[[Image:Splash-planar new.jpg|right|800px720px]]<strong><font color="#015865" size="4">Fast Full-Wave Simulator For Modeling Multilayer Planar Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== 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 Maxwell’s equations features collectively known as opposed to their differential forms that are used in the finite element or finite difference time domain methods[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.
In EM[[Image:Info_icon.Picasso, the background structure is a planar layered substrate that consists of one or png|30px]] Click here to learn more laterally infinite material layers always stacked along the Z-axis. In other words, the dimensions of the layers are infinite along the X and Y axes. Your substrate can be a dielectric half-space, or a single conductor-backed dielectric layer (as in microstrip components or patch antennas), or simply the unbounded free space, or any arbitrary multilayer stack-up configuration. In the special case of a free space substrate, EM.Picasso behaves similar to about '''[[Getting_Started_with_EM.Cube | EM.LiberaCube Modeling Environment]]'s Surface MoM simulator. Metallic traces are placed at the boundaries between the substrate or superstrate layers. These are modeled by perfect electric conductor (PEC) traces or conductive sheet traces of finite thickness and finite conductivity. Some layers might be separated by infinite perfectly conducting ground planes. The two sides of a ground plane can be electromagnetically coupled through one or more slots (apertures). Such slots are modeled by magnetic surface currents. Furthermore, the metallic traces can be interconnected or connected to ground planes using embedded objects. Such objects can be used to model circuit vias, plated-through holes or dielectric inserts. These are modeled as volume polarization currents''.
In a planar MoM simulation, the unknown electric and magnetic currents are discretized as a collection === Advantages & Limitations of elementary currents with small finite spatial extentsEM. As a result, the governing integral equations reduce to a system of linear algebraic equations, whose solution determines the amplitudes of all the elementary currents defined over the planar structurePicasso's mesh. Once the total currents are known, you can calculate the fields everywhere in the structure.Planar MoM Simulator ===
[[Image:Info_iconEM.png|40pxPicasso]] Click here assumes that your planar structure has a substrate (background structure) of infinite lateral extents. In addition, the planar 2.5-D assumption restricts the 3D objects of your physical structure to learn more about embedded prismatic objects that can only support vertical currents. These assumptions limit the variety and scope of the applications of [[EM.Picasso]]. For example, you cannot use [[EM.Picasso]] to analyze a patch antenna with a finite-sized dielectric substrate. If the substrate edge effects are of concern in your modeling problem, you must use [[EM.Tempo]] instead. On the other hand, since [[EM.Picasso]]'s Planar MoM simulation engine incorporates the Green's functions of the background structure into the analysis, only the finite-sized traces like microstrips and slots are discretized by the mesh generator. As a result, the size of [[EM.Picasso]]'s computational problem is normally much smaller than that of [[Planar Method EM.Tempo]]. In addition, [[EM.Picasso]] generates a hybrid rectangular-triangular mesh of Moments | Theory your planar structure with a large number of Planar Method equal-sized rectangular cells. Taking full advantage of Momentsall the symmetry and invariance properties of dyadic Green's functions often results in very fast computation times that easily make up for [[EM.Picasso]]'''s limited applications. A particularly efficient application of [[EM.Picasso]] is the modeling of periodic multilayer structures at oblique incidence angles.
=== Advantages & Limitations <table><tr><td> [[Image:ART PATCH Fig12.png|thumb|left|480px|The hybrid planar mesh of EMthe slot-coupled patch antenna array.Picasso's Planar MoM Simulator ===]]</td></tr></table>
== EM.Picasso assumes that your planar structure has Features at a substrate (background structure) of infinite lateral extents. In addition, the planar 2.5-D assumption restricts the 3D objects of your physical structure to embedded prismatic objects that can only support vertical currents. These assumptions limit the variety and scope of the applications of EM.Picasso. For example, you cannot use EM.Picasso to analyze a patch antenna with a finite-sized dielectric substrate. If the substrate edge effects are of concern in your modeling problem, you must use [[EM.Tempo]] instead. On the other hand, since EM.Picasso's Planar MoM simulation engine incorporates the Green's functions of the background structure into the analysis, only the finite-sized traces like microstrips and slots are discretized by the mesh generator. As a result, the size of EM.Picasso's computational problem is normally much smaller than that of [[EM.Tempo]]. In addition, EM.Picasso generates a hybrid rectangular-triangular mesh of your planar structure with a large number of equal-sized rectangular cells. Taking full advantage of all the symmetry and invariance properties of dyadic Green's functions often results in very fast computation times that easily make up for EM.Picasso's limited applications. A particularly efficient application of EM.Picasso is the modeling of periodic multilayer structures at oblique incidence angles.Glance ==
== Building a Planar = Structure Definition ===
<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.
</table>
[[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|Insert…}} 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.
<table>
<tr>
<td> [[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.]] </td>
</tr>
</table>
<table>
<tr>
=== 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:
* '''{| 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|}
Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]. You can define two types of metallic traces in [[EM.Picasso]]: '''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 traces, on the other hand, 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 objects.
'''Slot Traces''' are used to model cut-out slots and apertures in PEC ground planes. Planar slot objects are always assumed to lie on an infinite horizontal PEC ground plane with zero thickness, which is not explicitly displayed in the project workspace and its presence is implied. They are modeled by surface magnetic currents. When a slot is excited, tangential electric fields are formed on the aperture, which can be modeled as finite magnetic surface currents confined to the area of the slot. In other words, instead of modeling the electric surface currents 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) 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 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. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining Materials in EM.Cube]]'''.
{{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]]'''.
<table>
<tr>
<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>
</tr>
</table>
=== 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.}}
<table>
# 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 φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a 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 a signal source mesh cell. In fact, a lumped element is equivalent to an infinitesimally narrow gap that induces electric is placed in the path of current flow, across which the device's governing equations are enforced. Using Kirkhoff's laws, these device equations normally establish a relationship between the currents on metal parts and voltages across the device or circuit. Crossing the bridge to Maxwell's domain, the device equations must now be cast into a from o boundary conditions that relate the electric and magnetic currents on slot traces. The excitation source you choose depends on the observables you seek in your projectand fields. [[EM.Picasso provides the following source types for exciting planar structures]] allows you to define passive circuit elements:'''Resistors''' (R), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations of them.
* '''[[Common_Excitation_Source_Types_in_EMImage:Info_icon.Cube#Lumped_.26_Gap_Sources png| Gap Sources40px]]'''* Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Probe_Sources Modeling_Lumped_Elements_in_the_MoM_Solvers |Probe SourcesDefining Lumped Elements]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#De-Embedded_Sources | De-embedded Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Hertzian_Dipole_Sources |Short Dipole Sources]]'''* '''[[Common_Excitation_Source_Types_in_EM.Cube#Plane_Wave_Sources | Plane Wave Sources]]'''* '''[[Hybrid_Modeling_using_Multiple_Simulation_Engines#Working_with_Huygens_Sources | Huygens Sources]]'''
For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal. Gap sources are placed across metal or slot traces. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parametersImage:Info_icon.png|40px]] can be calculated accurately. To calculate the scattering characteristics of Click here for a planar structure, e.g. its radar cross section (RCS), you excite it with a plane wave source. Short dipole sources are used to explore propagation general discussion of points sources along a layered structure. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure possibly in another '''[[EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.Cube26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]] computational module and bring them as a new source to excite your planar structure'''.
A rectangle strip object on a PEC or conductive sheet trace can be regarded as a strip transmission line that carries electric currents along its length (local X direction). {{Note|The characteristic impedance of the line lumped circuit is a function calculated at the operating frequency of its width (local Y direction). A gap source is placed somewhere along the length and across project using the width of such a rectangle strip objectspecified R, thus creating an infinitesimally narrow gap at its locationL and C values. In this caseAs you change the frequency, the gap source represents an ideal voltage source in series with a lumped value of the impedance that is connected across the gap passed to excite the strip transmission line. When the impedance is zero, the gap acts like an ideal lumped source and creates a uniform electric field across the gap. The source pumps electric current into the line. If the voltage source is shorted (having a zero amplitude), then the gap acts like a series lumped element on the transmission linePlanar MoM engine will change.}}
A rectangle strip object on a PMC trace can be regarded as 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 slot gap source is placed somewhere along the length and across the width of the rectangle strip object on a PMC trace and creates an infinitesimally narrow gap at its location. In this case, the slot gap source represents an ideal current source with a shunt lumped admittance that is connected across the slot to excite the slot transmission line. When the admittance is zero, the gap acts like an ideal current filament, which creates electric fields across the slot, equivalent to a magnetic current flowing into the slot line. If the current source is open (having a zero amplitude), then the gap acts like a shunt (parallel) lumped element on the slot line. As you will see later, a coplanar waveguide (CPW) can be realized using two parallel slot lines with two aligned, collocated gap sources.=== Calculating Scattering Parameters Using Prony's Method ===
[[Image:Info_iconThe calculation of the scattering (S) parameters is usually an important objective of modeling planar structures especially for planar circuits like filters, couplers, etc.png|40px]] Click here As you saw earlier, you can use lumped sources like gaps and probes and even active lumped elements to learn calculate the circuit characteristics of planar structures. The admittance / impedance calculations based on the gap voltages and currents are accurate at RF and lower microwave frequencies or when the port transmission lines are narrow. In such cases, the electric or magnetic current distributions across the width of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized. At higher frequencies, however, a more about '''[[Planar MoM Source Types]]'''robust method is needed for calculating the port parameters.
[[Image:Info_iconOne can calculate the scattering parameters of a planar structure directly by analyzing the current distribution patterns on the port transmission lines.png|40px]] Click here The discontinuity at the end of a port line typically gives rise to learn more about a standing wave pattern that can clearly be discerned in the line'''[[Common_Excitation_Source_Types_in_EMs current distribution. From the location of the current minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, i.Cube#Defining_Finite-Sized_Source_Arrays | Using Source Arrays e. the S<sub>11</sub> parameter. A more robust technique is Prony’s method, which is used for Modeling Antenna Arrays]]'''exponential approximation of functions.A complex function f(x) can be expanded as a sum of complex exponentials in the following form:
:<math> f(x) \approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math><!--[[ImageFile:PMOM64PMOM73.png|thumb|600px|EM.Picasso's Lumped Element dialog.]]=== Modeling Lumped Elements in EM.Picasso ===-->
Lumped elements where c<sub>i</sub> are complex coefficients and γ<sub>i</sub> are components, devicesin general, or circuits whose overall dimensions are very small compared to the wavelengthcomplex exponents. As a result, they are considered to be dimensionless compared to From the dimensions physics of a mesh cell. In facttransmission lines, a lumped element is equivalent to an infinitesimally narrow gap we know 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 lossless lines may support one or circuitmore propagating modes with pure real propagation constants (real γ<sub>i</sub> exponents). Crossing the bridge to Maxwell's domainMoreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary γ<sub>i</sub> exponents) that decay along the device equations must now be cast into a line as you move away from o boundary conditions that relate the electric and magnetic currents and fields. EM.Picasso allows you to define passive circuit elements: '''Resistors''' (R), '''Capacitors''' (C), '''Inductors''' (L), and series and parallel combinations location of themsuch discontinuities.
[[Image:Info_icon.png|40px]] Click here In practical planar structures for which you want to learn more about '''[[Modeling_Lumped_Elementscalculate the scattering parameters,_Circuits_%26_Devices_in_EMeach port line normally supports one, and only one, dominant propagating mode.Cube#Defining_Lumped_Elements_in_EMMulti-mode transmission lines are seldom used for practical RF and microwave applications.Picasso_Nonetheless, each port line carries a superposition of incident and reflected dominant-mode propagating signals.26_EMAn incident signal, by convention, is one that propagates along the line towards the discontinuity, where the phase reference plane is usually established.Libera | Defining Lumped Elements]]'A reflected signal is one that propagates away from the port plane. Prony's 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, the scattering matrix of the multi-port structure is then calculated. 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.
<table><tr><td> [[Image:Info_iconPMOM71.png|40px]] Click here for thumb|600px|Minimum and maximum current locations of the standing wave pattern on a microstrip line feeding a general discussion of '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EMpatch antenna.Cube#Linear_Passive_Devices | Linear Passive Devices]]'''.</td></tr>{{Note|The impedance of the lumped circuit is calculated at the operating frequency of the project using the specified R, L and C values. As you change the frequency, the value of the impedance that is passed to the Planar MoM engine will change.}}</table>
=== Defining Independent & Coupled Ports ===
Ports are used in a planar structure to order and index the sources for calculation of circuit [[parameters]] such as scattering (S), impedance (Z) and admittance (Y) [[parameters]]. In [[EM.Cube]]'s [[Planar ModulePicasso]], you can use one or more of the following types of sources to define ports:
* Gap Sources
* De-Embedded Sources
Ports are defined in the '''Observables''' section of the Navigation Treenavigation tree. Right click on the '''Port Definition''' item You can define any number of ports equal to or less than the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the default port assignmentstotal number of sources in your project. If you have N sources in your planar structure, then N default ports are defined, with one port assigned to each source according to their order on the Navigation Treenavigation tree. Note that your project can have mixed gap and probes sources as well as active lumped element sourceson PEC and slot traces or vias. You can also couple ports together to define coupled transmission lines such as coupled strips (CPS) or coplanar waveguides (CPW).
'''You can define any number of ports equal [[Image:Info_icon.png|40px]] Click here to or less than learn more about the total number of sources in your project.''' The Port List of the dialog shows a list of all the ports in ascending order, with their associated sources and the port's characteristic impedance, which is 50S by default[[Glossary_of_EM. You can delete any port by selecting it from the Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port List and clicking the '''Delete''' button of the dialog. Keep in mind that after deleting a port, you will have a source in your project without any port assignment and make sure that is what you intend. You can change the characteristic impedance of a port by selecting it from the Port List and clicking the '''Edit''' button of the dialog. This opens up the Edit Port dialog, where you can enter a new value in the box labeled '''ImpedanceDefinition Observable]]'''.
[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#The_Port_Definition_Observable Modeling_Coupled_Sources_.26_Ports | Port Definition ObservableModeling Coupled Ports]]'''.
[[Image:Info_icon== EM.png|40px]] Click here to learn more about Picasso'''[[Common_Excitation_Source_Types_in_EM.Cube#Modeling_Coupled_Ports | Modeling Coupled Ports]]'''.s Simulation Data & Observables ==
== Running Planar 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 Simulations ==simulation. Some of these data are 2D by nature and some are 3D. The output simulation data generated by [[EM.Picasso]] can be categorized into the following groups:
The first step of planning a planar MoM simulation is defining your planar structure{| 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. This consists png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of the background structure plus all the finite-sized EM.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 trace objects and possibly embedded metal or dielectric objects that are interspersed among the substrate layerstraces | style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. The background stackpng]]| style="width:150px;" | Near-up is defined 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 Layer Stackfrequency domain| style="width:250px;" | None|-up dialog, which automatically opens up as soon as you enter the | style="width:30px;" | [[Planar ModuleFile:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM. The metal and slot traces and embedded object sets are listed in Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the Navigation Treeradiation pattern and additional radiation characteristics such as directivity, which also shows all the geometrical 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 (CADRCS) objects you draw in |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the project workspace under each object group at different 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/Zparameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-planes| 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 a 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|}
The next step is Click on each category to decide on the excitation scheme. If your planar structure has one or learn more ports and you seek to calculate its port characteristics, then you have to choose one of the lumped source types or a de-embedded source. If you are interested details about it in the scattering characteristics of your planar structure, then you must define a plane wave source. Before you can run a planar MoM simulation, you also need to decide on the project's observables. These are the simulation data that you expect [[EM.Cube]] to generate as the outcome Glossary of the numerical simulation. [[EM.Cube]]'s [[Planar ModuleSimulation Observables & Graph Types]] offers the following observables:.
* Current Distribution* Field Sensors* Far Fields (Radiation Patterns If your planar structure is excited by gap sources or Radar Cross Sectionprobe sources or de-embedded sources, and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y)* Huygens Surfaces* parameters of the designated ports. The scattering parameters are defined based on the port impedances specified in the project's Port Characteristics* Periodic CharacteristicsDefinition dialog. If more than one port has been defined in the project, the S/Z/Y matrices of the multiport network are calculated.
If you run a simulation without having defined any observables, no Electric and magnetic currents are the fundamental output data will be generated at the end of the a planar MoM simulation. Some observables require a certain type After the numerical solution of excitation source. For example, port characteristics will be calculated only if the project contains a port definitionMoM linear system, which in turn requires they are found using the existence of at least one gap or probe or de-embedded source. The periodic characteristics (reflection solution vector '''[I]''' and transmission coefficients) are calculated only if the structure has a periodic domain definitions of the electric and excited by a plane wave source.magnetic vectorial basis functions:
:<math> \mathbf{[X]}_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{cases} \mathbf{J(r)} =\sum_{n= Planar Module's Simulation Modes =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>
The simplest simulation type in [[EMNote that currents are complex vector quantities.Cube]] is an analysisEach electric or magnetic current has three X, Y and Z components, and each complex component has a magnitude and phase. In this modeYou can visualize the surface electric currents on metal (PEC) and conductive sheet traces, surface magnetic currents on slot (PMC) traces and vertical volume currents on the planar structure PEV vias and embedded dielectric objects. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in your the project workspace is meshed at , superimposed on the center frequency surface of the projectphysical objects. [[EM.Cube]] generates an input file at this single frequencyIn order to view the current distributions, and you must first define them as observables before running the Planar planar MoM simulation engine is run once. Upon completion of At the planar MoM simulation, a number top of data files are generated depending on the observables you have defined Current Distribution dialog and in your project. An analysis is the section titled '''Active Trace / Set''', you can select a single-run simulationtrace or embedded object set where you want to observe the current distribution.
[[EM.Cube]] offers {{Note|You have to define a number of multi-run simulation modes. In such cases, the Planar MoM simulation engine is run multiple times. At separate current distribution observable for each engine run, certain [[parameters]] are varied and a collection of simulation data are generated. At the end of a multi-run simulation, you can graph the simulation results in EM.Grid individual trace or you can animate the 3D simulation data from the Navigation Tree. For example, in a frequency sweep, the frequency of the project is varied over its specified bandwidth. Port characteristics are usually plotted vs. frequency, representing your planar structure's frequency response. In an angular sweep, the θ or φ angle of incidence of a plane wave source is varied over their respective ranges. [[EMembedded object set.Cube]]'s [[Planar Module]] currently provides the following types of multi-run simulation modes:}}
* Frequency Sweep<table>* Parametric Sweep<tr>* <td> [[OptimizationImage:PMOM85new.png|thumb|left|600px|The current distribution map of a patch antenna.]]</td>* HDMR Sweep</tr></table>
[[File:PMOM80EM.pngPicasso]]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.
Figure 1: Selecting a simulation mode {{Note|Keep in mind that since [[Planar ModuleEM.Picasso]]'s Simulation Run dialoguses a planar MoM solver, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}
=== Running A Planar MoM Analysis ===<table><tr><td> [[Image:PMOM116.png|thumb|left|600px|Near-zone electric field map above a microstrip-fed patch antenna.]] </td></tr><tr><td> [[Image:PMOM117.png|thumb|left|600px|Near-zone magnetic field map above a microstrip-fed patch antenna.]] </td></tr></table>
To run a planar MoM analysis of your project structure, open the Run Simulation Dialog by clicking the '''Run''' Even though [[File:run_iconEM.pngPicasso]] button on the '''Simulate Toolbar''' or select '''Menu''' '''s MoM engine does not need a radiation box, you still have to define a >quot;''' '''Simulate Far Field>quot;''' '''Run''' or use the keyboard shortcut '''Ctrl+R'''observable for radiation pattern calculation. The '''Analysis''' option of the '''Simulation Mode''' dropdown list This is selected by default. Once you click the '''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 because far field calculations take time. After the simulation is successfully completed, a message pops up and reports the end of simulation. In certain cases like calculating scattering you have to instruct [[parametersEM.Cube]] of to perform these calculations. Once a circuit or reflection / transmission characteristics of a periodic surfaceplanar MoM simulation is finished, some results three far field items are also reported added under the Far Field item in the Output WindowNavigation Tree. At These are the end of a simulationfar field component in θ direction, you need to click the far field component in φ direction and the "Total" far field. The 2D radiation pattern graphs can be plotted from the '''CloseData Manager''' button . A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the Output Window to return to the project workspaceXY, YZ, ZX and user defined plane cuts.
[[FileImage:PMOM78Info_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> [[Planar ModuleImage:PMOM119.png|thumb|left|600px|3D polar radiation pattern plot of a microstrip-fed patch antenna.]]'s Simulation Run dialog.</td></tr></table>
=== Stages Of A Planar MoM Analysis ===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.
<table><tr><td> [[EMImage:PMOM125.Cube]]'s Planar MoM simulation engine uses a particular formulation png|thumb|left|600px|An example of the method 3D monostatic radar cross section plot of moments called mixed potential integral equation (MPIE)a patch antenna. Due to high-order singularities, the dyadic Green's functions for electric fields generated by electric currents as well as the dyadic Green's functions for magnetic fields generated by magnetic currents have very slow convergence behaviors. Instead of using these slowly converging dyadic Green's function, the MPIE formulation uses vector and scalar potentials. These include vector electric potential '''A(r)''', scalar electric potential K]] <sup/td>Φ</suptr>'''(r)''', vector magnetic potential '''F(r)''' and scalar magnetic potential K<sup>Ψ</suptable>'''(r)'''. These potentials have singularities of lower orders. As a result, they coverage relatively faster. The speed of their convergence is further increased drastically using special singularity extraction techniques.
A planar MoM simulation consists of two major stages: matrix fill and linear system inversion. In the first stage, the moment matrix and excitation vector are calculated. In the second stage, the MoM system of linear equations is inverted using one of the several available matrix solvers to find the unknown coefficients of all the basis functions. The unknown electric and magnetic currents are linear superpositions of all these elementary solutions. These can be visualized == Discretizing a Planar Structure in [[EM.Cube]] using the current distribution observables. Having determined all the electric and magnetic currents in your planar structure, [[EM.Cube]] can then calculate the near fields on prescribed planes. These are introduced as field sensor observables. The near-zone electric and magnetic fields are calculated using a spectral domain formulation of the dyadic Green's functions. Finally the far fields of the planar structure are calculated in the spherical coordinate system. These calculations are performed using the asymptotic form of the dyadic Green's functions using the "stationary phase method".Picasso ==
=== Setting Numerical Parameters ===The method of moments (MoM) discretizes all the finite-sized objects of a planar structure (excluding the background structure) into a set of elementary cells. Both the quality and resolution of the generated mesh greatly affect the accuracy of the MoM numerical solution. The mesh density gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the finite-sized geometrical objects. As a rule of thumb, a mesh density of about 20-30 cells per effective wavelength usually yields satisfactory results. But for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular output data that you seek in a simulation also influence your choice of mesh resolution. For example, far field characteristics like radiation patterns are less sensitive to the mesh density than field distributions on structures with a highly irregular shapes and boundaries.
A planar MoM simulation involves a number of numerical <table><tr><td> [[parameters]] that take preset default values unless you change themImage:PMOM31. You can access these [[parameters]] and change their values by clicking the '''png|thumb|400px|The Planar Mesh Settings''' button next to the '''Select Engine''' dropdown list in the [[Planar Module]]'s Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the default numerical parameter values intact. However, it is useful to familiarize yourself with these [[parameters]], as they may affect the accuracy of your numerical results.</td></tr></table>
The Planar MoM Engine Settings Dialog is organized in a number of sectionsEM. Here we describe some Picasso provides two types of the numerical [[parameters]]. The "'''Matrix Fill'''" section of the dialog deals with the operations involving the dyadic Green's functions. You can set mesh for a value for the '''Convergence Rate for Integration''', which is 1Eplanar structure: a pure triangular surface mesh and a hybrid triangular-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 rectangular surface wave poles are captured in the complex integration plane using contour deformationmesh. You can change the maximum number of iterations involved in this deformed contour integrationIn both case, whose default value is 20EM. When the substrate is very thin with respect Picasso attempts 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, create a thin substrate layer is defined to a have a thickness less than 0.01λ<sub>eff</sub>highly regular mesh, where λ<sub>eff</sub> is the effective wavelength. You can modify the definition of "Thin Substrate" by entering a value for '''Thin Substrate Threshold''' different than the default 0.01. The parameter '''Max Coupling Range''' determines the distance threshold in wavelength between the observation and source points after which most of the Green's interactions are neglected. This distance by default is set to 1,000 wavelengthscells have almost equal areas. For electrically small planar structureswith regular, the phase variation across the structure may be negligible. In such casesmostly rectangular shapes, a fast quasi-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''hybrid mesh generator usually leads to faster computation times.
In the "Spectral Domain Integration" section of the dialog, you can set a value [[Image:Info_icon.png|30px]] Click here to learn more about '''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[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. The next parameter, '''NoCube. Radial Integration Divisions per k<sub>0</sub>''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k<sub>0</sub>27s_Mesh_Generators | Working with Mesh Generator]]. 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 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.
[[FileImage:PMOM79Info_icon.png|30px]]Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Picasso's Triangular Surface Mesh Generator]]'''.
Figure 1<table><tr><td> [[Image: The Planar MoM Engine Settings dialogPMOM48F.png|thumb|left|420px|Geometry of a multilayer slot-coupled patch array.]] </td></tr><tr><td> [[Image:PMOM48G.png|thumb|left|420px|Hybrid planar mesh of the slot-coupled patch array.]] </td></tr></table>
=== Planar Module's Linear System Solvers ===<table><tr><td> [[Image:PMOM48H.png|thumb|left|420px|Details of the hybrid planar mesh of the slot-coupled patch array around discontinuities.]] </td></tr></table>
After the MoM impedance matrix '''[Z]''' (not to be confused with the impedance [[parameters]]) 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:=== The Hybrid Planar Mesh Generator ===
:<math> \mathbf{[Z]}_{N\times N} \cdot \mathbf{[I]}_{N\times 1} = \mathbf{[V]}_{N\times 1} </math><!--[[File:PMOM81EM.Picasso's hybrid planar mesh generator tries to produce as many rectangular cells as possible especially in the case of objects with rectangular or linear boundaries. In connection or junction areas between adjacent objects or close to highly curved boundaries, triangular cells are used to fill the "irregular" regions in a conformal and consistent manner.png]]-->
where '''[I]''' is The mesh density gives a measure of the solution vector, which contains the unknown amplitudes number of all the basis functions cells per effective wavelength that represent the unknown electric and magnetic currents are placed in various regions of finite extents in your planar structure. In the above equationThe effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, N where e<sub>eff</sub> is the dimension of the linear system and equal to the total number of basis functions in the planar mesheffective permittivity. By default, [[EM.CubePicasso]]'s linear solvers compute the solution vector'''[I]''' generates a hybrid mesh with a mesh density of the above system20 cells per effective wavelength. You can instruct [[EM.Cube]] to write the MoM matrix and excitation and solution vectors into output data files The effective permittivity is defined differently for your examination. To do so, check the box labeled "'''Output MoM Matrix different types of traces and Vectors'''" in the Matrix Fill section of the Planar MoM Engine Settings dialogembedded object sets. These This is to make sure that enough cells are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectivelyplaced in areas that might feature higher field concentration.
There are a large number * For PEC and conductive sheet traces, the effective permittivity is defined as the larger of numerical methods for solving systems the permittivity of linear equations. These methods are generally divided into the two groups: direct solvers substrate layers just above and iterative solversbelow the metallic trace. Iterative solvers are usually based on matrix-vector multiplications. Direct solvers typically work faster for matrices of smal to medium size (N<3* For slot traces,000the effective permittivity is defined as the mean (average)of the permittivity of the two substrate layers just above and below the metallic trace. [[EM* For embedded object sets, the effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets.Cube]]'s [[Planar Module]] offers five linear solvers:
# LU Decomposition Method<table># Biconjugate Gradient Method (BiCG)<tr># Preconditioned Stabilized Biconjugate Gradient Method (BCG-STAB)<td> [[Image:PMOM32.png|thumb|360px|A comparison of triangular and planar hybrid meshes of a rectangular patch.]] </td># Generalized Minimal Residual Method (GMRES)<td> [[Image:PMOM30.png|thumb|360px|Mesh of two rectangular patches at two different substrate planes. The lower substrate layer has a higher permittivity.]] </td># Transpose-Free Quasi-Minimum Residual Method (TFQMR)</tr></table>
Of the above list, LU is a direct solver, while the rest are iterative solvers. 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 to a class === General Rules of solvers called '''Krylov Sub-space Methods'''. In particular, the GMRES method always provides guaranteed unconditional convergence.Planar Hybrid Mesh Generator ===
[[EM.Cube]]'s [[Planar Module]], by default, provides a "'''Automatic'''" solver option that picks the best method based on the settings and size The integrity 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, planar mesh and GMRES is used for asymmetric matrices. If its continuity in 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 junction areas directly affects the automatic solver option quality and manually set you own solver type. This is done using the '''Solver Type''' dropdown list in the "'''Linear System Solver'''" section accuracy of the Planar MoM Engine Settings dialogsimulation results. There are also a number of other [[parameters]] related to the solversEM. 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 s hybrid planar mesh generator has some rules that are used. In this case, the elements of the matrix are thresholded with respect catered to the larges element2. The default value of '''Threshold for Sparse Solver''' is 1E5-6, 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 [[parameters]] 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.D MoM simulations:
* If your computer has an Intel CPU, then [[EM.Cube]] offers special versions of all the above linear solvers that two connected rectangular objects have been optimized for Intel CPU platforms. These optimal solvers usually work 2-3 time faster than the same side dimensions along their generic counterparts. When you install [[EM.Cube]]common linear edge with perfect alignment, the option to use Intel-optimized solvers a rectangular junction mesh is already enabledproduced. However* If two connected rectangular objects have different side dimensions along their common linear edge or have edge offset, you can disable this option (e.g. if your computer has a non-Intel CPU). To do that, open set of triangular cells is generated along the [[EMedge of the object with the larger side.Cube]]'s Preferences Dialog from '''Menu > Edit > Preferences''' * Rectangle strip objects that host a gap source or using a lumped element always have a rectangular mesh around the keyboard shortcut '''Ctrl+H'''gap area. Select * If two objects reside on the Advanced tab of same Z-plane, belong to the dialog same trace group and uncheck have a common overlap area, they are first merged into a single object for the purpose of meshing using the box labeled "''' Use Optimized Solvers for Intel CPU'''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.
[[File:PMOM82.png]]
<table><tr><td> [[ImageFile:PMOM127PMOM36.png|thumb250px]] [[File:PMOM38.png|400px250px]] [[File:PMOM37.png|Settings adaptive frequency sweep parameters in EM250px]] </td></tr><tr><td> Two overlapping planar objects and a comparison of their triangular and hybrid planar meshes.Picasso's Frequency Settings Dialog</td></tr><tr><td> [[File:PMOM33.png|250px]][[File:PMOM35.png|250px]] [[File:PMOM34.png|250px]] </td>=== Running Uniform </tr><tr><td> Edge-connected rectangular planar objects and Adaptive Frequency Sweeps ===a comparison their triangular and hybrid planar meshes. </td></tr></table>
In a frequency sweep, the operating frequency of a planar structure is varied during each sweep run. <table><tr><td> [[EMFile:PMOM39.Cubepng|375px]]'s [[Planar ModuleFile:PMOM40.png|375px]] offers two types </td></tr><tr><td> Meshes of frequency sweep: Uniform short and Adaptivelong vertical PEC vias connecting two horizontal metallic strips. In a uniform frequency sweep, the frequency range and the number of frequency samples are specified. The samples are equally spaced over the frequency range. At the end of each individual frequency run, the output data are collected 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.Grid.td></tr></table>
To run a uniform frequency sweep, open === Refining 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 of '''Start Frequency'''and '''End Frequency''' as well as the '''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 that in a MoM simulation, changing the frequency results in a change of the mesh of the structure, too. This is because the mesh density is defined in terms of the number of cells per effective wavelength. By default, during a frequency sweep, [[EM.Cube]] fixes the mesh density at the highest frequency, i.e., at the "End Frequency". This usually results in a smoother frequency response. You have the option 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 in the '''Planar 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''' button.Locally ===
Frequency sweeps are often performed to study the frequency response of a planar structure. In particular, the variation of scattering [[parameters]] like S<sub>11</sub> (return loss) and S<sub>21</sub> (insertion loss) with frequency are of utmost interest. When analyzing resonant structures like patch antennas or planar filters over large frequency ranges, 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 is based on the fact that the frequency response of a physical, causal, multiport network can be represented mathematically using a rational function approximation. In other words, the S [[parameters]] of a circuit exhibit a finite number of poles and zeros over a given frequency range. [[EM.Cube]] first starts with very few frequency samples and tries important to fit rational functions of low orders apply the right mesh density to the scattering [[parameters]]. Then, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, capture all the possible rational functions geometrical details of higher orders are tried outyour planar structure. The process continues until adding new intermediate frequency samples does not improve the resolution of the This is especially true for "S<sub>ij</sub>field discontinuity" curves over regions such as junction areas between connected objects, where larger current concentrations are usually observed at sharp corners, or at the given frequency range. In that casejunction areas between metallic traces and PEC vias, as well as the curves are considered as having convergedareas around gap sources and lumped elements, which create voltage or current discontinuities.
You must have defined one or more ports The Planar Mesh Settings dialog gives a few options for customizing your planar structure run an adaptive frequency sweepmesh around geometrical and field discontinuities. Open the Frequency Settings dialog from the Simulation Run dialog and select the The check box labeled "'''Adaptive''' option of '''Frequency Sweep TypeRefine Mesh at Junctions'''" increases the mesh resolution at the connection area between rectangular objects. You have to set values for The check box labeled "'''Minimum Number of SamplesRefine Mesh at Gap Locations''' and '''Maximum Number of Samples'''. Their default values " might be particularly useful when gap sources or lumped elements are 3 and 9, respectivelyplaced on a short transmission line connected from both ends. You also set a value for the The check box labeled "'''Convergence CriterionRefine Mesh at Vias''', which has a default value of 0.1. At each iteration cycle, all " increases the S [[parameters]] are calculated at mesh resolution on the newly inserted frequency samples, cross section of embedded object sets and their average deviation from at the curves connection regions of the last cycle is measured as an errormetallic objects connected to them. When this error falls below EM.Picasso typically doubles the specified convergence criterion, mesh resolution locally at the iteration is endeddiscontinuity areas when the respective boxes are checked. If [[You should always visually inspect EM.Cube]] reaches the specified maximum number of iterations and the convergence criterion has not yet been met, the program will ask you whether Picasso's default generated mesh to continue see if the process or exit it and stopcurrent mesh settings have produced an acceptable mesh.
{{Note|For large frequency ranges, you Sometimes EM.Picasso's default mesh may have contain very narrow triangular cells due to increase both very small angles between two edges. In some rare cases, extremely small triangular cells may be generated, whose area is a small fraction of the minimum average mesh cell. These cases typically happen at the junctions and maximum number other discontinuity regions or at the boundary of sampleshighly irregular geometries with extremely fine details. MoreoverIn such cases, remeshing increasing or decreasing the mesh density by one or few cells per effective wavelength often resolves that problem and eliminates those defective cells. Nonetheless, EM.Picasso's planar structure at each frequency may prove more practical mesh generator offers an option to identify the defective triangular cells and either delete them or cure them. By curing we mean removing a narrow triangular cell and merging its two closely spaced nodes to fill the crack left behind. EM.Picasso by default deletes or cures all the triangular cells that have angles less than fixing 10º. Sometimes removing defective cells may inadvertently cause worse problems in the mesh at . You may choose to disable this feature and uncheck the highest frequencybox labeled "'''Remove Defective Triangular Cells'''" in the Planar Mesh Settings dialog. You can also change the value of the minimum allowable cell angle.}}
== Working with EM{{Note| Narrow, spiky triangular cells in a planar mesh are generally not desirable.Picasso Simulation Data ==You 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:PMOM130PMOM44.png|thumb|400pxleft|Changing the graph type by editing a data file's properties480px|Deleting or curing defective triangular cells: Case 1.]]=== EM</td></tr><tr><td> [[Image:PMOM42.Picasso's Output Simulation Data ===png|thumb|left|480px|Deleting or curing defective triangular cells: Case 2.]]</td></tr></table>
Depending on the source type and the types of observables defined == Running Planar MoM Simulations 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 can be categorized into the following groups:==
* '''Port Characteristics''': S, Z and Y [[Parameters]] and Voltage Standing Wave Ratio (VSWR)* '''Radiation Characteristics''': Radiation Patterns, Directivity, Total Radiated Power, Axial Ratio, Main Beam Theta and Phi, Radiation Efficiency, Half Power Beam Width (HPBW), Maximum Side Lobe Level (SLL), First Null Level (FNL), Front-to-Back Ratio (FBR), etc=== EM.* '''Scattering Characteristics''': Bi-static and Mono-static Radar Cross Section (RCS)* '''Periodic Characteristics''': Reflection and Transmission Coefficients* '''Current Distributions''': Electric and magnetic current amplitude and phase on all metal and slot traces and embedded objects* '''Near-Field Distributions''Picasso': Electric and magnetic field amplitude and phase on specified planes and their central axess Simulation Modes ===
=== Examining Port Characteristics ===[[EM.Picasso]] offers five Planar MoM simulation modes:
If your {| 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 is excited by gap sources or probe sources or de"As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-embedded sources, and one or more ports have been defined, | 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 engine calculates 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 scattering, impedance and admittance value(S/Z/Ys) 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;" | [[parametersParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]] | style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the designated ports. The scattering center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[parametersParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]] are defined based on | style="width:270px;" | Varies the port impedances specified in the project'value(s Port Definition dialog. If more than ) of one port has been defined in the or more project, variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the S/Z/Y matrices of the multiport network are calculated. center frequency fc| style="width:80px;" | None|}
At You can set the end of a planar MoM simulation, the values of S/Z/Y mode from [[parameters]] and VSWR data are calculated and reported in the output message windowEM. The S, Z and Y [[parametersPicasso]] are written into output ASCII data files of complex type with a "'''s "Simulation Run Dialog".CPX'''" extensionA single-frequency analysis is a single-run simulation. Every file begins with a header consisting of a few comment lines that start with All the "#" symbol. The complex values are arranged into two columns for other simulation modes in the real and imaginary partsabove list are considered multi-run simulations. In If you run a simulation without having defined any observables, no data will be generated at the case of multiport structures, every single element end of the S/Z/Y matrices is written into a separate complex data filesimulation. For exampleIn multi-run simulation modes, you will have certain parameters are varied and a collection of simulation data files like S11are generated.CPX, S21.CPX, ..., Z11.CPX, Z21.CPX, etc. The VSWR data are saved to an ASCII data file At the end of real type with a "'''.DAT'''" extension calledsweep simulation, VSWRyou can graph the simulation results in EM.DATGrid or you can animate the 3D simulation data from the navigation tree.
If you run an === Running a Single-Frequency Planar MoM Analysis === A single-frequency analysis, is the port characteristics have single complex values, which you can view using [[EM.Cube]]'s data manager. However, there are no curves to graph. You can plot the S/Z/Y [[parameters]] and VSWR data when you have data sets, which are generated at the end of any simplest type of sweep including a frequency sweep. In that case, the ".CPX" files have multiple rows corresponding to each value of the sweep parameter (e.g. frequency). [[EM.CubePicasso]]'s 2D graph data are plotted in EM.Grid, a versatile graphing utility. You can plot the port characteristics directly from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree simulation and select one of involves the itemsfollowing steps: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]].
In particular, it may be useful to plot * Set the S<sub>ii</sub> [[parameters]] on a Smith chart. To change units of your project and the format frequency of a data plot, select it in operation. Note that the Data Manager and click its default project unit is '''Editmillimeter''' button. In * 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 Edit File Dialogfinite-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, choose one of verify its integrity and change the options provided in mesh density if necessary.* Run the dropdown list labeled '''Graph Type'''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#Graphing_Port_Characteristics Simulate Toolbar''' or select '''Menu > Simulate > Run''' or use the keyboard shortcut {{key| Graphing Port Characteristics]]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><tr><td> [[Image:Info_iconPicasso L1 Fig18.png|40px]] Click here to learn more about thumb|left|480px|EM.Picasso'''[[Data_Visualization_and_Processing#Rational_Interpolation_of_Port_Characteristics | Rational Interpolation of Scattering Parameterss Simulation Run dialog.]]'''.</td></tr></table>
=== Visualizing Current Distributions Setting Numerical Parameters ===
Electric and magnetic currents are the fundamental output data of a A planar MoM simulationinvolves a number of numerical parameters that take preset default values unless you change them. After You can access these parameters and change their values by clicking the numerical solution of '''Settings''' button next to the MoM linear system, they are found using the solution vector '''[I]Select Engine''' drop-down list in [[EM.Picasso]]'s Simulation Run dialog. In most cases, you do not need to open this dialog and you can leave all the definitions of default numerical parameter values intact. However, it is useful to familiarize yourself with these parameters, as they may affect the electric and magnetic vectorial basis functions:accuracy of your numerical results.
:The Planar MoM Engine Settings Dialog is organized in a number of sections. Here we describe some of the numerical 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 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<mathsub> \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} eff</mathsub>, where λ<!-sub>eff</sub> is the effective wavelength. You can modify the definition of "Thin Substrate" by entering a value for '''Thin Substrate Threshold''' different than the default 0.01. The parameter '''Max Coupling Range''' determines the distance threshold in wavelength between the observation and source points after which the Green's interactions are neglected. This distance by default is set to 1,000 wavelengths. For electrically small structures, the phase variation across the structure may be negligible. In such cases, a fast quasi-[[File:PMOM83static analysis can be carried out.png]]You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-->Static Analysis'''.
Note that currents are complex vector quantities. Each electric or magnetic current has three XIn the "Spectral Domain Integration" section of the dialog, Y and Z componentsyou can set a value to '''Max Spectral Radius in k0''', and each complex component which has a magnitude and phasedefault value of 30. You can visualize This means that the surface electric currents on metal (PEC) infinite spectral-domain integrals in the spectral variable k<sub>ρ</sub> are pre-calculated and conductive sheet tracestabulated up to a limit of 30k<sub>0</sub>, surface magnetic currents on slot (PMC) traces and vertical volume currents where k<sub>0</sub> is the free space propagation constant. These integrals may converge much faster based on the PEV vias and embedded dielectric objectsspecified Convergence Rate for Integration described earlier. 3D color-coded intensity plots of electric and magnetic current distributions are visualized 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 project workspacereal k<sub>ρ</sub> axis, superimposed on the surface interval [0, Nk<sub>0</sub>] is subdivided into a large number of physical objectssub-intervals, within each an 8-point Gauss-Legendre quadrature is applied. In order to view the current distributionsThe next parameter, you must first define them as observables before running '''No. Radial Integration Divisions per k<sub>0</sub>''', determines how small these intervals should be. By default, 2 divisions are used for the planar MoM simulationinterval [0, k<sub>0</sub>]. At In other words, the top length of each integration sub-interval is k<sub>0</sub>/2. You can increase the Current Distribution dialog and resolution of integration by increasing this value above 2. Finally, instead of 2D Cartesian integration in the section titled spectral domain, a polar integration is performed. You can set the '''Active Trace / SetNo. of Angular Integration Points''', you can select which has a trace or embedded object set where you want to observe the current distribution. {{Note|You have to define a separate current distribution observable for each individual trace or embedded object setdefault value of 100.}}
[[Image:Info_iconEM.png|40pxPicasso]] 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_Current_Distribution_Maps | Visualizing 3D Current Distribution 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.
<table>
<tr>
<td> [[Image:PMOM84PMOM79.png|thumb|300pxleft|720px|EM.Picasso's Current Distribution Planar MoM Engine Settings dialog.]] </td><td> [[Image:PMOM85(1).png|thumb|420px|The current distribution map of a patch antenna.]] </td>
</tr>
</table>
=== Visualizing the Near Fields =Modeling Periodic Planar Structures in EM.Picasso ==
[[File:PMOM90EM.png|thumb|320px|[[Planar ModulePicasso]]'s Field Sensor dialog.]] EM.Picasso allows you to visualize simulate doubly periodic planar structures with periodicities along the near fields at a specific field sensor planeX and Y directions. Note that unlike Once you designate your planar structure as periodic, [[EM.CubePicasso]]'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 Planar MoM simulation, the fields are not available anywhere (as opposed engine uses a spectral domain solver to [[EManalyze it.Tempo]])In this case, and their computation requires integration of complex the dyadic Green's functions of a multilayer background periodic planar structure as opposed to take the free space Green's functionsform of doubly infinite summations rather than integrals.
{{Note[[Image:Info_icon.png|Keep in mind that since EM.Picasso uses a planar MoM solver, 30px]] Click here to learn more about the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable resultstheory of '''[[Basic_Principles_of_The_Method_of_Moments#Periodic_Planar_MoM_Simulation | Periodic Green's functions]]'''.}}
{{Note| [[Image:Info_iconEM.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Defining a Field Sensor ObservablePicasso]]'''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#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field MapsEM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''>''' '''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.
<table>
<tr>
<td> [[Image:PMOM116PMOM99.png|thumb|360px300px|Near-zone electric field map above a microstrip-fed patch antennaEM.]] </td><td> [[Image:PMOM117.png|thumb|360px|Near-zone magnetic field map above a microstrip-fed patch antennaPicasso's Periodicity Settings dialog.]] </td>
</tr>
</table>
=== Computing Radiation Pattern In many cases, your planar structure's traces or embedded objects are entirely enclosed inside the periodic unit cell and do not touch the boundary of Planar Structures ===the unit cell. [[EM.Picasso]] allows you to define periodic structures whose unit cells are interconnected. The interconnectivity applies only to PEC, PMC and conductive sheet traces, and embedded object sets are excluded. Your objects cannot cross the periodic domain. In other words, the neighboring unit cells cannot overlap one another. However, you can arrange objects with linear edges such that one or more flat edges line up with the domain's bounding box. In such cases, [[EM.Picasso]]'s planar MoM mesh generator will take into account the continuity of the currents across the adjacent connected unit cells and will create the connection basis functions at the right and top boundaries of the unit cell. It is clear that due to periodicity, the basis functions do not need to be extended at the left or bottom boundaries of the unit cell. As an example, consider a periodic metallic screen as shown in the figure on the right. The unit cell of this structure can be defined as a rectangular aperture in a PEC ground plane (marked as Unit Cell 1). In this case, the rectangle object is defined as a slot trace. Alternatively, you can define a unit cell in the form of a microstrip cross on a metal trace. In the latter case, however, the microstrip cross should extend across the unit cell and connect to the crosses in the neighboring cells in order to provide current continuity.
Even though EM.Pplanar MoM engine does not need a radiation box, you still have to define a "Far Field" observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct <table><tr><td> [[EMImage:image122.Cube]] to perform these calculations. Once png|thumb|400px|Modeling a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in 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 periodic screen using two different types of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cutsunit cell.]] </td></tr></table>
<table><tr><td> [[Image:Info_iconpmom_per5_tn.png|40pxthumb|300px|The PEC cross unit cell.]] Click here to learn more about the theory of '''</td><td> [[Computing_the_Far_Fields_%26_Radiation_CharacteristicsImage:pmom_per6_tn.png| Far Field Computations]]''thumb|300px|Planar mesh of the PEC cross unit cell. Note the cell extensions at the unit cell's boundaries.]] </td></tr></table>
[[Image:Info_icon.png|40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''=== Exciting Periodic Structures as Radiators in EM.Picasso ===
[[Image:Info_iconWhen a periodic planar structure is excited using a gap or probe source, it acts like an infinite periodic phased array.png|40px]] Click here All the periodic replicas of the unit cell structure are excited. You can even impose a phase progression across the infinite array to learn more about steer its beam. You can do this from the property dialog of the gap or probe source. At the bottom of the '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Planar Gap Circuit Source Dialog''' or '''Gap Source Dialog''', there is a button titled '''Periodic Scan...'''. You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the radiation patterns of a beam-steered antenna array, you have to define a finite-sized array factor in the Radiation Patterns]]Pattern dialog. You do this in the '''Impose Array Factor''' section of this dialog. The values of '''Element Spacing''' along the X and Y directions must be set equal to the value of '''Periodic Lattice Spacing'''along those directions.
<table><tr><td> [[Image:Info_iconPeriod5.png|40pxthumb|350px|Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] Click here to learn more about '''</td><td> [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs Image:Period5_ang.png| Plotting 2D Radiation Graphsthumb|350px|Setting the beam scan angles in Periodic Scan Angles dialog.]]</td></tr><tr><td> [[Image:Period6.png|thumb|350px|Setting the array factor in EM.Picasso'''s Radiation Pattern dialog.]] </td></tr></table>
<table>
<tr>
<td> [[FileImage:PMOM118Period7.png|thumb|300px360px|EM.Picasso's Radiation Pattern dialogpattern of an 8×8 finite-sized periodic printed dipole array with 0° phi and theta scan angles.]] </td><td> [[Image:PMOM119Period8.png|thumb|420px360px|3D polar radiation Radiation pattern plot of a microstripbeam-steered 8×8 finite-fed patch antennasized periodic printed dipole array with 45° phi and theta scan angles.]] </td>
</tr>
</table>
=== Radar Cross Section of Planar Exciting Periodic Structures Using Plane Waves in EM.Picasso ===
When a periodic planar structure is excited by using a plane wave source, it acts as a periodic surface that reflects or transmits the calculated far field data indeed represent the scattered fields of that planar structureincident wave. [[EM.Picasso]] can also calculate calculates the radar cross section (RCS) reflection and transmission coefficients of a periodic planar targetstructures. Note that in this case the RCS is defined for If you run a finitesingle-sized target frequency plane wave simulation, the reflection and transmission coefficients are reported in the presence Output Window at the end of an infinite background structurethe simulation. The scattered θ and φ components Note that these periodic characteristics depend on the polarization of the far-zone electric field are indeed what you see in incident plane wave. You set the 3D far field visualization of radiation polarization (scatteringTMz or TEz) patternsin the '''Plane Wave Dialog''' when defining your excitation source. Instead of radiation or scattering patterns, In this dialog you can instruct [[EMalso set the values of the incident '''Theta''' and '''Phi''' angles.Picasso]] to plot 3D visualizations At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called &sigmaquot;<sub>reflection.CPX&thetaquot;</sub>, and &sigmaquot;<sub>transmission.CPX&phiquot;</sub> and the total RCS.
{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[Image:Info_iconEM.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCSPicasso]]'''computes the reflection and transmission coefficients of the layered background structure of your project.}}
<table><tr><td>[[Image:Info_iconPMOM102.png|40pxthumb|580px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]] Click here to learn more about '''</td></tr></table> === Running a Periodic MoM Analysis === You run a periodic MoM analysis just like an aperiodic MoM simulation from [[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS GraphsEM.Picasso]]'s Run Dialog. Here, too, you can run a single-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you can define several observables for your project. If you open the Planar MoM Engine Settings dialog, you will see a section titled "Infinite Periodic Simulation". In this section, you can set the number of Floquet modes that will be computed in the periodic Green''s function summations. By default, the numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a total of 2500 Floquet terms will be computed for each periodic MoM simulation.
<table>
<tr>
<td> [[File:PMOM124.png|thumb|300px|EM.Picasso's Radar Cross Section dialog]] </td><td> [[Image:PMOM125PMOM98.png|thumb|420px600px|An example Changing the number of Floquet modes from the 3D mono-static radar cross section plot of a patch antennaPlanar MoM Engine Settings dialog.]] </td>
</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<psub>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° lt;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</psub>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]]'''
[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
