<tr>
</table>
[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Tutorial_Lessons Picasso_Documentation | EM.Picasso Tutorial Gateway]]'''
[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
| 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
|}
| 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 sourced sources imported from other [[EM.Cube]] modules
| style="width:300px;" | Imported from a Huygens surface data file
|}
<table>
<tr>
<td> [[Image:PMOM85(1)PMOM85new.png|thumb|left|480px600px|The current distribution map of a patch antenna.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[Image:PMOM116.png|thumb|left|480px600px|Near-zone electric field map above a microstrip-fed patch antenna.]] </td>
</tr>
<tr>
<td> [[Image:PMOM117.png|thumb|left|480px600px|Near-zone magnetic field map above a microstrip-fed patch antenna.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[Image:PMOM119.png|thumb|left|480px600px|3D polar radiation pattern plot of a microstrip-fed patch antenna.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[Image:PMOM125.png|thumb|left|480px600px|An example of the 3D monostatic radar cross section plot of a patch antenna.]] </td>
</tr>
</table>
</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 [[EM.Picasso]]'s '''[[Mesh_Generation_Schemes_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#The_Hybrid_Planar_Mesh_Generator The_Triangular_Surface_Mesh_Generator | Hybrid Planar Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about [[EM.Picasso]]'s '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator]]'''.
<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.
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.}}
=== 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 '''Probe Gap Source Dialog''', there is a section button titled '''Periodic Beam Scan Angles...'''. 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>
<tr>
<td>
[[Image:PMOM102.png|thumb|400px580px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]]
</td>
</tr>
[[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.
<!--
=== Modeling Finite-Sized Periodic Arrays ===
[[Image:Info_icon.png|40px]] Click here to learn about '''[[Modeling Finite-Sized Periodic Arrays Using NCCBF Technique]]'''.
-->
<br />