Changes

[[Image:Splash-planar new.jpg|right|720px]]<strong><font color="#015865" size="4">Fast Full-Wave Simulator For Modeling Multilayer Planar Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

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

Since its introduction in 2002, [[EM.Picasso assumes that your planar structure ]] has a substrate (background structure) of infinite lateral extents. Your substrate can be a dielectric half-space, or a single conductor-backed dielectric layer (as been successfully used by numerous users around the globe in microstrip components or patch antennas)industry, or simply the unbounded free space, or any arbitrary multilayer stack-up configurationacademia and government. In the special case of It has also undergone several evolutionary cycles including a free space substrate, total reconstruction based on our integrated [[EM.Picasso behaves similar Cube]] software foundation to expand its CAD and geometrical construction capabilities. [[EM.LiberaPicasso]]'s Surface MoM simulator. In all the other cases, it is important to keep in mind the infinite extents of the background substrate structure. For example, you cannot use EM.Picasso to analyze a patch antenna integration with a finite-sized dielectric substrate, if the substrate edge effects are of concern in your modeling problem. [[EM.TempoCube]] is recommended for the modeling facilitates import and export of finite-sized substrates. Since EM.Picasso's Planar MoM simulation engine incorporates the Green's functions many popular CAD formats (including DXF export of the background structure into the analysis, only the finite-sized layered traces like microstrips ) and slots are discretized by the mesh generator. As provides a result, the size of seamless interface with [[EM.PicassoCube]]'s computational problem is normally much smaller compared to the other techniques and solver. In addition, EM.Picasso generates a hybrid rectangular-triangular mesh of your planar structure with a large number of rectangular cells. This results in very fast computation times that oftentimes make up for the limited applications of EM.Picassosimulation tools.

=== An Overview [[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Basic Principles of The Method of Moments | Theory of Planar Method of Moments ===]]'''.

The Method of Moments (MoM) is a rigorous, full-wave numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwell’s equations as opposed to their differential forms that are used in the finite element or finite difference time domain methods.<table><tr><td> [[Image:PMOM11ART PATCH Fig title.png|thumb|250pxleft|EM.Picasso's Navigation Tree.]]In EM.Picasso, the background structure is usually a layered planar structure that consists of one or 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. 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 of elementary currents with small finite spatial extents. 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 structure's mesh. Once the total currents are known, you can calculate the fields everywhere in the structure. [[Image:MORE.png480px|40px]] Click here to learn more about the theory 3D radiation pattern of '''[[Planar Method of Moments]]'''. == Building a Planar Structure == [[Image:PMOM9.png|thumb|270px|EM.Picasso's Add Substrate Layer dialog.]]=== Understanding the Background Structure === EM.Picasso is intended for constructing and modeling 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 Zslot-axis. Objects of finite size are then interspersed among these substrate layers. The background structure in EM.Picasso is called the &quot;'''Layer Stack-up'''&quot;. The layer stack-up is always terminated from the top and bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material medium. Most planar structures used in RF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components require two bounding grounds (PEC half-spaces) both at their top and bottom.  === Planar Object Types === EM.Picasso groups objects by their trace type and their hierarchical location in the substrate layer stack-up. All the planar objects belonging to the same trace group are located on the same substrate layer boundary and have the same color. All the embedded objects belonging to the same embedded set lie inside the same substrate layer and have the same color and same material composition.  EM.Picasso provides the following types of objects for building a planar layered structure: # '''PEC Traces''': These represent infinitesimally thin metallic planar objects that are deposited or metallized on or between substrate layers. PEC objects are modeled by surface electric currents.# '''Slot Traces''': These are used to model slots and apertures in PEC ground planes. Slot objects are always assumed to lie on an infinite horizontal PEC ground plane coupled patch antenna array with zero thickness (which is not explicitly displayed in the project workspace). They are modeled by surface magnetic currents.# '''Conductive Sheet Traces:''' These represent imperfect metals. They have a finite conductivity and a very small thicknesscorporate feed network. A surface impedance boundary condition is enforced on the surface of such traces.# '''PEC Via Sets:''' These are metallic objects such as shorting pins, interconnect vias, plated-through holes, etc. that are grouped together as prismatic object sets. The embedded objects are modeled as vertical volume conduction currents.# '''Embedded Dielectric Sets:''' These are prismatic dielectric objects inserted inside a substrate layer. You can define a finite permittivity and conductivity for such objects, but their height is always the same as the height of their host layer. The embedded dielectric objects are modeled as vertical volume polarization currents. [[Image:MORE.png|40px]] Click here to learn more about '''[[Planar Traces & Object Types]]'''.</td>=== Defining the Layer Stack-Up ===</tr> When you start a new project in EM.Picasso, there is always a default background structure that consists of a finite vacuum layer sandwiched between a vacuum top half-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 &gt; Computational Domain &gt; Layer Stack-up Settings...'''</table>

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

You can add new layers to your project's stack[[EM.Picasso]] is the frequency-up or delete its layersdomain, or move layers up or down and thus change the layer hierarchy. To add a new background layer, click the arrow symbol on the full-wave '''Insert...Planar Module'''button at the bottom of the dialog and select '''Substrate Layer[[EM.Cube]]''' from the button's dropdown list, a comprehensive, integrated, modular electromagnetic modeling environment. A new dialog opens up where you can enter a label for [[EM.Picasso]] shares the new layer visual interface, 3D parametric CAD modeler, data visualization tools, and values for its material properties many more utilities and thickness in project unitsfeatures collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

You can delete a layer by selecting its row in the table and clicking the [[Image:Info_icon.png|30px]] Click here to learn more about '''Delete''' button[[Getting_Started_with_EM. To move a layer up and down, click on its row to select and highlight itCube | EM. Then click either the Cube Modeling Environment]]'''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 '''Edit''' button. The substrate layer dialog opens up, where you can change the layer's label and assigned color. In the material properties section === Advantages & Limitations of the dialog, you can change the name of the material and its properties: permittivity (e_r), permeability (µ_r), electric conductivity (s) and magnetic conductivity (s_m)EM. To define electrical losses, you can either assign a value for electric conductivity (s), or alternatively, define a loss tangent for the material. In the latter case, check the box labeled &quot;Picasso'''Specify Loss Tangent'''&quot; and enter a value for it. In this case, the electric conductivity field becomes greyed out and reflects the corresponding s value at the center frequency of the project. You can also set the thickness of any substrate layer in the project units except for the top and bottom half-spaces. Planar MoM Simulator ===

For better visualization of [[EM.Picasso]] assumes that your planar structure, EM.Picasso displays has a virtual domain in a default orange color to represent part of the infinite substrate (background structure. The size ) of this virtual domain is a quarter wavelength offset from infinite lateral extents. In addition, the largest bounding box that encompasses all planar 2.5-D assumption restricts the finite 3D objects in the project workspace. You of your physical structure to embedded prismatic objects that can change only support vertical currents. These assumptions limit the size variety and scope of the virtual domain or its display color from the Domain Settings dialogapplications of [[EM.Picasso]]. For example, which you can access either by clicking the '''Computational Domain''' cannot use [[File:domain_iconEM.pngPicasso]] button of to analyze a patch antenna with a finite-sized dielectric substrate. If the '''Simulate Toolbar'''substrate edge effects are of concern in your modeling problem, or by selecting '''Simulate &gt; Computational Domain &gt; Domain Settingsyou must use [[EM.Tempo]] instead.On the other hand, since [[EM.Picasso]]''' from s Planar MoM simulation engine incorporates the Simulate Menu or by right clicking the '''Virtual Domain''Green' item s functions of the Navigation Tree background structure into the analysis, only the finite-sized traces like microstrips and selecting slots are discretized by the mesh generator. As a result, the size of [[EM.Picasso]]'''Domain Settingss computational problem is normally much smaller than that of [[EM.Tempo]].In addition, [[EM.''' from 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 contextual menu, or using the keyboard shortcut 'symmetry and invariance properties of dyadic Green''Ctrl+A'''. Keep s functions often results in mind very fast computation times that the virtual domain is only easily make up for visualization purpose and does not affect the MoM simulation[[EM. The virtual domain also shows the substrate layers in translucent colorsPicasso]]'s limited applications. If you assign different colors to your substrate layers, you have get a better visualization A particularly efficient application of [[EM.Picasso]] is the modeling of periodic multilayer virtual domain box surrounding your project structurestructures at oblique incidence angles.

<td> [[Image:PMOM8(1)ART PATCH Fig12.png|thumb|550pxleft|EM.Picasso's Layer Stack480px|The hybrid planar mesh of the slot-up Settings dialog with the initial default valuescoupled patch antenna array.]] </td><td> [[Image:PMOM12.png|thumb|550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.]] </td></tr>

=== Defining Traces &amp; Object Sets =EM.Picasso Features at a Glance ==

When you start a new project in [[Planar Module]], the project workspace looks empty, and there are no finite objects in it. However, a default background structure is always present by default. 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. Definition ===

Traces and object sets can be defined either from Layer Stack<ul> <li> Multilayer stack-up Settings dialog 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 from the navigation tree.other offset periodic lattice topologies</li></ul>

In the '''Layer Stack-up Settings''' dialog=== Sources, you can add a new trace to the stack-up by clicking the arrow symbol on the '''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 other than default ones. 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.Loads &amp; Ports ===

EM<ul> <li> 2.Picasso has a special feature that makes construction 5-D mixed potential integral equation (MPIE) formulation of planar layered structures quite easy and straightforward</li> <li> 2. '''The active work plane 5-D spectral domain integral equation formulation of the project workspace is always set at the plane of the active trace.''' In [[EM.Cube]]'periodic layered structures</li> <li> Accurate scattering parameter extraction and de-embedding using Prony&#39;s other modulesmethod</li> <li> Plane wave excitation with arbitrary angles of incidence</li> <li> A variety of matrix solvers including LU, all objects are drawn in the XY plane (z = 0) by default. In [[Planar Module]], all new objects are drawn on a horizontal plane that is located at the ZBiCG 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-coordinate variable and multi-goal optimization of the currently active trace. As you change the active trace or add a new trace, you will also change the active work plane.structure</li> <li> Remote simulation capability</li> <li> Both Windows and Linux versions of Planar MoM simulation engine available</li></ul>

By default<ul> <li> Current distribution intensity plots</li> <li> Near field intensity plots (vectorial - amplitude &amp; 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, the last defined trace or embedded object set is activeside lobe levels and null parameters, etc. You can activate any trace or embedded object set at any time for drawing new objects. You can move one or more selected objects from any trace or embedded object set to another group </li> <li> Radiation pattern of the same type or an arbitrary array configuration of different type. First select an object in the project workspace planar structure or in the Navigation Tree. Then, right click on the highlighted selection periodic unit cell</li> <li> Reflection and select '''Move To Transmission Coefficients of Periodic Structures</li> <li> Monostatic and bi-static RCS&gtnbsp;''' from the contextual menu. This opens another sub-menu containing '''Planar''' and a list of all the other [[EM.Cube]] modules that have already defined object groups. Select '''Planar''' or any other available module</li> <li> Port characteristics: S/Y/Z parameters, VSWR and yet another subSmith chart</li> <li> Touchstone-menu opens up with a list of all the available traces and embedded object sets already defined in your project. Select the desired group, and all the selected objects will move style S parameter text files for direct export to that groupRF. When selecting multiple objects from the Navigation Tree, make sure that you hold the keyboard's '''Shift Key''' Spice or '''Ctrl Key''' down while selecting a group's name from the contextual menu.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 Module's Rules &amp; Limitations =Structure in EM.Picasso ==

# Terminating PEC ground planes at the top or bottom [[EM.Picasso]] is intended for construction and modeling of planar layered structures. By a planar structure are defined as PEC top or bottom half-spaces, respectively.# A PEC ground plane placed in the middle of we mean one that contains a background substrate stack-of laterally infinite extents, made up requires at least of one slot object to provide electromagnetic coupling between its top and bottom sides. In this case, a PMC trace is rather introduced at or more material layers all stacked up vertically along the given Z-plane, which implies the presence axis. Planar objects of an infinite PEC ground although it is not explicitly indicated finite size are interspersed among these substrate layers. The background structure in the Navigation Tree[[EM.# Metallic and slot traces cannot coexist on Picasso]] is called the same Z&quot;'''Layer Stack-planeup'''&quot;. However, you can The layer stack -up multiple PEC and conductive sheet traces at is always terminated from the same Ztop and bottom by two infinite half-coordinatespaces. Similarly, multiple PMC traces can The terminating half-spaces might be placed at the same Z-coordinate.# Metallic and slot traces are strictly defined at the interface planes between substrate layers. To define free space, or a suspended metallic trace in a substrate layer perfect conductor (as in the case of the center conductor of a striplinePEC ground), you must split the dielectric layer into two thinner layers or any material medium. Most planar structures used in RF and place your microwave applications such as microstrip-based components have a PEC trace ground at the interface between themtheir bottom.# The current version of the Planar MoM simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and no circumferential Some structures like stripline components are allowed on embedded objects. The 2.5-D assumption holds very well in sandwiched between two cases: grounds (a) when embedded objects are very thin with a very small cross section (with lateral dimensions less than 2PEC half-5% of the material wavelengthspaces) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the both their top and bottom.# The current release of [[EM.Cube]] allows any number of PEC via sets collocated in the same substrate layer. However, you can define only one embedded dielectric object set per substrate layer, and no vias sets collocated in the same layer. Note that the single set can host an arbitrary number of embedded dielectric objects of the same material properties.

<table><tr><td> [[Planar Module|Planar module]] does not allow construction of 3D CAD objectsImage:PMOM11. Instead, you draw the cross section of prismatic objects as planar [[Surface Objectspng|thumb|left|480px|surface objects]] parallel to the XY plane. [[EM.CubePicasso's navigation tree and trace types.]] then automatically extrudes these cross sections and constructs and displays 3D prisms over them. The prisms extend all the way across the thickness of the host substrate layer.</td></tr></table>

== Discretizing Planar Structures = Defining the Layer Stack-Up ===

When you start a new project in [[Image:PMOM32.png|thumb|450px|Planar hybrid and triangular meshes for rectangular patchesEM.Picasso]][[Image:PMOM30.png|thumb|450px|Mesh , there is always a default background structure that consists of two rectangular patches at two different planes. The lower substrate a finite vacuum layer has with a higher permittivitythickness 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 [[Image:PMOM31EM.png|thumb|400px|The Planar Mesh 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.]]=== Understanding ..''' from the Planar MoM Mesh ===contextual menu. Or alternatively, you can select the menu item '''Simulate &gt; Computational Domain &gt; Layer Stack-up Settings...'''

The method of moments (MoM) discretizes all the finiteStack-sized objects of up Settings dialog has two tabs: '''Layer Hierarchy''' and '''Embedded Sets'''. The Layer Hierarchy tab has a planar structure (excluding table that shows all the background structure) into a set of elementary cells. The accuracy of layers in hierarchical order from the MoM numerical solution depends greatly on top half-space to the quality and resolution of bottom half-space. It also lists the generated mesh. As a rule material composition of thumbeach layer, a mesh density Z-coordinate of about 20-30 cells per effective wavelength usually yields satisfactory results. Yet, for structures with lots the bottom of fine geometrical details or for highly resonant structureseach layer, higher mesh densities may be required. Also, the particular simulation data that you seek its thickness (in a project units) and material properties: permittivity (&epsilon;_r), permeability (&mu;_r), electric conductivity (&sigma;) and magnetic conductivity (&sigma;_m). There is also influence your choice a column that lists the names of mesh resolution. For exampleembedded object sets inside each substrate layer, far field characteristics like radiation patterns are less sensitive to the mesh density than field distributions on a structure with a highly irregular shape and a rugged boundaryif any.

EM.Picasso generates two types of mesh for a planar structure<table><tr><td> [[Image: a pure triangular and a hybrid triangular-rectangularPMOM8(1). In both case, png|thumb|550px|EM.Picasso attempts to create a highly regular mesh, in which most of 's Layer Stack-up Settings dialog with the cells have almost equal areasinitial default values. The hybrid mesh type tries ]] </td></tr></table> You can add new layers to produce as many rectangular cells as possible especially in the case of objects with rectangular your project's stack-up or linear boundaries. In connection delete its layers, or junction areas between adjacent objects move layers up or close to highly curved boundaries, down and thus change the use of triangular cells is clearly inevitablelayer hierarchy. EM.Picasso's default mesh type is hybrid. The uniformity or regularity of mesh is an important factor in warranting To add a stable 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 densitynew background layer, click the more cells are created arrow symbol on the geometrical objects. Keep in mind that only the finite-sized objects of your structure are discretized. The free-space wavelength is defined as <math>\lambda_0 = \tfrac{2\pi f}{ckey|Insert…}}</math>, where f is button at the center frequency bottom of your project the dialog and c is select '''Substrate Layer''' from the speed of light in the free spacebutton's dropdown list. The effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, A new dialog opens up where e_eff is the effective permittivity. By default, [[EM.Picasso]] generates you can enter a hybrid mesh with a mesh density of 20 cells per effective wavelength. The effective permittivity is defined differently label for different types of traces the new layer and embedded object setsvalues for its material properties and thickness in project units. This is to make sure that enough cells are placed You can delete a layer by selecting its row in areas that might feature higher field concentrationthe table and clicking the '''Delete''' button. For PEC To move a layer up and conductive sheet tracesdown, click on its row to select and highlight it. Then click either the effective permittivity is defined as '''Move Up''' or '''Move Down''' buttons consecutively to move the larger of selected layer to the permittivity of desired location in the two substrate layers just above and below stack-up. Note that you cannot delete or move the metallic tracetop or bottom half-spaces. For slot tracesAfter creating a substrate layer, you can always edit its properties in the effective permittivity is defined as Layer Stack-up Settings dialog. Click on any layer's row in the mean (average) of the permittivity of the two substrate layers just above table to select and below highlight it and then click the metallic trace{{key|Edit}} button. For embedded object setsThe substrate layer dialog opens up, where you can change the effective permittivity is defined layer's label and assigned color as the largest of the permittivities of all the substrate layers and embedded dielectric setswell as its constitutive parameters.  === A Note on the Junction Mesh ===

The integrity of the planar mesh and its continuity in the junction areas where adjacent objects are connected directly affects the simulation results[[Image:Info_icon. The most important rule png|30px]] Click here for a general discussion of object connections '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Assigning_Material_Properties_to_the_Physical_Structure | Materials in EM.Picasso is that only objects belonging to the same trace can be connected to one anotherCube]]'''. If two objects belong to the same trace (residing on the same Z-plane) and have a common overlap area, EM.Picasso first merges the two objects using the &quot;Boolean Union&quot; operation and converts them into a single object for the purpose of meshing. EM.Picasso's hybrid planar mesh generator has some additional rules:

* If two connected rectangular objects have the same side dimensions along the common linear edge with perfect alignment, a rectangular junction mesh is produced[[Image:Info_icon.* If two connected rectangular objects have different side dimensions along the common linear edge or have edge offset, a set of triangular cells is generated along the edge of the object with the large sidepng|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Using_EM.* Rectangular objects that contain gap source or lumped elements, always have a rectangular mesh around the gap areaCube.27s_Materials_List | Using EM.Cube's Materials Database]]'''.

If an embedded object like an interconnect via 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 located under or above a metallic trace 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 connected its display color from both top and bottomthe Domain Settings dialog, it is critical to create mesh continuity between which you can access either by clicking the embedded object and its connected metallic traces'''Computational Domain''' [[File:domain_icon. In other wordspng]] button of the '''Simulate Toolbar''', or using the generated mesh must ensure current continuity between keyboard shortcut {{key|Ctrl+A}}. Keep in mind that the vertical volume currents virtual domain is only for visualization purposes and horizontal surface currentsits size does not affect the MoM simulation. EMThe virtual domain also shows the substrate layers in translucent colors.Picasso’s planar mesh generator automatically handles situations If you assign different colors to your substrate layers, you have get a better visualization of this kind and generates all the required connection meshesmultilayer virtual domain box surrounding your project structure.

<td> [[FileImage:PMOM36PMOM12.png|250px]] [[File:PMOM38.pngthumb|250px]] [[File:PMOM37550px|EM.Picasso's Layer Stack-up Settings dialog showing a multilayer substrate configuration.png|250px]] </td>

<td> Two overlapping planar objects and their triangular and hybrid planar meshes. </td></tr><tr><td> [[FileImage:PMOM33PMOM9.png|250px]] [[File:PMOM35.pngthumb|250px]] [[File:PMOM34280px|EM.Picasso's Add Substrate Layer dialog.png|250px]] </td></tr><tr><td> Edge-connected rectangular planar objects and their triangular and hybrid planar meshes. </td></tr><tr><td> [[FileImage:PMOM39PMOM9A.png|375px]] [[File:PMOM40thumb|440px|A microstrip-fed, slot-coupled patch antenna on a double-layer substrate with a PEC ground plane in the middle hosting the coupling slot.png|375px]] </td></tr><tr><td> Meshes of short and long vertical PEC vias connecting two horizontal metallic strips. </td>

[[Image:PMOM44.png|thumb|400px|Deleting or curing defective triangular cells: Case 1.]][[Image:PMOM42.png|thumb|400px|Deleting or curing defective triangular cells: Case 2.]][[Image:PMOM45.png|thumb|300px|Locking the mesh density of an object group from its property dialog.]]=== Generating, Viewing & Customizing a Planar Mesh Object & Trace Types ===

You can generate and view a planar mesh by clicking the '''Show Mesh''' [[File:mesh_toolEM.pngPicasso]] button of the '''Simulate Toolbar''' or groups objects by selecting '''Menu &gt; Simulate &gt; Discretization &gt; Show Mesh''' or using their trace type and their hierarchical location in the keyboard shortcut '''Ctrl+M'''substrate layer stack-up. When the mesh A trace is a group of finite-sized planar objects that have the planar structure is displayed in [[EM.Cube]]’s project workspacesame material properties, its &quot;Mesh View&quot; mode is enabledsame color and same Z-coordinate. In this mode you can perform view operations like rotate view, pan or zoom, but you cannot create new All the planar objects belonging to the same metal or edit existing onesslot trace group are located on the same horizontal boundary plane in the layer stack-up. To exit All the mesh view mode, press embedded objects belonging to the keyboard's '''Esc Key''' or click same embedded set lie inside the '''Show Mesh''' [[File:mesh_tool.png]] button once againsame substrate layer and have same material composition.

Once a mesh is generated, it stays in the memory until the structure is changed or the mesh density or other settings are modified. Every time you view mesh, the one in the memory is displayed. You can force [[EM.Picasso]] to create a new mesh from the ground up by selecting '''Menu &gt; Simulate &gt; Discretization &gt; Regenerate Mesh''' or by right clicking on the '''Planar Mesh''' item in provides the '''Discretization''' section following types of the navigation tree and selecting '''Regenerate''' from the contextual menu.objects for building a planar layered structure:

You can change the settings {| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:250px;" | [[Glossary of the planar mesh including the mesh type and density from the Planar Mesh Settings DialogEM. You can also change these settings while in the mesh view modeCube's Materials, and you can update the changes to view the new mesh. To open the mesh settings dialogSources, either click Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Trace]]| style="width:300px;" | Modeling perfect metal traces on the '''Mesh Settings''' interface between two substrate layers| style="width:150px;" | Only surface objects|-| style="width:30px;" | [[File:mesh_settingsvoxel_group_icon.png]] button | style="width:250px;" | [[Glossary of the '''Simulate Toolbar''' or select ''EM.Cube'Menu s Materials, Sources, Devices &gtOther Physical Object Types#Conductive Sheet Trace |Conductive Sheet Trace]]| style="width:300px; Simulate &gt" | Modeling lossy metal traces with finite conductivity and finite metallization thickness| style="width:150px; Discretization &gt" | Only surface objects|-| style="width:30px; Mesh Settings." | [[File:pmc_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube'''s Materials, or by right click Sources, Devices & Other Physical Object Types#Slot Trace |Slot Trace]]| style="width:300px;" | Modeling cut-out slot traces and apertures on the '''Planar Mesh''' item in the '''Discretization''' section an infinite PEC ground plane | style="width:150px;" | Only surface objects|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:250px;" | [[Glossary of the Navigation Tree and select '''Mesh SettingsEM...''Cube' from the contextual menus Materials, or use the keyboard shortcut '''Ctrl+G'''. You can change the mesh algorithm from the dropdown list labeled '''Mesh Type'''Sources, which offers two optionsDevices & Other Physical Object Types#Embedded PEC Via Set |Embedded PEC Via Set]]| style="width: '''Hybrid''' 300px;" | Modeling small and '''Triangular'''. You can also enter a different value for '''Mesh Density''' in cells per effective wavelength (&lambdashort vertical vias and plated-through holes inside substrate layers| style="width:150px;_eff)" | Only surface objects|-| style="width:30px;" | [[File:diel_group_icon. For each value png]]| style="width:250px;" | [[Glossary of mesh densityEM.Cube's Materials, the dialog also shows the average Sources, Devices &quotOther Physical Object Types#Embedded Dielectric Object Set |Embedded Dielectric Object Set]]| style="width:300px;Cell Edge Length&quot" | Modeling small and short dielectric material inserts inside substrate layers| style="width:150px; in the free space" | Only surface objects|-| style="width:30px;" | [[File:Virt_group_icon. To get an idea png]]| style="width:250px;" | [[Glossary of the size of mesh cells on the traces and embedded object setsEM.Cube's Materials, Sources, divide this edge length by the square root 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 the effective permittivity a particular trace or set. Click the '''Apply''' button to make the changes effective.objects|}

=== Refining Click on each category to learn more details about it in the Planar Mesh Locally ===[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

It is very important to apply the right mesh density to capture all the geometrical details You can define two types of your metallic traces in [[EM.Picasso]]: '''PEC Traces''' and '''Conductive Sheet Traces'''. PEC traces represent infinitesimally thin (zero thickness) planar structure. This is especially true for &quot;field discontinuity&quot; regions such as junction areas between metal objects of different side dimensions, where larger current concentrations that are usually observed at sharp corners, deposited or metallized on or at the connection areas between metallic substrate layers. PEC objects are modeled by surface electric currents. Conductive sheet traces and PEC vias, as well as on the areas around gap sources and lumped elementsother hand, as these create voltage or current discontinuitiesrepresent imperfect metals. For large planar structures, using They have a higher mesh density may not always be a practical option since it will quickly lead to finite conductivity and a very large MoM matrix and thus growing the size of the numerical problemsmall thickness expressed in project units. EM.Picasso provides several ways of controlling A surface impedance boundary condition is enforced on the mesh surface of a planar structure locallyconductive sheet objects.

The Planar Mesh Settings dialog gives a few options for customizing your planar mesh around geometrical and field discontinuities. You can check the check box labeled &quot;'''Refine Mesh at JunctionsSlot Traces'''&quot;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 increases is not explicitly displayed in the mesh resolution at the connection area between rectangular objectsproject workspace and its presence is implied. Or you can check the check box labeled &quot;'''Refine Mesh at Gap Locations'''&quot;They are modeled by surface magnetic currents. When a slot is excited, which may prove particularly useful when gap sources or lumped elements tangential electric fields are placed formed on a short transmission line connected from both ends. Or you can check the check box labeled &quot;'''Refine Mesh at Vias'''&quot;aperture, which increases can be modeled as finite magnetic surface currents confined to the mesh resolution on the cross section area of embedded object sets and at the connection regions slot. In other words, instead of modeling the metallic 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 connected to them. [[EM.Picasso]] typically doubles provide the mesh resolution locally at electromagnetic coupling between the discontinuity areas when the respective boxes are checkedtwo sides of an infinite PEC ground plane.

You should always visually inspect Besides planar metal and slot traces, [[EM.Picasso's default generated mesh to see if the current mesh settings have produced an acceptable mesh. You may often need to change the mesh density or other [[parameters]] and regenerate allows you to insert prismatic embedded objects inside the meshsubstrate layers. Sometimes EM.Picasso's default mesh may contain very narrow triangular cells due to very small angles between two edges. In some rare cases, extremely small triangular cells may be generated, whose area The height of such embedded objects is a small fraction of always the average mesh cell. These cases typically happen at the junctions and other discontinuity regions or at same as the boundary height of highly irregular geometries with extremely fine detailstheir host substrate layer. In such cases, increasing or decreasing the mesh density by one or few cells per effective wavelength often resolves that problem Two types of embedded object sets are available: '''PEC Via Sets''' and eliminates those defective cells'''Embedded Dielectric Sets'''. NonethelessPEC via sets are metallic objects such as shorting pins, EMinterconnect vias, plated-through holes, etc.Picasso's planar mesh generator offers an option to identify the defective triangular cells all located 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 grouped together inside the crack left behindsame substrate layer. EMThe embedded via objects are modeled as vertical volume conduction currents.Picasso by default deletes or cures all the triangular cells that have angles less than 10º. Sometimes removing defective cells may inadvertently cause worse problems in the meshEmbedded dielectric sets are prismatic dielectric objects inserted inside a substrate layer. You may choose to disable this feature can define a finite permittivity and uncheck the box labeled &quot;'''Remove Defective Triangular Cells'''&quot; in the Planar Mesh Settings dialogconductivity for such objects. You can also change the value of the minimum allowable cell angleThe embedded dielectric objects are modeled as vertical volume polarization currents.

Another way of local mesh control is to lock the mesh density of certain traces or object sets. {{Note|The mesh density that you specify in the Planar Mesh Settings dialog is a global parameter and applies to all the traces and embedded object sets in your project. However, you can lock the mesh height of individual PEC, PMC and conductive sheet traces or an embedded objects sets. In that case, the locked mesh density takes precedence over the global density. Note that locking mesh of object groups, in principle, is different than refining the mesh at discontinuities. In the latter case, the mesh of connection areas is affected. However, objects belonging always identical to different traces cannot be connected to one another. Therefore, locking mesh can be useful primarily for isolated object groups that may require a higher (or lower) mesh resolution. You can lock the local mesh density by accessing the property dialog thickness of a specific trace or embedded object set and checking the box labeled '''Lock Mesh'''. This will enable the '''Mesh Density''' box, where you can accept the default global value or set any desired new valueits host substrate layer.}}

== Excitation Sources = Defining Traces &amp; Embedded Object Sets ===

Your planar 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 must 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 excited 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 some sort 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 signal source that induces electric currents on metal parts label and magnetic currents on slot tracesassign 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. The excitation source From here, you choose depends can move the trace down to the desired location on the observables layer hierarchy. Every time you seek define a new trace, it is also added under the respective category in your project. EMthe navigation tree.Picasso provides Alternatively, you can define a new trace from the following source types 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 exciting planar structures: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.

* [[Planar_MoM_Source_Types#Gap_Sources|Gap Sources]]* [[Planar_MoM_Source_Types#Probe_Sources|Probe Sources]]* [[Planar_MoM_Source_Types#DeEmbedded 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-Embedded_Sources|Dethrough 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 &quot;Embedded Sets&quot; tab of the stack-up dialog. This tab has a table that lists all the embedded Sources]]* [[Planar_MoM_Source_Types#Short_Dipole_Sourcesobject 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|Short Dipole Sources]]* [[Planar_MoM_Source_Types#Plane_Wave_Sources|Plane Wave Sources]]* [[#Huygens Sources|Huygens Sources]]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 &quot;'''Host Layer'''&quot; 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'''(&epsilon;_r) and '''Electric Conductivity'''(&sigma;) 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.

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 <table><tr><td> [[parameters]] can be calculated accuratelyImage:PMOM23. To calculate the scattering characteristics of a planar structure, epng|thumb|550px|EM.g. its radar cross section (RCS), you excite it with a plane wave source. Short dipole sources are used to explore propagation of points sources along a layered structure. Huygens sources are virtual equivalent sources that capture Picasso's Layer Stack-up dialog showing the radiated electric and magnetic fields from another structure possibly in another [[EMEmbedded Sets tab.Cube]] computational module and bring them as a new source to excite your planar structure. </td></tr></table> === Drawing Planar Objects on Horizontal Work Planes ===

[[Image:MOREAs soon as you start drawing geometrical objects in the project workspace, the '''Physical Structure''' section of the navigation tree gets populated.png|40px]] Click here 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 learn more about . 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 '''[[Planar MoM Source Types]]Activate'''from the contextual menu.

[[Image:PMOM52Info_icon.png|thumb|400px|EM.Picasso's Port Definition dialog.30px]]Click here to learn more about '''[[Image:PMOM53.pngBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules |thumb|300px|The Edit Port dialog.Moving Objects among Different Groups]][[Image:PMOM51(2)'''.png|thumb|600px|Coupling gap sources in the Port Definition dialog by associating more than one source with a single port.]]=== Defining Ports ===

Ports are used in a planar structure to order and index the sources for calculation of circuit <table><tr><td> [[parameters]] such as scattering (S), impedance (Z) and admittance (Y) [[parameters]]Image:PMOM23B. In [[png|thumb|280px|EM.Cube]]Picasso's [[Planar ModuleNavigation Tree populated with planar objects.]], you can use the following types of sources to define ports:</td></tr></table>

* Gap Sources* Probe Sources* Active Lumped Elements* De[[EM.Picasso]] has a special feature that makes construction of planar structures very convenient and straightforward. <u>The horizontal Z-Embedded Sourcesplane 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.

Ports are defined in the '''Observables''' section of the Navigation Tree{{Note| In [[EM. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens upPicasso]], showing the default port assignments. 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 cannot modify the Navigation Tree. Note that your project can have mixed gap Z-coordinate of an object as it is set and probes sources as well as active lumped element sources controlled by its host trace.}}

'''You can define any number of ports equal [[EM.Picasso]] does not allow you to draw 3D or less than the total number of sources in your projectsolid CAD objects.''' The Port List of the dialog shows a list of all the ports solid object buttons in ascending order, with their associated sources and the port's characteristic impedance, which is 50S by default. You can delete any port by selecting it from the Port List and clicking the ''Object Toolbar'Delete''' button of the dialogare disabled to prevent you from doing so. Keep in mind that after deleting a portIn order to create vias and embedded object, you will simply have a source in your project without any port assignment to draw their cross section geometry using planar surface CAD objects. [[EM.Picasso]] extrudes and make sure that is what you intendextends 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 change the characteristic impedance of a port enforce this extrusion manually by selecting it from the Port List and right-clicking the '''EditLayer Stack-up''' button item in the "Computational Domain" section of the dialog. This opens up the Edit Port dialog, where you can enter a new value in the box labeled navigation tree and selecting '''ImpedanceUpdate Planar Structure'''from the contextual menu.

{{Note| In [[Image:MOREEM.png|40px]] Click here to learn more about the theory of '''[[Computing Port Characteristics in Planar MoMPicasso]]''', you can only draw horizontal planar surface CAD objects.}}

Sources can be coupled to each other to model coupled strip lines (CPS) on metal traces or coplanar waveguides (CPW) on slot traces. Similarly, probe sources may be coupled to each other. Coupling two or more sources does not change the way they excite a planar structure. It is intended only for the purpose of S parameter calculation. The feed lines or vias which host the coupled sources are usually parallel and aligned with one another and they are all grouped together as a single transmission line represented by a single port. This single &quot;coupled&quot; port then interacts with other coupled or uncoupled ports=== EM.Picasso's Special Rules ===

You couple two # PEC ground planes at the top or more sources using the '''Port Definition Dialog'''. To do sobottom of a planar structure are regarded and modeled as PEC top or bottom half-spaces, you need to change the default port assignmentsrespectively. First, delete all # A PEC ground plane placed in the ports that are middle of a substrate stack-up requires at least one slot object to be coupled from the Port List of the dialogprovide electromagnetic coupling between its top and bottom sides. ThenIn this case, define a new port by clicking slot trace is rather introduced at the '''Add''' button of the dialog. This opens up the Add Port dialoggiven Z-plane, which consists also implies the presence of two tables: '''Available''' sources an infinite PEC ground.# Metallic and slot traces cannot coexist on the left same Z-plane. However, you can stack up multiple PEC and '''Associated''' sources on conductive sheet traces at the rightsame Z-coordinate. A right arrow ('''Similarly, multiple slot traces can be placed at the same Z--&gt;''') button coordinate.# Metallic and a left arrow ('''&lt;--''') button let you move slot traces are strictly defined at the sources freely interface planes between these two tablessubstrate layers. You will see To define a suspended metallic trace inside a dielectric layer (as in the &quot;Available&quot; table a list case of all the sources that center conductor of a stripline), you deleted earlier. You may even see more available sources. Select all must split the sources that you want to couple dielectric layer into two thinner substrate layers and move place your PEC trace at the interface between them to the &quot;Associated&quot; table on the right. You can make multiple selections using the keyboard# [[EM.Picasso]]'s '''Shift''' simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and '''Ctrl''' keysno circumferential components are allowed on embedded objects. Closing the Add Port dialog returns you to the Port Definition dialog, where you will now see the names 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 all the coupled sources next to material wavelength) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the name of the newly added porttop and bottom.

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

Your planar structure must be excited by some sort of signal source that induces electric surface currents on metal parts, magnetic surface currents on slot traces, and conduction or polarization volume currents on vertical vias and embedded objects. The excitation source you choose depends on the observables you seek in your project. [[Image:PMOM64.png|thumb|600px|EM.Picasso's Lumped Element dialog.]][[Imageprovides the following source types for exciting planar structures:PMOM49.png|thumb|600px|Defining gap sources on an array of rectangle strip objects with a Chebyshev amplitude distribution.]][[Image:PMOM50.png|thumb|500px|Defining gap source array weights using a data file.]]=== Modeling Lumped Elements in EM.Picasso ===

Lumped elements are components{| 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.Cube's Materials, devicesSources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source (or circuits whose overall dimensions are very small compared to the wavelength. As filament current source on slot traces)| style="width:300px;" | Associated with a result, they are considered to be dimensionless compared to the dimensions PEC rectangle strip|-| style="width:30px;" | [[File:probe_src_icon.png]]| [[Glossary of a mesh cellEM. In factCube's Materials, a lumped element is equivalent to Sources, Devices & Other Physical Object Types#Probe Gap Circuit Source |Probe Gap Circuit Source]]| style="width:300px;" | General-purpose voltage source for modeling coaxial feeds| style="width:300px;" | Associated with an infinitesimally narrow gap that is placed in the path embedded PEC via set|-| style="width:30px;" | [[File:waveport_src_icon.png]]| [[Glossary of current flowEM.Cube's Materials, across which 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 deviceopen end|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's governing equations are enforcedMaterials, 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 EM. Using KirkhoffCube's lawsMaterials, these device equations normally establish a relationship between the currents and voltages across the device or circuitSources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering & computation of reflection/transmission characteristics of periodic surfaces| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon. Crossing the bridge to Maxwellpng]]| [[Glossary of EM.Cube's domainMaterials, the device equations must now be cast into a Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from o boundary conditions that relate the electric and magnetic currents and fieldsother [[EM. Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

Click here on each category to learn more details about it in the theory [[Glossary of EM.Cube'''[[Computing_Port_Characteristics_in_Planar_MoM#Modeling_Lumped_Elements_in_Planar_MoM| Modeling Lumped Elements in Planar MoMs 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. [[EM.Picasso allows you to define passive circuit elements]] provides three types of lumped sources: '''Resistors'''(R)gap source, C'''apacitors'''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 inject a signal. 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 (Clocal X direction), I'''nductors'''. The characteristic impedance of the line is a function of its width (Llocal Y direction), . A gap source placed on a narrow metal strip creates a uniform electric field across the gap and series and parallel combinations 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 them the slot line is a function of its width (local Y direction). To define A gap source placed on a lumped RLC circuit in your planar structurenarrow slot represents an ideal current source. A slot gap acts like an ideal current filament, follow these steps: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 [[parameters]] can be calculated accurately.

* Open the Lumped Element Dialog by right clicking on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and selecting '''Insert New Source...'''* In the '''Gap Topology''' section of the dialog, select one of the two options: '''Gap on Line''' and '''Gap on Via'''.* In the '''Lumped Circuit Type''' section of the dialog, select one of the two options: '''Passive RLC''' and '''Active with Gap Source'''.* Depending on your choice of gap topology, in the '''Lumped Circuit Location''' section of the dialog, you will find either {{Note| You can realize a list of all the '''Rectangle Strip Objects''' or a list of all the '''PEC Via Objects''' available in the project workspace. Select the desired rectangle strip or embedded PEC via object.* In the box labeled '''Offset''', enter the distance of the lumped element from the start point of the rectangle strip line or from the bottom of the via object, whichever the case. The value of '''Offset''' by default is initially set to the center of the line or via.* In the '''Load Properties''' section, the series and shunt resistance values Rs and Rp are specified in Ohms, the series and shunt inductance values Ls and Lp are specified in nH coplanar waveguide (nanohenryCPW), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad)[[EM. Only the checked elements are taken into account in the total impedance calculation. By default, only the series resistor is checked Picasso]] using two parallel slot lines with a value of 50Stwo aligned, and all other circuit elements are initially greyed outcollocated gap sources.<br />}}

EM[[Image:Info_icon.Picasso allows you png|40px]] Click here to define a voltage source in series with a series-parallel RLC combination and place them across the gap. This is called an active lumped element. If you choose the learn more about '''Active with Gap [[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using SourceArrays for Modeling Antenna Arrays]]''' option of the '''Lumped Circuit Type''' section of the dialog, the right section of the dialog entitled '''Source Properties''' becomes enabled, where you can you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees. Also, the box labeled '''Direction''' becomes relevant in this case which contains a gap source. Otherwise, a passive RLC circuit does not have polarity.

If the project workspace contains an array A short dipole provides another way of rectangle strip objects or PEC via objects, the array object will exciting a planar structure in [[EM.Picasso]]. A short dipole source acts like an infinitesimally small ideal current source. You can also be listed as use an eligible object for lumped element placementincident plane wave to excite your planar structure in [[EM. A lumped element will then be placed on each element of the arrayPicasso]]. All In particular, you need a plane wave source to compute the lumped elements will have identical radar cross section of a planar structure. The direction, offset, resistance, inductance of incidence is defined by the θ and capacitance valuesφ angles of the unit propagation vector in the spherical coordinate system. If you define an active lumped element, you can prescribe certain amplitude The default values of the incidence angles are θ = 180° and/or phase distribution φ = 0° corresponding to a normally incident plane wave propagating along the gap -Z direction with a +X-polarized E-vector. Huygens sources just like in are virtual equivalent sources that capture the case of gap radiated electric and probe sourcesmagnetic fields from another structure that was previously analyzed in another [[EM. The available amplitude distributions include '''Uniform''', '''Binomial'''''', Chebyshev''' and '''Data File'''Cube]] computational module.

{{Note<table><tr><td> [[Image:PMOM64A.png|The impedance of the lumped circuit is calculated at the operating frequency of the project using the specified R, L thumb|550px|A multilayer planar structure containing a CPW line with a single coupled port and C values. As you change the frequency, the value of the impedance that is passed to the Planar MoM engine will changea lumped element on an overpassing metal strip.}}]] </td></tr></table>

=== Defining Source Arrays Modeling Lumped Elements in EM.Picasso ===

If the project workspace contains an array of rectangle strip objectsLumped elements are components, devices, or circuits whose overall dimensions are very small compared to the array object will also wavelength. As a result, they are considered to be listed as dimensionless compared to the dimensions of a mesh cell. In fact, a lumped element is equivalent to an eligible object for infinitesimally narrow gap source placement. A gap source will then be that is placed on each element in the path of current flow, across which the arraydevice's governing equations are enforced. All Using Kirkhoff's laws, these device equations normally establish a relationship between the gap sources will have identical direction currents and offsetvoltages across the device or circuit. Similarly, if Crossing the project workspace contains an array of PEC via objectsbridge to Maxwell's domain, the embedded array object will also device equations must now be listed as an eligible object for probe source placement. A probe source will then be placed on each via object of cast into a from o boundary conditions that relate the arrayelectric and magnetic currents and fields. All the probe sources will have identical direction [[EM.Picasso]] allows you to define passive circuit elements: '''Resistors''' (R), '''Capacitors''' (C), '''Inductors''' (L), and offsetseries and parallel combinations of them.

However, you can prescribe certain amplitude and/or phase distribution over the array of gap or probe sources[[Image:Info_icon. By default, all the gap or probe sources have identical amplitudes of 1V (or 1A for the slot case) and zero phase. The available amplitude distributions png|40px]] Click here to choose from include '''Uniform''', '''Binomial''' and '''Chebyshev''' and '''Date File'''. In the Chebyshev case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression''' in degrees along all three principal axes. You can view the amplitude and phase of individual sources by right clicking on the top '''Sources''' item in the Navigation Tree and selecting learn more about '''Show Source Label[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]''' from the contextual menu.

In {{Note|The impedance of the data file option, the complex amplitude are directly read in from a data file using a real - imaginary format. When this option lumped circuit is selected, you can either improvise calculated at the complex array weights or import them from an existing file. In the former case click the '''New Data File''' button. This opens up the [[Windows]] Notepad with default formatted data file that has a list operating frequency of all the array element indices with default 1+j0 amplitudes for all of them. You can replace project using the default complex specified R, L and C values with new one and save the Notepad data file, which brings . As you back to change the Gap Source dialog. To import the array weightsfrequency, click the '''Open Data File''' button, which opens value of the standard [[Windows]] Open dialog. You can then select the right data file from the one of your folders. It impedance that is important passed to note that the data file must have the correct format to be read by [[EM.Cube]]. For this reason, it is recommended that you first create a new data file with the right format using Notepad as described earlier and then save it for later usePlanar MoM engine will change.}}

== Running Planar MoM Simulations = Calculating Scattering Parameters Using Prony's Method ===

The first step calculation of planning a planar MoM simulation the scattering (S) parameters is defining your usually an important objective of modeling planar structurestructures especially for planar circuits like filters, couplers, etc. This consists of the background structure plus all the finite-sized metal As you saw earlier, you can use lumped sources like gaps and slot trace objects probes and possibly embedded metal or dielectric objects that are interspersed among even active lumped elements to calculate the substrate layerscircuit characteristics of planar structures. The background stack-up is defined in admittance / impedance calculations based on the Layer Stack-up dialog, which automatically opens up as soon as you enter the [[Planar Module]]. The metal and slot traces gap voltages and embedded object sets currents are listed in accurate at RF and lower microwave frequencies or when the Navigation Treeport transmission lines are narrow. In such cases, which also shows all the geometrical (CAD) objects you draw in electric or magnetic current distributions across the project workspace under each object group at different Z-planeswidth of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized. At higher frequencies, however, a more robust method is needed for calculating the port parameters.

The next step is to decide on One can calculate the excitation scheme. If your scattering parameters of a planar structure has one or more ports and you seek to calculate its port characteristics, then you have to choose one of directly by analyzing the lumped source types or a de-embedded sourcecurrent distribution patterns on the port transmission lines. If you are interested in The discontinuity at the scattering characteristics end of your planar structure, then you must define a plane port line typically gives rise to a standing wave source. Before you pattern that can run a planar MoM simulation, you also need to decide on clearly be discerned in the projectline's observablescurrent distribution. These are From the simulation data that you expect [[EM.Cube]] to generate as the outcome location of the numerical simulationcurrent minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, i. [[EMe.Cube]]'s [[Planar Module]] offers the S₁₁ parameter. A more robust technique is Prony’s method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following observablesform:

* Current Distribution* Field Sensors* Far Fields :<math> f(Radiation Patterns or Radar Cross Sectionx)\approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math>* Huygens Surfaces* Port Characteristics* Periodic Characteristics<!--[[File:PMOM73.png]]-->

If you run a simulation without having defined any observableswhere c_i are complex coefficients and &gamma;_i are, no data will be generated at in general, complex exponents. From the end physics of the simulation. Some observables require a certain type of excitation source. For exampletransmission lines, port characteristics will be calculated only if the project contains a port definition, which in turn requires the existence of at least we know that lossless lines may support one gap or probe or de-embedded sourcemore propagating modes with pure real propagation constants (real &gamma;_i exponents). The periodic characteristics Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (reflection and transmission coefficientsimaginary &gamma;_i exponents) are calculated only if that decay along the structure has a periodic domain and excited by a plane wave sourceline as you move away from the location of such discontinuities.

=== Planar ModuleIn practical planar structures for which you want to calculate the scattering parameters, each port line normally supports one, and only one, dominant propagating mode. Multi-mode transmission lines are seldom used for practical RF and microwave applications. Nonetheless, each port line carries a superposition of incident and reflected dominant-mode propagating signals. An incident signal, by convention, is one that propagates along the line towards the discontinuity, where the phase reference plane is usually established. A reflected signal is one that propagates away from the port plane. Prony's Simulation Modes ===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.

The simplest simulation type in <table><tr><td> [[EMImage:PMOM71.Cube]] is an analysis. In this mode, the planar structure in your project workspace is meshed at the center frequency of the project. [[EM.Cube]] generates an input file at this single frequency, png|thumb|600px|Minimum and the Planar MoM simulation engine is run once. Upon completion maximum current locations of the planar MoM simulation, a number of data files are generated depending standing wave pattern on the observables you have defined in your project. An analysis is a single-run simulationmicrostrip line feeding a patch antenna.]] </td></tr></table>

[[EM.Cube]] offers a number of multi-run simulation modes. In such cases, the Planar MoM simulation engine is run multiple times. At 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 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 === Defining Independent &theta; or &phi; angle of incidence of a plane wave source is varied over their respective ranges. [[EM.Cube]]'s [[Planar Module]] currently provides the following types of multi-run simulation modes:Coupled Ports ===

* Frequency Sweep* Parametric Sweep* R/T Macromodel* Huygens Sweep* 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 [[OptimizationEM.Picasso]]* HDMR, you can use one or more of the following types of sources to define ports:

Figure 1: Selecting a simulation mode Ports are defined in [[Planar Module]]the 's Simulation Run dialog''Observables''' section of the navigation tree. You can define any number of ports equal to or less than the total number of sources in your project. If you have N sources in your planar structure, then N default ports are defined, with one port assigned to each source according to their order on the navigation tree. Note that your project can have mixed gap and probes sources as well as active lumped element sources on PEC and slot traces or vias. You can also couple ports together to define coupled transmission lines such as coupled strips (CPS) or coplanar waveguides (CPW).

To run a planar MoM analysis of your project structure, open the Run Simulation Dialog by clicking the '''Run''' [[FileImage:run_iconInfo_icon.png|40px]] button on the Click here to learn more about '''Simulate Toolbar''' or select '''Menu''' '''&gt;''' '''Simulate &gt;''' '''Run''' or use the keyboard shortcut '''Ctrl+R'''. The '''Analysis''' option of the '''Simulation Mode''' dropdown list 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 time. After the simulation is successfully completed, a message pops up and reports the end of simulation. In certain cases like calculating scattering [[parametersPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Ports]] of a circuit or reflection / transmission characteristics of a periodic surface, some results are also reported in the Output Window. At the end of a simulation, you need to click the '''Close''' button of the Output Window to return to the project workspace.

[[File:PMOM78== EM.png]]Picasso's Simulation Data & Observables ==

Figure 1: Depending on the source type and the types of observables defined in a project, a number of output data are generated at the end of a planar MoM simulation. Some of these data are 2D by nature and some are 3D. The output simulation data generated by [[Planar ModuleEM.Picasso]]'s Simulation Run dialog.can be categorized into the following groups:

{| class="wikitable"|-! scope="col"| Icon! scope= Stages Of A Planar MoM Analysis "col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal traces and magnetic surface current distribution on slot traces | style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:period_icon.png]]| style="width:150px;" | Periodic Characteristics| style="width:150px;" | No observable required | style="width:300px;" | Computing the reflection and transmission coefficients of 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|}

Click on each category to learn more details about it in the [[Glossary of EM.Cube]]'s Planar MoM simulation engine uses a particular formulation of the method of moments called mixed potential integral equation (MPIE). Due to high-order singularities, the dyadic Green's functions for electric fields generated by electric currents as well as the dyadic Green's functions for magnetic fields generated by magnetic currents have very slow convergence behaviors. Instead of using these slowly converging dyadic Green's function, the MPIE formulation uses vector and scalar potentials. These include vector electric potential '''A(r)''', scalar electric potential K^{Simulation Observables &Phi;}'''(r)''', vector magnetic potential '''F(r)''' and scalar magnetic potential K^&Psi;'''(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 techniquesGraph Types]].

A If your planar MoM simulation consists of two major stages: matrix fill and linear system inversion. In the first stagestructure is excited by gap sources or probe sources or de-embedded sources, the moment matrix and excitation vector are calculated. In the second stageone or more ports have been defined, the planar MoM system of linear equations is inverted using one of engine calculates the several available matrix solvers to find the unknown coefficients scattering, impedance and admittance (S/Z/Y) parameters of all the basis functionsdesignated ports. The unknown electric and magnetic currents scattering parameters are linear superpositions of all these elementary solutions. These can be visualized in [[EM.Cube]] using defined based on the current distribution observables. Having determined all the electric and magnetic currents port impedances specified 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 Greenproject's functionsPort Definition dialog. Finally If more than one port has been defined in the project, the far fields S/Z/Y matrices of the planar structure multiport network are calculated in the spherical coordinate system. These calculations are performed using the asymptotic form of the dyadic Green's functions using the &quot;stationary phase method&quot;.

A planar MoM simulation involves a number of numerical :<math> \mathbf{[[parametersX]] that take preset default values unless you change them. You can access these [[parameters]] and change their values by clicking the '''Settings''' button next to the '''Select Engine''' dropdown list in the [[Planar Module]]'s Simulation Run dialog. In most }_{N\times 1} = \begin{bmatrix} I^{(J)} \\ \\ V^{(M)} \end{bmatrix} \quad \Rightarrow \quad \begin{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.} \mathbf{J(r)} = \sum_{n=1}^N I_n^{(J)} \mathbf{f_n^{(J)} (r)} \\ \\ \mathbf{M(r)} = \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math>

The Planar MoM Engine Settings Dialog is organized in Note that currents are complex vector quantities. Each electric or magnetic current has three X, Y and Z components, and each complex component has a number of sections. Here we describe some of the numerical [[parameters]]. The &quot;'''Matrix Fill'''&quot; section of the dialog deals with the operations involving the dyadic Green's functionsmagnitude and phase. You can set a value for visualize the '''Convergence Rate for Integration'''surface electric currents on metal (PEC) and conductive sheet traces, which is 1Esurface magnetic currents on slot (PMC) traces and vertical volume currents on the PEV vias and embedded dielectric objects. 3D color-5 by default. This is used for the convergence test coded intensity plots of all the infinite integrals electric and magnetic current distributions are visualized in the calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossyproject workspace, superimposed on 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 20physical objects. When the substrate is very thin with respect In order to view the wavelengthcurrent distributions, you must first define them as observables before running the dyadic Green's functions exhibit numerical instabilityplanar MoM simulation. Additional singularity extraction measures are taken to avoid numerical instability but at At the expense top of increased computation time. By default, a thin substrate layer is defined to a have a thickness less than 0.01&lambda;_eff, where &lambda;_eff is the effective wavelength. You can modify Current Distribution dialog and in the definition of &quot;Thin Substrate&quot; by entering a value for section titled '''Thin Substrate ThresholdActive Trace / Set''' 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, you can select a fast quasi-static analysis can be carried out. You can trace or embedded object set this threshold in wavelengths in where you want to observe the box labeled '''Max Dimensions for Quasi-Static Analysis'''current distribution.

In the &quot;Spectral Domain Integration&quot; section of the dialog, you can set a value {{Note|You have to '''Max Spectral Radius in k0''', which has define a default value of 30. This means that the infinite spectral-domain integrals in the spectral variable k_&rho; are pre-calculated and tabulated up to a limit of 30k₀, where k₀ is the free space propagation constant. These integrals may converge much faster based on the specified Convergence Rate separate current distribution observable for Integration described earlier. However, in certain cases involving highly oscillatory integrands, much larger integration limits like 100k₀ might be needed to warrant adequate convergence. For spectral-domain integration along the real k_&rho; axis, the interval [0, Nk₀] is subdivided into a large number of sub-intervals, within each an 8-point Gauss-Legendre quadrature is applied. The next parameter, '''No. Radial Integration Divisions per k₀''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k₀]. In other words, the length of each integration sub-interval is k₀/2. 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 individual trace or embedded object set the '''No. of Angular Integration Points''', which has a default value of 100.}}

<table><tr><td> [[FileImage:PMOM79PMOM85new.png|thumb|left|600px|The current distribution map of a patch antenna.]]</td></tr></table>

Figure 1: The Planar [[EM.Picasso]] allows you to visualize the near fields at a specific field sensor plane. Note that unlike [[EM.Cube]]'s other computational modules, near field calculations in [[EM.Picasso]] usually takes a significant amount of time. This is due to the fact that at the end of a planar MoM Engine Settings dialogsimulation, 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.

After the MoM impedance matrix '''<table><tr><td> [Z]''' (not to be confused with the impedance [[parametersImage:PMOM116.png|thumb|left|600px|Near-zone electric field map above a microstrip-fed patch antenna.]]) and excitation vector '''</td></tr><tr><td> [V]''' have been computed through the matrix fill process, the planar MoM simulation engine is ready to solve the system of linear equations[Image:PMOM117.png|thumb|left|600px|Near-zone magnetic field map above a microstrip-fed patch antenna.]] </td></tr></table>

:<math> \mathbf{Even though [Z]}_{N\times N} \cdot \mathbf{[IEM.Picasso]}_{N\times 1} = \mathbf{[V]}_{N\times 1} </math><!--'s MoM engine does not need a radiation box, you still have to define a &quot;Far Field&quot; observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct [[File:PMOM81EM.pngCube]]-->to perform these calculations. Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the &quot;Total&quot; far field. The 2D radiation pattern graphs can be plotted from the '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.

where '''[I]''' is the solution vector, which contains the unknown amplitudes of all the basis functions that represent the unknown electric and magnetic currents of finite extents in your planar structure. In the above equation, N is the dimension of the linear system and equal to the total number of basis functions in the planar mesh. [[EMImage:Info_icon.Cubepng|30px]]'s linear solvers compute Click here to learn more about the solution vectortheory of '''[I]''' of the above system. You can instruct [[EM.CubeDefining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]] to write the MoM matrix and excitation and solution vectors into output data files for your examination. To do so, check the box labeled &quot;'''Output MoM Matrix and Vectors'''&quot; in the Matrix Fill section of the Planar MoM Engine Settings dialog. These are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectively.

There are a large number of numerical methods for solving systems of linear equations. These methods are generally divided into two groups<table><tr><td> [[Image: direct solvers and iterative solversPMOM119. Iterative solvers are usually based on matrixpng|thumb|left|600px|3D polar radiation pattern plot of a microstrip-vector multiplicationsfed patch antenna. Direct solvers typically work faster for matrices of smal to medium size (N&lt;3,000). [[EM.Cube]]'s [[Planar Module]] offers five linear solvers:</td></tr></table>

# LU Decomposition Method# Biconjugate Gradient Method 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 (BiCGRCS)# Preconditioned Stabilized Biconjugate Gradient Method (BCG-STAB)# Generalized Minimal Residual Method (GMRES)# Transposeof a planar target. Note that in this case the RCS is defined for a finite-Free Quasisized target in the presence of an infinite background structure. The scattered &theta; and &phi; components of the far-Minimum Residual Method zone electric field are indeed what you see in the 3D far field visualization of radiation (TFQMRscattering)patterns. Instead of radiation or scattering patterns, you can instruct [[EM.Picasso]] to plot 3D visualizations of &sigma;_&theta;, &sigma;_&phi; and the total RCS.

Of the above list, LU is a direct solver, while the rest are iterative solvers<table><tr><td> [[Image:PMOM125. 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 png|thumb|left|600px|An example of solvers called '''Krylov Sub-space Methods'''. In particular, the GMRES method always provides guaranteed unconditional convergence3D monostatic radar cross section plot of a patch antenna.]] </td></tr></table>

[[EM.Cube]]'s [[Planar Module]], by default, provides a &quot;'''Automatic'''&quot; solver option that picks the best method based on the settings and size of the numerical problem. For linear systems with a size less than N = 3,000, the LU solver is used. For larger systems, BiCG is used when dealing with symmetric matrices, and GMRES is used for asymmetric matrices. If the size of the linear system exceeds N = 15,000, the sparse version of the iterative solvers is used, utilizing Discretizing a row-indexed sparse storage scheme. You can override the automatic solver option and manually set you own solver type. This is done using the '''Solver Type''' dropdown list Planar Structure in the &quot;'''Linear System Solver'''&quot; section of the Planar MoM Engine Settings dialog. There are also a number of other [[parameters]] related to the solvers. The default value of '''Tolerance of Iterative Solver''' is 1E-3, which can be increased for more ill-conditioned systems. The maximum number of iterations is usually expressed as a multiple of the systems size. The default value of '''Max No. of Solver Iterations / System Size''' is 3. For extremely large systems, sparse versions of iterative solvers are used. In this case, the elements of the matrix are thresholded with respect to the larges element. The default value of '''Threshold for Sparse Solver''' is 1E-6, meaning that all the matrix elements whose magnitude is less than 1E-6 times the large matrix elements are set equal to zero. There are two more [[parameters]] that are related to the Automatic Solver option. These are &quot;''' User Iterative Solver When System Size &gt;'''&quot; with a default value of 3,000 and &quot;''' Use SParse Storage When System Size &gt;''' &quot; with a default value of 15,000. In other words, you control the automatic solver when to switch between direct and iterative solvers and when to switch to the sparse version of iterative solversEM.Picasso ==

If your computer has an Intel CPU, then [[EM.Cube]] offers special versions The method of moments (MoM) discretizes all the above linear solvers that have been optimized for Intel CPU platforms. These optimal solvers usually work 2finite-3 time faster than their generic counterpartssized objects of a planar structure (excluding the background structure) into a set of elementary cells. When you install [[EMBoth the quality and resolution of the generated mesh greatly affect the accuracy of the MoM numerical solution.Cube]]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 option to use Intelmore cells are created on the finite-optimized solvers is already enabledsized geometrical objects. HoweverAs a rule of thumb, you can disable this option (e.g. if your computer has a nonmesh density of about 20-Intel CPU)30 cells per effective wavelength usually yields satisfactory results. To do thatBut for structures with lots of fine geometrical details or for highly resonant structures, open the [[EMhigher mesh densities may be required.Cube]]'s Preferences Dialog from '''Menu &gt; Edit &gt; Preferences''' or using the keyboard shortcut '''Ctrl+H'''The particular output data that you seek in a simulation also influence your choice of mesh resolution. Select For example, far field characteristics like radiation patterns are less sensitive to the Advanced tab of the dialog mesh density than field distributions on structures with a highly irregular shapes and uncheck the box labeled &quot;''' Use Optimized Solvers for Intel CPU'''&quot;boundaries.

<table><tr><td> [[FileImage:PMOM82PMOM31.png|thumb|400px|The Planar Mesh Settings dialog.]]</td></tr></table>

[[ImageEM.Picasso provides two types of mesh for a planar structure:PMOM127a pure triangular surface mesh and a hybrid triangular-rectangular surface mesh.png|thumb|400px|Settings adaptive frequency sweep parameters in In both case, EM.Picasso's Frequency Settings Dialogattempts to create a highly regular mesh, in which most of the cells have almost equal areas.]]=== Running Uniform and Adaptive Frequency Sweeps ===For planar structures with regular, mostly rectangular shapes, the hybrid mesh generator usually leads to faster computation times.

In a frequency sweep, the operating frequency of a planar structure is varied during each sweep run. [[EMImage:Info_icon.Cubepng|30px]]Click here to learn more about '''s [[Planar Module]] offers two types of frequency sweep: Uniform and AdaptivePreparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. In a uniform frequency sweep, the frequency range and the number of frequency samples are specified. The samples are equally spaced over the frequency rangeCube. 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.Grid27s_Mesh_Generators | Working with Mesh Generator]]'''.

To run a uniform frequency sweep, open the '''Simulation Run Dialog''', and select the '''Frequency Sweep''' option from the dropdown list labeled '''Simulation Mode'''. When you choose the frequency sweep option, the '''Settings''' button next to the simulation mode dropdown list becomes enabled. Clicking this button opens the '''Frequency Settings''' dialog. The '''Frequency Range'''is initially set equal to your project's center frequency minus and plus half bandwidth. But you can change the values 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, [[EMImage:Info_icon.Cubepng|30px]] fixes the mesh density at the highest frequency, i.e., at the &quot;End Frequency&quot;. This usually results in a smoother frequency response. You have the option Click here to fix the mesh at the center frequency of the project or let learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.CubePicasso's Triangular Surface Mesh Generator]] &quot;remesh&quot; the planar structure at each frequency sample during a frequency sweep. You can make one of these three choices using the radio button in the '''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.

Frequency sweeps are often performed to study the frequency response <table><tr><td> [[Image:PMOM48F.png|thumb|left|420px|Geometry of a planar structuremultilayer slot-coupled patch array. In particular, the variation of scattering [[parameters]] like S<sub/td>11</subtr> (return loss) and S<subtr>21</subtd> (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. [[EMImage:PMOM48G.Cube]]'s [[Planar Module]] offers a powerful adaptive frequency sweep option for this purpose. It is based on the fact that the frequency response png|thumb|left|420px|Hybrid planar mesh 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 rangeslot-coupled patch array. [[EM.Cube]] first starts with very few frequency samples and tries to fit rational functions of low orders to the scattering [[parameters]]. Then, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, all the possible rational functions of higher orders are tried out. The process continues until adding new intermediate frequency samples does not improve the resolution of the &quot;S<sub/td>ij</subtr></table>&quot; curves over the given frequency range. In that case, the curves are considered as having converged.

You must have defined one or more ports for your planar structure run an adaptive frequency sweep<table><tr><td> [[Image:PMOM48H. Open the Frequency Settings dialog from the Simulation Run dialog and select the '''Adaptive''' option png|thumb|left|420px|Details of '''Frequency Sweep Type'''. You have to set values for '''Minimum Number of Samples''' and '''Maximum Number of Samples'''. Their default values are 3 and 9, respectively. You also set a value for the '''Convergence Criterion''', which has a default value of 0.1. At each iteration cycle, all the S [[parameters]] are calculated at the newly inserted frequency samples, and their average deviation from the curves hybrid planar mesh of the last cycle is measured as an errorslot-coupled patch array around discontinuities. When this error falls below the specified convergence criterion, the iteration is ended. If [[EM.Cube]] reaches the specified maximum number of iterations and the convergence criterion has not yet been met, the program will ask you whether to continue the process or exit it and stop.</td></tr></table>

== Working EM.Picasso's hybrid planar mesh generator tries to produce as many rectangular cells as possible especially in the case of objects with Planar MoM Simulation Data ==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.

[[Image:PMOM130.png|thumb|400px|Changing the graph type by editing a data file's properties.]][[Image:PMOM134.png|thumb|400px|The S₁₁ parameter plotted on mesh density gives a Smith Chart graph measure of the number of cells per effective wavelength that are placed in EM.Grid.]][[Image:PMOM131.png|thumb|300px|EM.Picasso's Smart Fit dialog.]][[Image:PMOM133(2)various regions of your planar structure.png|thumb|300px|The Seffective wavelength is defined as <submath>11\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</submath> parameter plot of a two-port structure in magnitude-phase format.]][[Image:PMOM132(2).png|thumb|300px|The smoothed version of the S, where e_11eff parameter plot of is the two-port structure using effective permittivity. By default, [[EM.CubePicasso]]'s Smart Fitgenerates a hybrid mesh with a mesh density of 20 cells per effective wavelength. The effective permittivity is defined differently for different types of traces and embedded object sets. This is to make sure that enough cells are placed in areas that might feature higher field concentration.]]=== Planar Module's Output Simulation Data ===

Depending on the source type * For PEC and conductive sheet traces, the types of observables effective permittivity is defined in a project, a number as the larger of output data are generated at the end permittivity of a planar MoM simulationthe two substrate layers just above and below the metallic trace. Some * For slot traces, the effective permittivity is defined as the mean (average) of these data are 2D by nature the permittivity of the two substrate layers just above and some are 3D. The output simulation data generated by [[EMbelow the metallic trace.Cube]]'s [[Planar Module]] can be categorized into * For embedded object sets, the following groups:effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets.

* '''Port Characteristics'''<table><tr><td> [[Image: S, Z PMOM32.png|thumb|360px|A comparison of triangular and Y [[Parametersplanar hybrid meshes of a rectangular patch.]] and Voltage Standing Wave Ratio (VSWR)</td>* '''Radiation Characteristics'''<td> [[Image: 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), etcPMOM30.png|thumb|360px|Mesh of two rectangular patches at two different substrate planes.The lower substrate layer has a higher permittivity.]] </td>* '''Scattering Characteristics''': Bi-static and Mono-static Radar Cross Section (RCS)</tr>* '''Periodic Characteristics''': Reflection and Transmission Coefficients* '''Current Distributions''': Electric and magnetic current amplitude and phase on all metal and slot traces and embedded objects* '''Near-Field Distributions''': Electric and magnetic field amplitude and phase on specified planes and their central axes</table>

At the end === General Rules of an analysis, the 2D quantities usually have a single value that is written into an ASCII data file. Complex-valued quantities are written into complex data files with a &quot;'''.CPX'''&quot; extension. Real-valued quantities are written into real data files with a &quot;'''.DAT'''&quot; extension. Polar 2D radiation pattern data and some other radiation characteristics are written into angular data files with a &quot;'''.ANG'''&quot; extension. In this latter file type, polar data are stored as functions of an angle expressed in degrees. At the end of a sweep simulation of one of the many types available (frequency, angular, parametric, etc.), the ASCII output data files are populated with rows that correspond to the samples of the sweep variable(s). If a sweep simulation involves N sweep [[variables]], then the first N columns of the output data files show the samples of those sweep [[variables]]. All the 2D data files are listed in the '''2D Data Files''' tab of [[EM.Cube]]'s '''Data Manager'''. You can view the contents of these data files by selecting their row in the data manager and clicking the '''View''' button of the dialog.Planar Hybrid Mesh Generator ===

3D output data, on the other hand, are defined as functions The integrity of the space coordinates and are usually of vectorial nature. Cartesian-type and planar mesh-type data such as current distributions and near-field field distributions are expressed as functions of its continuity in the Cartesian (X, Y, Z) coordinates. Spherical-type data like far-field radiation patterns and RCS are expressed as functions of junction areas directly affects the spherical angles (&theta;, &phi;). The 3D radiation patterns are written into a file with a &quot;'''.RAD'''&quot; extension. This file contains the complex values of the &theta;- quality and &phi;-components accuracy of the far-zone electric field (E_&theta; and E_&phi;) as well as the total far field magnitude as functions of the spherical observation angles &theta; and &phi;simulation results. The 3D RCS patterns are written into a file with a &quot;'''EM.RCSPicasso'''&quot; extension. This file contains the real values of the &theta;- and &phi;-polarized RCS values as well as the total RCS as functions of the spherical observation angles &theta; and &phi;. The current distributions s hybrid planar mesh generator has some rules that are written into data files with a &quot;'''catered to 2.CUR'''&quot; extension. They contain the real and imaginary parts of the X, Y and Z components of electric ('''J''') and magnetic ('''M''') current on each cells together with the definition of all the node coordinates and node indices of the cells. The near5-field distributions are written into data files with a &quot;'''.SEN'''&quot; extension. They contain the amplitude and phase of the X, Y and Z components of electric ('''E''') and magnetic ('''H''') fields as functions of the coordinates of sampling points. All the 3D data files are listed in the '''3D Data Files''' tab of [[EM.Cube]]'s '''Data Manager'''. You can view the contents of these data files by selecting their row in the data manager and clicking the '''View''' button of the dialog.D MoM simulations:

:<mathtable><tr><td>\mathbf{ [S] = [Y_0File:PMOM36.png|250px]] \cdot ([Z[File:PMOM38.png|250px]]-[Z_0[File:PMOM37.png|250px]) \cdot (] </td></tr><tr><td> Two overlapping planar objects and a comparison of their triangular and hybrid planar meshes. </td></tr><tr><td> [Z[File:PMOM33.png|250px]]+[Z_0[File:PMOM35.png|250px]])^{-1} \cdot [Z_0[File:PMOM34.png|250px] }] </td></tr><tr><td> Edge-connected rectangular planar objects and a comparison their triangular and hybrid planar meshes. </td></tr></mathtable>

:<mathtable><tr><td>\mathbf{ [Y[File:PMOM39.png|375px]] = [Z[File:PMOM40.png|375px]^{-1} } ] </td></tr><tr><td> Meshes of short and long vertical PEC vias connecting two horizontal metallic strips. </td></tr></mathtable>

:<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot ([U]+[S]) \cdot ([U]-[S])^{-1} \cdot [\sqrt{Z_0}] }</math><!--[[File:PMOM121.png]]-->== Refining the Planar Mesh Locally ===

where <math>\mathbf{[U]}</math> It is very important to apply the right mesh density to capture all the identity matrix geometrical details of order Nyour planar structure. This is especially true for &quot;field discontinuity&quot; regions such as junction areas between connected objects, <math>\mathbf{[Z_0]}</math> and <math>\mathbf{[Y_0]}</math> are diagonal matrices whose diagonal elements where larger current concentrations are usually observed at sharp corners, or at the port characteristic impedances junction areas between metallic traces and admittances, respectivelyPEC vias, as well as the areas around gap sources and <math>\mathbf{[\sqrt{Z_0}]}</math> is a diagonal matrix whose diagonal lumped elements are the square roots of port characteristic impedances, which create voltage or current discontinuities. The voltage standing wave ratio (VSWR) of the structure at the first port is also computed:

:<math>\text{VSWR} = \frac{|V_{max}|}{|V_{min}|} = \frac{1+|S_{11}|}{1-|S_{11}|}</math><!--[[File:PMOM122The Planar Mesh Settings dialog gives a few options for customizing your planar mesh around geometrical and field discontinuities. The check box labeled &quot;'''Refine Mesh at Junctions'''&quot; increases the mesh resolution at the connection area between rectangular objects. The check box labeled &quot;'''Refine Mesh at Gap Locations'''&quot; might be particularly useful when gap sources or lumped elements are placed on a short transmission line connected from both ends. The check box labeled &quot;'''Refine Mesh at Vias'''&quot; increases the mesh resolution on the cross section of embedded object sets and at the connection regions of the metallic objects connected to them. EM.Picasso typically doubles the mesh resolution locally at the discontinuity areas when the respective boxes are checked. You should always visually inspect EM.Picasso's default generated mesh to see if the current mesh settings have produced an acceptable mesh.png]]-->

At the end of a planar MoM simulation, the values of S/Z/Y [[parameters]] and VSWR data are calculated and reported in the output message windowSometimes EM. The S, Z and Y [[parameters]] are written into output ASCII data files of complex type with a &quot;''Picasso's default mesh may contain very narrow triangular cells due to very small angles between two edges.CPX'''&quot; extension. Every file begins with In some rare cases, extremely small triangular cells may be generated, whose area is a header consisting small fraction of a few comment lines that start with the &quot;#&quot; symbolaverage mesh cell. The complex values are arranged into two columns for These cases typically happen at the real junctions and imaginary partsother discontinuity regions or at the boundary of highly irregular geometries with extremely fine details. In the case of multiport structuressuch cases, every single element of increasing or decreasing the S/Z/Y matrices is written into a separate complex data filemesh density by one or few cells per effective wavelength often resolves that problem and eliminates those defective cells. For exampleNonetheless, you will have data files like S11EM.CPX, S21Picasso's planar mesh generator offers an option to identify the defective triangular cells and either delete them or cure them.CPX, By curing we mean removing a narrow triangular cell and merging its two closely spaced nodes to fill the crack left behind.EM.Picasso by default deletes or cures all the triangular cells that have angles less than 10º., Z11Sometimes removing defective cells may inadvertently cause worse problems in the mesh.CPX, Z21.CPX, etc. The VSWR data are saved You may choose to an ASCII data file of real type with a disable this feature and uncheck the box labeled &quot;'''.DATRemove Defective Triangular Cells'''&quot; extension called, VSWRin the Planar Mesh Settings dialog.DATYou can also change the value of the minimum allowable cell angle.

If you run an analysis{{Note| Narrow, 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 type of sweep including spiky triangular cells in a frequency sweep. In that case, the &quot;.CPX&quot; files have multiple rows corresponding to each value of the sweep parameter (e.g. frequency). [[EM.Cube]]'s 2D graph data planar mesh are plotted in EM.Grid, a versatile graphing utilitygenerally not desirable. You can plot the port characteristics directly from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section should get rid of the Navigation Tree and select one of either by changing the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', mesh density or using the hybrid planar mesh generator'''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]]s additional mesh refinement options.}}

You can also see a list of all the port characteristics data files in <table><tr><td> [[EMImage:PMOM44.png|thumb|left|480px|Deleting or curing defective triangular cells: Case 1.Cube]]'s Data Manager. To open data manager, click the '''Data Manager''' </td></tr><tr><td> [[FileImage:data_manager_iconPMOM42.png]] button of the '''Simulate Toolbar''' |thumb|left|480px|Deleting or select '''Simulate &gt; Data Manager''' from the menu bar, or right click on the '''Data Manager''' item of the Navigation Tree and select '''Open Data Manager'''curing defective triangular cells: Case 2... from the contextual menu. You can also use the keyboard shortcut '''Ctrl+D''' at any time. Select any data file by clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You can change the format of complex data plots. In general complex data can be plotted in three forms:</td></tr></table>

In particular, it may be useful to plot the S_ii [[parameters]] on a Smith chart=== EM. To change the format of a data plot, select it in the Data Manager and click its Picasso'''Edit''' button. In the Edit File Dialog, choose one of the options provided in the dropdown list labeled '''Graph Type'''.s Simulation Modes ===

The adaptive frequency sweep described earlier is an iterative process, whereby the {| 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 simulation engine is Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the planar MoM solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a certain number specified set of frequency samples at each iteration cycle. The or adds more frequency samples are progressively built up, and rational fits for these data are found at each iteration cyclein an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. A decision is then made whether to continue more iterationsCube#Running_Parametric_Sweep_Simulations_in_EM. At Cube | Parametric Sweep]]| style="width:270px;" | Varies the end value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the whole process, a total number of scattering parameter data samples have been generated, and new smooth data corresponding to the best rational fits are written into new data files for graphing. center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[EMParametric_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 center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[planar ModuleParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]] also allows you | style="width:270px;" | Varies the value(s) of one or more project variables to generate a rational fit for all or any existing scattering parameter data as a post-processing operation without a need to run additional simulation engine compact model| style="width:80px;" | Multiple runs.| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|}

You can interpolate all set the scattering simulation mode from [[parameters]] together or select individual [[parametersEM.Picasso]]'s "Simulation Run Dialog". You do this postA single-processing operation from the Navigation Treefrequency analysis is a single-run simulation. Right click on All the '''Port Definition''' item other simulation modes in the '''Observables''' section of the Navigation Tree and select Smart Fit. At the top of the Smart Fit Dialog, there is a dropdown above list labeled '''Interpolate''', which gives a list of all the available S parameter data for rational interpolationare considered multi-run simulations. The default option is &quot;All Available [[Parameters]]&quot;. Then If you see run a box labeled '''Number of Available Samples'''simulation without having defined any observables, whose value is read from no data will be generated at the data content end of the selected complex simulation.CPX In multi-run simulation modes, certain parameters are varied and a collection of simulation data filefiles are generated. Based on At the number end of available data samplesa sweep simulation, you can graph the dialog reports the '''Maximum Interpolant Order'''simulation results in EM. You Grid or you can choose any integer number for '''Interpolant Order''', animate the 3D simulation data from 1 to the maximum allowednavigation tree.

{{Note|Interpolant order more than 15 will suffer from numerical instabilities even if you have === Running a very large number Single-Frequency Planar MoM Analysis === A single-frequency analysis is the simplest type of data samples[[EM.}}Picasso]] simulation and involves the following steps:

You can use * Set the '''Update''' button units of your project and the dialog to generate the interpolated data for a given orderfrequency of operation. The new data are written to a complex data file with Note that the same name as the selected S parameter and a &quot;default project unit is '''_RationalFitmillimeter'''&quot; suffix. While this dialog is still open, * Define you can plot 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 new data either directly from the Navigation Tree finite-sized metal and slot trace objects and possibly embedded metal or from dielectric objects that are interspersed among the Data Managersubstrate layers. If you are not satisfied with * Define an excitation source and observables for your project.* Examine the resultsplanar mesh, you can return to verify its integrity and change the Smart Fit dialog and try a higher or lower interpolant order and compare mesh density if necessary.* Run the Planar MoM simulation engine.* Visualize the new output simulation data.

Electric and magnetic currents are the fundamental output data of a planar MoM simulation<table><tr><td> [[Image:Picasso L1 Fig18. After the numerical solution of the MoM linear system, they are found using the solution vector png|thumb|left|480px|EM.Picasso'''[Is Simulation Run dialog.]''' and the definitions of the electric and magnetic vectorial basis functions:] </td></tr></table>

:<math> \mathbf{[I]}_{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)} Setting Numerical Parameters == \sum_{k=1}^K V_k^{(M)} \mathbf{f_k^{(M)} (r)} \end{cases} </math><!--[[File:PMOM83.png]]-->

Note A planar MoM simulation involves a number of numerical parameters that currents are complex vector quantities. Each electric or magnetic current has three X, Y and Z components, and each complex component has a magnitude and phasetake preset default values unless you change them. You can visualize access these parameters and change their values by clicking the surface electric currents on metal (PEC) and conductive sheet traces'''Settings''' button next to the '''Select Engine''' drop-down list in [[EM.Picasso]]'s Simulation Run dialog. In most cases, surface magnetic currents on slot (PMC) traces you do not need to open this dialog and vertical volume currents on you can leave all the PEV vias and embedded dielectric objectsdefault numerical parameter values intact. 3D color-coded intensity plots of electric and magnetic current distributions are visualized in the project workspaceHowever, it is useful to familiarize yourself with these parameters, superimposed on as they may affect the surface accuracy of physical objectsyour numerical results.

In order to view the current distributions, you must first define them as observables before running the planar The Planar MoM simulationEngine Settings Dialog is organized in a number of sections. To do that, right click on Here we describe some of the numerical parameters. The &quot;'''Current Distributions''' item in the '''ObservablesMatrix Fill''' &quot; section of the Navigation Tree and select dialog deals with the operations involving the dyadic Green's functions. You can set a value for the ''Insert New Observable...'Convergence Rate for Integration''', which is 1E-5 by default. The Current Distribution Dialog opens up. At This is used for the top convergence test of all the dialog and infinite integrals in the section titled '''Active Trace / Set''calculation of the Hankel transform of spectral-domain dyadic Green's functions. When the substrate is lossy, you the surface wave poles are captured in the complex integration plane using contour deformation. You can select 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 trace or embedded object set where you want thin substrate layer is defined to observe a have a thickness less than 0.01&lambda;_eff, where &lambda;_eff is the current distributioneffective wavelength. You can also select modify the current map type from two options: definition of &quot;Thin Substrate&quot; by entering a value for '''ConfettiThin Substrate Threshold''' and different than the default 0.01. The parameter '''ConeMax Coupling Range'''. The former produces an intensity plot for current amplitude determines the distance threshold in wavelength between the observation and phasesource points after which the Green's interactions are neglected. This distance by default is set to 1,000 wavelengths. For electrically small structures, while the latter generates phase variation across the structure may be negligible. In such cases, a 3D vector plotfast quasi-static analysis can be carried out. You can set this threshold in wavelengths in the box labeled '''Max Dimensions for Quasi-Static Analysis'''.

In the &quot;Spectral Domain Integration&quot; section of the dialog, you can set a value to '''Max Spectral Radius in k0''', which has a default value of 30. This means that the infinite spectral-domain integrals in the spectral variable k_&rho; are pre-calculated and tabulated up to a limit of 30k₀, where k₀ 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 100k₀ might be needed to warrant adequate convergence. For spectral-domain integration along the real k_&rho; axis, the interval [[File:PMOM840, Nk₀] is subdivided into a large number of sub-intervals, within each an 8-point Gauss-Legendre quadrature is applied.png]The next parameter, '''No. Radial Integration Divisions per k₀''', determines how small these intervals should be. By default, 2 divisions are used for the interval [0, k₀]. In other words, the length of each integration sub-interval is k₀/2. You can increase the resolution of integration by increasing this value above 2. Finally, instead of 2D Cartesian integration in the spectral domain, a polar integration is performed. You can set the '''No. of Angular Integration Points''', which has a default value of 100.

Figure 1: The [[Planar ModuleEM.Picasso]]provides a large selection of linear system solvers including both direct and iterative methods. [[EM.Picasso]], by default, provides a &quot;'s Current Distribution ''Automatic'''&quot; 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 [[EM.Cube]] to write the MoM matrix and excitation and solution vectors into output data files for your examination. To do so, check the box labeled &quot;'''Output MoM Matrix and Vectors'''&quot; in the Matrix Fill section of the Planar MoM Engine Settings dialog. These are written into three files called mom.dat1, exc.dat1 and soln.dat1, respectively.

Once you close the current distribution <table><tr><td> [[Image:PMOM79.png|thumb|left|720px|EM.Picasso's Planar MoM Engine Settings dialog, the label of the selected trace or object set is added under the '''Current Distributions''' node of the Navigation Tree. ]] </td></tr></table>

{{Note|You have to define a separate current distribution observable for each individual trace or embedded object set== Modeling Periodic Planar Structures in EM.}}Picasso ==

At [[EM.Picasso]] allows you to simulate doubly periodic planar structures with periodicities along the end of a X and Y directions. Once you designate your planar structure as periodic, [[EM.Picasso]]'s Planar MoM simulationengine uses a spectral domain solver to analyze it. In this case, the current distribution nodes in the Navigation Tree become populated by the magnitude and phase plots dyadic Green's functions of periodic planar structure take the three vectorial components form of the electric ('''J''') and magnetic ('''M''') currents as well as the total electric and magnetic currents defined in the following manner:doubly infinite summations rather than integrals.

[[Image:<math> Info_icon.png| \mathbf{J_{tot}} 30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Method_of_Moments#Periodic_Planar_MoM_Simulation | = \sqrt{|J_x|^2 + |J_y|^2 + |J_z|^2}</math>Periodic Green's functions]]'''.

:<math> | \mathbf{M_{tot}} Note| = \sqrt{|M_x|^2 + |M_y|^2 + |M_z|^2}</math><!--[[File:PMOM87EM.pngPicasso]]-->can handle both regular and skewed periodic lattices.}}

[[File:PMOM85(1)=== Defining a Periodic Structure in EM.png|800px]]Picasso ===

Figure 2: The current distribution map An infinite periodic structure in [[EM.Picasso]] is represented by a &quot;'''Periodic Unit Cell'''&quot;. To define a periodic structure, you must open [[EM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''&gt;''' '''Simulate &gt; 'Computational Domain &gt; Periodicity Settings...''' from the menu bar. In the Periodicity Settings Dialog, check the box labeled '''Periodic Structure'''. This will enable the section titled''&quot;''Lattice Properties&quot;. You can define the periods along the X and Y axes using the boxes labeled '''Spacing'''. In a patch antennaperiodic 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> [[FileImage:PMOM86(2)PMOM99.png|800pxthumb|300px|EM.Picasso's Periodicity Settings dialog.]]</td></tr></table>

Figure 3: Vectorial In many cases, your planar structure's traces or embedded objects are entirely enclosed inside the periodic unit cell and do not touch the boundary of the unit cell. [[EM.Picasso]] allows you to define periodic structures whose unit cells are interconnected. The interconnectivity applies only to PEC, PMC and conductive sheet traces, and embedded object sets are excluded. Your objects cannot cross the periodic domain. In other words, the neighboring unit cells cannot overlap one another. However, you can arrange objects with linear edges such that one or more flat edges line up with the domain's bounding box. In such cases, [[EM.Picasso]]'s planar MoM mesh generator will take into account the continuity of the currents across the adjacent connected unit cells and will create the connection basis functions at the right and top boundaries of the unit cell. It is clear that due to periodicity, the basis functions do not need to be extended at the left or bottom boundaries of the unit cell. As an example, consider a periodic metallic screen as shown in the figure on the right. The unit cell of this structure can be defined as a rectangular aperture in a PEC ground plane (conemarked as Unit Cell 1) visualization of . In this case, the current distribution rectangle object is defined as a slot trace. Alternatively, you can define a unit cell in the form of a microstrip cross on a patch antennametal 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.

<table><tr><td> [[FileImage:PMOM90pmom_per5_tn.png|thumb|300px|[[Planar Module]]'s Field Sensor dialogThe PEC cross unit cell.]]</td>In order to view the near field distributions, you must first define field sensor observables before running the planar MoM simulation<td> [[Image:pmom_per6_tn. To do that, right click on the '''Field Sensors''' item in the '''Observables''' section png|thumb|300px|Planar mesh of the Navigation Tree and select '''Insert New ObservablePEC cross unit cell...'''. The Field Sensor Dialog opens up. At Note the top of cell extensions at the dialog and in the section titled unit cell'''Sensor Plane Location''', first you need to set the plane of near field calculation. In the dropdown box labeled '''Direction''', you have three options X, Y, and Z, representing the&quot;normals&quot; to the XY, YZ and ZX planes, respectively. The default direction is Z, i.e. XY plane parallel to the substrate layers. In the three boxes labeled '''Coordinates''', you set the coordinates of the center of the plane. Then, you specify the '''Size''' of the plane in project units, and finally set the '''Number of Samples''' along the two sides of the sensor plane. The larger the number of samples, the smoother the near field map will appears boundaries.]] </td></tr></table>

In the section titled Output Settings, you can also select the field map type from two options: '''Confetti''' and '''Cone'''. The former produces an intensity plot for field amplitude and phase, while the latter generates a 3D vector plot. In the confetti case, you have an option to check the box labeled '''Data Interpolation''', which creates a smooth and blended (digitally filtered) map. In the cone case, you can set the size of the vector cones that represent the field direction. At the end of a sweep simulation, multiple field map are produced and added to the Navigation Tree. You can animate these maps. However, during the sweep only one field type is stored, either the E-field or H-field. You can choose the field type for multiple plots using the radio buttons === Exciting Periodic Structures as Radiators in the section titled '''Field Display - Multiple Plots'''. The default choice is the E-fieldEM.Picasso ===

Once you close When a periodic planar structure is excited using a gap or probe source, it acts like an infinite periodic phased array. All the Field Sensor periodic replicas of the unit cell structure are excited. You can even impose a phase progression across the infinite array to steer its beam. You can do this from the property dialogof the gap or probe source. At the bottom of the '''Planar Gap Circuit Source Dialog''' or '''Gap Source Dialog''', its name there is added under the a button titled '''Field SensorsPeriodic Scan...''' node of the Navigation Tree. At You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the end radiation patterns of a planar MoM simulationbeam-steered antenna array, you have to define a finite-sized array factor in the field sensor nodes Radiation Pattern dialog. You do this in the Navigation Tree become populated by the magnitude and phase plots of the three vectorial components of the electric ('''EImpose Array Factor''') and magnetic (section of this dialog. The values of '''HElement Spacing''') field as well as along the total electric X and magnetic fields defined in Y directions must be set equal to the following manner:value of '''Periodic Lattice Spacing''' along those directions.

:<mathtable> <tr><td> [[Image:Period5.png|\mathbf{E_{tot}}thumb| = \sqrt{350px|E_x|^2 + |E_y|^2 + |E_z|^2} Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] </mathtd>:<mathtd> [[Image:Period5_ang.png|\mathbf{H_{tot}}thumb| = \sqrt{350px|H_x|^2 + |H_y|^2 + |H_z|^2} Setting the beam scan angles in Periodic Scan Angles dialog.]] </mathtd><!--/tr><tr><td> [[FileImage:PMOM88Period6.png|thumb|350px|Setting the array factor in EM.Picasso's Radiation Pattern dialog.]]--</td></tr></table>

Note that unlike <table><tr><td> [[EMImage:Period7.png|thumb|360px|Radiation pattern of an 8×8 finite-sized periodic printed dipole array with 0&deg; phi and theta scan angles.Cube]]'s other computational modules, near field calculations in the </td><td> [[Planar Module]] usually takes substantial timeImage:Period8. This is due to the fact that at the end png|thumb|360px|Radiation pattern of a planar MoM simulation, the fields are not available anywhere (as opposed to the [[FDTD Module]]), beam-steered 8×8 finite-sized periodic printed dipole array with 45&deg; phi and their computation requires integration of complex dyadic Green's functions (as opposed to [[MoM3D Moduletheta scan angles.]]'s free space Green's functions).</td></tr></table>

[[File:PMOM116=== Exciting Periodic Structures Using Plane Waves in EM.png|800px]]Picasso ===

Near-zone electric field map above When a microstripperiodic planar structure is excited using a plane wave source, it acts as a periodic surface that reflects or transmits the incident wave. [[EM.Picasso ]] calculates the reflection and transmission coefficients of periodic planar structures. If you run a single-fed patch antennafrequency plane wave simulation, the reflection and transmission coefficients are reported in the Output Window at the end of the simulation. Note that these periodic characteristics depend on the polarization of the incident plane wave. You set the polarization (TMz or TEz) in the '''Plane Wave Dialog''' when defining your excitation source. In this dialog you also set the values of the incident '''Theta''' and '''Phi''' angles. At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called &quot;reflection.CPX&quot; and &quot;transmission.CPX&quot;.

{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[File:PMOM117EM.png|800pxPicasso]]computes the reflection and transmission coefficients of the layered background structure of your project.}}

Near-zone magnetic field map above <table><tr><td>[[Image:PMOM102.png|thumb|580px|A periodic planar layered structure with slot traces excited by a microstrip-fed patch antennanormally incident plane wave source.]]</td></tr></table>

=== Visualizing The Far Fields Running a Periodic MoM Analysis ===

You run a periodic MoM analysis just like an aperiodic MoM simulation from [[File:PMOM118EM.png|thumb|300px|[[Planar ModulePicasso]]'s Radiation Pattern dialog]]Even though the planar MoM engine does not need Run Dialog. Here, too, you can run a radiation boxsingle-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you still have to can define a &quot;Far Field&quot; observable several observables for radiation pattern calculationyour project. This is because far field calculations take time and If you have to instruct [[EM.Cube]] to perform these calculations. To define open the Planar MoM Engine Settings dialog, you will see a far field, right click the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Radiation Patterntitled "Infinite Periodic Simulation"...'''. The Radiation Pattern Dialog opens up. You may accept the default settingsIn this section, or you can change set the value number of '''Angle Increment''', which is expressed Floquet modes that will be computed in degrees. You can also choose to '''Normalize 2D Patterns''the periodic Green's function summations. In that caseBy default, the maximum value numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a 2D paten graph will have a value total of 1; otherwise, the actual far field values in V/m 2500 Floquet terms will be used on the graphcomputed for each periodic MoM simulation.

Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the &quot;Total&quot; far field. The 3D plots can be viewed in the project workspace by clicking on each item. The view of the 3D far field plot can be changed with the available view operations such as rotate view, pan, zoom, etc. If the structure blocks the view of the radiation pattern, you can simply hide or freeze the whole structure or parts of it. In a 3D radiation pattern plot, the fields are always normalized to the maximum value of the total far field for visualization purpose: :<mathtable>|\mathbf{E_{ff,tot}}| = \sqrt{ |E_{\theta}|^2 + |E_{\phi}|^2 }</mathtr><!--[[File:PMOM89.png]]--td> [[FileImage:PMOM119PMOM98.png|800px]] Figure: 3D polar radiation pattern plot of a microstrip-fed patch antenna. [[File:PMOM120.pngthumb|800px]] Figure: 3D vectorial (cone) radiation pattern plot 600px|Changing the number of a microstrip-fed patch antenna. The 2D radiation pattern graphs can be plotted Floquet modes from [[EMthe Planar MoM Engine Settings dialog.Cube]]'s '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.</td>=== Radar Cross Section of Planar Structures ===</tr></table>

You learned earlier how to use [[File:PMOM124EM.png|thumb|300px|Planar Module's Radar Cross Section dialogCube]]'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.

When a planar structure is [[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 calculated far field data indeed represent planar MoM engine calculates the scattered fields reflection and transmission coefficients of the periodic surface. Note that planar structureyou can conceptually consider a periodic surface as a two-port network, where Port 1 is the top half-space and Port 2 is the bottom half-space. In that case, the reflection coefficient R is equivalent to S₁₁ parameter, while the transmission coefficient T is equivalent to S₂₁ parameter. This is, of course, the case when the periodic surface is illuminated by the plane wave source from the top half-space, corresponding to 90°&lt; &theta; = 180°. You can also illuminate the periodic surface by the plane wave source from the bottom half-space, corresponding to 0° = &theta; &lt; 90°. In this case, the reflection coefficient R and transmission coefficient T are equivalent to S₂₂ and S₁₂ parameters, respectively. Having these interpretations in mind, [[EM.Cube]] can also calculate enables the radar cross section (RCS) &quot;'''Adaptive Frequency Sweep'''&quot; option of a the '''Frequency Settings Dialog''' when your planar target:structure has a periodic domain together with a plane wave source.

:<math> \sigma_{\theta} !--= 4\pi r^2 \dfrac{|E_{\theta}^{scat}|^2}{|E^{inc}|^2}, \quad \sigma_{\phi} = 4\pi r^2 \dfrac{|E_{\phi}^{scat}|^2}{|E^{inc}|^2}, \quad \sigma = \sigma_{\theta} + \sigma_{\phi} Modeling Finite-Sized Periodic Arrays === 4\pi r^2 \dfrac{|E_{tot}^{scat}|^2}{|E^{inc}|^2} </math><!--[[File:PMOM123.png]]-->

[[Image:Info_icon.png|40px]] Click here to learn about '''Note that in this case the RCS is defined for a finite[[Modeling Finite-sized target in the presence of an infinite background structure.Sized Periodic Arrays Using NCCBF Technique]]''' The scattered &theta; and &phi; 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.Cube]] to plot 3D visualizations of &sigma;_&theta;, &sigma;_&phi; and the total RCS. To do so, you must define an RCS observable instead of a radiation pattern. Follow these steps:

At the end of a planar MoM simulation, in the far field section of the Navigation Tree, you will have the &theta; and &phi; components of RCS as well as the total radar cross section. You can view a 3D visualization of these quantities by clicking on their entries in the Navigation Tree. The RCS values are expressed in m<suphr>2</sup>. The 3D plots are normalized to the maximum RCS value, which is also displayed in the legend box.

[[FileImage:PMOM125Top_icon.png|800px30px]]'''[[EM.Picasso#Product_Overview | Back to the Top of the Page]]'''

Figure 2[[Image: An example of the 3D mono-static radar cross section plot of a patch antennaTutorial_icon.png|30px]] '''[[EM.Cube#EM.Picasso_Documentation | EM.Picasso Tutorial Gateway]]'''

<p>&nbsp;</p>[[Image:BACKBack_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''