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[[Image:Splash-planar new.jpg|right|800px720px]]<strong><font color="#015865" size="4">Fast Full-Wave Simulator For Modeling Multilayer Planar Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

[[Image:PMOM14EM.png|thumb|400px|A typical planar layered structurePicasso]]EM.Picasso^® is a versatile planar structure simulator for modeling and design of printed antennas, planar microwave circuits, and layered periodic structures. [[EM.Picasso]]'s simulation engine is based on a 2.5-D full-wave Method of Moments (MoM) formulation that provides the ultimate modeling accuracy and computational speed for open-boundary multilayer structures. It can handle planar structures with arbitrary numbers of metal layouts, slot traces, vertical interconnects and lumped elements interspersed among different substrate layers.

{{Note|Since its introduction in 2002, [[EM.Picasso is ]] has been successfully used by numerous users around the frequency-domainglobe in industry, full-wave '''academia and government. It has also undergone several evolutionary cycles including a total reconstruction based on our integrated [[Planar ModuleEM.Cube]]''' of '''software foundation to expand its CAD and geometrical construction capabilities. [[EM.CubePicasso]]''', a comprehensive, integrated, modular electromagnetic modeling environment. s integration with [[EM.Picasso shares the visual interface, 3D parametric CAD modeler, data visualization tools, Cube]] facilitates import and export of many more utilities popular CAD formats (including DXF export of layered traces) and features collectively known as '''[[CubeCAD]]''' provides a seamless interface with all of [[EM.Cube]]'s other computational modulessimulation tools.}}

[[Image:Info_icon.png|40px30px]] Click here to learn more about the '''[[Getting_Started_with_EM.CUBE Basic Principles of The Method of Moments | EM.Cube Modeling EnvironmentTheory of Planar Method of Moments]]'''.

<table><tr><td> [[Image:Info_iconART PATCH Fig title.png|40px]] Click here to learn more about the basic functionality thumb|left|480px|3D radiation pattern of '''[[CubeCADa slot-coupled patch antenna array with a corporate feed network.]]'''.</td></tr></table>

=== An Overview of EM.Picasso as the Planar Method Module of Moments EM.Cube ===

The Method of Moments (MoM) [[EM.Picasso]] is a rigorousthe frequency-domain, full-wave numerical technique for solving open boundary electromagnetic problems'''Planar Module''' of '''[[EM. Using this techniqueCube]]''', you can analyze a comprehensive, integrated, modular electromagnetic radiationmodeling environment. [[EM.Picasso]] shares the visual interface, 3D 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 that are used in the finite element or finite difference time domain methods[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

In EM[[Image:Info_icon.Picasso, the background structure is a planar layered substrate that consists of one or png|30px]] Click here to learn more laterally infinite material layers always stacked along the Z-axis. In other words, the dimensions of the layers are infinite along the X and Y axes. Your substrate can be a dielectric half-space, or a single conductor-backed dielectric layer (as in microstrip components or patch antennas), or simply the unbounded free space, or any arbitrary multilayer stack-up configuration. In the special case of a free space substrate, EM.Picasso behaves similar to about '''[[Getting_Started_with_EM.Cube | EM.LiberaCube Modeling Environment]]'s Surface MoM simulator. Metallic traces are placed at the boundaries between the substrate or superstrate layers. These are modeled by perfect electric conductor (PEC) traces or conductive sheet traces of finite thickness and finite conductivity. Some layers might be separated by infinite perfectly conducting ground planes. The two sides of a ground plane can be electromagnetically coupled through one or more slots (apertures). Such slots are modeled by magnetic surface currents. Furthermore, the metallic traces can be interconnected or connected to ground planes using embedded objects. Such objects can be used to model circuit vias, plated-through holes or dielectric inserts. These are modeled as volume polarization currents''.

In a planar MoM simulation, the unknown electric and magnetic currents are discretized as a collection === Advantages & Limitations of elementary currents with small finite spatial extentsEM. As a result, the governing integral equations reduce to a system of linear algebraic equations, whose solution determines the amplitudes of all the elementary currents defined over the planar structurePicasso's mesh. Once the total currents are known, you can calculate the fields everywhere in the structure.Planar MoM Simulator ===

[[Image:Info_iconEM.png|40pxPicasso]] Click here assumes that your planar structure has a substrate (background structure) of infinite lateral extents. In addition, the planar 2.5-D assumption restricts the 3D objects of your physical structure to learn more about embedded prismatic objects that can only support vertical currents. These assumptions limit the variety and scope of the applications of [[EM.Picasso]]. For example, you cannot use [[EM.Picasso]] to analyze a patch antenna with a finite-sized dielectric substrate. If the substrate edge effects are of concern in your modeling problem, you must use [[EM.Tempo]] instead. On the other hand, since [[EM.Picasso]]'s Planar MoM simulation engine incorporates the Green's functions of the background structure into the analysis, only the finite-sized traces like microstrips and slots are discretized by the mesh generator. As a result, the size of [[EM.Picasso]]'s computational problem is normally much smaller than that of [[Planar Method EM.Tempo]]. In addition, [[EM.Picasso]] generates a hybrid rectangular-triangular mesh of Moments | Theory your planar structure with a large number of Planar Method equal-sized rectangular cells. Taking full advantage of Momentsall the symmetry and invariance properties of dyadic Green's functions often results in very fast computation times that easily make up for [[EM.Picasso]]'''s limited applications. A particularly efficient application of [[EM.Picasso]] is the modeling of periodic multilayer structures at oblique incidence angles.

=== Advantages & Limitations <table><tr><td> [[Image:ART PATCH Fig12.png|thumb|left|480px|The hybrid planar mesh of EMthe slot-coupled patch antenna array.Picasso's Planar MoM Simulator ===]]</td></tr></table>

== EM.Picasso assumes that your planar structure has Features at a substrate (background structure) of infinite lateral extents. In addition, the planar 2.5-D assumption restricts the 3D objects of your physical structure to embedded prismatic objects that can only support vertical currents. These assumptions limit the variety and scope of the applications of EM.Picasso. For example, you cannot use EM.Picasso to analyze a patch antenna with a finite-sized dielectric substrate. If the substrate edge effects are of concern in your modeling problem, you must use [[EM.Tempo]] instead. On the other hand, since EM.Picasso's Planar MoM simulation engine incorporates the Green's functions of the background structure into the analysis, only the finite-sized traces like microstrips and slots are discretized by the mesh generator. As a result, the size of EM.Picasso's computational problem is normally much smaller than that of [[EM.Tempo]]. In addition, EM.Picasso generates a hybrid rectangular-triangular mesh of your planar structure with a large number of equal-sized rectangular cells. Taking full advantage of all the symmetry and invariance properties of dyadic Green's functions often results in very fast computation times that easily make up for EM.Picasso's limited applications. A particularly efficient application of EM.Picasso is the modeling of periodic multilayer structures at oblique incidence angles.Glance ==

== Building a Planar = Structure Definition ===

EM.Picasso is intended for construction and modeling of planar layered structures. By a planar structure we mean one that contains a background substrate of laterally infinite extents=== Sources, made up of one or more material layers all stacked up vertically along the Z-axis. Planar objects of finite size are interspersed among these substrate layers. The background structure in EM.Picasso is called the Loads &quotamp;'''Layer Stack-up'''&quot;. The layer stack-up is always terminated from the top and bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material medium. Most planar structures used in RF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components require two bounding grounds (PEC half-spaces) both at their top and bottom.Ports ===

EM.Picasso provides the following types <ul> <li> Optimized hybrid mesh with rectangular and triangular cells</li> <li> Regular triangular surface mesh</li> <li> Local meshing of trace groups</li> <li> Local mesh editing of objects for building a planar layered structure:polymesh objects</li> <li> Fast mesh generation of array objects</li></ul>

[[Image:Info_icon<ul> <li> 2.png|40px]] Click here to learn more about '''[[Planar Traces & Object Types]]'''5-D mixed potential integral equation (MPIE) formulation of planar layered structures</li> <li> 2.5-D spectral domain integral equation formulation of periodic layered structures</li> <li> Accurate scattering parameter extraction and de-embedding using Prony&#39;s method</li> <li> Plane wave excitation with arbitrary angles of incidence</li> <li> A variety of matrix solvers including LU, BiCG and GMRES</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Generation of reflection and transmission coefficient macromodels</li> <li> Multi-variable and multi-goal optimization of structure</li> <li> Remote simulation capability</li> <li> Both Windows and Linux versions of Planar MoM simulation engine available</li></ul>

=== Defining the Layer Stack-Up Data Generation &amp; Visualization ===

When you start a new project in EM.Picasso, there is always a default background structure that consists of a finite vacuum layer sandwiched between a vacuum top half<ul> <li> Current distribution intensity plots</li> <li> Near field intensity plots (vectorial -space amplitude &amp; phase)</li> <li> Far field radiation patterns: 3D pattern visualization and a PEC bottom half-space. Every time you open EM.Picasso or switched to it from [[EM.Cube]]'s other modules2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, the '''Stack-up Settings Dialog''' opens upside lobe levels and null parameters, etc. This is where you define </li> <li> Radiation pattern of an arbitrary array configuration of the entire background planar structure. Once you close this dialog, you can open it again by right clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section or periodic unit cell</li> <li> Reflection and Transmission Coefficients of the navigation tree Periodic Structures</li> <li> Monostatic and selecting '''Layer Stackbi-up Settings...''' from the contextual menu. Or alternatively, you can select the menu item '''Simulate static RCS&gtnbsp; Computational Domain &gt; Layer Stack</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-up Settingsstyle S parameter text files for direct export to RF...'''Spice or its Device Editor</li> <li> Huygens surface generation</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

The Stack-up Settings dialog has two tabs: '''Layer Hierarchy''' and '''Embedded Sets'''. The Layer Hierarchy tab has == Building a table that shows all the background layers Planar Structure in hierarchical order from the top half-space to the bottom half-space. It also lists the material label of each layer, Z-coordinate of the bottom of each layer, its thickness (in project units) and material properties: permittivity (e_r), permeability (µ_r), electric conductivity (s) and magnetic conductivity (s_m). There is also a column that lists the names of embedded object sets inside each substrate layer, if anyEM.Picasso ==

You can add new layers to your project's stack-up or delete its layers, or move layers up or down [[EM.Picasso]] is intended for construction and thus change the layer hierarchymodeling of planar layered structures. To add By a planar structure we mean one that contains a new background layersubstrate of laterally infinite extents, click the arrow symbol on made up of one or more material layers all stacked up vertically along the '''InsertZ-axis.Planar objects of finite size are interspersed among these substrate layers.The background structure in [[EM.'''button at Picasso]] is called the bottom of the dialog and select &quot;'''Substrate LayerStack-up''' from the button's dropdown list&quot;. A new dialog opens The layer stack-up where you can enter a label for is always terminated from the new layer top and values for its bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material properties and thickness medium. Most planar structures used in project unitsRF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components are sandwiched between two grounds (PEC half-spaces) from both their top and bottom.

You can delete a layer by selecting its row in the <table and clicking the '''Delete''' button><tr><td> [[Image:PMOM11. To move a layer up and down, click on its row to select and highlight itpng|thumb|left|480px|EM. Then click either the Picasso'''Move Up''' or '''Move Down''' buttons consecutively to move the selected layer to the desired location in the stack-up. Note that you cannot delete or move the top or bottom half-spacess navigation tree and trace types.]]</td></tr></table>

After creating a substrate layer, you can always edit its properties in === Defining the Layer Stack-up Settings dialog. Click on any layer's row in the table to select and highlight it and then click the '''Edit''' button. The substrate layer dialog opens up, where you can change the layer's label and assigned color. In the material properties section of the dialog, you can change the name of the material and its properties: permittivity (e_r), permeability (µ_r), electric conductivity (s) and magnetic conductivity (s_m). To define electrical losses, you can either assign a value for electric conductivity (s), or alternatively, define a loss tangent for the material. In the latter case, check the box labeled &quot;'''Specify Loss Tangent'''&quot; and enter a value for it. In this case, the electric conductivity field becomes greyed out and reflects the corresponding s value at the center frequency of the project. You can also set the thickness of any substrate layer in the project units except for the top and bottom half-spaces. Up ===

When you start a new project in [[Image:Info_iconEM.png|40pxPicasso]] Click here , there is always a default background structure that consists of a finite vacuum layer with a thickness of one project unit sandwiched between a vacuum top half-space and a PEC bottom half-space. Every time you open [[EM.Picasso]] or switched to learn more about '''it from [[Defining Materials in EM.Cube]]'s other modules, the '''Stack-up Settings Dialog''' opens up.This is where you define the entire background structure. Once you close this dialog, you can open it again by right-clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Layer Stack-up Settings...''' from the contextual menu. Or alternatively, you can select the menu item '''Simulate &gt; Computational Domain &gt; Layer Stack-up Settings...'''

For better visualization of your planar structure, EM.Picasso displays a virtual domain in a default orange color to represent part of the infinite background structure. The size of this virtual domain is a quarter wavelength offset from the largest bounding box that encompasses all the finite objects in the project workspace. You can change the size of the virtual domain or its display color from the Domain Stack-up Settings dialog, which you can access either by clicking the has two tabs: '''Computational DomainLayer Hierarchy''' [[File:domain_icon.png]] button of the and '''Simulate ToolbarEmbedded Sets''', or by selecting '''Simulate &gt; Computational Domain &gt; Domain Settings...''' The Layer Hierarchy tab has a table that shows all the background layers in hierarchical order from the Simulate Menu or by right clicking top half-space to the '''Virtual Domain''' item of the Navigation Tree and selecting '''Domain Settingsbottom half-space...''' from It also lists the contextual menumaterial composition of each layer, or using Z-coordinate of the keyboard shortcut '''Ctrl+A'''. Keep bottom of each layer, its thickness (in mind that the virtual domain is only for visualization purpose project units) and does not affect the MoM simulationmaterial properties: permittivity (&epsilon;_r), permeability (&mu;_r), electric conductivity (&sigma;) and magnetic conductivity (&sigma;_m). The virtual domain There is also shows a column that lists the names of embedded object sets inside each substrate layers in translucent colors. If you assign different colors to your substrate layerslayer, you have get a better visualization of multilayer virtual domain box surrounding your project structureif any.

When you start a new project in [[Planar ModuleImage:Info_icon.png|30px]], the project workspace looks empty, and there are no finite objects in itClick here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Using_EM. However, a default background structure is always present by defaultCube. Objects are defined as part of traces or embedded sets27s_Materials_List | Using EM. Once defined, you can see a list of project objects in the Cube'''Physical Structures Materials Database]]''' section of the navigation tree.

Traces and object sets For better visualization of your planar structure, [[EM.Picasso]] displays a virtual domain in a default orange color to represent part of the infinite background structure. The size of this virtual domain is a quarter wavelength offset from the largest bounding box that encompasses all the finite objects in the project workspace. You can be defined either change the size of the virtual domain or its display color from Layer Stack-up the Domain Settings dialog , which you can access either by clicking the '''Computational Domain''' [[File:domain_icon.png]] button of the '''Simulate Toolbar''', or from using the keyboard shortcut {{key|Ctrl+A}}. Keep in mind that the virtual domain is only for visualization purposes and its size does not affect the MoM simulation. The virtual domain also shows the navigation treesubstrate layers in translucent colors. If you assign different colors to your substrate layers, you have get a better visualization of multilayer virtual domain box surrounding your project structure.

In the ''<table><tr><td> [[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings''' dialog, you can add showing a new trace to the stack-up by clicking the arrow symbol on the multilayer substrate configuration.]] </td></tr></table> <table><tr><td> [[Image:PMOM9.png|thumb|280px|EM.Picasso'''Insert''' button of the s Add Substrate Layer dialog. You have to choose from '''Metal (PEC)''', '''Slot (PMC)''' or '''Conductive Sheet''' options]] </td><td> [[Image:PMOM9A. png|thumb|440px|A respective dialog opens upmicrostrip-fed, where you can enter slot-coupled patch antenna on a label and assign double-layer substrate with a color other than default ones. Once a new trace is defined, it is added, by default, to PEC ground plane in the top of middle hosting the stack-up coupling slot.]] </td></tr></table underneath the top half-space. From here, you can move the trace down to the desired location on the layer hierarchy.>

Every time you define a new trace, it is also added under the respective category in the Navigation Tree[[EM. Alternatively, you can define a new trace from the Navigation Tree Picasso]] groups objects by right clicking on one of the their trace type names and selecting '''Insert New PEC Tracetheir hierarchical location in the substrate layer stack-up...'''or '''Insert New PMC Trace...'''or '''Insert New Conductive Sheet Trace...'''A respective dialog opens up for setting trace is a group of finite-sized planar objects that have the trace same material properties. Once you close this dialog, it takes you directly to the Layer Stacksame color and same Z-up Settings dialog so that you can set coordinate. All the right position of planar objects belonging to the same metal or slot trace group are located on the same horizontal boundary plane in the layer stack-up. All the embedded objects belonging to the same embedded set lie inside the same substrate layer and have same material composition.

As soon as you start drawing geometrical objects in the project workspace{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, the Sources, Devices & Other Physical Structure section of Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Trace]]| style="width:300px;" | Modeling perfect metal traces on the Navigation Tree gets populatedinterface between two substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[File:voxel_group_icon. The names png]]| style="width:250px;" | [[Glossary of traces are added under their respective trace type categoryEM.Cube's Materials, Sources, Devices & Other Physical Object Types#Conductive Sheet Trace |Conductive Sheet Trace]]| style="width:300px;" | Modeling lossy metal traces with finite conductivity and the names of finite metallization thickness| style="width:150px;" | Only surface objects appear under their respective trace group|-| style="width:30px;" | [[File:pmc_group_icon. At any timepng]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, one Sources, Devices & Other Physical Object Types#Slot Trace |Slot Trace]]| style="width:300px;" | Modeling cut-out slot traces and only one trace is active in the project workspace. An active trace is where all the new apertures on an infinite PEC ground plane | style="width:150px;" | Only surface objects you draw belong to|-| style="width:30px;" | [[File:pec_group_icon. When you define a new tracepng]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, it is set as active Sources, Devices & Other Physical Object Types#Embedded PEC Via Set |Embedded PEC Via Set]]| style="width:300px;" | Modeling small and you can immediately start drawing new short vertical vias and plated-through holes inside substrate layers| style="width:150px;" | Only surface objects on that trace|-| style="width:30px;" | [[File:diel_group_icon. You can also set any trace active at any time by right clicking its name on the Navigation Tree and selecting 'png]]| style="width:250px;" | [[Glossary of EM.Cube''Activate''' from the contextual menus Materials, Sources, Devices & Other Physical Object Types#Embedded Dielectric Object Set |Embedded Dielectric Object Set]]| style="width:300px;" | Modeling small and short dielectric material inserts inside substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[File:Virt_group_icon. The name png]]| style="width:250px;" | [[Glossary of the active trace is always displayed in bold letter in the Navigation TreeEM.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|}

EM.Picasso has a special feature that makes construction of planar structures quite easy and straightforward. '''The active work plane of Click on each category to learn more details about it in the project workspace is always set at the plane of the active trace.''' In [[Glossary of EM.Cube]]'s other modulesMaterials, all objects are drawn in the XY plane (z = 0) by default. In [[Planar ModuleSources, Devices & Other Physical Object Types]], all new objects are drawn on a horizontal plane that is located at the Z-coordinate of the currently active trace. As you change the active trace or add a new trace, you will also change the active work plane.

You can manage your project's layer hierarchy from the Layer Stack-up Settings dialog. You can add, delete and move around substrate layers, define two types of metallic and slot traces in [[EM.Picasso]]: '''PEC Traces''' and embedded object sets'''Conductive Sheet Traces'''. Metallic and slot PEC traces can move among the interface planes represent infinitesimally thin (zero thickness) planar metal objects that are deposited or metallized on or between neighboring substrate layers. Embedded object sets including PEC vias and finite dielectric objects can move from substrate layer into anotherare modeled by surface electric currents. When you delete a trace from the Layer Stack-up Settings dialogConductive sheet traces, all of its objects are deleted from on the project workspaceother hand, toorepresent imperfect metals. You can also delete metallic They have a finite conductivity and slot traces or embedded object sets from the Navigation Treea very small thickness expressed in project units. To do so, right click A surface impedance boundary condition is enforced on the name surface of the trace or object set in the Navigation Tree and select '''Delete''' from the contextual menu. You can also delete all the traces or object sets of the same type from the contextual menu of the respective type category in the Navigation Treeconductive sheet objects.

By default, the last defined trace or embedded object set is active'''Slot Traces''' are used to model cut-out slots and apertures in PEC ground planes. You can activate any trace or embedded object set at any time for drawing new Planar slot objects. You can move one or more selected objects from any trace or embedded object set are always assumed to another group of the same type or of different type. First select lie on an object infinite horizontal PEC ground plane with zero thickness, which is not explicitly displayed in the project workspace or in the Navigation Treeand its presence is implied. ThenThey are modeled by surface magnetic currents. When a slot is excited, right click tangential electric fields are formed on the highlighted selection and select '''Move To &gt;''' from aperture, which can be modeled as finite magnetic surface currents confined to the contextual menu. This opens another sub-menu containing '''Planar''' and a list area of all the other [[EMslot.Cube]] modules that have already defined object groups. Select '''Planar''' or any In other available modulewords, and yet another sub-menu opens up with a list instead of all modeling the available traces and embedded object sets already defined in your project. Select electric surface currents on an infinite PEC ground around the desired groupslot, and all one can alternatively model the selected objects will move to that groupfinite-extent magnetic surface currents on a perfect magnetic conductor (PMC) trace. When selecting multiple Slot (PMC) objects from provide the Navigation Tree, make sure that you hold electromagnetic coupling between the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a group's name from the contextual menutwo sides of an infinite PEC ground plane.

=== Planar ModuleBesides planar metal and slot traces, [[EM.Picasso]] allows you to insert prismatic embedded objects inside the substrate layers. The height of such embedded objects is always the same as the height of their host substrate layer. Two types of embedded object sets are available: 's Rules &amp; Limitations ===''PEC Via Sets''' and '''Embedded Dielectric Sets'''. PEC via sets are metallic objects such as shorting pins, interconnect vias, plated-through holes, etc. all located and grouped together inside the same substrate layer. The embedded via objects are modeled as vertical volume conduction currents. Embedded dielectric sets are prismatic dielectric objects inserted inside a substrate layer. You can define a finite permittivity and conductivity for such objects. The embedded dielectric objects are modeled as vertical volume polarization currents.

# Terminating PEC ground planes at the top or bottom {{Note|The height of a planar structure are defined as PEC top or bottom half-spaces, respectively.# A PEC ground plane placed in the middle of a substrate stack-up requires at least one slot an embedded object is always identical to provide electromagnetic coupling between its top and bottom sides. In this case, a PMC trace is rather introduced at the given Z-plane, which implies the presence thickness of an infinite PEC ground although it is not explicitly indicated in the Navigation Tree.# Metallic and slot traces cannot coexist on the same Z-plane. However, you can stack up multiple PEC and conductive sheet traces at the same Z-coordinate. Similarly, multiple PMC traces can be placed at the same Z-coordinate.# Metallic and slot traces are strictly defined at the interface planes between substrate layers. To define a suspended metallic trace in a its host substrate layer (as in the case of the center conductor of a stripline), you must split the dielectric layer into two thinner layers and place your PEC trace at the interface between them.# The current version of the Planar MoM simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and no circumferential components are allowed on embedded objects. The 2.5-D assumption holds very well in two cases: (a) when embedded objects are very thin with a very small cross section (with lateral dimensions less than 2-5% of the material wavelength) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the top and bottom.# The current release of [[EM.Cube]] allows any number of PEC via sets collocated in the same substrate layer. However, you can define only one embedded dielectric object set per substrate layer, and no vias sets collocated in the same layer. Note that the single set can host an arbitrary number of embedded dielectric objects of the same material properties.}}

[[Image:PMOM31Embedded object sets represent short material insertions inside substrate layers.png|thumb|400px|The Planar Mesh They can be metal or dielectric. Metallic embedded objects can be used to model vias, plated-through holes, shorting pins and interconnects. These are called PEC via sets. Embedded dielectric objects can be used to model air voids, thin films and material inserts in metamaterial structures. Embedded objects can be defined either from the Layer Stack-up Settings dialogor directly from the navigation tree.]]The method Open the &quot;Embedded Sets&quot; tab of moments (MoM) discretizes all the finitestack-sized objects of up dialog. This tab has a planar structure (excluding table that lists all the background structure) into embedded object sets along with their material type, the host substrate layer, the host material and their height. To add a new object set of elementary cells. The accuracy of , click the MoM numerical solution depends greatly arrow symbol on the quality {{key|Insert}} button of the dialog and resolution select one of the generated meshtwo options, '''PEC Via Set''' or '''Embedded Dielectric Set''', from the dropdown list. As This opens up a rule new dialog where first you have to set the host layer of thumb, the new object set. A dropdown list labeled &quot;'''Host Layer'''&quot; gives a mesh density list of about 20-30 cells per effective wavelength usually yields satisfactory resultsall the available finite substrate layers. YetYou can also set the properties of the embedded object set, for structures with lots including its label, color and material properties. Keep in mind that you cannot control the height of fine geometrical details or for highly resonant structuresembedded objects. Moreover, higher mesh densities may be requiredyou cannot assign material properties to PEC via sets, while you can set values for the '''Permittivity'''(&epsilon;_r) and '''Electric Conductivity'''(&sigma;) of embedded dielectric sets. AlsoVacuum is the default material choice. To define an embedded set from the navigation tree, right-click on the particular simulation data that you seek '''Embedded Object Sets''' item in a project also influence your choice the '''Physical Structure''' section of mesh resolutionthe navigation tree and select either '''Insert New PEC Via Set. For example..''' or '''Insert New Embedded Dielectric Set...''' The respective New Embedded Object Set dialog opens up, far field characteristics like radiation patterns are less sensitive where you can set the properties of the new object set. As soon as you close this dialog, it takes you to the mesh density than field distributions Layer Stack-up Settings dialog, where you can verify the location of the new object set on a structure with a highly irregular shape and a rugged boundarythe layer hierarchy.

EM.Picasso generates two types of mesh for a planar structure<table><tr><td> [[Image: a pure triangular and a hybrid triangular-rectangular. In both case, EM.Picasso attempts to create a highly regular mesh, in which most of the cells have almost equal areas. The hybrid mesh type 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, the use of triangular cells is clearly inevitablePMOM23. png|thumb|550px|EM.Picasso's default mesh type is hybrid. The uniformity or regularity of mesh is an important factor in warranting a stable MoM numerical solutionLayer Stack-up dialog showing the Embedded Sets tab. ]] </td></tr></table> === Drawing Planar Objects on Horizontal Work Planes ===

The mesh density gives a measure of the number of cells per effective wavelength that are placed As soon as you start drawing geometrical objects in various regions of your planar structure. The higher the mesh densityproject workspace, the more cells are created on '''Physical Structure''' section of the geometrical objectsnavigation tree gets populated. Keep in mind that only the finite-sized objects The names of your structure traces are discretized. The free-space wavelength is defined as <math>\lambda_0 = \tfrac{2\pi f}{c}</math>added under their respective trace type category, where f is and the center frequency names of your project objects appear under their respective trace group. At any time, one and c only one trace is active in the speed project workspace. The name of light the active trace in the free spacenavigation tree is always displayed in bold letters. The effective wavelength An active trace is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e_eff is all the effective permittivitynew objects you draw belong to. By default, [[EM.Picasso]] generates a hybrid mesh with a mesh density of 20 cells per effective wavelength. The effective permittivity is the last defined differently for different types of traces and trace or embedded object sets. This set is to make sure that enough cells are placed in areas that might feature higher field concentrationactive. 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 You can immediately start drawing new objects on the metallic active 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 You can also set any trace. For embedded or object sets, set group active at any time by right-clicking on its name on the effective permittivity is defined as navigation tree and selecting '''Activate''' from the largest of the permittivities of all the substrate layers and embedded dielectric setscontextual menu.

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.CubeBuilding Geometrical Constructions in CubeCAD#Working_with_Mesh_Generator Transferring Objects Among Different Groups or Modules | Working with Mesh Generator Moving Objects among Different Groups]]'''.

<table><tr><td> [[Image:Info_iconPMOM23B.png|40px]] Click here to learn more about thumb|280px|EM.Picasso's '''[[Mesh_Generation_Schemes_in_EMNavigation Tree populated with planar objects.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator]]'''.</td></tr></table>

[[Image:Info_iconEM.png|40pxPicasso]] Click here to learn more about EMhas a special feature that makes construction of planar structures very convenient and straightforward.Picasso's '''[[Mesh_Generation_Schemes_in_EM<u>The horizontal Z-plane of the active trace or object set group is always set as the active work plane of the project workspace.Cube#The_Hybrid_Planar_Mesh_Generator | Hybrid Planar Mesh Generator]]'''</u> That means all new objects are drawn at the Z-coordinate of the currently active trace. As you change the active trace group or add a new one, the active work plane changes accordingly.

{{Note| In [[Image:Info_iconEM.png|40pxPicasso]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#General_Rules_of_Planar_Hybrid_Mesh_Generator| General Rules , you cannot modify the Z-coordinate of Planar Hybrid Mesh Generator]]'''an object as it is set and controlled by its host trace.}}

[[Image:Info_iconEM.png|40pxPicasso]] Click here does not allow you to learn more about draw 3D or solid CAD objects. The solid object buttons in the '''Object Toolbar''' are disabled to prevent you from doing so. In order to create vias and embedded object, you simply have to draw their cross section geometry using planar surface CAD objects. [[Mesh_Generation_Schemes_in_EMEM.Cube#Refining_the_Planar_Mesh_Locally| Refining the Planar Mesh LocallyPicasso]]extrudes and extends these planar objects across their host layer automatically and displays them as 3D wireframe, prismatic objects. The automatic extrusion of embedded objects happens after mesh generation and before every planar MoM simulation. You can enforce this extrusion manually by right-clicking the '''Layer Stack-up''' item in the "Computational Domain" section of the navigation tree and selecting '''Update Planar Structure''' from the contextual menu. {{Note| In [[EM.Picasso]], you can only draw horizontal planar surface CAD objects.}}

<td> [[Image:PMOM48FPMOM23A.png|thumb|350px620px|Geometry of A planar structure with a multilayer slottwo-coupled patch array.]] </td><td> [[Image:PMOM48G.png|thumb|370px|Hybrid planar mesh layer conductor-backed substrate, two PEC patches located at the tops of the slot-coupled lower and upper substrate layers, four PEC vias located inside the lower substrate layer between the lower patch arrayand bottom ground and an embedded dielectric film located inside the top substrate layer sandwiched between the two patches.]] </td>

<td> [[Image:PMOM48HPMOM64A.png|thumb|350px550px|Details of the hybrid A multilayer planar mesh of the slot-structure containing a CPW line with a single coupled patch array around discontinuitiesport and a lumped element on an overpassing metal strip.]] </td>

== Excitation Sources = Modeling Lumped Elements in EM.Picasso ===

Your planar structure must Lumped elements are components, devices, or circuits whose overall dimensions are very small compared to the wavelength. As a result, they are considered to be excited by some sort dimensionless compared to the dimensions of a signal source mesh cell. In fact, a lumped element is equivalent to an infinitesimally narrow gap that induces electric is placed in the path of current flow, across which the device's governing equations are enforced. Using Kirkhoff's laws, these device equations normally establish a relationship between the currents on metal parts and voltages across the device or circuit. Crossing the bridge to Maxwell's domain, the device equations must now be cast into a from o boundary conditions that relate the electric and magnetic currents on slot traces. The excitation source you choose depends on the observables you seek in your projectand fields. [[EM.Picasso provides the following source types for exciting planar structures]] allows you to define passive circuit elements:'''Resistors''' (R), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations of them.

* '''[[Common_Excitation_Source_Types_in_EMImage:Info_icon.Cube#Lumped_.26_Gap_Sources png| Gap Sources40px]]'''* Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Probe_Sources Modeling_Lumped_Elements_in_the_MoM_Solvers |Probe SourcesDefining Lumped Elements]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#De-Embedded_Sources | De-embedded Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Hertzian_Dipole_Sources |Short Dipole Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Plane_Wave_Sources | Plane Wave Sources]]'''* '''[[Hybrid_Modeling_using_Multiple_Simulation_Engines#Working_with_Huygens_Sources | Huygens Sources]]'''

For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal. Gap sources are placed across metal or slot traces. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parametersImage:Info_icon.png|40px]] can be calculated accurately. To calculate the scattering characteristics of Click here for a planar structure, e.g. its radar cross section (RCS), you excite it with a plane wave source. Short dipole sources are used to explore propagation general discussion of points sources along a layered structure. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure possibly in another '''[[EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.Cube26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]] computational module and bring them as a new source to excite your planar structure'''.

[[Image:Info_icon.png{{Note|40px]] Click here The impedance of the lumped circuit is calculated at the operating frequency of the project using the specified R, L and C values. As you change the frequency, the value of the impedance that is passed to learn more about '''[[the Planar MoM Source Types]]'''engine will change.}}

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.Cube#Defining_Finite-Sized_Source_Arrays | === Calculating Scattering Parameters Using Source Arrays for Modeling Antenna Arrays]]''Prony'.s Method ===

[[Image:PMOM64The calculation of the scattering (S) parameters is usually an important objective of modeling planar structures especially for planar circuits like filters, couplers, etc.png|thumb|600px|EMAs you saw earlier, you can use lumped sources like gaps and probes and even active lumped elements to calculate the circuit characteristics of planar structures.Picasso's Lumped Element dialogThe admittance / impedance calculations based on the gap voltages and currents are accurate at RF and lower microwave frequencies or when the port transmission lines are narrow.]]=== Modeling Lumped Elements in EMIn such cases, the electric or magnetic current distributions across the width of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized. At higher frequencies, however, a more robust method is needed for calculating the port parameters.Picasso ===

Lumped elements are components, devices, or circuits whose overall dimensions are very small compared to One can calculate the wavelength. As scattering parameters of a result, they are considered to be dimensionless compared to planar structure directly by analyzing the current distribution patterns on the dimensions port transmission lines. The discontinuity at the end of a mesh cell. In fact, port line typically gives rise to a lumped element is equivalent to an infinitesimally narrow gap standing wave pattern that is placed can clearly be discerned in the path of current flow, across which the deviceline's governing equations are enforcedcurrent distribution. Using Kirkhoff's laws, these device equations normally establish a relationship between From the currents location of the current minima and voltages across maxima and their relative levels, one can determine the device or circuit. Crossing reflection coefficient at the bridge to Maxwell's domaindiscontinuity, i.e. the device equations must now be cast into a from o boundary conditions that relate the electric and magnetic currents and fieldsS₁₁ parameter. EMA more robust technique is Prony’s method, which is used for exponential approximation of functions.Picasso allows you to define passive circuit elements: '''Resistors''' A complex function f(Rx), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations can be expanded as a sum of them. complex exponentials in the following form:

:<math> f(x) \approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math><!--[[ImageFile:Info_iconPMOM73.png|40px]] Click here to learn more about '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.Cube#Defining_Lumped_Elements_in_EM.Picasso_.26_EM.Libera | Defining Lumped Elements]]'''.-->

[[Image:Info_icon.png|40px]] Click here for a where c_i are complex coefficients and &gamma;_i are, in general discussion , complex exponents. From the physics of '''[[Modeling_Lumped_Elementstransmission lines,_Circuits_%26_Devices_in_EMwe know that lossless lines may support one or more propagating modes with pure real propagation constants (real &gamma;_i exponents).Cube| Linear Passive Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary & Nonlinear Active Devices]]'''gamma;_i exponents) that decay along the line as you move away from the location of such discontinuities.

{{Note|The impedance of In practical planar structures for which you want to calculate the lumped circuit scattering parameters, each port line normally supports one, and only one, dominant propagating mode. Multi-mode transmission lines are seldom used for practical RF and microwave applications. Nonetheless, each port line carries a superposition of incident and reflected dominant-mode propagating signals. An incident signal, by convention, is calculated at one that propagates along the operating frequency of the project using line towards the specified Rdiscontinuity, L where the phase reference plane is usually established. A reflected signal is one that propagates away from the port plane. Prony's method can be used to extract the incident and C valuesreflected propagating and evanescent exponential waves from the standing wave data. As you change From a knowledge of the frequencyamplitudes (expansion coefficients) of the incident and reflected dominant propagating modes at all ports, the value scattering matrix of the impedance that multi-port structure is passed to then calculated. In Prony's method, the Planar MoM engine will changequality of the S parameter extraction results depends on the quality of the current samples and whether the port lines exhibit a dominant single-mode behavior. Clean current samples can be drawn in a region far from sources or discontinuities, typically a quarter wavelength away from the two ends of a feed line.}}

[[Image:PMOM52.png|thumb|400px|EM.Picasso's Port Definition dialog.]]<table>[[Image:PMOM53.png|thumb|300px|The Edit Port dialog.]]<tr><td> [[Image:PMOM51(2)PMOM71.png|thumb|600px|Coupling gap sources in Minimum and maximum current locations of the Port Definition dialog by associating more than one source with standing wave pattern on a single portmicrostrip line feeding a patch antenna.]]</td></tr></table>

=== Defining Independent & Coupled Ports ===

Ports are used in a planar structure to order and index the sources for calculation of circuit [[parameters]] such as scattering (S), impedance (Z) and admittance (Y) [[parameters]]. In [[EM.Cube]]'s [[Planar ModulePicasso]], you can use one or more of the following types of sources to define ports:

Ports are defined in the '''Observables''' section of the Navigation Treenavigation tree. Right click on the '''Port Definition''' item You can define any number of ports equal to or less than the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the default port assignmentstotal number of sources in your project. If you have N sources in your planar structure, then N default ports are defined, with one port assigned to each source according to their order on the Navigation Treenavigation tree. Note that your project can have mixed gap and probes sources as well as active lumped element sourceson PEC and slot traces or vias. You can also couple ports together to define coupled transmission lines such as coupled strips (CPS) or coplanar waveguides (CPW).

'''You can define any number of ports equal [[Image:Info_icon.png|40px]] Click here to or less than learn more about the total number of sources in your project.''' The Port List of the dialog shows a list of all the ports in ascending order, with their associated sources and the port's characteristic impedance, which is 50S by default[[Glossary_of_EM. You can delete any port by selecting it from the Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port List and clicking the '''Delete''' button of the dialog. Keep in mind that after deleting a port, you will have a source in your project without any port assignment and make sure that is what you intend. You can change the characteristic impedance of a port by selecting it from the Port List and clicking the '''Edit''' button of the dialog. This opens up the Edit Port dialog, where you can enter a new value in the box labeled '''ImpedanceDefinition Observable]]'''.

[[Image:Info_icon.png|40px]] Click here to learn more about the theory of '''[[Computing Port Characteristics in Planar MoMPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Ports]]'''.

=== Modeling Coupled Ports =EM.Picasso's Simulation Data & Observables ==

Sources can be coupled to each other to model coupled strip lines (CPS) on metal traces or coplanar waveguides (CPW) Depending on slot traces. Similarlythe source type and the types of observables defined in a project, probe sources may be coupled to each other. Coupling two or more sources does not change a number of output data are generated at the way they excite end of a planar structureMoM simulation. It is intended only for the purpose Some of S parameter calculation. The feed lines or vias which host the coupled sources these data are usually parallel and aligned with one another 2D by nature and they some are all grouped together as a single transmission line represented 3D. The output simulation data generated by a single port. This single &quot;coupled&quot; port then interacts with other coupled or uncoupled ports[[EM.Picasso]] can be categorized into the following groups:

You couple two or more sources using the '''Port Definition Dialog'''{| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon. To do so, you need to change the default port assignments. First, delete all the ports that are to be coupled from the Port List png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of the dialogEM. Then, define a new port by clicking the Cube'''Add''' button of the dialog. This opens up the Add Port dialog, which consists of two tabless Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width: '''Available''' sources 300px;" | Computing electric surface current distribution on the left metal traces and '''Associated''' sources magnetic surface current distribution on the rightslot traces | style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. A right arrow (''png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-&gtField Sensor]] | style="width:300px;''') button " | Computing electric and magnetic field components on a left arrow ('''&ltspecified 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''') button let you move s Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the sources freely between these two tablesradiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. You will see in the &quot| style="width:250px;Available&quot" | None|-| style="width:30px; table a list " | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of all the sources that you deleted earlierEM. You may even see more available sources. Select all Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the sources that you want to couple bistatic and move them to the &quotmonostatic RCS of a target| style="width:250px;Associated&quot" | Requires a plane wave source|-| style="width:30px; table on the right" | [[File:port_icon. You can make multiple selections using the keyboardpng]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's '''Shift''' and '''Ctrl''' keys. Closing the Add Simulation Observables & Graph Types#Port dialog returns you to the Definition |Port Definition dialog, where you will now see ]] | style="width:300px;" | Computing the names S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of all these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:period_icon.png]]| style="width:150px;" | Periodic Characteristics| style="width:150px;" | No observable required | style="width:300px;" | Computing the coupled sources next to the name reflection and transmission coefficients of the newly added porta periodic surface| style="width:250px;" | Requires a plane wave source and periodic boundary conditions |-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}

{{Note|It is your responsibility Click on each category to set up coupled ports and coupled learn more details about it in the [[Transmission LinesGlossary of EM.Cube's Simulation Observables & Graph Types]] properly. For example, to excite the desirable odd mode of a coplanar waveguide (CPW), you need to create two rectangular slots parallel to and aligned with each other and place two gap sources on them with the same offsets and opposite polarities. To excite the even mode of the CPW, you use the same polarity for the two collocated gap sources. Whether you define a coupled port for the CPW or not, the right definition of sources will excite the proper mode. The couple ports are needed only for correct calculation of the port characteristics.}}

== Running Planar If your planar structure is excited by gap sources or probe sources or de-embedded sources, and one or more ports have been defined, the planar MoM Simulations ==engine calculates the scattering, impedance and admittance (S/Z/Y) parameters of the designated ports. The scattering parameters are defined based on the port impedances specified in the project's Port Definition dialog. If more than one port has been defined in the project, the S/Z/Y matrices of the multiport network are calculated.

The first step Electric and magnetic currents are the fundamental output data of planning a planar MoM simulation is defining your planar structure. This consists After the numerical solution of the background structure plus all the finite-sized metal and slot trace objects and possibly embedded metal or dielectric objects that MoM linear system, they are interspersed among found using the substrate layers. The background stack-up is defined in the Layer Stack-up dialog, which automatically opens up as soon as you enter the [solution vector '''[Planar ModuleI]]. The metal ''' and slot traces and embedded object sets are listed in the Navigation Tree, which also shows all definitions of the geometrical (CAD) objects you draw in the project workspace under each object group at different Z-planes.electric and magnetic vectorial basis functions:

The next step is to decide on the excitation scheme. If your planar structure has one or more ports and you seek to calculate its port characteristics, then you have to choose one of the lumped source types or a de-embedded source. If you are interested in the scattering characteristics of your planar structure, then you must define a plane wave source. Before you can run a planar MoM simulation, you also need to decide on the project's observables. These are the simulation data that you expect :<math> \mathbf{[[EM.CubeX]] to generate as the outcome of the numerical simulation. [[EM.Cube]]'s [[Planar Module]] offers the following observables:}_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math>

* Note that currents are complex vector quantities. Each electric or magnetic current has three X, Y and Z components, and each complex component has a magnitude and phase. You can visualize the surface electric currents on metal (PEC) and conductive sheet traces, surface magnetic currents on slot (PMC) traces and vertical volume currents on the PEV vias and embedded dielectric objects. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the project workspace, superimposed on the surface of physical objects. In order to view the current distributions, you must first define them as observables before running the planar MoM simulation. At the top of the Current Distribution* Field Sensors* Far Fields (Radiation Patterns dialog and in the section titled '''Active Trace / Set''', you can select a trace or Radar Cross Section)* Huygens Surfaces* Port Characteristics* Periodic Characteristicsembedded object set where you want to observe the current distribution.

If you run {{Note|You have to define a simulation without having defined any observables, no data will be generated at the end of the simulation. Some observables require a certain type of excitation source. For example, port characteristics will be calculated only if the project contains a port definition, which in turn requires the existence of at least one gap separate current distribution observable for each individual trace or probe or de-embedded source. The periodic characteristics (reflection and transmission coefficients) are calculated only if the structure has a periodic domain and excited by a plane wave sourceobject set.}}

The simplest simulation type in [[EM.CubePicasso]] is an analysis. In this mode, allows you to visualize the planar structure in your project workspace is meshed near fields at the center frequency of the projecta specific field sensor plane. Note that unlike [[EM.Cube]] generates an input file at this single frequency's other computational modules, and the Planar MoM simulation engine is run oncenear field calculations in [[EM. Upon completion Picasso]] usually takes a significant amount of time. This is due to the fact that at the end of a planar MoM simulation, a number of data files are generated depending on the observables you have defined in your projectfields are not available anywhere (as opposed to [[EM. An analysis is Tempo]]), and their computation requires integration of complex dyadic Green's functions of a single-run simulationmultilayer background structure as opposed to the free space Green's functions.

{{Note|Keep in mind that since [[EM.CubePicasso]] offers uses a number of multi-run simulation modes. In such casesplanar MoM solver, the Planar MoM simulation engine calculated field value at the source point is run multiple timesinfinite. At each engine run, certain [[parameters]] are varied and a collection of simulation data are generated. At the end of As a multi-run simulationresult, you can graph the simulation results in EM.Grid field sensors must be placed at adequate distances (at least one or you can animate the 3D simulation data few wavelengths) away from the Navigation Treescatterers to produce acceptable results. For example, in a frequency sweep, the frequency of the project is varied over its specified bandwidth. Port characteristics are usually plotted vs. frequency, representing your planar structure's frequency response. In an angular sweep, the &theta; or &phi; angle of incidence of a plane wave source is varied over their respective ranges. [[EM.Cube]]'s [[Planar Module]] currently provides the following types of multi-run simulation modes:}}

* Frequency Sweep<table>* Parametric Sweep<tr>* <td> [[OptimizationImage:PMOM116.png|thumb|left|600px|Near-zone electric field map above a microstrip-fed patch antenna.]]</td>* HDMR Sweep</tr><tr><td> [[Image:PMOM117.png|thumb|left|600px|Near-zone magnetic field map above a microstrip-fed patch antenna.]] </td></tr></table>

Even though [[File:PMOM80EM.pngPicasso]]'s MoM engine does not need a radiation box, you still have to define a &quot;Far Field&quot; observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct [[EM.Cube]] to perform these calculations. Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the &quot;Total&quot; far field. The 2D radiation pattern graphs can be plotted from the '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.

Figure 1[[Image: Selecting a simulation mode in Info_icon.png|30px]] Click here to learn more about the theory of '''[[Planar ModuleDefining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'s Simulation Run dialog''.

To run When a planar MoM analysis of your project structureis excited by a plane wave source, open the Run Simulation Dialog by clicking calculated far field data indeed represent the '''Run''' scattered fields of that planar structure. [[File:run_iconEM.pngPicasso]] button on can also calculate the '''Simulate Toolbar''' or select '''Menu''' '''radar cross section (RCS) of a planar target. Note that in this case the RCS is defined for a finite-sized target in the presence of an infinite background structure. The scattered &gttheta;''' '''Simulate and &gtphi;''' '''Run''' or use the keyboard shortcut '''Ctrl+R'''. The '''Analysis''' option components of the '''Simulation Mode''' dropdown list is selected by default. Once far-zone electric field are indeed what you click see in the '''Run''' button, the simulation starts. A new window, called the '''Output Window''', opens up that reports the different stages 3D far field visualization of simulation and the percentage of the tasks completed at any timeradiation (scattering) patterns. After the simulation is successfully completed, a message pops up and reports the end Instead of simulation. In certain cases like calculating radiation or scattering patterns, you can instruct [[parametersEM.Picasso]] to plot 3D visualizations of a circuit or reflection &sigma;<sub>&theta;</ transmission characteristics of a periodic surfacesub>, some results are also reported in the Output Window. At the end of a simulation, you need to click the '''Close''' button of the Output Window to return to &sigma;_&phi; and the project workspacetotal RCS.

<table><tr><td> [[FileImage:PMOM78PMOM125.png|thumb|left|600px|An example of the 3D monostatic radar cross section plot of a patch antenna.]]</td></tr></table>

Figure 1: [[== Discretizing a Planar Module]]'s Simulation Run dialogStructure in EM.Picasso ==

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

<table><tr><td> [[EMImage:PMOM31.png|thumb|400px|The Planar Mesh Settings dialog.Cube]]'s Planar MoM simulation engine uses a particular formulation of the method of moments called mixed potential integral equation (MPIE). Due to high-order singularities, the dyadic Green's functions for electric fields generated by electric currents as well as the dyadic Green's functions for magnetic fields generated by magnetic currents have very slow convergence behaviors. Instead of using these slowly converging dyadic Green's function, the MPIE formulation uses vector and scalar potentials. These include vector electric potential '''A(r)''', scalar electric potential K<sup/td>&Phi;</suptr>'''(r)''', vector magnetic potential '''F(r)''' and scalar magnetic potential K<sup>&Psi;</suptable>'''(r)'''. These potentials have singularities of lower orders. As a result, they coverage relatively faster. The speed of their convergence is further increased drastically using special singularity extraction techniques.

A EM.Picasso provides two types of mesh for a planar MoM simulation consists of two major stagesstructure: matrix fill a pure triangular surface mesh and linear system inversiona hybrid triangular-rectangular surface mesh. In the first stageboth case, the moment matrix and excitation vector are calculatedEM. In the second stagePicasso attempts to create a highly regular mesh, the MoM system of linear equations is inverted using one in which most of the several available matrix solvers to find the unknown coefficients of all the basis functionscells have almost equal areas. The unknown electric and magnetic currents are linear superpositions of all these elementary solutions. These can be visualized in [[EM.Cube]] using the current distribution observables. Having determined all the electric and magnetic currents in your For planar structurestructures with regular, mostly rectangular shapes, [[EM.Cube]] can then calculate the near fields on prescribed planes. These are introduced as field sensor observables. The near-zone electric and magnetic fields are calculated using a spectral domain formulation of the dyadic Green's functions. Finally the far fields of the planar structure are calculated in the spherical coordinate system. These calculations are performed using the asymptotic form of the dyadic Green's functions using the &quot;stationary phase method&quot;hybrid mesh generator usually leads to faster computation times.

A planar MoM simulation involves a number of numerical [[parameters]] that take preset default values unless you change themImage:Info_icon. You can access these [[parameterspng|30px]] and change their values by clicking the '''Settings''' button next Click here to the learn more about '''Select Engine''' dropdown list in the [[Planar Module]]Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Picasso's Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the default numerical parameter values intact. However, it is useful to familiarize yourself with these [[parametersTriangular Surface Mesh Generator]], as they may affect the accuracy of your numerical results'''.

The Planar MoM Engine Settings Dialog is organized in a number of sections. Here we describe some of the numerical <table><tr><td> [[parameters]]Image:PMOM48F. The &quot;'''Matrix Fill'''&quot; section png|thumb|left|420px|Geometry of the dialog deals with the operations involving the dyadic Green's functions. You can set a value for the '''Convergence Rate for Integration''', which is 1Emultilayer slot-5 by defaultcoupled patch array. This is used for the convergence test of all the infinite integrals in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, the surface wave poles are captured in the complex integration plane using contour deformation. You can change the maximum number of iterations involved in this deformed contour integration, whose default value is 20. When the substrate is very thin with respect to the wavelength, the dyadic Green's functions exhibit numerical instability. Additional singularity extraction measures are taken to avoid numerical instability but at the expense of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01&lambda;]] <sub/td>eff</subtr>, where &lambda;<subtr>eff</subtd> is the effective wavelength[[Image:PMOM48G. You can modify the definition png|thumb|left|420px|Hybrid planar mesh of &quot;Thin Substrate&quot; by entering a value for '''Thin Substrate Threshold''' different than the default 0.01. The parameter '''Max Coupling Range''' determines the distance threshold in wavelength between the observation and source points after which the Green's interactions are neglected. This distance by default is set to 1,000 wavelengths. For electrically small structures, the phase variation across the structure may be negligible. In such cases, a fast quasislot-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''coupled patch array.]] </td></tr></table>

In the &quot;Spectral Domain Integration&quot; section of the dialog, you can set a value to '''Max Spectral Radius in k0''', which has a default value of 30. This means that the infinite spectral-domain integrals in the spectral variable k<subtable>&rho;</subtr> are pre-calculated and tabulated up to a limit of 30k<subtd>0</sub>, where k₀ is the free space propagation constant[[Image:PMOM48H. These integrals may converge much faster based on png|thumb|left|420px|Details of the specified Convergence Rate for Integration described earlier. However, in certain cases involving highly oscillatory integrands, much larger integration limits like 100k₀ might be needed to warrant adequate convergence. For spectral-domain integration along hybrid planar mesh of the real k_&rho; axis, the interval [0, Nk₀] is subdivided into a large number of subslot-intervals, within each an 8-point Gauss-Legendre quadrature is appliedcoupled patch array around discontinuities. The next parameter, '''No. Radial Integration Divisions per k<sub>0]] </subtd>''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k<sub>0</subtr>]. In other words, the length of each integration sub-interval is k<sub>0</subtable>/2. You can increase the resolution of integration by increasing this value above 2. Finally, instead of 2D Cartesian integration in the spectral domain, a polar integration is performed. You can set the '''No. of Angular Integration Points''', which has a default value of 100.

Figure 1: The Planar MoM Engine Settings dialogEM.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} === Planar Module's Linear System Solvers ===\tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e_eff 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.

After * For PEC and conductive sheet traces, the MoM impedance matrix '''[Z]''' (not to be confused with effective permittivity is defined as the impedance [[parameters]]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 excitation vector '''[V]''' have been computed through below the matrix fill processmetallic trace. * For embedded object sets, the planar MoM simulation engine effective permittivity is ready to solve defined as the system largest of linear equations:the permittivities of all the substrate layers and embedded dielectric sets.

:<mathtable><tr><td> \mathbf{[Z]}_{N\times N} \cdot \mathbf{[IImage:PMOM32.png|thumb|360px|A comparison of triangular and planar hybrid meshes of a rectangular patch.]}_{N\times 1} = \mathbf{[V]}_{N\times 1} </mathtd><!--td> [[FileImage:PMOM81PMOM30.png|thumb|360px|Mesh of two rectangular patches at two different substrate planes. The lower substrate layer has a higher permittivity.]]--</td></tr></table>

where '''[I]''' is the solution vector, which contains the unknown amplitudes === General Rules of all the basis functions that represent the unknown electric and magnetic currents of finite extents in your planar structure. In the above equation, N is the dimension of the linear system and equal to the total number of basis functions in the planar mesh. [[EM.Cube]]'s linear solvers compute the solution vector'''[I]''' of the above system. You can instruct [[EM.Cube]] to write the MoM matrix and excitation and solution vectors into output data files for your examination. To do so, check the box labeled &quot;'''Output MoM Matrix and Vectors'''&quot; in the Matrix Fill section of the Planar MoM Engine Settings dialog. These are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectively.Hybrid Mesh Generator ===

There are a large number The integrity of numerical methods for solving systems of linear equations. These methods are generally divided into two groups: direct solvers the planar mesh and iterative solvers. Iterative solvers are usually based on matrix-vector multiplications. Direct solvers typically work faster for matrices its continuity in the junction areas directly affects the quality and accuracy of smal to medium size (N&lt;3,000)the simulation results. [[EM.Cube]]Picasso's [[Planar Module]] offers five linear solvershybrid planar mesh generator has some rules that are catered to 2.5-D MoM simulations:

# LU Decomposition Method* If two connected rectangular objects have the same side dimensions along their common linear edge with perfect alignment, a rectangular junction mesh is produced.# Biconjugate Gradient Method (BiCG)* If two connected rectangular objects have different side dimensions along their common linear edge or have edge offset, a set of triangular cells is generated along the edge of the object with the larger side.# Preconditioned Stabilized Biconjugate Gradient Method (BCG* Rectangle strip objects that host a gap source or a lumped element always have a rectangular mesh around the gap area.* If two objects reside on the same Z-STAB)plane, belong to the same trace group and have a common overlap area, they are first merged into a single object for the purpose of meshing using the &quot;Boolean Union&quot; operation. # Generalized Minimal Residual Method (GMRES)# Transpose* Embedded objects have prismatic meshes along the Z-Free Quasi-Minimum Residual Method (TFQMR)axis.* If an embedded object is located underneath or above a metallic trace object or connected from both top and bottom, it is meshed first and its mesh is then reflected on all of its attached horizontal trace objects.

<table><tr><td> [[EMFile:PMOM36.Cubepng|250px]]'s [[Planar ModuleFile:PMOM38.png|250px]], by default, provides a &quot;'''Automatic'''&quot; solver option that picks the best method based on the settings [[File:PMOM37.png|250px]] </td></tr><tr><td> Two overlapping planar objects and size of the numerical problem. For linear systems with a size less than N = 3,000, the LU solver is used. For larger systems, BiCG is used when dealing with symmetric matrices, and GMRES is used for asymmetric matrices. If the size comparison of the linear system exceeds N = 15,000, the sparse version of the iterative solvers is used, utilizing a row-indexed sparse storage scheme. You can override the automatic solver option their triangular and manually set you own solver typehybrid planar meshes. This is done using the '''Solver Type''' dropdown list in the &quot;'''Linear System Solver'''&quot; section of the Planar MoM Engine Settings dialog</td></tr><tr><td> [[File:PMOM33. There are also a number of other png|250px]] [[parametersFile:PMOM35.png|250px]] related to the solvers. The default value of '''Tolerance of Iterative Solver''' is 1E-3, which can be increased for more ill-conditioned systems. The maximum number of iterations is usually expressed as a multiple of the systems size. The default value of '''Max No. of Solver Iterations / System Size''' is 3. For extremely large systems, sparse versions of iterative solvers are used. In this case, the elements of the matrix are thresholded with respect to the larges element. The default value of '''Threshold for Sparse Solver''' is 1E-6, meaning that all the matrix elements whose magnitude is less than 1E-6 times the large matrix elements are set equal to zero. There are two more [[parametersFile:PMOM34.png|250px]] that are related to the Automatic Solver option. These are &quot;''' User Iterative Solver When System Size &gt;'''&quot; with a default value of 3,000 </td></tr><tr><td> Edge-connected rectangular planar objects and &quot;''' Use SParse Storage When System Size &gt;''' &quot; with a default value of 15,000. In other words, you control the automatic solver when to switch between direct comparison their triangular and iterative solvers and when to switch to the sparse version of iterative solvershybrid planar meshes.</td></tr></table>

If your computer has an Intel CPU, then <table><tr><td> [[EMFile:PMOM39.Cubepng|375px]] offers special versions of all the above linear solvers that have been optimized for Intel CPU platforms. These optimal solvers usually work 2-3 time faster than their generic counterparts. When you install [[EMFile:PMOM40.Cubepng|375px]], the option to use Intel-optimized solvers is already enabled. However, you can disable this option (e.g. if your computer has a non-Intel CPU). To do that, open the [[EM.Cube]]'s Preferences Dialog from '''Menu &gt; Edit &gt; Preferences''' or using the keyboard shortcut '''Ctrl+H'''. Select the Advanced tab </td></tr><tr><td> Meshes of the dialog short and uncheck the box labeled &quot;''' Use Optimized Solvers for Intel CPU'''&quot;long vertical PEC vias connecting two horizontal metallic strips.</td></tr></table>

[[Image:PMOM127It is very important to apply the right mesh density to capture all the geometrical details of your planar structure.png|thumb|400px|Settings adaptive frequency sweep parameters in EM.Picasso's Frequency Settings Dialog.]]=== Running Uniform 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 Adaptive Frequency Sweeps ===PEC vias, as well as the areas around gap sources and lumped elements, which create voltage or current discontinuities.

In a frequency sweep, the operating frequency of The Planar Mesh Settings dialog gives a few options for customizing your planar structure is varied during each sweep run. [[EM.Cube]]'s [[Planar Module]] offers two types of frequency sweep: Uniform mesh around geometrical and Adaptivefield discontinuities. In a uniform frequency sweep, The check box labeled &quot;'''Refine Mesh at Junctions'''&quot; increases the frequency range and mesh resolution at the number of frequency samples are specifiedconnection area between rectangular objects. The samples check box labeled &quot;'''Refine Mesh at Gap Locations'''&quot; might be particularly useful when gap sources or lumped elements are equally spaced over the frequency rangeplaced on a short transmission line connected from both ends. At The check box labeled &quot;'''Refine Mesh at Vias'''&quot; increases the end of each individual frequency run, mesh resolution on the output data are collected cross section of embedded object sets and stored. At at the end connection regions of the frequency sweep, metallic objects connected to them. EM.Picasso typically doubles the 3D data can be visualized and/or animated, and mesh resolution locally at the 2D data can be graphed in discontinuity areas when the respective boxes are checked. You should always visually inspect EM.GridPicasso's default generated mesh to see if the current mesh settings have produced an acceptable mesh.

To run a uniform frequency sweep, open the '''Simulation Run Dialog''', and select the '''Frequency Sweep''' option from the dropdown list labeled '''Simulation Mode'''Sometimes EM. When you choose the frequency sweep option, the Picasso'''Settings''' button next s default mesh may contain very narrow triangular cells due to the simulation mode dropdown list becomes enabledvery small angles between two edges. Clicking this button opens In some rare cases, extremely small triangular cells may be generated, whose area is a small fraction of the '''Frequency Settings''' dialogaverage mesh cell. The '''Frequency Range'''is initially set equal to your project's center frequency minus and plus half bandwidth. But you can change These cases typically happen at the values of '''Start Frequency'''junctions and '''End Frequency''' as well as other discontinuity regions or at the '''Number boundary of Samples'''highly irregular geometries with extremely fine details. The dialog offers two options for '''Frequency Sweep Type''': '''Uniform''' In such cases, increasing or '''Adaptive'''. Select the former type. It is very important to note that in a MoM simulation, changing the frequency results in a change of the mesh of the structure, too. This is because decreasing the mesh density is defined in terms of the number of by one or few cells per effective wavelengthoften resolves that problem and eliminates those defective cells. By defaultNonetheless, during a frequency sweep, [[EM.Cube]] fixes the Picasso's planar mesh density at generator offers an option to identify the highest frequency, idefective triangular cells and either delete them or cure them.eBy curing we mean removing a narrow triangular cell and merging its two closely spaced nodes to fill the crack left behind., at EM.Picasso by default deletes or cures all the &quot;End Frequency&quot;triangular cells that have angles less than 10º. This usually results Sometimes removing defective cells may inadvertently cause worse problems in a smoother frequency responsethe mesh. You have the option may choose to fix disable this feature and uncheck the mesh at the center frequency of the project or let [[EM.Cube]] box labeled &quot;remesh'''Remove Defective Triangular Cells'''&quot; the planar structure at each frequency sample during a frequency sweep. You can make one of these three choices using the radio button in the '''Planar Mesh Settings''' section of the dialog. Closing the Frequency Settings dialog returns you to the Simulation Run dialog, where you You can start also change the planar MoM frequency sweep simulation by clicking value of the '''Run''' buttonminimum allowable cell angle.

Frequency sweeps are often performed to study the frequency response of {{Note| Narrow, spiky triangular cells in a planar structure. In particular, the variation of scattering [[parameters]] like S₁₁ (return loss) and S₂₁ (insertion loss) with frequency mesh are of utmost interestgenerally not desirable. When analyzing resonant structures like patch antennas or planar filters over large frequency ranges, you may have to sweep a large number You should get rid of frequency samples to capture their behavior with adequate details. The resonant peaks the either by changing the mesh density or notches are often missed due to using the lack of enough resolution. [[EM.Cube]]hybrid planar mesh generator's [[Planar Module]] offers a powerful adaptive frequency sweep option for this purpose. It is based on the fact that the frequency response of a physical, causal, multiport network can be represented mathematically using a rational function approximation. In other words, the S [[parameters]] of a circuit exhibit a finite number of poles and zeros over a given frequency range. [[EM.Cube]] first starts with very few frequency samples and tries to fit rational functions of low orders to the scattering [[parameters]]. Then, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, all the possible rational functions of higher orders are tried out. The process continues until adding new intermediate frequency samples does not improve the resolution of the &quot;S_ij&quot; curves over the given frequency range. In that case, the curves are considered as having convergedadditional mesh refinement options.}}

You must have defined one <table><tr><td> [[Image:PMOM44.png|thumb|left|480px|Deleting or more ports for your planar structure run an adaptive frequency sweep. Open the Frequency Settings dialog from the Simulation Run dialog and select the '''Adaptive''' option of '''Frequency Sweep Type'''. You have to set values for '''Minimum Number of Samples''' and '''Maximum Number of Samples'''. Their default values are 3 and 9, respectively. You also set a value for the '''Convergence Criterion''', which has a default value of 0.curing defective triangular cells: Case 1. At each iteration cycle, all the S [[parameters]] are calculated at the newly inserted frequency samples, and their average deviation from the curves of the last cycle is measured as an error. When this error falls below the specified convergence criterion, the iteration is ended. If </td></tr><tr><td> [[EMImage:PMOM42.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 2.Cube]] reaches the specified maximum number of iterations and the convergence criterion has not yet been met, the program will ask you whether to continue the process or exit it and stop.</td></tr></table>

{{Note|For large frequency ranges, you may have to increase both the minimum and maximum number of samples== Running Planar MoM Simulations in EM. Moreover, remeshing the planar structure at each frequency may prove more practical than fixing the mesh at the highest frequency.}}Picasso ==

== Working with = EM.Picasso 's Simulation Data Modes ===

[[Image:PMOM130.png|thumb|400px|Changing the graph type by editing a data file's propertiesEM.Picasso]]=== EM.Picasso's Output Simulation Data ===offers five Planar MoM simulation modes:

Depending on the source type and the types {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of observables defined in Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a project, a number of output data are generated Single-Frequency Planar MoM Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the end center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of a the planar MoM simulationsolver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. Some Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of these data are 2D by nature and some are 3Done 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. The output simulation data generated by EMCube#Performing_Optimization_in_EM.Picasso can be categorized into 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 following groupscenter frequency fc| style="width:80px;" | None|}

* '''Port Characteristics''': S, Z and Y You can set the simulation mode from [[ParametersEM.Picasso]] and Voltage Standing Wave Ratio (VSWR)* '''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), Fronts "Simulation Run Dialog". A single-tofrequency analysis is a single-Back Ratio (FBR)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, etcno data will be generated at the end of the simulation.* '''Scattering Characteristics''': BiIn multi-static run simulation modes, certain parameters are varied and Mono-static Radar Cross Section (RCS)* '''Periodic Characteristics''': Reflection and Transmission Coefficients* '''Current Distributions''': Electric and magnetic current amplitude and phase on all metal and slot traces and embedded objects* '''Near-Field Distributions''': Electric and magnetic field amplitude and phase on specified planes and their central axesa 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.

=== Examining Port Characteristics Running a Single-Frequency Planar MoM Analysis === A single-frequency analysis is the simplest type of [[EM.Picasso]] simulation and involves the following steps:

If * Set the units of your planar structure is excited by gap sources or probe sources or de-embedded sources, project and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y) [[parameters]] frequency of operation. Note that the designated portsdefault project unit is '''millimeter'''. The scattering * Define you background structure and its layer properties and trace types. * Construct your planar structure using [[parametersBuilding_Geometrical_Constructions_in_CubeCAD | CubeCAD]] are defined based on 's drawing tools to create all the port impedances specified in finite-sized metal and slot trace objects and possibly embedded metal or dielectric objects that are interspersed among the substrate layers.* Define an excitation source and observables for your project's Port Definition dialog. If more than one port has been defined in * Examine the projectplanar mesh, verify its integrity and change the S/Z/Y matrices of mesh density if necessary.* Run the multiport network are calculatedPlanar MoM simulation engine.* Visualize the output simulation data.

At the end of To run a planar MoM simulationanalysis of your project structure, open the values of S/Z/Y Run Simulation Dialog by clicking the '''Run''' [[parametersFile:run_icon.png]] and VSWR data are calculated and reported in button on the output message window'''Simulate Toolbar''' or select '''Menu > Simulate > Run''' or use the keyboard shortcut {{key|Ctrl+R}}. The S, Z and Y [[parameters]] are written into output ASCII data files '''Single-Frequency Analysis''' option of complex type with a &quot;the '''.CPXSimulation Mode'''&quot; extensiondropdown list is selected by default. Every file begins with a header consisting of a few comment lines that start with Once you click the &quot;#&quot; symbol{{key|Run}} button, the simulation starts. The complex values are arranged into two columns for A new window called the real "Output Window" opens up that reports the different stages of simulation and imaginary parts. In the case of multiport structures, every single element percentage of the S/Z/Y matrices tasks completed at any time. After the simulation is written into successfully completed, a separate complex data filemessage pops up and reports the end of simulation. For example, you will have data files In certain cases like S11.CPX, S21.CPX, ..., Z11.CPX, Z21.CPX, etc. The VSWR data are saved to an ASCII data file calculating scattering parameters of real type with a &quot;'''.DAT'''&quot; extension calledcircuit or reflection / transmission characteristics of a periodic surface, VSWR.DATsome results are also reported in the output window.

If you run an analysis, the port characteristics have single complex values, which you can view using <table><tr><td> [[EMImage:Picasso L1 Fig18.Cube]]'s data manager. However, there are no curves to graph. You can plot the S/Z/Y [[parameters]] and VSWR data when you have data sets, which are generated at the end of any type of sweep including a frequency sweep. In that case, the &quot;.CPX&quot; files have multiple rows corresponding to each value of the sweep parameter (e.g. frequency). [[png|thumb|left|480px|EM.Cube]]Picasso's 2D graph data are plotted in EMSimulation Run dialog.Grid, a versatile graphing utility. You can plot the port characteristics directly from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]].</td></tr></table>

[[Image:Info_iconA planar MoM simulation involves a number of numerical parameters that take preset default values unless you change them.png|40px]] Click here You can access these parameters and change their values by clicking the '''Settings''' button next to learn more about the '''Select Engine''' drop-down list in [[Data_Visualization_and_Processing#Graphing_Port_Characteristics | Graphing Port CharacteristicsEM.Picasso]]'''s Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the default numerical parameter values intact. However, it is useful to familiarize yourself with these parameters, as they may affect the accuracy of your numerical results.

[[Image:Info_iconThe Planar MoM Engine Settings Dialog is organized in a number of sections.png|40px]] Click here to learn more about Here we describe some of the numerical parameters. The &quot;'''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation Matrix Fill'''&quot; section of Scattering Parameters]]the dialog deals with the operations involving the dyadic Green's functions. You can set a value for the '''Convergence Rate for Integration''', which is 1E-5 by default. This is used for the convergence test of all the infinite integrals in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, the surface wave poles are captured in the complex integration plane using contour deformation. You can change the maximum number of iterations involved in this deformed contour integration, whose default value is 20. When the substrate is very thin with respect to the wavelength, the dyadic Green's functions exhibit numerical instability. Additional singularity extraction measures are taken to avoid numerical instability but at the expense of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01&lambda;_eff, where &lambda;_eff is the effective wavelength. You can modify the definition of &quot;Thin Substrate&quot; by entering a value for '''Thin Substrate Threshold''' different than the default 0.01. The parameter '''Max Coupling Range''' determines the distance threshold in wavelength between the observation and source points after which the Green's interactions are neglected. This distance by default is set to 1,000 wavelengths. For electrically small structures, the phase variation across the structure may be negligible. In such cases, a fast quasi-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''.

Electric and magnetic currents are the fundamental output data of [[EM.Picasso]] provides a planar MoM simulation. After the numerical solution large selection of the MoM linear systemsolvers including both direct and iterative methods. [[EM.Picasso]], they are found using the solution vector by default, provides a &quot;'''[I]Automatic''' and &quot; solver option that picks the definitions best method based on the settings and size of the electric and magnetic vectorial basis functions: :<math> \mathbf{[X]}_{numerical problem. For linear systems with a size less than N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math><!--[[File:PMOM833,000, the LU solver is used.png]]--> Note that currents are complex vector quantities. Each electric or magnetic current has three XFor larger systems, Y and Z componentsBiCG is used when dealing with symmetric matrices, and each complex component has a magnitude and phaseGMRES is used for asymmetric matrices. You can visualize instruct [[EM.Cube]] to write the surface electric currents on metal (PEC) MoM matrix and conductive sheet traces, surface magnetic currents on slot (PMC) traces excitation and vertical volume currents on the PEV vias and embedded dielectric objectssolution vectors into output data files for your examination. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the project workspaceTo do so, superimposed on check the surface of physical objects. In order to view the current distributions, you must first define them as observables before running the planar MoM simulation. At the top of the Current Distribution dialog and in the section titled box labeled &quot;'''Active Trace / SetOutput MoM Matrix and Vectors''', you can select a trace or embedded object set where you want to observe &quot; in the Matrix Fill section of the current distributionPlanar MoM Engine Settings dialog.  {{Note|You have to define a separate current distribution observable for each individual trace or embedded object setThese are written into three files called mom.}} [[Image:Info_icondat1, exc.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''dat1 and soln.dat1, respectively.

<td> [[Image:PMOM84PMOM79.png|thumb|300pxleft|720px|EM.Picasso's Current Distribution Planar MoM Engine Settings dialog.]] </td><td> [[Image:PMOM85(1).png|thumb|420px|The current distribution map of a patch antenna.]] </td>

=== Visualizing the Near Fields =Modeling Periodic Planar Structures in EM.Picasso == [[EM.Picasso]] allows you to simulate doubly periodic planar structures with periodicities along the X and Y directions. Once you designate your planar structure as periodic, [[EM.Picasso]]'s Planar MoM simulation engine uses a spectral domain solver to analyze it. In this case, the dyadic Green's functions of periodic planar structure take the form of doubly infinite summations rather than integrals.  [[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Method_of_Moments#Periodic_Planar_MoM_Simulation | Periodic Green's functions]]'''.

[[File:PMOM90.png|thumb|320px{{Note|[[Planar Module]]'s Field Sensor dialog.]] EM.Picasso allows you to visualize the near fields at a specific field sensor plane. Note that unlike [[EM.Cube]]'s other computational modules, near field calculations in EM.Picasso usually takes a significant amount of time. This is due to the fact that at the end of a planar MoM simulation, the fields are not available anywhere (as opposed to [[EM.Tempo]]), can handle both regular and their computation requires integration of complex dyadic Green's functions of a multilayer background structure as opposed to the free space Green's functionsskewed periodic lattices.}}

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | === Defining a Field Sensor Observable]]'''Periodic Structure in EM.Picasso ===

An infinite periodic structure in [[Image:Info_iconEM.png|40pxPicasso]] Click here to learn more about is represented by a &quot;'''Periodic Unit Cell'''&quot;. To define a periodic structure, you must open [[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field MapsEM.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.

<td> [[Image:PMOM116PMOM99.png|thumb|360px300px|Near-zone electric field map above a microstrip-fed patch antennaEM.]] </td><td> [[Image:PMOM117.png|thumb|360px|Near-zone magnetic field map above a microstrip-fed patch antennaPicasso's Periodicity Settings dialog.]] </td>

=== Computing Radiation Pattern 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 Planar Structures ===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.

Even though EM.Pplanar MoM engine does not need a radiation box, you still have to define a &quot;Far Field&quot; observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct <table><tr><td> [[EMImage:image122.Cube]] to perform these calculations. Once png|thumb|400px|Modeling a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the &quot;Total&quot; far field. The 2D radiation pattern graphs can be plotted from the '''Data Manager'''. A total periodic screen using two different types of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cutsunit cell.]] </td></tr></table>

<table><tr><td> [[Image:Info_iconpmom_per5_tn.png|40pxthumb|300px|The PEC cross unit cell.]] Click here to learn more about the theory of '''</td><td> [[Computing_the_Far_Fields_%26_Radiation_CharacteristicsImage:pmom_per6_tn.png| Far Field Computations]]''thumb|300px|Planar mesh of the PEC cross unit cell. Note the cell extensions at the unit cell's boundaries.]] </td></tr></table>

[[Image:Info_icon.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 ]]'''=== Exciting Periodic Structures as Radiators in EM.Picasso ===

[[Image:Info_iconWhen a periodic planar structure is excited using a gap or probe source, it acts like an infinite periodic phased array.png|40px]] Click here All the periodic replicas of the unit cell structure are excited. You can even impose a phase progression across the infinite array to learn more about steer its beam. You can do this from the property dialog of the gap or probe source. At the bottom of the '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Planar Gap Circuit Source Dialog''' or '''Gap Source Dialog''', there is a button titled '''Periodic Scan...'''. You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the radiation patterns of a beam-steered antenna array, you have to define a finite-sized array factor in the Radiation Patterns]]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:Info_iconPeriod5.png|40pxthumb|350px|Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] Click here to learn more about '''</td><td> [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs Image:Period5_ang.png| Plotting 2D Radiation Graphsthumb|350px|Setting the beam scan angles in Periodic Scan Angles dialog.]]</td></tr><tr><td> [[Image:Period6.png|thumb|350px|Setting the array factor in EM.Picasso'''s Radiation Pattern dialog.]] </td></tr></table>

<td> [[FileImage:PMOM118Period7.png|thumb|300px360px|EM.Picasso's Radiation Pattern dialogpattern of an 8×8 finite-sized periodic printed dipole array with 0&deg; phi and theta scan angles.]] </td><td> [[Image:PMOM119Period8.png|thumb|420px360px|3D polar radiation Radiation pattern plot of a microstripbeam-steered 8×8 finite-fed patch antennasized periodic printed dipole array with 45&deg; phi and theta scan angles.]] </td>

=== Radar Cross Section of Planar Exciting Periodic Structures Using Plane Waves in EM.Picasso ===

When a periodic planar structure is excited by using a plane wave source, it acts as a periodic surface that reflects or transmits the calculated far field data indeed represent the scattered fields of that planar structureincident wave. [[EM.Picasso]] can also calculate calculates the radar cross section (RCS) reflection and transmission coefficients of a periodic planar targetstructures. Note that in this case the RCS is defined for If you run a finitesingle-sized target frequency plane wave simulation, the reflection and transmission coefficients are reported in the presence Output Window at the end of an infinite background structurethe simulation. The scattered &theta; and &phi; components Note that these periodic characteristics depend on the polarization of the far-zone electric field are indeed what you see in incident plane wave. You set the 3D far field visualization of radiation polarization (scatteringTMz or TEz) patternsin the '''Plane Wave Dialog''' when defining your excitation source. Instead of radiation or scattering patterns, In this dialog you can instruct [[EMalso set the values of the incident '''Theta''' and '''Phi''' angles.Picasso]] to plot 3D visualizations At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called &sigmaquot;_{reflection.CPX&thetaquot;}, and &sigmaquot;_{transmission.CPX&phiquot;} and the total RCS.

{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[Image:Info_iconEM.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCSPicasso]]'''computes the reflection and transmission coefficients of the layered background structure of your project.}}

<table><tr><td>[[Image:Info_iconPMOM102.png|40pxthumb|580px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]] Click here to learn more about '''</td></tr></table> === Running a Periodic MoM Analysis === You run a periodic MoM analysis just like an aperiodic MoM simulation from [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS GraphsEM.Picasso]]'s Run Dialog. Here, too, you can run a single-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you can define several observables for your project. If you open the Planar MoM Engine Settings dialog, you will see a section titled "Infinite Periodic Simulation". In this section, you can set the number of Floquet modes that will be computed in the periodic Green''s function summations. By default, the numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a total of 2500 Floquet terms will be computed for each periodic MoM simulation.

<td> [[File:PMOM124.png|thumb|300px|EM.Picasso's Radar Cross Section dialog]] </td><td> [[Image:PMOM125PMOM98.png|thumb|420px600px|An example Changing the number of Floquet modes from the 3D mono-static radar cross section plot of a patch antennaPlanar MoM Engine Settings dialog.]] </td>

You learned earlier how to use [[EM.Cube]]'s powerful, adaptive frequency sweep utility to study the frequency response of a planar structure. Adaptive frequency sweep uses rational function interpolation to generate smooth curves of the scattering parameters with a relatively small number of full-wave simulation runs in a progressive manner. Therefore, you need a port definition in your planar structure to be able to run an adaptive frequency sweep. This is clear in the case of an infinite periodic phased array, where your periodic unit cell structure must be excited using either a gap source or a probe source. You run an adaptive frequency sweep of an infinite periodic phased array in exactly the same way to do for regular, aperiodic, planar structures. [[EM.Cube]]'s Planar Modules also allows you to run an adaptive frequency sweep of periodic surfaces excited by a plane wave source. In this case, the planar MoM engine calculates the reflection and transmission coefficients of the periodic surface. Note that you can conceptually consider a periodic surface as a two-port network, where Port 1 is the top half-space and Port 2 is the bottom half-space. In that case, the reflection coefficient R is equivalent to S<psub>11</sub> 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°&nbsplt;&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 S<sub>22</psub>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]]'''.--> <br /> <hr> [[Image:Top_icon.png|48px30px]] '''[[EM.Picasso#An_EM.Picasso_Primer Product_Overview | Back to the Top of the Page]]''' [[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Tutorial Gateway]]'''

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