theta and Phi observation angles in the degrees. These [[parameters]] indeed set the resolution maximum number of far field calculations. The default values are 5 degrees. After closing the radiation pattern dialog, BiCG iterations by setting a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked new value for further editing. 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|40px]] Click here to learn more about '''[[Maxwell%27s_Equations#Definition_of_the_Far_Radiation_Zone | Computing the Far Fields & Radiation Characteristics]]'''Max. [[Image:Info_iconNo.png|40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]Solver Iterations / System Size'''.
<table>
<tr>
<td> [[Image:wire_pic38_tnMOM9B.png|thumb|280pxleft|The 3D radiation pattern of the circular loop antenna: Theta component480px|EM.]] </td><td> [[Image:wire_pic39_tn.png|thumb|280px|The 3D radiation pattern of the circular loop antenna: Phi componentLibera's Wire MoM Engine Settings dialog.]] </td><td> [[Image:wire_pic40_tn.png|thumb|280px|The total radiation pattern of the circular loop antenna.]] </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 === Computing Radar Cross Section === 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 [[Image:MOM13.png|thumb|380px|EM.Libera's Radar Cross Section dialog.]] When your structure is excited by a plane wave source, to write the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) contents of a target. Three RCS quantities are computed: the φ MoM matrix and θ components of the radar cross section as well as the total radar cross section: σ<sub>θ</sub>, σ<sub>φ</sub>, excitation and σ<sub>tot</sub>. In addition, EM.Libera calculates two types of RCS for each structure: solutions vectors into data files with '''Bi-Static RCS.DAT1''' and file extensions. These files can be accessed from the '''Mono-Static RCSInput/Output Files'''. In bi-static RCS, tab of 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 anglesData Manager. 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 both case of mono-static RCS, the Wire MoM simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ<sub>0</sub> and φ<sub>0</sub> are varied over the 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. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' option to open uncheck the Radar Cross Section Dialog. Use the '''Label''' check box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''"Superpose Incident plane Wave Fields". The former This option applies when your structure is the default choice. The resolution of RCS calculation is specified excited by '''Angle Increment''' expressed in degrees. By default, the θ and φ angles are incremented by 5 degrees. At the end of a Wire MoM simulation, besides calculating the RCS data over the entire (spherical) 3-D space, a number of 2-D RCS graphs are also generatedplane wave source. These are RCS cuts at certain planesWhen checked, which include the three principal XY, YZ and ZX planes plus one additional constant φ-cut. This latter cut is at φ=45° by default. You can assign another phi angle in degrees in the box labeled '''Non-Principal Phi Plane'''. At the end of a Wire MoM 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 sensors plot the navigation tree. The 2D RCS graphs can be plotted from the data manager exactly in the same way that you plot 2D radiation pattern graphs. A total of eight 2D RCS graphs are available: 4 polar electric and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, EM.Libera calculates some other quantities magnetic field distributions including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable)incident field. In this caseOtherwise, only the RCS needs to be computed at a fixed pair of phi scattered electric and theta angles. These angles magnetic field distributions are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the '''Radar Cross Section Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith. {{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}} [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]'''visualized.
<table>
<tr>
<td> [[Image:wire_pic51_tnMOM9.png|thumb|300pxleft|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png640px|thumb|300px|The RCS of a metal plate structure: σ<sub>φ</sub>EM.]] </td><td> [[Image:wire_pic53_tn.png|thumb|300px|The total RCS of a metal plate structure: σ<sub>tot</sub>Libera's Surface MoM Engine Settings dialog.]] </td>
</tr>
</table>
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