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[[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

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| 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;" | Imported from a Huygens surface data file

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== Discretizing a Planar Structure in EM.Picasso ==

The method of moments (MoM) discretizes all the finite-sized objects of a planar structure (excluding the background structure) into a set of elementary cells. Both the quality and resolution of the generated mesh greatly affect the accuracy of the MoM numerical solution. The mesh density gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the finite-sized geometrical objects. As a rule of thumb, a mesh density of about 20-30 cells per effective wavelength usually yields satisfactory results. But for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular output data that you seek in a simulation also influence your choice of mesh resolution. For example, far field characteristics like radiation patterns are less sensitive to the mesh density than field distributions on structures with a highly irregular shapes and boundaries.

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<td> [[Image:PMOM48H.png|thumb|left|420px|Details of the hybrid planar mesh of the slot-coupled patch array around discontinuities.]] </td>

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=== General Rules of Planar Hybrid Mesh Generator ===

* 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 &quot;field discontinuity&quot; 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.

{{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.}}

[[EM.Picasso]] allows you to simulate doubly periodic planar structures with periodicities along the X and Y directions. Once you designate your planar structure as periodic, [[EM.Picasso]]'s Planar MoM simulation engine uses a spectral domain solver to analyze it. In this case, the dyadic Green's functions of periodic planar structure take the form of doubly infinite summations rather than integrals.

{{Note| [[EM.Picasso]] can handle both regular and skewed periodic lattices.}}

=== Defining a Periodic Structure in EM.Picasso ===

An infinite periodic structure in [[EM.Picasso]] is represented by a &quot;'''Periodic Unit Cell'''&quot;. To define a periodic structure, you must open [[EM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''&gt;''' '''Simulate &gt; 'Computational Domain &gt; Periodicity Settings...''' from the menu bar. In the Periodicity Settings Dialog, check the box labeled '''Periodic Structure'''. This will enable the section titled''&quot;''Lattice Properties&quot;. You can define the periods along the X and Y axes using the boxes labeled '''Spacing'''. In a periodic structure, the virtual domain is replaced by a default blue periodic domain that is always centered around the origin of coordinates. Keep in mind that the periodic unit cell must always be centered at the origin of coordinates. The relative position of the structure within this centered unit cell will change the phase of the results.

In many cases, your planar structure's traces or embedded objects are entirely enclosed inside the periodic unit cell and do not touch the boundary of the unit cell. [[EM.Picasso]] allows you to define periodic structures whose unit cells are interconnected. The interconnectivity applies only to PEC, PMC and conductive sheet traces, and embedded object sets are excluded. Your objects cannot cross the periodic domain. In other words, the neighboring unit cells cannot overlap one another. However, you can arrange objects with linear edges such that one or more flat edges line up with the domain's bounding box. In such cases, [[EM.Picasso]]'s planar MoM mesh generator will take into account the continuity of the currents across the adjacent connected unit cells and will create the connection basis functions at the right and top boundaries of the unit cell. It is clear that due to periodicity, the basis functions do not need to be extended at the left or bottom boundaries of the unit cell. As an example, consider a periodic metallic screen as shown in the figure on the right. The unit cell of this structure can be defined as a rectangular aperture in a PEC ground plane (marked as Unit Cell 1). In this case, the rectangle object is defined as a slot trace. Alternatively, you can define a unit cell in the form of a microstrip cross on a metal trace. In the latter case, however, the microstrip cross should extend across the unit cell and connect to the crosses in the neighboring cells in order to provide current continuity.

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=== Exciting Periodic Structures as Radiators in EM.Picasso ===

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<td> [[Image:Period5.png|thumb|350px|Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] </td>

<td> [[Image:Period6.png|thumb|350px|Setting the array factor in EM.Picasso's Radiation Pattern dialog.]] </td>

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{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[EM.Picasso]] computes the reflection and transmission coefficients of the layered background structure of your project.}}

=== Running a Periodic MoM Analysis ===

[[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 S₁₁ parameter, while the transmission coefficient T is equivalent to S₂₁ 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°&lt; &theta; = 180°. You can also illuminate the periodic surface by the plane wave source from the bottom half-space, corresponding to 0° = &theta; &lt; 90°. In this case, the reflection coefficient R and transmission coefficient T are equivalent to S₂₂ and S₁₂ parameters, respectively. Having these interpretations in mind, [[EM.Cube]] enables the &quot;'''Adaptive Frequency Sweep'''&quot; 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]]'''.

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