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[[Image:Splash-mom.jpg|right|720px]]<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space 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:planar-ico.png | link=EM.Picasso]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

[[EM.Libera ]] is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structure simulator for modeling metallic structures made up of metal and dielectric structuresregions or a combination of them. It features two full-wave Method of Moments (MoM) separate simulation engines, one based on a Wire Surface MoM formulation solver and the other based on a Surface MoM formulation. In general, a surface Wire MoM solver is used to simulate your physical structure, which may involve metallic that work independently and dielectric objects provide different types of arbitrary shapes as well as composite structures that contain joined solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric regions. If objects in your project workspace contains at least one line or curve object, EMphysical structure.Libera then invokes its The Wire MoM solver. In that case, can only handle metallic structure can be modeled, and all wireframe structures. [[EM.Libera]] selects the surface and solid PEC simulation engine automatically based on the types of objects are meshed as wireframespresent in your project workspace.

{{Note|You can use [[EM.Libera either for modeling metallic wire objects and wireframe structures ]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling metallicPEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric ad composite structures that do not contain lines or curvesregions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.}}

=== A Overview {{Note|In general, [[EM.Libera]] uses the surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, [[EM.Libera]] switches to the Wire MoM solver.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of the '''[[Basic Principles of The Method of Moments | 3D Method Of 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 used in the finite element or finite difference time domain methods.<table><tr><td>In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem. The given structure is immersed in the free space. The unknown currents or fields are discretized as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields are called basis functions. They obviously have a vectorial nature and must satisfy [[Maxwell's EquationsImage:Yagi Pattern.png|thumb|500px|Maxwell's equations]] and relevant boundary conditions individually. The actual currents or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudes. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structure. EM.Libera offers two distinct 3D MoM simulation engines. The first one is a Wire MoM solver, which is based on Pocklington's integral equation. This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wirefar-type antennas and arrays. The second engine features a powerful Surface MoM solver. It can model metallic surfaces and solids as well as solid dielectric objects. The Surface MoM solver uses a surface integral equation formulation of [[Maxwell's Equations|Maxwell's equations]]. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. For the modeling radiation pattern of the dielectric regions of the physical structure , the soexpanded Yagi-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problemsUda antenna array with 13 directors. [[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[3D Method of Moments]]'''.</td>== Constructing the Physical Structure &amp; 3D Mesh Generation ==</tr></table>

=== Defining Groups Of PEC Objects EM.Libera as the MoM3D Module of EM.Cube ===

You can use [[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] EM.Libera features two different simulation engines: Wire MoM either for simulating arbitrary 3D metallic, dielectric and Surface MoM. Both simulation engines can handle metallic composite surfaces and volumetric structures. The Wire MoM engine models or for modeling wire objects and metallic objects as perfect electric conductor (PEC) wireframe structures, while the Surface MoM engine treats them as PEC surfaces. The PEC objects can be lines, curves, surfaces or solids[[EM. All the PEC objects are created under Libera]] also serves as the frequency-domain, full-wave '''PECMoM3D Module''' node in the '''Physical Structure''' section of the Navigation Tree. Objects are grouped together by their color. You can insert different PEC groups with different colors. A new PEC group can be defined by simply right clicking on the '''PEC''' item in the Navigation Tree and selecting '''Insert New PEC..[[EM.Cube]]''' from the contextual menu, a comprehensive, integrated, modular electromagnetic modeling environment. A dialog for setting up the PEC properties opens up[[EM. From this dialog you can change Libera]] shares the name visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of the group or its color[[EM. Note that PEC object do not have any material properties that can be editedCube]]'s other computational modules.

Of === Advantages & Limitations of EM.Libera's two simulation engines, only the Surface MoM solver can handle dielectric objects. Dielectric objects are created under the '''Dielectric''' node in the '''Physical Structure''' section of the Navigation Tree. They are grouped together by their color and material properties. You can insert different dielectric groups with different colors and different permittivity e_r and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when &sigma; &rarr; &infin;.Wire MoM Solvers ===

To define The method of moments uses an open-boundary formulation of Maxwell's equations which does not require a new Dielectric groupdiscretization of the entire computational domain, follow these steps:but only the finite-sized objects within it. As a result, [[EM.Libera]]'s typical mesh size is typically much smaller that that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]'s triangular surface mesh provides a more accurate representation of your physical structure than [[EM.Tempo]]'s staircase brick volume mesh, which often requires a fairly high mesh density to capture the geometric details of curved surfaces. These can be serious advantages when deciding on which solver to use for analyzing highly resonant structures. In that respect, [[EM.Libera]] and [[EM.Picasso]] are similar as both utilize MoM solvers and surface mesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.

* Right click on the [[EM.Libera]]'''Dielectric''' item of the Navigation Tree s Wire MoM solver can be used to simulate thin wires and select '''Insert New Dielectricwireframe structures very fast and accurately.This is particularly useful for modeling wire-type antennas and arrays..''' from One of the contextual menucurrent limitations of [[EM.* Specify a '''Label'''Libera]], '''Color''' (however, is its inability to mix wire structures with dielectric objects. If your physical structure contains one ore more wire objects, then all the PEC surface and optional Texture) and the electromagnetic properties solid CAD objects of the dielectric material project workspace are reduced to be created: '''Relative Permittivity''' (e_r) wireframe models in order to perform a Wire MoM simulation. Also note that Surface MoM simulation of composite structures containing conjoined metal and '''Electric Conductivity''' (s).* You dielectric parts may also choose from a list take long computation times due to the slow convergence of preloaded material the iterative linear solver for such typesof numerical problems. Click the button labeled '''Material''' to open Since [[EM.CubeLibera]]'s Materials dialog. Select the desired material from the list or type the first letter uses a surface integral equation formulation of a material to find dielectric objects, itcan only handle homogeneous dielectric regions. For examplestructures that involve multiple interconnected dielectric and metal regions such as planar circuits, typing '''V''' selects '''Vacuum''' in the list. Once it is highly recommended that you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automaticallyuse either [[EM.* Click the '''OK''' button of the dielectric material dialog to accept the changes and close itTempo]] or [[EM.Picasso]] instead.

<td> [[Image:wire_pic2Hemi current.png|thumb|350px500px|EM.Libera's PEC dialogThe computed surface current distribution on a metallic dome structure excited by a plane wave source.]] </td><td> [[Image:wire_pic3.png|thumb|350px|EM.Libera's Dielectric dialog.]] </td>

=== Moving Objects Between Groups &amp; Modules =EM.Libera Features at a Glance ==

By default, the last object group that was defined n the navigation tree is active. The current active group is always listed in bold letters in the navigation tree. All the new objects are inserted under the current active group. A group can be activated by right-clicking on its entry in the navigation tree and then selecting the '''Active''' item of the contextual menu. You can move one or more selected objects to any desired PEC group. Right click on the highlighted selection and select '''Move To [[File:larrow_tn.png]] MoM3D [[File:larrow_tn.png]]''' from the contextual menu. This opens another sub-menu with a list of all the available PEC groups already defined in the [[PO Module]]. Select the desired PEC group, and all the selected objects will move to that group. The objects can be selected either in the project workspace, or their names can be selected from the Navigation Tree. In the latter case, make sure that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a PEC group's name from the contextual menu. In a similar way, you can move one or more objects from a === Physical Optics PEC group to [[EM.Cube|EM.CUBE]]'s other modules. In this case, the sub-[[menus]] of the''' Move To [[File:larrow_tn.png]]''' item of the contextual menu will indicate all the [[EM.Cube|EM.CUBE]] modules that have valid groups for transfer of the select objects.Structure Definition ===

# Setting the <ul> <li> Polygonized mesh properties.of curves and wireframe mesh of surfaces and solids for Wire MoM simulation</li># Generating the <li> User defined wire radius</li> <li> Connection of wires/lines to wireframe surfaces and solids using polymesh objects</li> <li> Surface triangular mesh.of surfaces and solids for Surface MoM simulation</li># Verifying the <li> Local mesh.editing of polymesh objects</li></ul>

The commercial release of [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides a === 3D Wire MoM solver. In this simulation engine, all the metallic objects are discretized as a wire-frame structure. Wires, line and curves are discretized as polylines made up of small linear cells (segments).Surface and [[Solid Objects|solid objects]] are discretized as a wire-frame mesh with triangular cells. The MoM3D mesh generator meshes the wires based on a specified mesh sampling rate expressed in cells/&lambda₀. Curves are first polygonized and converted into '''Polyline''' Objects, whose edge lengths follow the specified mesh sampling rate. In the case of [[Solid Objects|solid objects]], only their surface and faces are discretized using a triangular wireframe mesh, which is regarded as a grid of interconnected wires. Two algorithms are offered for generation of a triangular wireframe mesh. The default algorithm is '''Regular Wireframe'''. This mesh generator creates wireframe elements that have almost equal edge lengths. The other algorithm is '''Structured Wireframe''', which usually creates a very structured wireframe with a large number of aligned wireframe elements.amp; Surface MoM Simulations ===

To view the [[MoM3D Module]]'s <ul> <li> 3D Pocklington integral equation formulation of wire-frame meshstructures</li> <li> 3D electric field integral equation (EFIE), click on the [[File:mesh_tool_tn.png]] button magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of the '''Compute Toolbar''' or select '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Shoe Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the wire-frame mesh is displayed in the Project Workspace, [[EM.Cube|EM.CUBE]]'s mesh view mode is enabled. In this mode, you can perform view operations like rotate view, pan, zoom, etc. However, you cannot select or move or edit PEC structures</li> <li> PMCHWT formulation of homogeneous dielectric objects. While the mesh view is enabled, the '''Show Mesh''' [[File:mesh_tool.png]] button remains depressed. To get back to the Normal View mode, click this button one more time, or deselect '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Show Mesh''' to remove its check mark or simply click the '''Esc Key''' </li> <li> AIM acceleration of the keyboard.&quot;Show Mesh&quot; generates a new mesh Surface MoM solver</li> <li> Uniform and displays it if there is none in the memory, fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or it simply displays an existing mesh in the memory. This is a useful feature because generating a wiresource parameters</li> <li> Multi-frame mesh may take a long time depending on the complexity variable and size multi-goal optimization of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory scene</li> <li> Fully parallelized Surface MoM solver using MPI</li> <li> Both Windows and force [[EM.Cube|EM.CUBE]] to generate a mesh from the ground up by selecting '''Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Discretization [[File:larrow_tn.png]] Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item Linux versions of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.Wire MoM simulation engine available</li></ul>

The regular wireframe mesh <ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude &amp; phase)</li> <li> Huygens surface data generation for use in MoM3D or other [[EM.Cube]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of a PEC spherean arbitrary array configuraition of the wire structure</li> <li> Bi-static and mono-static radar cross section: 3D visualization and 2D graphs</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

=== Customizing Building the Mesh =Physical Structure in EM.Libera ==

All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of the navigation tree. In [[File:wire_pic4EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s mesh settings dialog]][[File, you can create three different types of objects:PO5.png|thumb|300px|The Tessellation Options dialog.]]

To set the wire{| class="wikitable"|-frame mesh properties, click on the ! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[File:mesh_tool_tnpec_group_icon.png]] button | style="width:150px;" | [[Glossary of the '''Compute Toolbar''' or select EM.Cube'''Menu s Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects| None|-| style="width:30px;" | [[File:larrow_tnthin_group_icon.png]] Compute | style="width:150px;" | [[File:larrow_tnGlossary of EM.pngCube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]] Discretization | style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[File:larrow_tndiel_group_icon.png]] Mesh Settings...'''or right click on the '''3-D Mesh''' item in the '''Discretization''' section or the Navigation Tree and select '''Mesh Settings...''' from the contextual menu. The MoM3D Mesh Settings Dialog opens up. You can change the mesh generation algorithm from the drop-down list labeled '''Mesh Type''' and select one of the two options| style="width: '''Regular Wireframe''' or '''Structured Wireframe'''150px;" | [[Glossary of EM. You can also set the '''Mesh Sampling Rate''Cube's Materials, whose default value is 20 Cells/&lambda;₀.By defaultSources, [[Surface ObjectsDevices & Other Physical Object Types#Dielectric Material |surface objectsDielectric Material]] or solids are wire| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-framed at the mesh cell size| style="width:30px;" | [[File:Virt_group_icon. Therefore, each wire segment of the wire-frame mesh contains one cell. Another parameter that can affect the shape of the mesh especially in the case of png]]| style="width:150px;" | [[Solid ObjectsGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group |solid objectsVirtual Object]] is the '''Curvature Angle Tolerance'''. This parameter expressed in degrees determines the apex angle | style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of the triangular cells of the structured mesh. Lower values of the angle tolerance will results in more pointed triangular cells.objects| None |}

Click on each category to learn more details about it in the [[File:wire_pic6_tnGlossary of EM.png|800pxCube's Materials, Sources, Devices & Other Physical Object Types]].

Four-port view Both of the structured wireframe mesh [[EM.Libera]]'s two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and volumetric metal objects under '''PEC Objects'''. In other words, you can draw lines, polylines and other curve objects as thin wires, which have a radius parameters expressed in project units. All types of solid and surface CAD objects can be drawn in a PEC spheregroup. Only solid CAD objects can be drawn under '''Dielectric Objects'''.

=== <table><tr><td>[[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] Mesh of Connected Objects === </td></tr></table>

All Once a new object group node has been created on the [[Solid Objects|solid objects]] belonging to navigation tree, it becomes the same PEC "Active" group are merged together using of the Boolean union operation before meshing. If your structure contains attachedproject workspace, interconnected which is always listed in bold letters. When you draw a new CAD object such as a Box or overlapping [[Solid Objects|solid objects]]a Sphere, their internal common faces are removed and it is inserted under the currently active group. There is only one object group that is active at any time. Any object type can be made active by right clicking on its name in the surface navigation tree and selecting the '''Activate''' item of the external faces contextual menu. It is meshed. Similarlyrecommended that you first create object groups, all the [[Surface Objects|surface and then draw new CAD objects]] belonging to under the same PEC active object group are merged together before meshing. However, following if you start a new [[EM.Cube|EM.CUBELibera]]'s union rulesproject from scratch, a solid and start drawing a surface new object cannot not be &quot;unioned&quot; together. Thereforewithout having previously defined any object groups, their meshes will not connect even if the two objects belong to the same a new default PEC object groupis created and added to the navigation tree to hold your new CAD object.

You can connect a line object to a touching surface. To connect lines to surfaces and allow for current continuity, you must make sure that the box labeled '''Connect Lines to Touching Surfaces''' is checked in the '''Mesh Settings Dialog'''. If the end of a line lies on a flat surface, [[EMImage:Info_icon.Cubepng|EM.CUBE30px]] will detect that and create the connection automatically. However, this may not always be the case if the surface is not flat and has curvature. In such cases, you have Click here to specifically instruct learn more about '''[[EM.CubeBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules |EM.CUBEMoving Objects among Different Groups]] to enforce the connection. An example of this case is shown in the figure below'''.

{{Note|In [[File:wire_pic7_tnEM.png|260pxCube]] , you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[File:wire_pic8_tnBuilding_Geometrical_Constructions_in_CubeCAD | CubeCAD]].pngFrom [[Building_Geometrical_Constructions_in_CubeCAD |260pxCubeCAD]] , you can then move the imported objects to [[File:wire_pic9_tnEM.png|260pxLibera]].}}

The line object at the top of a PEC sphere and the structure== EM.Libera's mesh without and with proximity mesh connection enforced.Excitation Sources ==

{| 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, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |EMStrip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source | style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:gap_src_icon.CUBEpng]] applies the global mesh sampling rate to discretize all the objects in the Project Workspace| [[Glossary of EM. HoweverCube's Materials, you can lock the mesh sampling rate of any Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source| style="width:300px;" | Associated with an PEC group to a desired value different than the global rate. To do soor thin wire line or polyline, open the property dialog works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of a PEC group by right clicking on its name in the Navigation Tree and select EM.Cube'''Properties.s Materials, 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.Cube''' from the contextual menus Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon. At the bottom png]]| [[Glossary of the dialog, check the box labeled '''Lock Mesh'''EM. This will enable the '''Sampling Rate''Cube' boxs Materials, where you can set a desired valueSources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM. The default value is equal to the global mesh sampling rate. Keep in mind that objects that belong to different PEC groups are not merged during the mesh generation even if they overlap or are intended to be connected to one another.<br /> Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

Click on each category to learn more details about it in the [[File:wire_pic10Glossary of EM.pngCube's Materials, Sources, Devices & Other Physical Object Types]].

Locking For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on the mesh sampling rate path of the current and is used to define an ideal voltage source. Wire gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''PEC groupRectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source.

A short dipole provides another simple way of exciting a 3D structure in [[EM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are &theta; =180° and &phi; == Gaps Sources On Wires === 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current. In [[EMImage:Info_icon.Cubepng|40px]]'s [[MoM3D Module]], a gap is used Click here to define an excitation source in the form of an ideal voltage source. Gap sources can be placed only on learn more about '''Line''' and '''Polyline''' objects. '''If you want to excite a curved wire antennas such as a circular loop or helix with a gap source, first you have to convert the curve object into a polyline using [[EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'s Polygonize Tool.''' The gap splits the wire into two segment with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. To define a new gap source, follow these steps:

* Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.<table>* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object<tr><td> [[Image:wire_pic14_tn. png|thumb|left|640px|A wire gap symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.* In the case one side of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, representing a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automaticallypolygonized circular loop.]] </td>* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.</tr><tr></table>

<table><tr><td> [[FileImage:wire_pic14_tnpo_phys16_tn.png|thumb|left|420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]]</td></tr>A gap source placed on one side of a polyline representing a polygonized circular loop.</table>

[[File:wire_pic15.png|thumb|300px|[[MoM3D Module]]'s lumped element dialog]] In [[EM.Cube]]'s [[MoM3D ModuleLibera]], you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. Unlike the [[FDTD Module]]'s single-device lumped loads that connect between two adjacent nodes, the [[MoM3D ModuleEM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below: [[File:image106.png]] [[File:wire_pic16_tn.png|thumb|200px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wire]]

To define a new lumped element, follow these steps[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

* Right click on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the two options[[Image: '''Passive RLC''' or '''Active with Gap Source'''Info_icon. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction png|40px]] Click here for the source.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance general discussion of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side26_Nonlinear_Passive_. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* 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 (nanohenry), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad). The impedance of the circuit is calculated at the operating frequency of the project. Only the elements that have been checked are taken into account. By default, only the series resistor has a value of 50&Sigma; and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the '''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees.* If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical direction, offset, resistance, inductance and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression26_Active_Devices | Linear Passive Devices]]''' in degrees along all three principal axes.

Ports are used to order and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the Navigation Tree. 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 up, showing the total number of existing sources in the workspacenavigation tree. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. This includes both gap sources and active lumped elements (which contain gap sources). In the '''Port Association''' section of this dialog, you can go over each one of the sources and associate them with a desired port. Note that you can associate more than one source with same given port. In this case, you will have a coupled port. All the coupled sources are listed as associated with a single port. However, you cannot associate the same source with more than one port. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50&SigmaOmega;. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedancesby default.

{{Note|In [[EMImage:Info_icon.Cubepng|40px]] you cannot assign ports Click here to an array object, even if it contains sources on its elements. To calculate learn more about the S '''[[parametersGlossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]] of an antenna array, you have to construct it using individual elements, not as an array object'''.}}

<table><tr><td> [[FileImage:port-definitionMOM7A.png|thumb|360px|Two metallic strips hosting a gap source and a lumped element.]] </td><td> [[Image:MOM7B.png|thumb|360px|The surface mesh of the two strips with a gap source and a lumped element.]]</td></tr></table>

The [[MoM3D Module]]== EM.Libera's port definition dialog.Simulation Data & Observables ==

At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: {| class="wikitable"|-! scope="col"| Icon! scope= Sources "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 &ampGraph Types#Current Distribution |Current Distribution]]| style="width:300px; Loads On Arrays Of Wire Radiators " | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires| 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: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|}

If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A gap source will be placed Click on each element of the array. All the gap sources will have identical direction and offset. However, you can prescribe certain amplitude and/or phase distributions. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need category to set a value for maximum side lobe level ('''SLL''') learn more details about it in dBthe [[Glossary of EM. You can also define Cube'''Phase Progression''' in degrees along all three principal axess Simulation Observables & Graph Types]].

Depending on the types of objects present in your project workspace, [[File:wire_pic12EM.pngLibera]] performs either a Surface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted. [[File:wire_pic13_tn.png]]

The <table><tr><td> [[MoM3D ModuleImage:wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a PEC plate.]]'s gap source dialog and gaps sources defined on an array of dipole wires with binomial weight </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution and 90° phase progressionplot of the monopole antenna connected above the PEC plate.]] </td></tr></table>

<table><tr><td> [[FileImage:wire_pic17wire_pic32_tn.png|thumb|300px360px|The short dipole source dialogElectric field plot of the circular loop antenna.]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]]</td></tr></table>

A short dipole provides You need to define a simple way far field observable if you want to plot radiation patterns of exciting a your physical structure in the [[MoM3D ModuleEM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. To define After a short dipole source3D MoM simulation is finished, follow these steps:three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.

* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source[[Image:Info_icon...''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialog, you can set the coordinate of the center of the short dipole. By default, the source is placed at the origin of the world coordinate system at (0,0,0).You can type in new coordinates or use the spin buttons png|30px]] Click here to move learn more about the dipole around.* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' theory of the dipole in project units.* In the '''Direction Unit Vector[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitude.

When you simulate a wire structure in the <table><tr><td> [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your project. This is used not only to visualize the current distribution in the project workspace but also to save the current solution into an ASCII data file. This data file is called &quot;MoM.IDI&quot; by default and has a '''.IDI''' file extensionImage:wire_pic38_tn. png|thumb|230px|The current data are saved as line segments representing each 3D radiation pattern of the wire cells together with the complex current at the center of each cellcircular loop antenna: Theta component. In the ]] </td><td> [[MoM3D Module]], you can import the current data from an existing '''Image:wire_pic39_tn.IDI''' file to serve as a set png|thumb|230px|The 3D radiation pattern of short dipoles for excitation. To import a wire current solution, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Sourcecircular loop antenna: Phi component...''' from the contextual menu. This opens up the standard [[Windows]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find it, select it and click the '''Open''' button of the dialog. This will create as many short dipole sources on the </td><td> [[PO Module]]'s Navigation Tree as the Image:wire_pic40_tn.png|thumb|230px|The total number radiation pattern of mesh cells in the Wire MoM solutioncircular loop antenna. From this point on, each of the imported dipoles behave like a regular short dipole source. You can open the property dialog of each individual source and modify its [[parameters]].</td></tr></table>

[[File:po_phys15To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the navigation tree.png|thumb|300px|plane wave dialog]]

{{Note| The wire-frame structure in 3D RCS plot is always displayed at the [[MoM3D Module]] can be excited by an incident plane wave. In particularorigin of the spherical coordinate system, a plane wave source can be used (0,0,0), with respect to compute which the radar cross section of a metallic target. A plane wave far radiation zone is defined by its propagation vector indicating . Oftentimes, this might not be the direction scattering center of incidence and its polarizationyour physical structure. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:}}

<table><tr><td> [[Image:wire_pic51_tn.png|thumb|230px|The direction RCS of incidence is defined through the a metal plate structure: &thetasigma; and _{&phitheta; angles of the unit propagation vector in the spherical coordinate system}. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi''']] </td><td> [[Image:wire_pic52_tn. png|thumb|230px|The default values are RCS of a metal plate structure: &thetasigma; = 180° and _{&phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM}z.]] </subtd> and TE<subtd>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively[[Image:wire_pic53_tn. png|thumb|230px|The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case total RCS of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfieda metal plate structure: '''ê . ê''' = 1 and '''ê × k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (&thetasigma; = 180°)_tot.]] </td></tr></table>

* Right click === A Note on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source..EM.Libera''' The Plane wave Dialog opens up.* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selected, you also need to enter the X, Y, Z components of the '''E-Field Vector'''.s Mesh Types ===

{{Note|In the spherical coordinate system[[EM.Libera]] features two simulation engines, normal plane wave incidence from Wire MoM and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the top of the domain downward corresponds connection points between two or more wires, junction basis functions are generated to &theta; of 180&deg;ensure current continuity. }}

On the other hands, [[File:po_phys16_tnEM.pngLibera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.

Figure[[Image: Illuminating a metallic sphere Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with an obliquely incident plane wave sourceMesh Generator]]'''.

Once you have set up your metal structure in You can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Cube|EM.CUBELibera]]'s [[MoM3D Module]], have defined sources and observables and have examined the quality of the Wire MoM simulator. When you structure's wire-frame meshcontains at least one PEC line, you are ready to run a simulation. To open the Run Simulation Dialogpolyline or any curve CAD object, click the '''Run''' [[File:run_iconEM.pngLibera]] button will automatically invoke its linear wireframe mesh generator. This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the '''Compute Toolbar''' or select Menu [[File:larrow_tnspecified mesh density.png]] Compute It also polygonizes rounded [[File:larrow_tn.pngCurve Objects|curve objects]] Run...or use into polylines with side lengths that are determined by the keyboard shortcut '''Ctrl+R'''specified mesh density. To start the simulation click the '''Run''' button of this dialog. Once the Wire MoM simulation starts, a new dialog called '''Output Window''' opens up Note that reports the various stages of Wire MoM simulation, displays the running time polygonizing operation is temporary and shows the percentage of completion solely for certain tasks during the Wire MoM simulation process. A prompt announces the completion he purpose of the Wire MoM simulationmesh generation. At this timeAs for surface and solid CAD objects, [[EM.Cube|EM.CUBE]] generates a wireframe mesh of these objects is created which consists of a large number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections interconnected linear (RCSwire) if the structure is excited by a plane wave sourceelements.

You have the choice to run a '''Fixed Frequency''' simulation, which is the default choice, or run a '''Frequency Sweep''{{Note| The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. In the former case, the simulation will be carried out at the It also discretizes surface and solid CAD objects temporarily using CubeCAD'''Center Frequency''' of the project. This frequency can be changed from the Frequency Dialog of the project or you can click the Frequency Settings button of the Run Dialog to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, toos Polymesh tool.}}

In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type<table><tr><td> [[Image: Adaptive''' or '''Uniform'''Mesh6. In png|thumb|200px|The geometry of an expanding helix with a uniform sweep, equally spaced samples circular ground.]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the frequency are used between helix with the Start and End frequencies. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog. The default '''Number mesh density of Samples''' is 10cells/&lambda;₀.In the case ]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of adaptive sweep, you have to specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts helix with a few initial frequency samples, where the Wire MoM engine is runmesh density of 25 cells/&lambda;₀. Then, the intermediary samples are calculated in a progressive manner]] </td><td> [[Image:Mesh9. At each iteration, png|thumb|200px|Wireframe mesh of the frequency samples are used to calculate helix with a rational approximation mesh density of the S parameter response over the specified frequency range. The process stops when the error criterion is met50 cells/&lambda;₀.]] </td></tr></table>

Figure: The output windowAll the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the surface objects belonging to the same PEC group are merged together and their internal edges are removed before meshing. Note that a solid and a surface object belonging to the same PEC group might not always be merged properly.

A Wire MoM simulation involves a number of numerical <table><tr><td> [[parameters]] that normally take default values unless you change themImage:MOM3. You can access these [[parameters]] and change their values by clicking on the '''Settings''' button next to the &quot;Select Engine&quot; drop-down list in the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialogpng|thumb|300px|EM. In the '''Solver''' section of the dialog, you can choose the type of linear solver. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the [[MoM3D Module]]. The BiCG solver is iterative. Once selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''. The Wire MoM simulator is based on PocklingtonLibera's integral equation method. In this method, the wires are assumed to have a very small radius. The basis functions are placed on the axis of the &quot;wire cylinder&quot;, while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functions. In the &quot;Source Singularity&quot; section of the Mesh Hierarchy dialog, you can specify the '''Wire Radius''' . [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] assumes an identical wire radius for all wires and wireframe structures. This radius is expressed in free space wavelengths and its default value is 0.001&lambda; <sub/td>0</subtr></table>. The value of the wire radius has a direct influence on the wire's computed reactance.

<table><tr><td> [[FileImage:wire_pic21MOM1.png|thumb|360px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM2.png|thumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]]</td></tr></table>

You can run {{Note|In [[EM.Cube|EM.CUBE]]'s MoM3D simulation engine in the sweep mode, whereby a parameter like frequency, plane wave angles of incidence or a user defined variable is varied over a specified range at predetermined samples. The output data polymesh objects are saved into data file for visualization regarded as already-meshed objects and plottingare not re-meshed again during a simulation. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types of sweep:}}

To run a MoM3D sweep, open the [[Image:Info_icon.png|30px]] Click here to learn more about '''Run Simulation Dialog[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool | Converting Object to Polymesh]]''' and select one of the above sweep types from the '''Simulation Mode''' drop-down list in this dialog[[EM. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabledCube]]. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:

# Fix mesh Once an object is converted to a polymesh, you can place your wire at the highest frequencyany of its nodes.# Fix mesh at In that case, [[EM.Libera]]'s Wire MoM engine will sense the center frequency.# Re-mesh at each frequencycoincident nodes between line segments and will create a junction basis function to ensure current continuity.

The <table><tr><td> [[MoM3D Module]] offers two types of frequency sweepImage: adaptive or uniformMOM4. In a uniform sweep, equally spaced frequency samples are generated between the start and end frequencies. In the case png|thumb|360px|Geometry of an adaptive sweep, you must specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is initially run. Then, the intermediary frequency samples are calculated and inserted in a progressive manner. At each iteration, the frequency samples are used monopole wire connected to calculate a rational approximation of the scattering parameter response over the specified frequency rangePEC plate. The process stops when the specified error criterion is met in a mean-square sense]] </td><td> [[Image:MOM5. The adaptive sweep simulation results are always continuous and smooth. This is due to png|thumb|360px|Placing the fact that a rational function curve is fitted through wire on the discrete frequency data points. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. However, you have to make sure that the process converges. Otherwise, you might get an entirely wrong, but still perfectly smooth, curve at the end polymesh version of the simulationPEC plate.]] </td></tr></table>

[[File:wire_pic22== Running 3D MoM Simulations in EM.png]] [[File:wire_pic24.png]]Libera ==

The [[MoM3D Module]]=== EM.Libera's run simulation dialog with frequency sweep selected and the frequency settings dialog.Simulation Modes ===

In a parametric sweep, one or more user defined Once you have set up your structure in [[variablesEM.Libera]] are varied at , have defined sources and observables and have examined the same time over their specified ranges. This creates a parametric space with the total number quality of samples equal to the product of the number of samples for each variable. The user defined [[variables]] are defined using [[EM.Cube|EM.CUBE]]structure's '''[[Variables]] Dialog'''mesh, you are ready to run a 3D MoM simulation. For a description of [[EM.Cube|EM.CUBELibera]] [[variables]], please refer to the [[CubeCAD|CUBECAD]] manual or the &quot;Parametric Sweep&quot; sections of the FDTD or [[Planar Module]] manuals.offers five simulation modes:

{| class="wikitable"|-! scope= Working with 3D MoM "col"| Simulation Data Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|}

At In a single-frequency analysis, the end structure of your project workspace is meshed at the center frequency of the project and analyzed by one of a MoM3D simulation, [[EM.Cube|EM.CUBELibera]]'s Wire two MoM engine generates a number of output data files that contain all the computed simulation datasolvers. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currentsIf your project contains at least one line or curve object, you must first define current sensors before running the Wire MoM simulationsolver is automatically selected. To do thisOtherwise, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added Surface MoM solver will always be used to the Navigation Treesimulate your numerical problem. Unlike the [[Planar Module]]In either case, in the [[MoM3D Module]] you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire MoM simulation engine type is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -&pi; and &pi;set automatically.

Current distribution maps are displayed with some default settings and options. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Run Simulation Dialog, click the ''' by right clicking on the specific plot entry in the Navigation Tree and selecting Run'''Properties[[File:run_icon...''' or by double clicking on the surface png]] button of the plot's legend box. Two ''Simulate Toolbar'scale''or select ' options are available: '''Linear''' and '''dBMenu > Simulate > Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. With the '''Linear''' (By default) option selected, the current value Surface MoM solver is always normalized to the maximum total current in that plane, and the normalized scale is mapped between the minimum and maximum valuesselected as your simulation engine. If To start the '''dB''' option is selectedsimulation, click the normalized current is converted to dB scale. The plot limits (bounds) can be set individually for every current distribution plot. In the '''Limits''' section {{key|Run}} button of the plot's property this dialog, you see four options: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select Once the user defined option and enter 3D MoM simulation starts, a new values for the dialog called '''LowerOutput Window''' and '''Upper''' limits. The last two options are used to remove opens up that reports the outlier data within various stages of MoM simulation, displays the 95% running time and 99% confidence intervals, respectively. In other words, shows the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution percentage of completion for certain tasks during the dataMoM simulation process. Three color maps are offered: '''Default''', '''Rainbow''' and '''Grayscale'''. You can hide A prompt announces the legend box by deselecting the box labeled '''Show Legend Box'''. You can also change the foreground and background colors completion of the legend boxMoM simulation.

<table><tr><td> [[Image:MORELibera L1 Fig13.png|40pxthumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] Click here to learn more about '''</td></tr><tr><td> [[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps Image:MOM3D MAN10.png| Visualizing 3D Current Distribution Maps]]''thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td></tr></table>

Figure: A monopole antenna connected above MoM simulations involve a PEC plate number of numerical parameters that normally take default values unless you change them. You can access these parameters and its current distribution with change their values by clicking on the default plot settings'''Settings''' button next to the &quot;Select Engine&quot; dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.

[[File:wire_pic28First we discuss the Wire MoM Engine Settings dialog.png|360px]] [[File:wire_pic29_tnIn the '''Solver''' section of this dialog, you can choose the type of '''Linear Solver'''. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.png|440px]]

Figure: The output plot settings dialog, and the current distribution of the monopole-plate structure with a user defined upper limit.<table><tr>=== Scattering Parameters and Port Characteristics === <td>  If the project structure is excited by gap sources, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) [[parameters]] of the selected ports, all based on the port impedances specified in the project's &quot;Port Definition&quot;. If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. The S [[parameters]] are written into output ASCII data files. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with &quot;#&quot;. The admittance (Y) and impedance (Z) [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of the structure at the first port is also computed and saved to a real data '''.DAT''' file. You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the itemsImage: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''MOM9B. In the first three cases, another sub-menu gives a list of individual port [[parameters]]. Keep in mind that in multi-port structures, each individual port parameter has its own graph. You can also see a list of all the port characteristics data files in [[EM.Cubepng|thumb|left|480px|EM.CUBE]]Libera's data managerWire MoM Engine Settings dialog. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by clicking and highlighting its '''ID''' 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 change the format of complex data plots. In general complex data can be plotted in three forms:</td># Magnitude and Phase</tr># Real and Imaginary Parts# Smith Chart</table>

The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In particularthe "Integral Equation" section of the dialog, it may be useful to plot you can choose among the S_ii [[parameters]] on a Smith chartthree PEC formulations: EFIE, MFIE and CFIE. To change The EFIE formulation is the format default option. In the case of the CFIE formulation, you can set a data plotvalue for the "Alpha" parameter, go to which determines the row in weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is &alpha; = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Data Manager DialogError Tolerance''' that contains a specific complex data file's name and click on the fourth column under the title '''Graph TypeMax. No. of Solver Iterations'''. The selected table cell turns into a dropdown list that contains When the system size is large, typically above three formats3000, [[EM. Select Libera]] uses an acceleration technique called the desired format and click Adaptive Integral Method (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05&lambda;₀. [[EM.Libera]]'''Plot''' button s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the data manager dialog to plot MPI-parallelized solver can speed up your simulations significantly. In the data in "MPI Settings" of the new formatdialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.

For both Wire MoM and Surface MoM solvers, you can instruct [[Image:MOREEM.png|40pxLibera]] Click here to learn more about write the contents of the MoM matrix and excitation and solutions vectors into data files with '''[[Data_Visualization_and_Processing#Graphing_Port_Characteristics | Graphing Port Characteristics]].DAT1'''file extensions. These files can be accessed from the '''Input/Output Files''' tab of the Data Manager. In both case, you have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your structure is excited by a plane wave source. When checked, the field sensors plot the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualized.

=== Near Field Visualization === <table><tr><td> [[FileImage:wire_pic30MOM9.png|thumb|300px|[[MoM3D Module]]'s field sensor dialog]] [[EM.Cube|EM.CUBE]] allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps: * Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBE]] creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -&pi; and &pi;. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps 640px| Visualizing 3D Near Field Maps]]'''. [[File:wire_pic31_tn.png]] Figure: A circular loop antenna fed by a gap source. [[File:wire_pic32_tn.png|400px]] [[File:wire_pic33_tn.png|400px]] Electric and magnetic field plots of the circular loop antenna. === Visualizing 3D Radiation Patterns === [[File:wire_pic37.png|thumb|300px|[[MoM3D Module]]'s radiation pattern dialog]] Unlike the FDTD method, the method of moments does not need a far field box to perform near-to-far-field transformations. But you still need to define a far field observable if you want to plot radiation patterns in EM.Libera. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output s Surface MoM Engine Settings section allows you to change the '''Angle Increment''' for both Theta and Phi observation angles in the degrees. These [[parameters]] indeed set the resolution of far field calculations. The default values are 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked for further editing. After a 3D MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.  [[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field Computations]]'''.</td></tr>[[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''. [[File:wire_pic38_tn.png|260px]] [[File:wire_pic39_tn.png|260px]] [[File:wire_pic40_tn.png|260px]] 3D radiation pattern of the circular loop antenna: (Left) Theta component, (Center) Phi components, and (Right) total far field. === Modeling Antenna Arrays ===  In view of far field characteristics, [[EM.Cube|EM.CUBE]] can handle antenna arrays in two different ways. The first approach is full-wave and requires building an array of radiating elements using the '''Array Tool''' and feeding individual array elements using some type of excitation. This method is very accurate and takes into account all the inter-element coupling effects. At the end of the Wire MoM simulation of the array structure, you can plot the radiation patterns and other far field characteristics of the antenna array just like any other wire-frame structure. The second approach is based on the &quot;Array Factor&quot; concept and ignores any inter-element coupling effects. In this approach, you can regard the structure in the project workspace as a single radiating element. A specified array factor can be calculated and multiplied by the element pattern to estimate the radiation pattern of the overall radiating array. To define an array factor, open the '''Radiation Pattern Dialog''' of the project. In the section titled '''Impose Array Factor''', you will see a default value of 1 for the '''Number of Elements''' along the three X, Y and Z directions. This implies a single radiator, which is your structure in the project workspace. There are also default zero values for the '''Element Spacing''' along the X, Y and Z directions. You should change both the number of elements and element spacing in the X, Y or Z directions to define any desired finite array lattice. For example, you can define a linear array by setting the number of elements to 1 in two directions and entering a larger value for the number of elements along the third direction. The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some [[parameters]] of interest in such structures include the '''Half Power Beam Width (HPBW)''', '''Maximum Side Lobe Level (SLL)''' and '''First Null [[Parameters]]''' such as first null level and first null beam width. You can have [[EM.Cube|EM.CUBE]] calculate all such [[parameters]] if you check the relevant boxes in the &quot;Additional Radiation Characteristics&quot; section of the '''Radiation Pattern Dialog'''. These quantities are saved into ASCII data files of similar names with '''.DAT''' file extensions. In particular, you can plot such data files at the end of a sweep simulation.</table>

[[FileImage:wire_pic47Top_icon.png|30px]]'''[[EM.Libera#Product_Overview | Back to the Top of the Page]]'''

Defining a finite-sized 4-element array factor in the radiation pattern dialog. [[FileImage:wire_pic48_tnTutorial_icon.png|400px]] [[File:wire_pic46_tn.png|400px]] Radiation pattern of a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array object. === Computing Radar Cross Section ===  [[File:wire_pic49.png|thumb|300px|[[MoM3D Module30px]]'s RCS dialog]]  When your structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) of a target. Three RCS quantities are computed: the &phi; and &theta; components of the radar cross section as well as the total radar cross section: &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, EM.Libera calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀ and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀ and the RCS is measured and plotted at the echo angles 180°-&theta;₀ and &phi;₀.It is clear that in the case of mono-static RCS, the Wire MoM simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta;₀ and &phi;₀ are varied over the intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recordedEM. To calculate RCS, first you have to define an RCS observable instead of a radiation patternCube#EM. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the &theta; and &phi; angles are incremented by 5 degrees. At the end of a Wire MoM simulation, besides calculating the RCS data over the entire (spherical) 3-D space, a number of 2-D RCS graphs are also generated. These are RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant &phi;-cut. This latter cut is at &phi;=45° by default. You can assign another phi angle in degrees in the box labeled '''Non-Principal Phi Plane'''. At the end of a Wire MoM simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_totare added under the far field section of the navigation tree. The 2D RCS graphs can be plotted from the data manager exactly in the same way that you plot 2D radiation pattern graphs. A total of eight 2D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, Libera_Documentation | EM.Libera calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, the RCS needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth &amp; Elevation''' in the &quot;Output Settings&quot; section of the '''Radar Cross Section Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith. {{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}} [[Image:MORE.png|40pxTutorial Gateway]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]'''. <table><tr><td> [[Image:wire_pic51_tn.png|thumb|300px|The RCS of a metal plate structure: &sigma;_&theta;.]] </td><td> [[Image:wire_pic52_tn.png|thumb|300px|The RCS of a metal plate structure: &sigma;_&phi;.]] </td><td> [[Image:wire_pic53_tn.png|thumb|300px|The total RCS of a metal plate structure: &sigma;_tot.]] </td></tr></table>

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