[[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]]'''Â [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== EM.Picasso in a Nutshell ===
[[Image:PMOM14EM.png|thumb|400px|A typical planar layered structurePicasso]]EM.Picasso<sup>®</sup> is a versatile planar structure simulator for modeling and design of printed antennas, planar microwave circuits, and layered periodic structures. [[EM.Picasso]]'s simulation engine is based on a 2.5-D full-wave Method of Moments (MoM) formulation that provides the ultimate modeling accuracy and computational speed for open-boundary multilayer structures. It can handle planar structures with arbitrary numbers of metal layouts, slot traces, vertical interconnects and lumped elements interspersed among different substrate layers.
{{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 Maxwellâs 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 ===
<ul> <li> Multilayer stack-up with unlimited number of substrate layers and trace planes</li> <li> PEC and conductive sheet traces for modeling ideal and non-ideal metallic layouts</li> <li> PMC traces for modeling slot layouts</li> <li> Vertical metal interconnects and embedded dielectric objects</li> <li> Full periodic structure capability with inter-connected unit cells</li> <li> Periodicity offset parameters to model triangular, hexagonal or other offset periodic lattice topologies</li></ul> === Sources, Loads & Ports === <ul> <li> Gap sources on lines</li> <li> De-embedded sources on lines for S parameter calculations</li> <li> Probe (coaxial feed) sources on vias</li> <li> Gap arrays with amplitude distribution and phase progression</li> <li> Periodic gaps with beam scanning</li> <li> Multi-port and coupled port definitions</li> <li> RLC lumped elements on strips with series-parallel combinations</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh solution as collection of short dipoles</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-ray excitation capability (ray data imported from [[Image:PMOM11EM.png|thumb|280px|Terrano]] or external files)</li> <li> Huygens sources imported from other [[EM.Picasso's Navigation Tree.Cube]]modules</li></ul> === Mesh Generation === <ul> <li> Optimized hybrid mesh with rectangular and triangular cells</li> <li> Regular triangular surface mesh</li> <li> Local meshing of trace groups</li> <li> Local mesh editing of planar polymesh objects</li> <li> Fast mesh generation of array objects</li></ul> === Planar MoM Simulation === <ul> <li> 2.5-D mixed potential integral equation (MPIE) formulation of planar layered structures</li> <li> 2.5-D spectral domain integral equation formulation of periodic layered structures</li> <li> Accurate scattering parameter extraction and de-embedding using Prony's method</li> <li> Plane wave excitation with arbitrary angles of incidence</li> <li> A variety of matrix solvers including LU, BiCG and GMRES</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Generation of reflection and transmission coefficient macromodels</li> <li> Multi-variable and multi-goal optimization of structure</li> <li> Remote simulation capability</li> <li> Both Windows and Linux versions of Planar MoM simulation engine available</li></ul> === Data Generation & Visualization === <ul> <li> Current distribution intensity plots</li> <li> Near field intensity plots (vectorial - amplitude & phase)</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of an arbitrary array configuration of the planar structure or periodic unit cell</li> <li> Reflection and Transmission Coefficients of Periodic Structures</li> <li> Monostatic and bi-static RCS </li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li> <li> Huygens surface generation</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul> == Building a Planar Structure in EM.Picasso == [[EM.Picasso]] is intended for construction and modeling of planar layered structures. By a planar structure we mean one that contains a background substrate of laterally infinite extents, made up of one or more material layers all stacked up vertically along the Z-axis. Planar objects of finite size are interspersed among these substrate layers. The background structure in [[EM.Picasso ]] is called the "'''Layer Stack-up'''". The layer stack-up is always terminated from the top and bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material medium. Most planar structures used in RF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components are sandwiched between two grounds (PEC half-spaces) from both their top and bottom. <table><tr><td> [[Image:PMOM11.png|thumb|left|480px|EM.Picasso's navigation tree and trace types.]]</td></tr></table>
=== Defining the Layer Stack-Up ===
When you start a new project in [[EM.Picasso]], there is always a default background structure that consists of a finite vacuum layer with a thickness of one project unit sandwiched between a vacuum top half-space and a PEC bottom half-space. Every time you open [[EM.Picasso ]] or switched to it from [[EM.Cube]]'s other modules, the '''Stack-up Settings Dialog''' opens up. This is where you define the entire background structure. Once you close this dialog, you can open it again by right-clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Layer Stack-up Settings...''' from the contextual menu. Or alternatively, you can select the menu item '''Simulate > Computational Domain > Layer Stack-up Settings...'''
The Stack-up Settings dialog has two tabs: '''Layer Hierarchy''' and '''Embedded Sets'''. The Layer Hierarchy tab has a table that shows all the background layers in hierarchical order from the top half-space to the bottom half-space. It also lists the material composition of each layer, Z-coordinate of the bottom of each layer, its thickness (in project units) and material properties: permittivity (ε<sub>r</sub>), permeability (μ<sub>r</sub>), electric conductivity (σ) and magnetic conductivity (σ<sub>m</sub>). There is also a column that lists the names of embedded object sets inside each substrate layer, if any.
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[[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.]] You can add new layers to your project's stack-up or delete its layers, or move layers up or down and thus change the layer hierarchy. To add a new background layer, click the arrow symbol on the {{key|Insertâ¦}} button at the bottom of the dialog and select '''Substrate Layer''' from the button's dropdown list. A new dialog opens up where you can enter a label for the new layer and values for its material properties and thickness in project units. You can delete a layer by selecting its row in the table and clicking the '''Delete''' button. To move a layer up and down, click on its row to select and highlight it. Then click either the '''Move Up''' or '''Move Down''' buttons consecutively to move the selected layer to the desired location in the stack-up. Note that you cannot delete or move the top or bottom half-spaces. After creating a substrate layer, you can always edit its properties in the Layer Stack-up Settings dialog. Click on any layer's row in the table to select and highlight it and then click the {{key|Edit}} button. The substrate layer dialog opens up, where you can change the layer's label and assigned color as well as its constitutive [[parameters]].
[[Image:Info_icon.png|40px30px]] Click here for a general discussion of '''[[Defining Materials in EM.Cube Preparing_Physical_Structures_for_Electromagnetic_Simulation#Assigning_Material_Properties_to_the_Physical_Structure | Materials in EM.Cube]]'''.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Defining_Materials_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Using_EM.Cube.27s_Materials_List | Using EM.Cube's Materials Database]]'''.
For better visualization of your planar structure, [[EM.Picasso ]] displays a virtual domain in a default orange color to represent part of the infinite background structure. The size of this virtual domain is a quarter wavelength offset from the largest bounding box that encompasses all the finite objects in the project workspace. You can change the size of the virtual domain or its display color from the Domain Settings dialog, which you can access either by clicking the '''Computational Domain''' [[File:domain_icon.png]] button of the '''Simulate Toolbar''', or using the keyboard shortcut {{key|Ctrl+A}}. Keep in mind that the virtual domain is only for visualization purposes and its size does not affect the MoM simulation. The virtual domain also shows the substrate layers in translucent colors. If you assign different colors to your substrate layers, you have get a better visualization of multilayer virtual domain box surrounding your project structure.
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<td> [[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.]] </td>
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=== Planar Object & Trace Types ===
[[EM.Picasso ]] groups objects by their trace type and their hierarchical location in the substrate layer stack-up. A trace is a group of finite-sized planar objects that have the same material properties, same color and same Z-coordinate. All the planar objects belonging to the same metal or slot trace group are located on the same horizontal boundary plane in the layer stack-up. All the embedded objects belonging to the same embedded set lie inside the same substrate layer and have same material composition.
[[EM.Picasso ]] provides the following types of objects for building a planar layered structure (click on each type to learn more about it):
* '''{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[Defining_Materials_in_EMFile:pec_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect_Electric_Conductors_.26_Metal_Traces Perfect Electric Conductor (PEC) | Perfect Electric Conductor (PEC Traces) Trace]]''' * '''| style="width:300px;" | Modeling perfect metal traces on the interface between two substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[Defining_Materials_in_EMFile:voxel_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance_Surfaces_.26_Conductive_Sheet_Traces Conductive Sheet Trace | Conductive Sheet TracesTrace]]''' * '''| style="width:300px;" | Modeling lossy metal traces with finite conductivity and finite metallization thickness| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[Defining_Materials_in_EMFile:pmc_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect_Magnetic_Conductors_.26_Slot_Traces Slot Trace | Slot TracesTrace]]'''* '''| style="width:300px;" | Modeling cut-out slot traces and apertures on an infinite PEC ground plane | style="width:150px;" | Only surface objects|-| style="width:30px;" | [[Defining_Materials_in_EMFile:pec_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect_Electric_Conductors_.26_Metal_Traces Embedded PEC Via Set | Embedded PEC Via SetsSet]]''' * '''| style="width:300px;" | Modeling small and short vertical vias and plated-through holes inside substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[Defining_Materials_in_EMFile:diel_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Defining_Dielectric_Materials Embedded Dielectric Object Set | Embedded Dielectric SetsObject Set]]| style="width:300px;" | Modeling small and short dielectric material inserts inside substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube''' s Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:150px;" | All types of objects|}
You can define two types Click on each category to learn more details about it in the [[Glossary of metallic traces in EM.Picasso: Cube'''PEC Traces''' and '''Conductive Sheet Traces'''. PEC traces represent infinitesimally thin (zero thickness) planar metal objects that are deposited or metallized on or between substrate layers. PEC objects are modeled by surface electric currents. Conductive sheet tracess Materials, on the other handSources, represent imperfect metals. They have a finite conductivity and a very small thickness expressed in project units. A surface impedance boundary condition is enforced on the surface of conductive sheet objectsDevices & Other Physical Object Types]].
You can define two types of metallic traces in [[EM.Picasso]]: '''Slot PEC Traces''' are used to model cut-out slots and apertures in '''Conductive Sheet Traces'''. PEC ground planes. Planar slot traces represent infinitesimally thin (zero thickness) planar metal objects that are always assumed to lie deposited or metallized on an infinite horizontal or between substrate layers. PEC ground plane with zero thickness, which is not explicitly displayed in the project workspace and its presence is implied. They objects are modeled by surface magnetic electric currents. When a slot is excitedConductive sheet traces, tangential electric fields are formed on the apertureother hand, which can be modeled as represent imperfect metals. They have a finite magnetic surface currents confined to the area of the slotconductivity and a very small thickness expressed in project units. In other words, instead of modeling the electric A surface currents impedance boundary condition is enforced on an infinite PEC ground around the slot, one can alternatively model the finite-extent magnetic surface currents on a perfect magnetic conductor (PMC) trace. Slot (PMC) of conductive sheet objects provide the electromagnetic coupling between the two sides of an infinite PEC ground plane.
Besides planar metal and slot traces, EM.Picasso allows you to insert prismatic embedded objects inside the substrate layers. The height of such embedded objects is always the same as the height of their host substrate layer. Two types of embedded object sets are available: '''PEC Via SetsSlot Traces''' are used to model cut-out slots and '''Embedded Dielectric Sets'''apertures in PEC ground planes. Planar slot objects are always assumed to lie on an infinite horizontal PEC via sets are metallic objects such as shorting pinsground plane with zero thickness, interconnect vias, plated-through holes, etc. all located which is not explicitly displayed in the project workspace and grouped together inside the same substrate layerits presence is implied. The embedded via objects They are modeled as vertical volume conduction by surface magnetic currents. Embedded dielectric sets When a slot is excited, tangential electric fields are prismatic dielectric objects inserted inside a substrate layerformed on the aperture, which can be modeled as finite magnetic surface currents confined to the area of the slot. You In other words, instead of modeling the electric surface currents on an infinite PEC ground around the slot, one can define alternatively model the finite-extent magnetic surface currents on a finite permittivity and conductivity for such objectsperfect magnetic conductor (PMC) trace. The embedded dielectric Slot (PMC) objects are modeled as vertical volume polarization currentsprovide the electromagnetic coupling between the two sides of an infinite PEC ground plane.
Besides planar metal and slot traces, [[Image:Info_iconEM.png|40pxPicasso]] Click here allows you to learn more about 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: '''[[Defining Materials in EM.Cube]]PEC Via Sets'''and '''Embedded Dielectric Sets'''. PEC via sets are metallic objects such as shorting pins, interconnect vias, plated-through holes, etc. all located and grouped together inside the same substrate layer. The embedded via objects are modeled as vertical volume conduction currents. Embedded dielectric sets are prismatic dielectric objects inserted inside a substrate layer. You can define a finite permittivity and conductivity for such objects. The embedded dielectric objects are modeled as vertical volume polarization currents.
{{Note|The height of an embedded object is always identical to the thickness of its host substrate layer.}}
=== Defining Traces & Embedded Object Sets ===
[[Image:PMOM23.png|thumb|550px|EM.Picasso's Layer Stack-up dialog showing the Embedded Sets tab.]] When you start a new project in [[EM.Picasso]], the project workspace looks empty, and there are no finite objects in it. However, a default background structure is always present. Finite objects are defined as part of traces or embedded sets. Once defined, you can see a list of project objects in the '''Physical Structure''' section of the navigation tree. Traces and object sets can be defined either from Layer Stack-up Settings dialog or from the navigation tree. In the '''Layer Stack-up Settings''' dialog, you can add a new trace to the stack-up by clicking the arrow symbol on the {{key|Insert}} button of the dialog. You have to choose from '''Metal (PEC)''', '''Slot (PMC)''' or '''Conductive Sheet''' options. A respective dialog opens up, where you can enter a label and assign a color. Once a new trace is defined, it is added, by default, to the top of the stack-up table underneath the top half-space. From here, you can move the trace down to the desired location on the layer hierarchy. Every time you define a new trace, it is also added under the respective category in the navigation tree. Alternatively, you can define a new trace from the navigation tree by right-clicking on one of the trace type names and selecting '''Insert New PEC Trace...'''or '''Insert New PMC Trace...'''or '''Insert New Conductive Sheet Trace...''' A respective dialog opens up for setting the trace properties. Once you close this dialog, it takes you directly to the Layer Stack-up Settings dialog so that you can set the right position of the trace on the stack-up.
Embedded object sets represent short material insertions inside substrate layers. They can be metal or dielectric. Metallic embedded objects can be used to model vias, plated-through holes, shorting pins and interconnects. These are called PEC via sets. Embedded dielectric objects can be used to model air voids, thin films and material inserts in metamaterial structures. Embedded objects can be defined either from the Layer Stack-up Settings dialog or directly from the navigation tree. Open the "Embedded Sets" tab of the stack-up dialog. This tab has a table that lists all the embedded object sets along with their material type, the host substrate layer, the host material and their height. To add a new object set, click the arrow symbol on the {{key|Insert}} button of the dialog and select one of the two options, '''PEC Via Set''' or '''Embedded Dielectric Set''', from the dropdown list. This opens up a new dialog where first you have to set the host layer of the new object set. A dropdown list labeled "'''Host Layer'''" gives a list of all the available finite substrate layers. You can also set the properties of the embedded object set, including its label, color and material properties. Keep in mind that you cannot control the height of embedded objects. Moreover, you cannot assign material properties to PEC via sets, while you can set values for the '''Permittivity'''(ε<sub>r</sub>) and '''Electric Conductivity'''(σ) of embedded dielectric sets. Vacuum is the default material choice. To define an embedded set from the navigation tree, right-click on the '''Embedded Object Sets''' item in the '''Physical Structure''' section of the navigation tree and select either '''Insert New PEC Via Set...''' or '''Insert New Embedded Dielectric Set...''' The respective New Embedded Object Set dialog opens up, where you can set the properties of the new object set. As soon as you close this dialog, it takes you to the Layer Stack-up Settings dialog, where you can verify the location of the new object set on the layer hierarchy.
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining Materials in EM.Cube]]'''.
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<td> [[Image:PMOM21PMOM23.png|thumb|300px550px|EM.Picasso's PEC Via Set Layer Stack-up dialog.]] </td><td> [[Image:PMOM22.png|thumb|300px|EM.Picasso's showing the Embedded Dielectric SetdialogSets tab.]] </td>
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=== Drawing Planar Objects on Horizontal Work Planes ===
[[Image:PMOM23B.png|thumb|280px|EM.Picasso's Navigation Tree populated with planar objects.]]
As soon as you start drawing geometrical objects in the project workspace, the '''Physical Structure''' section of the navigation tree gets populated. The names of traces are added under their respective trace type category, and the names of objects appear under their respective trace group. At any time, one and only one trace is active in the project workspace. The name of the active trace in the navigation tree is always displayed in bold letters. An active trace is where all the new objects you draw belong to. By default, the last defined trace or embedded object set is active. You can immediately start drawing new objects on the active trace. You can also set any trace or object set group active at any time by right-clicking on its name on the navigation tree and selecting '''Activate''' from the contextual menu.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Defining_Materials_in_EM.CubeBuilding Geometrical Constructions in CubeCAD#Defining_a_New_Material_Group Transferring Objects Among Different Groups or Modules | Defining a New Trace GroupMoving Objects among Different Groups]]'''.
<table><tr><td> [[Image:Info_iconPMOM23B.png|40px]] Click here to learn more about thumb|280px|EM.Picasso'''[[Defining_Materials_in_EMs Navigation Tree populated with planar objects.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Trace Groups]]'''.</td></tr></table>
[[EM.Picasso ]] has a special feature that makes construction of planar structures very convenient and straightforward. <u>The horizontal Z-plane of the active trace or object set group is always set as the active work plane of the project workspace.</u> That means all new objects are drawn at the Z-coordinate of the currently active trace. As you change the active trace group or add a new one, the active work plane changes accordingly.
{{Note| In [[EM.Picasso]], you cannot modify the Z-coordinate of an object as it is set and controlled by its host trace.}}
[[EM.Picasso ]] does not allow you to draw 3D or solid CAD objects. The solid object buttons in the '''Object Toolbar''' are disabled to prevent you from doing so. In order to create vias and embedded object, you simply have to draw their cross section geometry using planar surface CAD objects. [[EM.Picasso ]] extrudes and extends these planar objects across their host layer automatically and displays them as 3D wireframe, prismatic objects. The automatic extrusion of embedded objects happens after mesh generation and before every planar MoM simulation. You can enforce this extrusion manually by right-clicking the '''Layer Stack-up''' item in the "Computational Domain" section of the navigation tree and selecting '''Update Planar Structure''' from the contextual menu.
{{Note| In [[EM.Picasso]], you can only draw horizontal planar surface CAD objects.}}
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# Metallic and slot traces cannot coexist on the same Z-plane. However, you can stack up multiple PEC and conductive sheet traces at the same Z-coordinate. Similarly, multiple slot traces can be placed at the same Z-coordinate.
# Metallic and slot traces are strictly defined at the interface planes between substrate layers. To define a suspended metallic trace inside a dielectric layer (as in the case of the center conductor of a stripline), you must split the dielectric layer into two thinner substrate layers and place your PEC trace at the interface between them.
# [[EM.Picasso]]'s simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and no circumferential components are allowed on embedded objects. The 2.5-D assumption holds very well in two cases: (a) when embedded objects are very thin with a very small cross section (with lateral dimensions less than 2-5% of the material wavelength) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the top and bottom.
== Discretizing the Planar Structure EM.Picasso's Excitation Sources ==
[[Image:PMOM31.png|thumb|400px|The Planar Mesh Settings dialog.]]The method of moments (MoM) discretizes all the finite-sized objects of a Your 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 must be excited by some sort of cells per effective wavelength signal source that are placed in various regions of your planar structure. The higher the mesh densityinduces electric surface currents on metal parts, the more cells are created magnetic surface currents on the finite-sized geometrical objects. As a rule of thumbslot traces, a mesh density of about 20-30 cells per effective wavelength usually yields satisfactory results. But for structures with lots of fine geometrical details and conduction or for highly resonant structures, higher mesh densities may be requiredpolarization volume currents on vertical vias and embedded objects. The particular output data that excitation source you choose depends on the observables you seek in a simulation also influence your choice of mesh resolutionproject. For example, far field characteristics like radiation patterns are less sensitive to [[EM.Picasso]] provides the mesh density than field distributions on following source types for exciting planar structures with a highly irregular shapes and boundaries.:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.Picasso provides two types Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source (or filament current source on slot traces)| style="width:300px;" | Associated with a PEC rectangle strip|-| style="width:30px;" | [[File:probe_src_icon.png]]| [[Glossary of mesh EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Probe Gap Circuit Source |Probe Gap Circuit Source]]| style="width:300px;" | General-purpose voltage source for a planar structuremodeling coaxial feeds| style="width: a pure triangular surface mesh and a hybrid triangular300px;" | Associated with an embedded PEC via set|-rectangular surface mesh| style="width:30px;" | [[File:waveport_src_icon.png]]| [[Glossary of EM. In both caseCube's Materials, Sources, Devices & Other Physical Object Types#Scattering Wave Port |Scattering Wave Port Source]]| style="width:300px;" | Used for S-parameter computations| style="width:300px;" | Associated with an open-ended PEC rectangle strip, extends long from the open end|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Picasso attempts to create a highly regular meshCube's Materials, in which most Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of the cells have almost equal areasEM. For planar structures with regularCube's Materials, mostly rectangular shapesSources, the hybrid mesh generator usually leads to faster Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering & computation timesof reflection/transmission characteristics of periodic surfaces| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon. png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}
[[Image:Info_icon.png|40px]] Click here on each category to learn more details about '''it in the [[Mesh_Generation_Schemes_in_EMGlossary of EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator 's Materials, Sources, Devices & Other Physical Object Types]]'''.
For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[Image:Info_iconEM.png|40pxPicasso]] Click here provides three types of lumped sources: gap source, probe source and de-embedded source. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to learn more about EMinject a signal.Picasso's '''Gap sources are placed across metal or slot traces. A rectangle strip object on a PEC or conductive sheet trace acts like a strip transmission line that carries electric currents along its length (local X direction). The characteristic impedance of the line is a function of its width (local Y direction). A gap source placed on a narrow metal strip creates a uniform electric field across the gap and pumps electric current into the line. A rectangle strip object on a slot trace acts like a slot transmission line on an infinite PEC ground plane that carries a magnetic current along its length (local X direction). The characteristic impedance of the slot line is a function of its width (local Y direction). A gap source placed on a narrow slot represents an ideal current source. A slot gap acts like an ideal current filament, which creates electric fields across the slot, equivalent to a magnetic current flowing into the slot line. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[Mesh_Generation_Schemes_in_EM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generatorparameters]]'''can be calculated accurately.
{{Note| You can realize a coplanar waveguide (CPW) in [[Image:Info_icon.png|40px]] Click here to learn more about EM.Picasso's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Hybrid_Planar_Mesh_Generator | Hybrid Planar Mesh Generator]]'''using two parallel slot lines with two aligned, collocated gap sources.}}
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#General_Rules_of_Planar_Hybrid_Mesh_GeneratorModeling_Finite-Sized_Source_Arrays | General Rules of Planar Hybrid Mesh GeneratorUsing Source Arrays for Modeling Antenna Arrays]]'''.
A short dipole provides another way of exciting a planar structure in [[Image:Info_iconEM.png|40pxPicasso]] Click here . A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to learn more about '''excite your planar structure in [[Mesh_Generation_Schemes_in_EMEM.Cube#Refining_the_Planar_Mesh_Locally| Refining Picasso]]. In particular, you need a plane wave source to compute the Planar Mesh Locallyradar cross section of a planar structure. The direction of incidence is defined by the θ and Ï angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and Ï = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]]'''computational module.
<table>
<tr>
<td> [[Image:PMOM48FPMOM64A.png|thumb|350px550px|Geometry of a A multilayer slot-coupled patch array.]] </td><td> [[Image:PMOM48G.png|thumb|370px|Hybrid planar mesh of the slot-structure containing a CPW line with a single coupled patch array.]] </td></tr></table><table><tr><td> [[Image:PMOM48H.png|thumb|350px|Details of the hybrid planar mesh of the slot-coupled patch array around discontinuitiesport and a lumped element on an overpassing metal strip.]] </td>
</tr>
</table>
== 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 signal source a mesh cell. In fact, a lumped element is equivalent to an infinitesimally narrow gap that induces electric surface currents on metal partsis placed in the path of current flow, magnetic surface currents on slot tracesacross which the device's governing equations are enforced. Using Kirkhoff's laws, these device equations normally establish a relationship between the currents and conduction voltages across the device or polarization volume 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 vertical vias and embedded objects. The excitation source you choose depends on the observables you seek in your projectfields. [[EM.Picasso provides the following source types for exciting planar structures (click on each type ]] allows you to learn more about it)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. EM.Picasso provides three types of lumped sources[[Image: gap source, probe source and de-embedded sourceInfo_icon. A lumped source is indeed png|40px]] Click here for a gap discontinuity that is placed on the path general discussion of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal'''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_. Gap sources are placed across metal or slot traces26_Nonlinear_Passive_. A rectangle strip object on a PEC or conductive sheet trace acts like a strip transmission line that carries electric currents along its length (local X direction). The characteristic impedance of the line is a function of its width (local Y direction). A gap source placed on a narrow metal strip creates a uniform electric field across the gap and pumps electric current into the line. A rectangle strip object on a slot trace acts like a slot transmission line on an infinite PEC ground plane that carries a magnetic current along its length (local X direction). The characteristic impedance of the slot line is a function of its width (local Y direction). A gap source placed on a narrow slot represents an ideal current source. A slot gap acts like an ideal current filament, which creates electric fields across the slot, equivalent to a magnetic current flowing into the slot line. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parameters26_Active_Devices | Linear Passive Devices]] can be calculated accurately'''.
{{Note| You can realize a coplanar waveguide (CPW) in EM.Picasso The impedance of the lumped circuit is calculated at the operating frequency of the project using two parallel slot lines with two alignedthe specified R, L and C values. As you change the frequency, collocated gap sourcesthe value of the impedance that is passed to the Planar MoM 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 ===
A short dipole provides another way The calculation of exciting a the scattering (S) parameters is usually an important objective of modeling planar structure in EM.Picasso. A short dipole source acts structures especially for planar circuits like an infinitesimally small ideal current sourcefilters, couplers, etc. You As you saw earlier, you can also use an incident plane wave lumped sources like gaps and probes and even active lumped elements to excite your planar structure in EM.Picasso. In particular, you need a plane wave source to compute calculate the radar cross section circuit characteristics of a planar structurestructures. The direction of incidence is defined by admittance / impedance calculations based on the θ gap voltages and Ï angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles currents are θ = 180° accurate at RF and Ï = 0° corresponding to a normally incident plane wave propagating along lower microwave frequencies or when the -Z direction with a +X-polarized E-vector. Huygens sources port transmission lines are virtual equivalent sources that capture narrow. In such cases, the radiated electric and or magnetic fields from another structure that was previously analyzed in another [[EMcurrent distributions across the width of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized.Cube]] computational moduleAt higher frequencies, however, a more robust method is needed for calculating the port parameters.
[[Image:PMOM64A.png|thumb|550px|A multilayer One can calculate the scattering parameters of a planar structure containing directly by analyzing the current distribution patterns on the port transmission lines. The discontinuity at the end of a CPW port line with typically gives rise to a single coupled port standing wave pattern that can clearly be discerned in the line's current distribution. From the location of the current minima and a lumped element on an overpassing metal stripmaxima and their relative levels, one can determine the reflection coefficient at the discontinuity, i.]]=== Modeling Lumped Elements in EMe.Picasso ===the S<sub>11</sub> parameter. A more robust technique is Pronyâs method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following form:
Lumped elements are components, devices, or circuits whose overall dimensions are very small compared to the wavelength. As a result, they are considered to be dimensionless compared to the dimensions of a mesh cell. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of current flow, across which the device's governing equations are enforced. Using Kirkhoff's laws, these device equations normally establish a relationship between the currents and voltages across the device or circuit. Crossing the bridge to Maxwell's domain, the device equations must now be cast into a from o boundary conditions that relate the electric and magnetic currents and fields. EM.Picasso allows you to define passive circuit elements: '''Resistors''' <math> f(Rx), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations of them\approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math><!--[[File:PMOM73. png]]-->
[[Image:Info_iconwhere c<sub>i</sub> are complex coefficients and γ<sub>i</sub> are, in general, complex exponents.png|40px]] Click here to learn more about '''[[Modeling_Lumped_ElementsFrom the physics of transmission lines,_Circuits_%26_Devices_in_EMwe know that lossless lines may support one or more propagating modes with pure real propagation constants (real γ<sub>i</sub> exponents).Cube#Defining_Lumped_Elements_in_EM.Picasso_.26_EM.Libera | Defining Lumped Elements]]'''Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary γ<sub>i</sub> exponents) that decay along the line as you move away from the location of such discontinuities.
[[Image:Info_iconIn practical planar structures for which you want to calculate the scattering parameters, each port line normally supports one, and only one, dominant propagating mode.png|40px]] Click here Multi-mode transmission lines are seldom used for practical RF and microwave applications. Nonetheless, each port line carries a general discussion superposition of incident and reflected dominant-mode propagating signals. An incident signal, by convention, is one that propagates along the line towards the discontinuity, where the phase reference plane is usually established. A reflected signal is one that propagates away from the port plane. Prony'''[[Modeling_Lumped_Elementss method can be used to extract the incident and reflected propagating and evanescent exponential waves from the standing wave data. From a knowledge of the amplitudes (expansion coefficients) of the incident and reflected dominant propagating modes at all ports,_Circuits_%26_Devices_in_EMthe scattering matrix of the multi-port structure is then calculated.Cube#Linear_Passive_Devices | Linear Passive Devices]]''In Prony's method, the quality of the S parameter extraction results depends on the quality of the current samples and whether the port lines exhibit a dominant single-mode behavior. Clean current samples can be drawn in a region far from sources or discontinuities, typically a quarter wavelength away from the two ends of a feed line.
{{Note<table><tr><td> [[Image:PMOM71.png|The impedance of the lumped circuit is calculated at the operating frequency of the project using the specified R, L thumb|600px|Minimum and C values. As you change the frequency, the value maximum current locations of the impedance that is passed to the Planar MoM engine will changestanding wave pattern on a microstrip line feeding a patch antenna.}}]] </td></tr></table>
=== Defining Independent & Coupled Ports ===
Ports are used in a planar structure to order and index the sources for calculation of circuit [[parameters]] such as scattering (S), impedance (Z) and admittance (Y) [[parameters]]. In [[EM.Picasso]], you can use one or more of the following types of sources to define ports:
* Gap Sources
* De-Embedded Sources
Ports are defined in the '''Observables''' section of the navigation tree. You can define any number of ports equal to or less than the total number of sources in your project. If you have N sources in your planar structure, then N default ports are defined, with one port assigned to each source according to their order on the navigation tree. Note that your project can have mixed gap and probes sources as well as active lumped element sources on PEC and slot traces or vias. You can also couple ports together to define coupled [[Transmission Lines|transmission lines]] such as coupled strips (CPS) or coplanar waveguides (CPW).
[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Common_Excitation_Source_Types_in_EMGlossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#The_Port_Definition_Observable Port_Definition_Observable | Port Definition Observable]]'''.
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Ports Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Ports]]'''.
== Running Planar MoM Simulations EM.Picasso's Simulation Data & Observables ==
=== Depending on the source type and the types of observables defined in a project, a number of output data are generated at the end of a planar MoM simulation. Some of these data are 2D by nature and some are 3D. The output simulation data generated by [[EM.Picasso's Simulation Modes ===]] can be categorized into the following groups:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Picasso offers five Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal traces and magnetic surface current distribution on slot traces | style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types : lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:period_icon.png]]| style="width:150px;" | Periodic Characteristics| style="width:150px;" | No observable required | style="width:300px;" | Computing the reflection and transmission coefficients of Planar MoM simulationsa 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|}
* Single-Frequency Analysis* Frequency Sweep* Parametric Sweep* Click on each category to learn more details about it in the [[OptimizationGlossary of EM.Cube's Simulation Observables & Graph Types]]* HDMR Sweep.
A single-frequency analysis 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 simplest type planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y) parameters of EMthe designated ports.Picasso simulation and involves The scattering parameters are defined based on the following steps: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.
* Set the units of your project Electric and magnetic currents are the frequency fundamental output data of operationa planar MoM simulation. Note that After the default project unit is numerical solution of the MoM linear system, they are found using the solution vector '''millimeter[I]'''. * Define you background structure and its layer properties and trace types. * Construct your planar structure using [[CubeCAD]]'s drawing tools to create all the finite-sized metal and slot trace objects and possibly embedded metal or dielectric objects that are interspersed among definitions of the substrate layers.* Define an excitation source electric and observables for your project.* Examine the planar mesh, verify its integrity and change the mesh density if necessary.* Run the Planar MoM simulation engine.* Visualize the output simulation data.magnetic vectorial basis functions:
:<math> \mathbf{[[Image:PMOM80.png|thumb|400px|EM.Picasso's Simulation Run dialog.]X]}_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math>
If you run 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 simulation without having defined any observablesmagnitude and phase. You can visualize the surface electric currents on metal (PEC) and conductive sheet traces, no data will be generated at surface magnetic currents on slot (PMC) traces and vertical volume currents on the end PEV vias and embedded dielectric objects. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the simulation. An analysis is a single-run simulationproject workspace, superimposed on the surface of physical objects. In multi-run simulation modesorder to view the current distributions, certain [[parameters]] are varied and a collection of you must first define them as observables before running the planar MoM simulation data are generated. At the end top of a multi-run simulationthe Current Distribution dialog and in the section titled '''Active Trace / Set''', you can graph the simulation results in EM.Grid select a trace or embedded object set where you can animate the 3D simulation data from want to observe the navigation treecurrent distribution.
=== Running A Planar MoM Analysis ==={{Note|You have to define a separate current distribution observable for each individual trace or embedded object set.}}
To run a planar MoM analysis of your project structure, open the Run Simulation Dialog by clicking the '''Run''' <table><tr><td> [[FileImage:run_iconPMOM85new.png]] button on the '''Simulate Toolbar''' or select '''Menu > Simulate > Run''' or use the keyboard shortcut {{key|Ctrl+R}}. thumb|left|600px|The '''Single-Frequency Analysis''' option current distribution map of the '''Simulation Mode''' dropdown list is selected by default. Once you click the {{key|Run}} button, the simulation starts. A new window called the "Output Window" opens up that reports the different stages of simulation and the percentage of the tasks completed at any time. After the simulation is successfully completed, a message pops up and reports the end of simulationpatch antenna. In certain cases like calculating scattering [[parameters]] of a circuit or reflection </td></ transmission characteristics of a periodic surface, some results are also reported in the output window. tr></table>
=== Setting Numerical Parameters ===[[EM.Picasso]] allows you to visualize the near fields at a specific field sensor plane. Note that unlike [[EM.Cube]]'s other computational modules, near field calculations in [[EM.Picasso]] usually takes a significant amount of time. This is due to the fact that at the end of a planar MoM simulation, the fields are not available anywhere (as opposed to [[EM.Tempo]]), and their computation requires integration of complex dyadic Green's functions of a multilayer background structure as opposed to the free space Green's functions.
A planar MoM simulation involves a number of numerical {{Note|Keep in mind that since [[parameters]] that take preset default values unless you change themEM. You can access these [[parametersPicasso]] and change their values by clicking uses a planar MoM solver, the '''Settings''' button next to calculated field value at the '''Select Engine''' dropdown list in the [[Planar Module]]'s Simulation Run dialogsource point is infinite. In most casesAs a result, you do not need to open this dialog and you can leave all the default numerical parameter values intact. However, it is useful field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to familiarize yourself with these [[parameters]], as they may affect the accuracy of your numerical produce acceptable 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:PMOM116. The "'''Matrix Fill'''" section of the dialog deals with the operations involving the dyadic Green's functions. You can set png|thumb|left|600px|Near-zone electric field map above a value for the '''Convergence Rate for Integration''', which is 1Emicrostrip-5 by defaultfed patch antenna. This is used for the convergence test of all the infinite integrals in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, the surface wave poles are captured in the complex integration plane using contour deformation. You can change the maximum number of iterations involved in this deformed contour integration, whose default value is 20. When the substrate is very thin with respect to the wavelength, the dyadic Green's functions exhibit numerical instability. Additional singularity extraction measures are taken to avoid numerical instability but at the expense of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01λ]] <sub/td>eff</subtr>, where λ<subtr>eff</subtd> is the effective wavelength[[Image:PMOM117. You can modify the definition of "Thin Substrate" by entering png|thumb|left|600px|Near-zone magnetic field map above 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 quasimicrostrip-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''fed patch antenna.]] </td></tr></table>
In the Even though [[EM.Picasso]]'s MoM engine does not need a radiation box, you still have to define a "Spectral Domain IntegrationFar Field" section of the dialog, you can set a value to '''Max Spectral Radius in k0''', which has a default value of 30observable for radiation pattern calculation. This means that the infinite spectral-domain integrals in the spectral variable k<sub>ρ</sub> are pre-calculated is because far field calculations take time and tabulated up you have to instruct [[EM.Cube]] to perform these calculations. Once a limit of 30k<sub>0</sub>, where k<sub>0</sub> planar MoM simulation is finished, three far field items are added under the free space propagation constantFar Field item in the Navigation Tree. These integrals may converge much faster based on are the specified Convergence Rate for Integration described earlier. However, far field component in certain cases involving highly oscillatory integrandsθ direction, much larger integration limits like 100k<sub>0</sub> might be needed to warrant adequate convergence. For spectral-domain integration along the real k<sub>far field component in &rhophi;</sub> axis, direction and the interval [0, Nk<sub>0</sub>] is subdivided into a large number of sub-intervals, within each an 8-point Gauss-Legendre quadrature is applied"Total" far field. The next parameter, 2D radiation pattern graphs can be plotted from the '''No. Radial Integration Divisions per k<sub>0</sub>Data Manager''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k<sub>0</sub>]. In other words, the length of each integration sub-interval is k<sub>0</sub>/2. You can increase the resolution of integration by increasing this value above 2. Finally, instead A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian integration in graphs for the spectral domainXY, a polar integration is performed. You can set the '''No. of Angular Integration Points'''YZ, which has a default value of 100ZX and user defined plane cuts.
[[FileImage:PMOM79Info_icon.png|30px]]Click here to learn more about the theory of '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.
Figure 1<table><tr><td> [[Image: The Planar MoM Engine Settings dialogPMOM119.png|thumb|left|600px|3D polar radiation pattern plot of a microstrip-fed patch antenna.]] </td></tr></table>
=== Planar Module's Linear System Solvers ===When a planar structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields of that planar structure. [[EM.Picasso]] can also calculate the radar cross section (RCS) of a planar target. Note that in this case the RCS is defined for a finite-sized target in the presence of an infinite background structure. The scattered θ and φ components of the far-zone electric field are indeed what you see in the 3D far field visualization of radiation (scattering) patterns. Instead of radiation or scattering patterns, you can instruct [[EM.Picasso]] to plot 3D visualizations of σ<sub>θ</sub>, σ<sub>φ</sub> and the total RCS.
After the MoM impedance matrix '''<table><tr><td> [Z]''' (not to be confused with [Image:PMOM125.png|thumb|left|600px|An example of the impedance [[parameters3D monostatic radar cross section plot of a patch antenna.]]) and excitation vector '''[V]''' have been computed through the matrix fill process, the planar MoM simulation engine is ready to solve the system of linear equations:</td></tr></table>
:<math> \mathbf{[Z]}_{N\times N} \cdot \mathbf{[I]}_{N\times 1} = \mathbf{[V]}_{N\times 1} </math><!--[[File:PMOM81= Discretizing a Planar Structure in EM.png]]-->Picasso ==
where '''[I]''' is the solution vector, which contains the unknown amplitudes The method of moments (MoM) discretizes all the basis functions that represent the unknown electric and magnetic currents finite-sized objects of finite extents in your a planar structure. In (excluding the above equation, N is the dimension background structure) into a set of elementary cells. Both the linear system quality and equal to the total number resolution of basis functions in the planar generated mesh. [[EM.Cube]]'s linear solvers compute greatly affect the solution vector'''[I]''' accuracy of the above system. You can instruct [[EM.Cube]] to write the MoM matrix and excitation and numerical solution vectors into output data files for your examination. To do so, check The mesh density gives a measure of the box labeled "'''Output MoM Matrix and Vectors'''" number of cells per effective wavelength that are placed in the Matrix Fill section various regions of the Planar MoM Engine Settings dialogyour planar structure. These The higher the mesh density, the more cells are written into three files called momcreated on the finite-sized geometrical objects.dat1As a rule of thumb, exca mesh density of about 20-30 cells per effective wavelength usually yields satisfactory results.dat1 and solnBut for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required.dat1The particular output data that you seek in a simulation also influence your choice of mesh resolution. For example, respectivelyfar field characteristics like radiation patterns are less sensitive to the mesh density than field distributions on structures with a highly irregular shapes and boundaries.
There are a large number of numerical methods for solving systems of linear equations. These methods are generally divided into two groups: direct solvers and iterative solvers. Iterative solvers are usually based on matrix-vector multiplications. Direct solvers typically work faster for matrices of smal to medium size (N<3,000). <table><tr><td> [[EMImage:PMOM31.Cube]]'s [[png|thumb|400px|The Planar ModuleMesh Settings dialog.]] offers five linear solvers:</td></tr></table>
# LU Decomposition Method# Biconjugate Gradient Method (BiCG)# Preconditioned Stabilized Biconjugate Gradient Method (BCGEM.Picasso provides two types of mesh for a planar structure: a pure triangular surface mesh and a hybrid triangular-STAB)# Generalized Minimal Residual Method (GMRES)# Transpose-Free Quasi-Minimum Residual Method (TFQMR)rectangular surface mesh. In both case, EM.Picasso attempts to create a highly regular mesh, in which most of the cells have almost equal areas. For planar structures with regular, mostly rectangular shapes, the hybrid mesh generator usually leads to faster computation times.
Of the above list, LU is a direct solver, while the rest are iterative solvers[[Image:Info_icon. BiCG is a relatively fast iterative solver, but it works only for symmetric matrices. You cannot use BiCG for periodic structures or planar structures that contain both metal and slot traces at different planes, as their MoM matrices are not symmetric. The three solvers BCG-STAB, GMRES and TtFQMR work well for both symmetric and asymmetric matrices and they also belong png|30px]] Click here to a class of solvers called learn more about '''Krylov Sub-space Methods[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''. In particular, the GMRES method always provides guaranteed unconditional convergence.
[[EMImage:Info_icon.Cubepng|30px]]Click here to learn more about 's [[Planar Module]], by default, provides a "'''Automatic'''" solver option that picks the best method based on the settings and size of the numerical problem. For linear systems with a size less than N = 3,000, the LU solver is used. For larger systems, BiCG is used when dealing with symmetric matrices, and GMRES is used for asymmetric matrices. If the size 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 and manually set you own solver type. This is done using the '''Solver Type''' dropdown list in the "'''Linear System Solver'''" section of the Planar MoM Engine Settings dialog. There are also a number of other [[parameters]] related to the solversPreparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM. The default value of Picasso'''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 [[parameterss Triangular Surface Mesh Generator]] that are related to the Automatic Solver option. These are "''' User Iterative Solver When System Size >'''" with a default value of 3,000 and "''' Use SParse Storage When System Size >''' " with a default value of 15,000. In other words, you control the automatic solver when to switch between direct and iterative solvers and when to switch to the sparse version of iterative solvers.
If your computer has an Intel CPU, then <table><tr><td> [[EMImage:PMOM48F.Cube]] offers special versions png|thumb|left|420px|Geometry of all the above linear solvers that have been optimized for Intel CPU platforms. These optimal solvers usually work 2a multilayer slot-3 time faster than their generic counterpartscoupled patch array. When you install ]] </td></tr><tr><td> [[EMImage:PMOM48G.Cube]], png|thumb|left|420px|Hybrid planar mesh of the option to use Intelslot-optimized solvers is already enabledcoupled patch array. 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 > Edit > Preferences''' or using the keyboard shortcut '''Ctrl+H'''. Select the Advanced tab of the dialog and uncheck the box labeled "''' Use Optimized Solvers for Intel CPU'''".</td></tr></table>
<table><tr><td> [[FileImage:PMOM82PMOM48H.png|thumb|left|420px|Details of the hybrid planar mesh of the slot-coupled patch array around discontinuities.]]</td></tr></table>
[[Image:PMOM127.png|thumb|400px|Settings adaptive frequency sweep parameters in EM.Picasso's Frequency Settings Dialog.]]=== Running Uniform and Adaptive Frequency Sweeps The Hybrid Planar Mesh Generator ===
In a frequency sweep, the operating frequency of a planar structure is varied during each sweep run. [[EM.Cube]]Picasso's [[Planar Module]] offers two types hybrid planar mesh generator tries to produce as many rectangular cells as possible especially in the case of frequency sweep: Uniform and Adaptiveobjects with rectangular or linear boundaries. In a uniform frequency sweepconnection or junction areas between adjacent objects or close to highly curved boundaries, the frequency range and the number of frequency samples triangular cells are specified. The samples are equally spaced over used to fill the frequency range. At the end of each individual frequency run, the output data are collected "irregular" regions in a conformal and stored. At the end of the frequency sweep, the 3D data can be visualized and/or animated, and the 2D data can be graphed in EM.Gridconsistent manner.
To run The mesh density gives a uniform frequency sweep, open the '''Simulation Run Dialog''', and select the '''Frequency Sweep''' option from the dropdown list labeled '''Simulation Mode'''. When you choose the frequency sweep option, the '''Settings''' button next to the simulation mode dropdown list becomes enabled. Clicking this button opens the '''Frequency Settings''' dialog. The '''Frequency Range'''is initially set equal to your project's center frequency minus and plus half bandwidth. But you can change the values measure of '''Start Frequency'''and '''End Frequency''' as well as the '''Number number of Samples'''. The dialog offers two options for '''Frequency Sweep Type''': '''Uniform''' or '''Adaptive'''. Select the former type. It is very important to note cells per effective wavelength that are placed in a MoM simulation, changing the frequency results in a change various regions of the mesh of the your planar structure, too. This The effective wavelength is because the mesh density defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e<sub>eff</sub> is defined in terms of the number of cells per effective wavelengthpermittivity. By default, during a frequency sweep, [[EM.CubePicasso]] fixes the generates a hybrid mesh with a mesh density at the highest frequency, iof 20 cells per effective wavelength.e., at the "End Frequency"The effective permittivity is defined differently for different types of traces and embedded object sets. This usually results in a smoother frequency response. You have the option is to fix the mesh at the center frequency of the project or let [[EM.Cube]] "remesh" the planar structure at each frequency sample during a frequency sweep. You can make one of these three choices using the radio button sure that enough cells are placed in the '''Mesh Settings''' section of the dialog. Closing the Frequency Settings dialog returns you to the Simulation Run dialog, where you can start the planar MoM frequency sweep simulation by clicking the '''Run''' buttonareas that might feature higher field concentration.
Frequency sweeps are often performed to study * For PEC and conductive sheet traces, the frequency response effective permittivity is defined as the larger of a planar structure. In particular, the variation permittivity of scattering [[parameters]] like S<sub>11</sub> (return loss) the two substrate layers just above and S<sub>21</sub> (insertion loss) with frequency are of utmost interestbelow the metallic trace. When analyzing resonant structures like patch antennas or planar filters over large frequency ranges* For slot traces, you may have to sweep a large number of frequency samples to capture their behavior with adequate details. The resonant peaks or notches are often missed due to the lack of enough resolution. [[EM.Cube]]'s [[Planar Module]] offers a powerful adaptive frequency sweep option for this purpose. It effective permittivity is based on defined as the fact that mean (average) of the frequency response permittivity 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 two substrate layers just above 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 below the scattering [[parameters]]metallic trace. Then* For embedded object sets, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, all effective permittivity is defined as the possible rational functions largest of higher orders are tried out. The process continues until adding new intermediate frequency samples does not improve the resolution permittivities of all the "S<sub>ij</sub>" curves over the given frequency range. In that case, the curves are considered as having convergedsubstrate layers and embedded dielectric sets.
You must have defined one or more ports for your planar structure run an adaptive frequency sweep<table><tr><td> [[Image:PMOM32. Open the Frequency Settings dialog from the Simulation Run dialog and select the '''Adaptive''' option png|thumb|360px|A comparison of '''Frequency Sweep Type'''. You have to set values for '''Minimum Number of Samples''' triangular and '''Maximum Number planar hybrid meshes 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 0rectangular patch.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><td> [[EMImage:PMOM30.Cube]] reaches the specified maximum number png|thumb|360px|Mesh of iterations and the convergence criterion two rectangular patches at two different substrate planes. The lower substrate layer has not yet been met, the program will ask you whether to continue the process or exit it and stopa higher permittivity.]] </td></tr></table>
{{Note|For large frequency ranges, you may have to increase both the minimum and maximum number === General Rules of samples. Moreover, remeshing the planar structure at each frequency may prove more practical than fixing the mesh at the highest frequency.}}Planar Hybrid Mesh Generator ===
== Working with The integrity of the planar mesh and its continuity in the junction areas directly affects the quality and accuracy of the simulation results. EM.Picasso Simulation Data =='s hybrid planar mesh generator has some rules that are catered to 2.5-D MoM simulations:
Depending on * If two connected rectangular objects have the source type and the types of observables defined in same side dimensions along their common linear edge with perfect alignment, a projectrectangular junction mesh is produced.* If two connected rectangular objects have different side dimensions along their common linear edge or have edge offset, a number set of output data are triangular cells is generated at along the end edge of the object with the larger side.* Rectangle strip objects that host a planar MoM simulationgap source or a lumped element always have a rectangular mesh around the gap area. Some of these data are 2D by nature * If two objects reside on the same Z-plane, belong to the same trace group and some have a common overlap area, they are 3D. The output simulation data generated by EM.Picasso can be categorized first merged into a single object for the following groups (click on each type to learn more about purpose of meshing using the "Boolean Union" operation. * Embedded objects have prismatic meshes along the Z-axis.* If an embedded object is located underneath or above a metallic trace object or connected from both top and bottom, it): is meshed first and its mesh is then reflected on all of its attached horizontal trace objects.
* '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Current Distributions]]''': Electric and magnetic current amplitude and phase on all metal and slot traces and embedded objects
* '''[[Data_Visualization_and_Processing#Computing_and_Graphing_Port_Characteristics | Port Characteristics]]''': S, Z and Y [[Parameters]] and Voltage Standing Wave Ratio (VSWR)
* '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Near-Field Distributions]]''': Electric and magnetic field amplitude and phase on specified planes and their central axes
* '''[[Data_Visualization_and_Processing#Far-Field_Observables | Radiation Characteristics]]''': Radiation Patterns, Directivity, Total Radiated Power, Axial Ratio, Main Beam Theta and Phi, Radiation Efficiency, Half Power Beam Width (HPBW), Maximum Side Lobe Level (SLL), First Null Level (FNL), Front-to-Back Ratio (FBR), etc.
* '''[[Data_Visualization_and_Processing#Computing_Radar_Cross_Section | Radar Cross Section]]''': Bi-static and Mono-static Radar Cross Section (RCS)
* '''Periodic Characteristics''': Reflection and Transmission Coefficients
If your <table><tr><td> [[File:PMOM36.png|250px]] [[File:PMOM38.png|250px]] [[File:PMOM37.png|250px]] </td></tr><tr><td> Two overlapping planar structure is excited by gap sources or probe sources or de-embedded sources, objects and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance a comparison of their triangular and admittance (Shybrid planar meshes. </Ztd></Y) tr><tr><td> [[parametersFile:PMOM33.png|250px]] of the designated ports. The scattering [[parametersFile:PMOM35.png|250px]] are defined based on the port impedances specified in the project's Port Definition dialog[[File:PMOM34. If more than one port has been defined in the project, the Spng|250px]] </Ztd></Y matrices of the multiport network are calculatedtr><tr><td> Edge-connected rectangular planar objects and a comparison their triangular and hybrid planar meshes. </td></tr></table>
<table><tr><td> [[ImageFile:Info_iconPMOM39.png|40px375px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Computing_and_Graphing_Port_Characteristics File:PMOM40.png| Computing and Graphing Port Characteristics375px]]'''</td></tr><tr><td> Meshes of short and long vertical PEC vias connecting two horizontal metallic strips.</td></tr></table>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation of Scattering Parameters]]'''.=== Refining the Planar Mesh Locally ===
Electric and magnetic currents are It is very important to apply the right mesh density to capture all the fundamental output data geometrical details of a your planar MoM simulationstructure. After the numerical solution of the MoM linear systemThis is especially true for "field discontinuity" regions such as junction areas between connected objects, they where larger current concentrations are found using usually observed at sharp corners, or at the solution vector '''[I]''' junction areas between metallic traces and PEC vias, as well as the definitions of the electric areas around gap sources and magnetic vectorial basis functions:lumped elements, which create voltage or current discontinuities.
:<math> \mathbf{[X]}_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math><!--[[File:PMOM83The Planar Mesh Settings dialog gives a few options for customizing your planar mesh around geometrical and field discontinuities. The check box labeled "'''Refine Mesh at Junctions'''" increases the mesh resolution at the connection area between rectangular objects. The check box labeled "'''Refine Mesh at Gap Locations'''" might be particularly useful when gap sources or lumped elements are placed on a short transmission line connected from both ends. The check box labeled "'''Refine Mesh at Vias'''" increases the mesh resolution on the cross section of embedded object sets and at the connection regions of the metallic objects connected to them. EM.Picasso typically doubles the mesh resolution locally at the discontinuity areas when the respective boxes are checked. You should always visually inspect EM.Picasso's default generated mesh to see if the current mesh settings have produced an acceptable mesh.png]]-->
Note that currents are complex vector quantitiesSometimes EM. Each electric or magnetic current has three XPicasso's default mesh may contain very narrow triangular cells due to very small angles between two edges. In some rare cases, Y and Z componentsextremely small triangular cells may be generated, and each complex component has whose area is a magnitude and phasesmall fraction of the average mesh cell. You can visualize These cases typically happen at the surface electric currents on metal (PEC) junctions and conductive sheet tracesother discontinuity regions or at the boundary of highly irregular geometries with extremely fine details. In such cases, surface magnetic currents on slot (PMC) traces and vertical volume currents on increasing or decreasing the PEV vias mesh density by one or few cells per effective wavelength often resolves that problem and embedded dielectric objectseliminates those defective cells. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the project workspaceNonetheless, superimposed on the surface of physical objectsEM. In order Picasso's planar mesh generator offers an option to view identify the current distributions, you must first define defective triangular cells and either delete them as observables before running or cure them. By curing we mean removing a narrow triangular cell and merging its two closely spaced nodes to fill the planar MoM simulationcrack left behind. At EM.Picasso by default deletes or cures all the top of triangular cells that have angles less than 10º. Sometimes removing defective cells may inadvertently cause worse problems in the Current Distribution dialog mesh. You may choose to disable this feature and in uncheck the section titled box labeled "'''Active Trace / SetRemove Defective Triangular Cells''', you " in the Planar Mesh Settings dialog. You can select a trace or embedded object set where you want to observe also change the value of the current distributionminimum allowable cell angle.
{{Note|Narrow, spiky triangular cells in a planar mesh are generally not desirable. You have should get rid of the either by changing the mesh density or using the hybrid planar mesh generator's additional mesh refinement options.}} <table><tr><td> [[Image:PMOM44.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 1.]]</td></tr><tr><td> [[Image:PMOM42.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 2.]]</td></tr></table> == Running Planar MoM Simulations in EM.Picasso == === EM.Picasso's Simulation Modes === [[EM.Picasso]] offers five Planar MoM simulation modes: {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency Planar MoM Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the planar MoM solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to define achieve a separate current distribution observable for each individual trace 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 embedded object more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|} You can setthe simulation mode from [[EM.Picasso]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree. === Running a Single-Frequency Planar MoM Analysis === A single-frequency analysis is the simplest type of [[EM.Picasso]] simulation and involves the following steps: * Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''. * Define you background structure and its layer properties and trace types. * Construct your planar structure using [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s drawing tools to create all the finite-sized metal and slot trace objects and possibly embedded metal or dielectric objects that are interspersed among the substrate layers.* Define an excitation source and observables for your project.* Examine the planar mesh, verify its integrity and change the mesh density if necessary.* Run the Planar MoM simulation engine.* Visualize the output simulation data.}}
To run a planar MoM analysis of your project structure, open the Run Simulation Dialog by clicking the '''Run''' [[ImageFile:Info_iconrun_icon.png|40px]] Click here to learn more about button on the '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps Simulate Toolbar''' or select '''Menu > Simulate > Run''' or use the keyboard shortcut {{key| Visualizing 3D Current Distribution Maps]]Ctrl+R}}. The '''Single-Frequency Analysis''' option of the '''Simulation Mode''' dropdown list is selected by default. Once you click the {{key|Run}} button, the simulation starts. A new window called the "Output Window" opens up that reports the different stages of simulation and the percentage of the tasks completed at any time. After the simulation is successfully completed, a message pops up and reports the end of simulation. In certain cases like calculating scattering parameters of a circuit or reflection / transmission characteristics of a periodic surface, some results are also reported in the output window.
<table>
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<td> [[Image:PMOM84Picasso L1 Fig18.png|thumb|300pxleft|480px|EM.Picasso's Current Distribution Simulation Run dialog.]] </td><td> [[Image:PMOM85(1).png|thumb|420px|The current distribution map of a patch antenna.]] </td>
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[[File:PMOM90.png|thumb|320px|[[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]]), and their computation requires integration of complex dyadic Green's functions of a multilayer background structure as opposed to the free space Green's functions.=== Setting Numerical Parameters ===
{{Note|Keep in mind A planar MoM simulation involves a number of numerical parameters that since take preset default values unless you change them. You can access these parameters and change their values by clicking the '''Settings''' button next to the '''Select Engine''' drop-down list in [[EM.Picasso uses a planar MoM solver]]'s Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the calculated field value at the source point is infinitedefault numerical parameter values intact. As a resultHowever, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers it is useful to produce acceptable 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 Here we describe some of the numerical parameters. The "'''Matrix Fill'''" section of the dialog deals with the operations involving the dyadic Green's functions. You can set a value for the '''Convergence Rate for Integration''', which is 1E-5 by default. This is used for the convergence test of all the infinite integrals in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, the surface wave poles are captured in the complex integration plane using contour deformation. You can change the maximum number of iterations involved in this deformed contour integration, whose default value is 20. When the substrate is very thin with respect to learn more about the wavelength, the dyadic Green's functions exhibit numerical instability. Additional singularity extraction measures are taken to avoid numerical instability but at the expense of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01λ<sub>eff</sub>, where λ<sub>eff</sub> is the effective wavelength. You can modify the definition of "Thin Substrate" by entering a value for ''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Defining '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 Field Sensor Observable]]fast quasi-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''.
In the "Spectral Domain Integration" section of the dialog, you can set a value to '''Max Spectral Radius in k0''', which has a default value of 30. This means that the infinite spectral-domain integrals in the spectral variable k<sub>ρ</sub> are pre-calculated and tabulated up to a limit of 30k<sub>0</sub>, where k<sub>0</sub> is the free space propagation constant. These integrals may converge much faster based on the specified Convergence Rate for Integration described earlier. However, in certain cases involving highly oscillatory integrands, much larger integration limits like 100k<sub>0</sub> might be needed to warrant adequate convergence. For spectral-domain integration along the real k<sub>ρ</sub> axis, the interval [0, Nk<sub>0</sub>] is subdivided into a large number of sub-intervals, within each an 8-point Gauss-Legendre quadrature is applied. The next parameter, '''No. Radial Integration Divisions per k<sub>0</sub>''', determines how small these intervals should be. By default, 2 divisions are used for the interval [Image:Info_icon0, k<sub>0</sub>].png|40pxIn other words, the length of each integration sub-interval is k<sub>0</sub>/2. You can increase the resolution of integration by increasing this value above 2. Finally, instead of 2D Cartesian integration in the spectral domain, a polar integration is performed. You can set the '''No. of Angular Integration Points''', which has a default value of 100. [[EM.Picasso]] Click here to learn more about provides a large selection of linear system solvers including both direct and iterative methods. [[EM.Picasso]], by default, provides a "'''Automatic'''" solver option that picks the best method based on the settings and size of the numerical problem. For linear systems with a size less than N = 3,000, the LU solver is used. For larger systems, BiCG is used when dealing with symmetric matrices, and GMRES is used for asymmetric matrices. You can instruct [[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field MapsEM.Cube]]to write the MoM matrix and excitation and solution vectors into output data files for your examination. To do so, check the box labeled "'''Output MoM Matrix and Vectors'''" in the Matrix Fill section of the Planar MoM Engine Settings dialog. These are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectively.
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<td> [[Image:PMOM116PMOM79.png|thumb|360pxleft|Near-zone electric field map above a microstrip-fed patch antenna720px|EM.]] </td><td> [[Image:PMOM117.png|thumb|360px|Near-zone magnetic field map above a microstrip-fed patch antennaPicasso's Planar MoM Engine Settings dialog.]] </td>
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Even though == Modeling Periodic Planar Structures in EM.Picasso's MoM engine does not need a radiation box, you still have to define a "Far Field" observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct [[EM.Cube]] to perform these calculations. Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in θ direction, the far field component in φ direction and the "Total" far field. The 2D radiation pattern graphs can be plotted from the '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.==
[[Image:Info_iconEM.png|40pxPicasso]] Click here allows you to learn more about '''simulate doubly periodic planar structures with periodicities along the X and Y directions. Once you designate your planar structure as periodic, [[Data_Visualization_and_Processing#Far-Field_Observables | Far Field ObservablesEM.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|40px30px]] Click here to learn more about the theory of '''[[Data_Visualization_and_ProcessingBasic_Principles_of_The_Method_of_Moments#Using_Array_Factors_to_Model_Antenna_Arrays Periodic_Planar_MoM_Simulation | Using Array Factors to Model Antenna Arrays Periodic Green's functions]]'''.
{{Note| [[Image:Info_iconEM.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation PatternsPicasso]]'''can handle both regular and skewed periodic lattices.}}
 === Defining a 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 "'''Periodic Unit Cell'''". To define a periodic structure, you must open [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation GraphsEM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''>''' '''Simulate > 'Computational Domain > Periodicity Settings...''' from the menu bar. In the Periodicity Settings Dialog, check the box labeled '''Periodic Structure'''. This will enable the section titled''"''Lattice Properties". You can define the periods along the X and Y axes using the boxes labeled '''Spacing'''. In a periodic structure, the virtual domain is replaced by a default blue periodic domain that is always centered around the origin of coordinates. Keep in mind that the periodic unit cell must always be centered at the origin of coordinates. The relative position of the structure within this centered unit cell will change the phase of the results.
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<td> [[FileImage:PMOM118PMOM99.png|thumb|300px|EM.Picasso's Radiation Pattern Periodicity Settings dialog.]] </td><td> [[Image:PMOM119.png|thumb|420px|3D polar radiation pattern plot of a microstrip-fed patch antenna.]] </td>
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When a In many cases, your planar structure is excited by a plane wave source, 's traces or embedded objects are entirely enclosed inside the calculated far field data indeed represent periodic unit cell and do not touch the scattered fields boundary of that planar structurethe 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 also calculate arrange objects with linear edges such that one or more flat edges line up with the radar cross section (RCS) of a domain's bounding box. In such cases, [[EM.Picasso]]'s planar targetMoM 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. Note It is clear that in this case due to periodicity, the RCS is defined for a finite-sized target in basis functions do not need to be extended at the presence left or bottom boundaries of the unit cell. As an infinite background structureexample, consider a periodic metallic screen as shown in the figure on the right. The scattered θ and φ components unit cell of the far-zone electric field are indeed what you see this structure can be defined as a rectangular aperture in the 3D far field visualization of radiation a PEC ground plane (scatteringmarked as Unit Cell 1) patterns. Instead of radiation or scattering patternsIn this case, the rectangle object is defined as a slot trace. Alternatively, you can instruct [[EM.Picasso]] to plot 3D visualizations define a unit cell in the form of σ<sub>θ</sub>a microstrip cross on a metal trace. In the latter case, σ<sub>φ</sub> however, the microstrip cross should extend across the unit cell and connect to the total RCScrosses in the neighboring cells in order to provide current continuity.
<table><tr><td> [[Image:Info_iconimage122.png|40pxthumb|400px|Modeling a periodic screen using two different types of unit cell.]] Click here to learn more about '''</td></tr></table>Â <table><tr><td> [[Data_Visualization_and_Processing#Computing_Radar_Cross_Section Image:pmom_per5_tn.png| Computing Radar Cross Sectionthumb|300px|The PEC cross unit cell.]]</td><td> [[Image:pmom_per6_tn.png|thumb|300px|Planar mesh of the PEC cross unit cell. Note the cell extensions at the unit cell'''s boundaries.]] </td></tr></table>Â === 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 steer its beam. You can do this from the property dialog of the gap or probe source. At the bottom of the '''Planar Gap Circuit Source Dialog''' or '''Gap Source Dialog''', there is a button titled '''Periodic Scan...'''. You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the radiation patterns of a beam-steered antenna array, you have to define a finite-sized array factor in the Radiation Pattern dialog. You do this in the '''Impose Array Factor''' section of this dialog. The values of '''Element Spacing''' along the X and Y directions must be set equal to learn more about the value of '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]Periodic Lattice Spacing'''along those directions.
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<td> [[FileImage:PMOM124Period5.png|thumb|300px350px|Setting periodic scan angles in EM.Picasso's Radar Cross Section Gap Source dialog.]] </td><td> [[Image:PMOM125Period5_ang.png|thumb|420px350px|An example of Setting the 3D mono-static radar cross section plot of a patch antennabeam 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>
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<ptable><tr><td> [[Image:Period7.png|thumb|360px|Radiation pattern of an 8Ã8 finite-sized periodic printed dipole array with 0 deg;phi and theta scan angles.]] </ptd><td> [[Image:Period8.png|thumb|360px|Radiation pattern of a beam-steered 8Ã8 finite-sized periodic printed dipole array with 45° phi and theta scan angles.]] </td></tr></table> === Exciting Periodic Structures Using Plane Waves in EM.Picasso === When a periodic planar structure is excited using a plane wave source, it acts as a periodic surface that reflects or transmits the incident wave. [[EM.Picasso ]] calculates the reflection and transmission coefficients of periodic planar structures. If you run a single-frequency plane wave simulation, the reflection and transmission coefficients are reported in the Output Window at the end of the simulation. Note that these periodic characteristics depend on the polarization of the incident plane wave. You set the polarization (TMz or TEz) in the '''Plane Wave Dialog''' when defining your excitation source. In this dialog you also set the values of the incident '''Theta''' and '''Phi''' angles. At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called "reflection.CPX" and "transmission.CPX".  {{Note|In the absence of any finite traces or embedded objects in the project workspace, [[EM.Picasso]] computes the reflection and transmission coefficients of the layered background structure of your project.}} <table><tr><td>[[Image:PMOM102.png|thumb|580px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]]</td></tr></table> === Running a Periodic MoM Analysis === You run a periodic MoM analysis just like an aperiodic MoM simulation from [[EM.Picasso]]'s Run Dialog. Here, too, you can run a single-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you can define several observables for your project. If you open the Planar MoM Engine Settings dialog, you will see a section titled "Infinite Periodic Simulation". In this section, you can set the number of Floquet modes that will be computed in the periodic Green's function summations. By default, the numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a total of 2500 Floquet terms will be computed for each periodic MoM simulation.  <table><tr><td>[[Image:PMOM98.png|thumb|600px|Changing the number of Floquet modes from the Planar MoM Engine Settings dialog.]]</td></tr></table> You learned earlier how to use [[EM.Cube]]'s powerful, adaptive frequency sweep utility to study the frequency response of a planar structure. Adaptive frequency sweep uses rational function interpolation to generate smooth curves of the scattering parameters with a relatively small number of full-wave simulation runs in a progressive manner. Therefore, you need a port definition in your planar structure to be able to run an adaptive frequency sweep. This is clear in the case of an infinite periodic phased array, where your periodic unit cell structure must be excited using either a gap source or a probe source. You run an adaptive frequency sweep of an infinite periodic phased array in exactly the same way to do for regular, aperiodic, planar structures. [[EM.Cube]]'s Planar Modules also allows you to run an adaptive frequency sweep of periodic surfaces excited by a plane wave source. In this case, the planar MoM engine calculates the reflection and transmission coefficients of the periodic surface. Note that you can conceptually consider a periodic surface as a two-port network, where Port 1 is the top half-space and Port 2 is the bottom half-space. In that case, the reflection coefficient R is equivalent to S<sub>11</sub> parameter, while the transmission coefficient T is equivalent to S<sub>21</sub> parameter. This is, of course, the case when the periodic surface is illuminated by the plane wave source from the top half-space, corresponding to 90°< θ = 180°. You can also illuminate the periodic surface by the plane wave source from the bottom half-space, corresponding to 0° = θ < 90°. In this case, the reflection coefficient R and transmission coefficient T are equivalent to S<sub>22</sub> and S<sub>12</sub> parameters, respectively. Having these interpretations in mind, [[EM.Cube]] enables the "'''Adaptive Frequency Sweep'''" option of the '''Frequency Settings Dialog''' when your planar structure has a periodic domain together with a plane wave source. <!--=== 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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