== An EM.Libera Primer == === EM.Libera in a Nutshell === EM.Libera is a 3D free-space structure simulator for modeling metallic and dielectric structures. It features two full-wave Method of Moments (MoM) simulation engines, one based on a Wire MoM formulation and the other based on a Surface MoM formulation. In general, a surface MoM solver is used to simulate your physical structure, which may involve metallic and dielectric objects of arbitrary shapes as well as composite structures that contain joined metal and dielectric regions. If your project workspace contains at least one line or curve object, EM.Libera then invokes its Wire MoM solver. In that case, only metallic structure can be modeled, and all the surface and solid PEC objects are meshed as wireframes.  {{Note|You can use EM.Libera either for modeling metallic wire objects and wireframe structures or for modeling metallic, dielectric ad composite structures that do not contain lines or curves.}}  === A Overview of 3D 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 Maxwellâs equations as opposed to their differential forms used in the finite element or finite difference time domain methods. 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 Equations|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 wire-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 of the dielectric regions of the physical structure , the so-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 problems. [[Image:MORESplash-mom.pngjpg|40pxright|720px]] Click here to learn more about the theory of '''[[3D Method of Moments]]'''. <strong><font color="#06569f" size= Constructing the Physical Structure & "4">3D Mesh Generation == === Defining Groups Of PEC Objects ===  [[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] EM.Libera features two different simulation engines: Wire MoM and And Surface MoM. Both simulation engines can handle metallic structures. The Wire MoM engine models 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. All the PEC objects are created under the '''PEC''' 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...''' from the contextual menu. A dialog for setting up the PEC properties opens up. From this dialog you can change the name of the group or its color. Note that PEC object do not have any material properties that can be edited. === Defining Dielectric Objects ===  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<sub>rSolvers For Simulating Free-Space Structures</subfont> and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when σ → ∞. To define a new Dielectric group, follow these steps: * Right click on the '''Dielectric''' item of the Navigation Tree and select '''Insert New Dielectric...''' from the contextual menu.* Specify a '''Label''', '''Color''' (and optional Texture) and the electromagnetic properties of the dielectric material to be created: '''Relative Permittivity''' (e<sub>r</substrong>) and '''Electric Conductivity''' (s).* You may also choose from a list of preloaded material types. Click the button labeled '''Material''' to open [[EM.Cube]]'s Materials dialog. Select the desired material from the list or type the first letter of a material to find it. For example, typing '''V''' selects '''Vacuum''' in the list. Once you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automatically.* Click the '''OK''' button of the dielectric material dialog to accept the changes and close it. {{Note|Under dielectric material groups, you cannot draw [[Surface Objects|[[Surface Objects|surface objects]]]] or [[Curve Objects|curve objects]].}}Â
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<td> [[Imageimage:wire_pic2Cube-icon.png|thumblink=Getting_Started_with_EM.Cube]] [[image:cad-ico.png |350pxlink=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png |link=EM.Libera's PEC dialogTempo]] [[image:prop-ico.png | link=EM.Terrano]] </td><td> [[Imageimage:wire_pic3static-ico.png|thumb|350pxlink=EM.Ferma]] [[image:planar-ico.png |link=EM.Libera's Dielectric dialogPicasso]] [[image:po-ico.png | link=EM.Illumina]] </td></tr>
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[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''
[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''=== Moving Objects Between Groups & Modules =Product Overview==
By default, the last object group that was defined n the navigation tree is active=== EM. The current active group is always listed Libera 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.Nutshell ===
== [[EM.Libera]] is a full-wave 3D Mesh Generation ==electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structures made up of metal and dielectric regions or a combination of them. It features two separate simulation engines, a Surface MoM solver and a Wire MoM solver, that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric objects in your physical structure. The Wire MoM solver can only handle metallic wireframe structures. [[EM.Libera]] selects the simulation engine automatically based on the types of objects present in your project workspace.
=== A Note on [[EM.Libera]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's Mesh Types ===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 PEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.
EM.Libera features two simulation engines, 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 connection points between two or more wires, junction basis functions are generated to ensure current continuity.  On the other hands{{Note|In general, [[EM.Libera's Surface MoM solver requires a triangular surface mesh of surface and [[Solid Objects|solid objects]].The mesh generating algorithm tries to generate regularized triangular cells with almost equal uses the 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 MoM solver 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. === Creating & Viewing the Mesh ===  The mesh generation process in EM.Libera involves three steps: # Setting the mesh properties.# Generating the mesh.# Verifying the mesh. The objects of analyze your physical structure are meshed based on a specified mesh density expressed in cells/λ<sub>0</sub>. The default mesh density is 10 cells/λ<sub>0</sub>. To view the PO mesh, click on the [[File:mesh_tool_tn.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the PO mesh is displayed in the If your project workspace, [[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 objects. While the mesh view is enabled, the '''Show Mesh''' [[File:mesh_tool.png]] button remains depressed. To get back to the normal view or select mode, click this button contains at least one more time, line or deselect '''Menu > Simulate > Discretization > Show Mesh''' to remove its check mark or simply click the '''Esc Key''' of the keyboard. "Show Mesh" generates a new mesh and displays it if there is none in the memorycurve object, or it simply displays an existing mesh in the memory. This is a useful feature because generating a PO mesh may take a long time depending on the complexity and size 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 and force [[EM.CubeLibera]] switches to generate a mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menuWire MoM solver. To set the PO mesh properties, click on the [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Mesh Settings... '''or right click on the '''3-D Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the value of '''Mesh Density''' to generate a triangular mesh with a higher or lower resolutions. Some additional mesh [[parameters]] can be access by clicking the {{key|Tessellation Options}} button of the dialog. In the Tessellation Options dialog, you can change '''Curvature Angle Tolerance''' expressed in degrees, which as a default value of 15°. This parameter can affect the shape of the mesh especially in the case of [[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|solid objects]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]. It determines the apex angle of the triangular cells of the primary tessellation mesh which is generated initially before cell regularization. Lower values of the angle tolerance result in a less smooth and more pointed mesh of curved surface like a sphere.
<table><tr><td> [[Image:PO2Info_icon.png|thumb|450px|Two ellipsoids of different (PEC and dielectric) compositions.30px]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoids.]] </td></tr></table>Â === Mesh of Connected Objects === Â [[Image:MOM3.png|thumb|350px|EM.Libera's Mesh Hierarchy dialog.]] All the objects belonging Click here to learn more about 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|solid objects]], their internal common faces are removed and only the surface theory of the external faces is meshed. Similarly, all the '''[[Surface Objects|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. Â When two objects belonging to two different material groups overlap or intersect each other, EM.Libera has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top Basic Principles of a PEC plate. The two object share a circular area at the base Method of the cylinder. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, EM.Libera does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu > Simulate < discretization < Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the top of the table. You can select an group from the table and change its hierarch using the {{key|Move Up}} or {{keyMoments |Move Down}} buttons 3D Method of the dialog. You can also change the color of junction cells that belong to each group. Â 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 Moments]]'''Connect Lines to Touching Surfaces''' is checked in the '''Mesh Settings Dialog'''. If the end of a line lies on a flat surface, [[EM.Cube|EM.CUBE]] 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 to specifically instruct [[EM.Cube|EM.CUBE]] to enforce the connection. An example of this case is shown in the figure below.
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<td> [[Image:MOM1.png|thumb|450px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM2Yagi Pattern.png|thumb|450px500px|The surface mesh 3D far-field radiation pattern of the dielectric cylinder and PEC plateexpanded Yagi-Uda antenna array with 13 directors.]] </td>
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=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces EM.Libera as the MoM3D Module of EM.Cube === Â You can use [[EM.Libera]] either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. [[EM.Libera]] also serves as the frequency-domain, full-wave '''MoM3D Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Libera]] shares the 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 [[EM.Cube]]'s other computational modules.
If the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure. From the point of view of this mesh generator, all PEC [[Surface ObjectsImage:Info_icon.png|surface objects30px]] and PEC Click here to learn more about '''[[Solid ObjectsGetting_Started_with_EM.Cube |solid objects]] are treated as wireframe objects. If you want to model a wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of the surface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.CubeModeling Environment]]'s polymesh objects to accomplish this objective''.
{{Note|In [[=== Advantages & Limitations of EM.Cube]], polymesh objects are regards as already-meshed objects and are not re-meshed again during a simulation.}} Libera's Surface MoM & Wire MoM Solvers ===
You can convert any surface object or solid object to The method of moments uses an open-boundary formulation of Maxwell's equations which does not require a discretization of the entire computational domain, but only the finite-sized objects within it. As a polymesh using result, [[CubeCADEM.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]]'Polymesh Tool'''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.
[[Image:MOREEM.png|40pxLibera]] Click here to learn more about '''s Wire MoM solver can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the current limitations of [[Discretizing_Objects#Converting_Objects_to_Polymesh | Converting Object to PolymeshEM.Libera]]''' , 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 solid CAD objects of the project workspace are reduced to wireframe models in order to perform a Wire MoM simulation. Also note that Surface MoM simulation of composite structures containing conjoined metal and dielectric parts may take long computation times due to the slow convergence of the iterative linear solver for such types of numerical problems. Since [[EM.Libera]] uses a surface integral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. For structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you use either [[EM.Tempo]] or [[EM.CubePicasso]]instead.
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<td> [[Image:MOM4Hemi current.png|thumb|450px500px|Geometry of The computed surface current distribution on a monopole wire connected to metallic dome structure excited by a PEC plateplane wave source.]] </td><td> [[Image:MOM5.png|thumb|450px|Placing the wire on the polymesh version of the PEC plate.]] </td>
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== Excitation Sources EM.Libera Features at a Glance ==
=== Gaps Sources on PEC Wires and Strips Physical Structure Definition ===
A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current. In EM.Libera, a gap is used to define an excitation source <ul> <li> Metal wires and curves in the form of an ideal voltage source. Gap sources can be placed on PEC '''Line''' free space</li> <li> Metal surfaces and '''Polyline''' solids in free space</li> <li> Homogeneous dielectric solid 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. in free space</li> <li> Import STL CAD files as native polymesh structures</li> <li> Export wireframe structures as STL CAD files</li></ul>
{{Note|If you want to excite a curved wire antennas such as a circular loop or helix with a gap source=== Sources, first you have to convert the curve object into a polyline using [[CubeCAD]]'s Polygonize Tool.}} Loads & Ports ===
<ul> <li> Gap sources can also be placed on wires (for Wire MoM) and gap sources on long, narrow, PEC '''Rectangle Strip''' objects to provide excitation metal strips (for the Surface MoM solver. The )</li> <li> Gap arrays with amplitude distribution and phase progression</li> <li> Multi-port port definition for gap splits the strip into two sources</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh solution as collection of short dipoles</li> <li> RLC lumped elements on wires and narrow strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connectedseries-parallel combinations</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source. Terrano]] or external files)</li> <li>To define a new gap source, follow these steps: Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>
* 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.* 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 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 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, 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 '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.=== Mesh Generation ===
[[File:wire_pic14_tn.png]]<ul> <li> Polygonized mesh of curves and wireframe mesh of surfaces and solids for Wire MoM simulation</li> <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> <li> Local mesh editing of polymesh objects</li></ul>
A gap source placed on one side of a polyline representing a polygonized circular loop.=== 3D Wire MoM & Surface MoM Simulations ===
[[Image:MORE.png|40px]] Click here to learn more about '''[[Using Sources & Loads in Antenna Arrays]]'''.<ul> <li> 3D Pocklington integral equation formulation of wire structures</li> <li> 3D electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of PEC structures</li> <li> PMCHWT formulation of homogeneous dielectric objects</li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Multi-variable and multi-goal optimization of scene</li> <li> Fully parallelized Surface MoM solver using MPI</li> <li> Both Windows and Linux versions of Wire MoM simulation engine available</li></ul>
=== Modeling Lumped Circuits Data Generation & Visualization ===
<ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude & phase)</li> <li> Huygens surface data generation for use in MoM3D or other [[File:wire_pic15EM.png|thumb|300px|[[MoM3D Module]]'s lumped element dialogCube]]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 an 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>
In [[== Building the Physical Structure in EM.Cube]]'s [[MoM3D Module]], 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 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 Module]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below: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:image106EM.pngLibera]], you can create three different types of objects:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[File:wire_pic16_tnpec_group_icon.png]]|thumbstyle="width:150px;" |200px[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Active lumped element with a voltage gap in series with an RC circuit placed on a dipole Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects| None|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wireradiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects| None |}
To define a new lumped elementClick on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, follow these steps:Sources, Devices & Other Physical Object Types]].
* Right click on the '''Lumped Elements''' item in the '''Sources''' section Both of the Navigation Tree and select '''Insert New Source..[[EM.Libera]]''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the s two options: '''Passive RLC''' or '''Active with Gap Source'''simulation engines, Wire MoM and Surface MoM, can handle metallic structures. Choosing the latter option enables the You define wires under '''Source PropertiesThin Wire''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line groups and polyline surface and volumetric metal 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 under '''DirectionPEC Objects''' 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.* In the case of a gap on a line objectother words, 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, 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 nextdraw lines, polylines and its side index and offset value are adjusted automatically.* In the '''Load Properties''' sectionother curve objects as thin wires, the series and shunt resistance values Rs and Rp are specified which have a radius parameters expressed 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 projectunits. Only the elements that have been checked are taken into account. By default, only the series resistor has a value All types of 50Σ solid 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 surface CAD objects can specify the '''Source Amplitude''' be drawn in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degreesa PEC group.* If the workspace contains an array of line or polyline Only solid CAD objects, the array object will can 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 drawn under '''UniformDielectric Objects''', '''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 Progression''' in degrees along all three principal axes.
=== <table><tr><td>[[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] Defining Ports === </td></tr></table>
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 Once a new object group node has been created on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens upnavigation tree, showing it becomes the total number "Active" group of existing sources in the project workspace, which is always listed in bold letters. By defaultWhen you draw a new CAD object such as a Box or a Sphere, as many ports as it is inserted under the total number of sources are createdcurrently active group. You can define There is only one object group that is active at any number of ports equal to or less than time. Any object type can be made active by right clicking on its name in the total number of sources. This includes both gap sources navigation tree and active lumped elements (which contain gap sources). In selecting the '''Port AssociationActivate''' section of this dialog, you can go over each one item of the sources and associate them with a desired portcontextual menu. Note It is recommended that you can associate more than one source with same given port. In this casefirst create object groups, you will have a coupled port. All and then draw new CAD objects under the coupled sources are listed as associated with a single portactive object group. However, if you cannot associate the same source with more than one portstart a new [[EM. FinallyLibera]] project from scratch, you can assign '''Port Impedance''' in Ohms. By and start drawing a new object without having previously defined any object groups, a new default, all port impedances are 50Σ. The table titled '''Port Configuration''' lists all PEC object group is created and added to the ports and their associated sources and port impedancesnavigation tree to hold your new CAD object.
{{Note|In [[EMImage:Info_icon.Cubepng|30px]] you cannot assign ports Click here to an array object, even if it contains sources on its elements. To calculate the S learn more about '''[[parametersBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]] of an antenna array, you have to construct it using individual elements, not as an array object'''.}}
{{Note|In [[File:port-definitionEM.pngCube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. From [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you can then move the imported objects to [[EM.Libera]].}}
The [[MoM3D Module]]== EM.Libera's port definition dialog.Excitation Sources ==
=== Hertzian Dipole Sources === Your 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, electric surface currents on metal surface and both electric magnetic surface currents on the surface of dielectric objects. The excitation source you choose depends on the observables you seek in your project. [[EM.Libera]] provides the following source types for exciting your physical structure:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:wire_pic17gap_src_icon.png]]|thumb[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" |The short dipole General-purpose point voltage source dialog| style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of EM.Cube's Materials, 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 or thin wire line or polyline, works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube'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's 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.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}
A short dipole provides a simple way of exciting a structure Click on each category to learn more details about it in the [[MoM3D ModuleGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]. A short dipole source acts like an infinitesimally small ideal current source. To define a short dipole source, follow these steps:
* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree For antennas and select '''Insert New Sourceplanar circuits, where you typically define one or more ports, you usually use lumped sources.[[EM..''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section Libera]] provides two types of the dialog, you can set the coordinate of the center of the short dipolelumped sources: strip gap and wire gap. By default, the source A Gap is an infinitesimally narrow discontinuity that is placed at on the origin path of the world coordinate system at (0,0,0).You can type in new coordinates or use the spin buttons current and is used to move the dipole arounddefine an ideal voltage source.* In the Wire gap sources must be placed on '''Source PropertiesThin Wire Line''' section, you can specify the and '''AmplitudeThin Polyline''' in Volts, objects to provide excitation for the '''Phase''' in degrees as well as Wire MoM solver. The gap splits the '''Length''' of wire into two lines with a an infinitesimally small spacing between them, across which the dipole in project unitsideal voltage source is connected.* In the '''Direction Unit Vector''' sectionStrip gap sources must be placed on long, you can specify the orientation of the short dipole by setting values for the components '''uX'''narrow, '''uYPEC Rectangle Strip''', and '''uZ''' of objects to provide excitation for the dipole's unit vectorSurface MoM solver. The default values correspond to gap splits the strip into two strips with a vertical (Z-directed) short dipole. The dialog normalizes an infinitesimally small spacing between them, across which the vector components upon closure even if your component values do not satisfy ideal voltage source is connected. Only narrow rectangle strip object that have a unit magnitudesingle mesh cell across their width can be used to host a gap source.
When {{Note|If you simulate a wire structure in the [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your project. This is used not only want 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 "MoM.IDI" by default and has excite a '''.IDI''' file extension. The current data are saved as line segments representing each of the curved wire cells together with the complex current at the center of each cell. In the [[MoM3D Module]], you can import the current data from an existing '''.IDI''' file to serve antenna such as a set of short dipoles for excitation. To import circular loop or helix with a wire current solutiongap source, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Source...''' from the contextual menu. This opens up the standard [[Windows]] Open dialog with the file type set first you have 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 convert the curve object into a polyline using [[PO ModuleCubeCAD]]'s Navigation Tree as the total number of mesh cells in the Wire MoM solution. 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]]Polygonize Tool.}}
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 θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ =180° and φ == Plane Wave Sources === 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.
[[FileImage:po_phys15Info_icon.png|thumb40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays |300px|plane wave dialogUsing Source Arrays in Antenna Arrays]]'''.
The wire-frame structure in the <table><tr><td> [[MoM3D Module]] can be excited by an incident plane waveImage:wire_pic14_tn. In particular, a plane wave png|thumb|left|640px|A wire gap source can be used to compute the radar cross section placed on one side of a metallic targetpolyline representing a polygonized circular loop. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:</td></tr><tr></table>
* TMz<table>* TEz<tr>* Custom Linear<td> [[Image:po_phys16_tn.png|thumb|left|420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]] </td>* LCPz</tr>* RCPz</table>
The direction of incidence is defined through the θ and φ 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'''. The default values are θ = 180° and φ = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM<sub>z</sub> and TE<sub>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case 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 satisfied: '''ê . ê''' = 1 and '''ê à k''' Modeling Lumped Circuits == 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 (θ = 180°).
To In [[EM.Libera]], you can define simple lumped elements in a plane wave 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 follow these steps. 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. [[EM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source[[Image:Info_icon...''' 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 png|40px]] Click here to enter the X, Y, Z components of the learn more about '''E-Field Vector[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.
{{Note[[Image:Info_icon.png|In the spherical coordinate system, normal plane wave incidence from the top 40px]] Click here for a general discussion of the domain downward corresponds to θ of 180°'''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''. }}
[[File:po_phys16_tn.png]]=== Defining Ports ===
Figure: Illuminating a metallic sphere with an obliquely incident plane wave sourcePorts are used to order and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the navigation 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. All port impedances are 50Ω by default.
== Running Wire MoM Simulations ==[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.
=== Running A Wire MoM Analysis === <table><tr><td> [[Image:MOM7A.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>
[[File:wire_pic19== EM.png|thumb|300px|[[MoM3D Module]]Libera's run simulation dialog]]Simulation Data & Observables ==
Once you have set up your metal structure in At the end of a 3D MoM simulation, [[EM.Cube|EM.CUBELibera]]'s 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. [[MoM3D ModuleEM.Libera]], have defined sources and observables and have examined currently offers the quality following types of the structure's wireobservables: {| class="wikitable"|-frame mesh, you are ready to run a simulation. To open the Run ! scope="col"| Icon! scope="col"| Simulation Dialog, click the '''Run''' Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:run_iconcurrdistr_icon.png]] button | style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of the EM.Cube'''Compute Toolbar''' or select Menu s Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | 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:larrow_tnfieldsensor_icon.png]] Compute | 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:larrow_tnfarfield_icon.png]] Run..| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.or use the keyboard shortcut ''Cube'Ctrl+R'''. To start s Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the simulation click the '''Run''' button 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 this dialogEM. Once the Wire MoM simulation starts, a new dialog called 'Cube''Output Window''' opens up that reports s Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the various stages of Wire MoM simulation, displays the running time bistatic and shows the percentage monostatic RCS of completion for certain tasks during the Wire MoM simulation processa target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon. A prompt announces the completion of the Wire MoM simulation. At this time, png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |EM.CUBEPort Definition]] generates a number of output data files that contain all | style="width:300px;" | Computing the computed simulation dataS/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. These include png]]| style="width:150px;" | Equivalent electric and magnetic surface current distributions, near field data, far | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field radiation pattern data on a box to be used later as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave Huygens sourcein other [[EM.Cube]] modules| style="width:250px;" | None|}
You have the choice Click on each category to run a '''Fixed Frequency''' simulation, which is learn more details about it in the default choice, or run a '''Frequency Sweep'''[[Glossary of EM. In the former case, the simulation will be carried out at the Cube'''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 Simulation Observables & Graph Types]].
In case you choose Frequency Sweep, Depending on the Frequency Settings dialog gives two options for '''Sweep Type: Adaptive''' or '''Uniform'''. In a uniform sweep, equally spaced samples types of the frequency are used between the Start and End frequencies. These are initially set by the objects present in your project Bandwidthworkspace, but you can change their values from the Frequency Settings dialog[[EM. The default '''Number of Samples''' is 10Libera]] performs either a Surface MoM simulation or a Wire MoM simulation.In the former case of adaptive sweep, you have to specify the '''Maximum Number electric and magnetic surface current distributions on the surface of Iterations''' as well as the '''Error'''PEC and dielectric objects can be visualized. An adaptive sweep simulation starts with a few initial frequency samples, where In the Wire MoM engine is run. Thenlatter case, the intermediary samples are calculated in a progressive manner. At each iteration, linear electric currents on all the frequency samples are used to calculate a rational approximation of the S parameter response over the specified frequency range. The process stops when the error criterion is metwires and wireframe objects can be plotted.
<table><tr><td> [[FileImage:wire_pic20wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a PEC plate.]] </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.]]</td></tr></table>
Figure: The output window{{Note|Keep in mind that since [[EM.Libera]] uses MoM solvers, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}
=== Setting Wire MoM Numerical Parameters === <table><tr><td> [[Image:wire_pic32_tn.png|thumb|360px|Electric 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 Wire MoM simulation involves You need to define a number of numerical [[parameters]] that normally take default values unless far field observable if you change them. You can access these [[parameters]] and change their values by clicking on the '''Settings''' button next want to the "Select Engine" drop-down list plot radiation patterns of your physical structure in the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialog. 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 ModuleEM.Libera]]. The BiCG solver is iterative. Once selected, you have to set After 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 3D MoM simulator simulation is based on Pocklington's integral equation method. In this methodfinished, the wires three radiation patterns plots are assumed added to have a very small radius. The basis functions are placed on the axis of far field entry in the "wire cylinder", while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functionsNavigation Tree. In These are the "Source Singularity" section of the dialogfar field component in Theta direction, 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 far field component in free space wavelengths Phi direction and its default value is 0.001λ<sub>0</sub>. The value of the wire radius has a direct influence on the wire's computed reactancetotal far field.
[[FileImage:wire_pic21Info_icon.png|30px]]Click here to learn more about the theory of '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.
<table><tr><td> [[Image:wire_pic38_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Theta component.]] </td><td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The wire MoM engine settings dialogtotal radiation pattern of the circular loop antenna.]] </td></tr></table>
=== 3D MoM Sweep Simulations === When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Libera]] calculates the radar cross section (RCS) of a target. Three RCS quantities are computed: the θ and φ components of the radar cross section as well as the total radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. 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 θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.
You can run [[EMTo calculate RCS, first you have to define an RCS observable instead of a radiation pattern.Cube|EM.CUBE]]'s MoM3D At the end of a PO simulation engine in , the sweep modethee RCS plots σ<sub>θ</sub>, whereby a parameter like frequencyσ<sub>φ</sub>, plane wave angles of incidence or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data file for visualization and plotting. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types σ<sub>tot</sub> are added under the far field section of sweep:the navigation tree.
# Frequency Sweep# Angular Sweep# Parametric Sweep{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}
To run a MoM3D sweep, open {{Note|Computing the '''Run Simulation Dialog''' and select one of the above sweep types from the '''Simulation Mode''' drop3D mono-down list in this dialog. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabled. 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 static RCS may take an enormous amount of frequency samplescomputation time. 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 at the highest frequency<table><tr><td> [[Image:wire_pic51_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td># Fix mesh at the center frequency<td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td># Re-mesh at each frequency<td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]] </td></tr></table>
The [[MoM3D Module]] offers two types of frequency sweep: adaptive or uniform. In a uniform sweep, equally spaced frequency samples are generated between the start and end frequencies. In the case 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 == 3D Mesh Generation in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a mean-square sense. The adaptive sweep simulation results are always continuous and smooth. This is due to the fact that a rational function curve is fitted through 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 of the simulationEM.Libera ==
[[File:wire_pic22=== A Note on EM.png]] [[File:wire_pic24.png]]Libera's Mesh Types ===
The [[MoM3D ModuleEM.Libera]]'s run features two simulation dialog with frequency sweep selected engines, 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 frequency settings dialogconnection points between two or more wires, junction basis functions are generated to ensure current continuity.
In a parametric sweepOn the other hands, one or more user defined [[variablesEM.Libera]] are varied at the same time over their specified ranges's Surface MoM solver requires a triangular surface mesh of surface and solid objects. This creates a parametric space The mesh generating algorithm tries to generate regularized triangular cells with the total number of samples almost equal to surface areas across the product entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the number of samples for each variablefree-space wavelength. The user defined [[variables]] are defined using [[EM.Cube|EM.CUBE]]'s '''[[Variables]] Dialog'''default mesh density is 10 cells per wavelength. For meshing surfaces, a description mesh density of [[EM7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength.Cube|EM.CUBE]] [[variables]]Alternatively, please refer to you can base the [[CubeCAD|CUBECAD]] manual or the "Parametric Sweep" sections definition of the FDTD or [[Planar Module]] manualsmesh density on "Cell Edge Length" expressed in project units.
== [[Image: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 3D MoM Simulation Data ==Mesh Generator]]'''.
=== Visualizing Wire Current Distributions === [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera's Triangular Surface Mesh Generator ]]'''.
<table><tr><td> [[FileImage:wire_pic25Mesh5.png|thumb|300px400px|[[MoM3D Module]]EM.Libera's current distribution Mesh Settings dialogshowing the parameters of the linear wireframe mesh generator.]]</td></tr></table>
At the end of a MoM3D simulation, [[EM.Cube|EM.CUBE]]'s Wire MoM engine generates a number of output data files that contain all the computed simulation data. === 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 currents, you must first define current sensors before running the Wire MoM simulation. To do this, 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 to the Navigation Tree. Unlike the [[Planar Module]], 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 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 -π and π.Linear Wireframe Mesh Generator ===
Current distribution maps are displayed You can analyze metallic wire structures very accurately with some default settings and optionsutmost computational efficiency using [[EM. You can customize the individual maps (totalLibera]]'s Wire MoM simulator. When you structure contains at least one PEC line, magnitudepolyline or any curve CAD object, phase, etc[[EM.)Libera]] will automatically invoke its linear wireframe mesh generator. To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree This mesh generator subdivides straight lines and selecting '''Properties...''' linear segments of polyline objects into or by double clicking on linear elements according to the surface of the plot's legend boxspecified mesh density. Two '''scale''' options It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are available: '''Linear''' and '''dB'''determined by the specified mesh density. With the '''Linear''' (default) option selected, the current value is always normalized to the maximum total current in Note that plane, and the normalized scale polygonizing operation is mapped between the minimum temporary and maximum values. If the '''dB''' option is selected, the normalized current is converted to dB scale. The plot limits (bounds) can be set individually solely for every current distribution plot. In the '''Limits''' section he purpose of the plot's property dialog, you see four options: '''Default''', '''User Defined''', '''95% Confmesh generation.''' and '''95% Conf.'''. Select the user defined option and enter new values As for the '''Lower''' surface and '''Upper''' limits. The last two options are used to remove the outlier data within the 95% and 99% confidence intervalssolid CAD objects, respectively. In other words, the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution wireframe mesh of the data. Three color maps are offered: '''Default''', '''Rainbow''' and '''Grayscale'''. You can hide the legend box by deselecting the box labeled '''Show Legend Box'''. You can also change the foreground and background colors these objects is created which consists of the legend boxa large number of interconnected linear (wire) elements.
[[Image:MORE.png{{Note|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. It also discretizes surface and solid CAD objects temporarily using CubeCAD's Polymesh tool.}}
<table><tr><td> [[FileImage:wire_pic26_tnMesh6.png|400pxthumb|200px|The geometry of an expanding helix with a circular ground.]] </td><td> [[FileImage:wire_pic27_tnMesh7.png|400pxthumb|200px|Wireframe mesh of the helix with the default mesh density of 10 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 25 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/λ<sub>0</sub>.]]</td></tr></table>
Figure: A monopole antenna connected above a PEC plate and its current distribution with the default plot settings.=== Mesh of Connected Objects ===
[[File:wire_pic28All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing.png|360px]] [[File:wire_pic29_tnIf 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.png|440px]]
Figure: When two objects belonging to two different material groups overlap or intersect each other, [[EM.Libera]] has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top of a PEC plate. The output plot settings dialogtwo object share a circular area at the base of the cylinder. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, [[EM.Libera]] does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu > Simulate > discretization > Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the current distribution top of the monopole-plate structure with a user defined upper limittable. You can select an group from the table and change its hierarchy using the {{key|Move Up}} or {{key|Move Down}} buttons of the dialog. You can also change the color of junction cells that belong to each group.
=== <table><tr><td> [[Image:MOM3.png|thumb|300px|EM.Libera's Mesh Hierarchy dialog.]] Scattering Parameters and Port Characteristics === </td></tr></table>
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) <table><tr><td> [[parameters]] of the selected ports, all based on the port impedances specified in the project's "Port Definition"Image:MOM1. If more than one port has been defined in the project, the scattering matrix of the multiport network is calculatedpng|thumb|360px|A dielectric cylinder attached to a PEC plate. 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 "#". The admittance (Y) and impedance (Z) </td><td> [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensionsImage:MOM2. png|thumb|360px|The voltage standing wave ratio surface mesh of the structure at the first port is also computed dielectric cylinder and saved to a real data '''.DAT''' filePEC plate.]] </td></tr></table>
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 items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. === Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===
[[Image:MOREIf the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure.png|40px]] Click here From the point of view of this mesh generator, all PEC surface objects and PEC solid objects are treated as wireframe objects. If you want to learn more about '''model a wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of the surface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[Data_Visualization_and_Processing#Graphing_Port_Characteristics | Graphing Port CharacteristicsEM.Cube]]'''s polymesh objects to accomplish this objective.
=== Near Field Visualization === {{Note|In [[EM.Cube]], polymesh objects are regarded as already-meshed objects and are not re-meshed again during a simulation.}}
[[File:wire_pic30.png|thumb|300px|[[MoM3D Module]]You can convert any surface object or solid object to a polymesh using CubeCAD's field sensor dialog]]'''Polymesh Tool'''.
[[EMImage:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool |Converting Object to Polymesh]]''' in [[EM.CUBECube]] 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 Once an object is converted to change the sensorâs name. a polymesh, you can also change the color place your wire at any of the field sensor plane using the '''Color''' buttonits nodes.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X'''In that case, '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBELibera]] creates a field sensor plane passing through 's Wire MoM engine will sense the origin of coordinates (0,0,0) coincident nodes between line segments 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 will create 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 Ã 100 project units. You can change the dimensions of the sensor plane junction basis function 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 timesensure current continuity.
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<table><tr><td> [[Image:MOM4. Once png|thumb|360px|Geometry of a Wire MoM simulation is finished, monopole wire connected to a total of 14 plots are added to every field sensor node in the Navigation TreePEC plate. These include ]] </td><td> [[Image:MOM5.png|thumb|360px|Placing 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 wire on the Project Workspace. A legend box appears in the upper right corner polymesh version of the field plot, which can be dragged around using the left mouse buttonPEC plate. 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 Atd></m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc.tr></table>
[[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing == Running 3D Near Field Maps]]'''MoM Simulations in EM.Libera ==
[[File:wire_pic31_tn=== EM.png]]Libera's Simulation Modes ===
Figure: A circular loop antenna fed by Once you have set up your structure in [[EM.Libera]], have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a gap source3D MoM simulation.[[EM.Libera]] offers five simulation modes:
{| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[File#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:wire_pic32_tn270px;" | 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.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube |400pxFrequency 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;" | [[FileParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:wire_pic33_tn270px;" | 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.pngCube#Performing_Optimization_in_EM.Cube |400pxOptimization]]| 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|}
Electric You can set the simulation mode from [[EM.Libera]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and magnetic field plots a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the circular loop antennanavigation tree.
=== Visualizing 3D Radiation Patterns Running a Single-Frequency MoM Analysis ===
In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed by one of [[File:wire_pic37EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s radiation pattern dialog]]two MoM solvers. If your project contains at least one line or curve object, the Wire MoM solver is automatically selected. Otherwise, the Surface MoM solver will always be used to simulate your numerical problem. In either case, the engine type is set automatically.
Unlike To open the FDTD methodRun Simulation Dialog, 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 click the '''Far FieldsRun''' item in [[File:run_icon.png]] button of the '''ObservablesSimulate Toolbar''' section of the Navigation Tree and selecting or select '''Insert New Radiation PatternMenu > Simulate > Run...''' from or use the contextual menukeyboard shortcut {{key|Ctrl+R}}. The Radiation Pattern dialog opens up. You can accept most of By default, the default settings in this dialogSurface MoM solver is selected as your simulation engine. The Output Settings section allows you to change To start the '''Angle Increment''' for both Theta and Phi observation angles in simulation, click the degrees. These [[parameters]] indeed set the resolution {{key|Run}} button of far field calculationsthis dialog. The default values are 5 degrees. After closing Once the radiation pattern dialog3D MoM simulation starts, a far field entry immediately appears with its given name under the new dialog called '''Far FieldsOutput Window''' item opens up that reports the various stages of MoM simulation, displays the Navigation Tree running time and can be right clicked shows the percentage of completion for further editing. After a 3D certain tasks during the MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Treeprocess. These are A prompt announces the far field component in Theta direction, completion of the far field component in Phi direction and the total far fieldMoM 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 the theory of '''</td></tr><tr><td> [[Computing_the_Far_Fields_%26_Radiation_CharacteristicsImage:MOM3D MAN10.png| Far Field Computations]]''thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td></tr></table>
[[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 ]]'''.=== Setting MoM Numerical Parameters ===
[[Image:MOREMoM simulations involve a number of numerical parameters that normally take default values unless you change them.png|40px]] Click here You can access these parameters and change their values by clicking on the '''Settings''' button next to learn more about the "Select Engine" dropdown list in the '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.
[[Image:MOREFirst we discuss the Wire MoM Engine Settings dialog.png|40px]] Click here In 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 learn more about set a '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]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'''.
<table><tr><td> [[FileImage:wire_pic38_tnMOM9B.png|260px]] [[File:wire_pic39_tn.pngthumb|260px]] [[File:wire_pic40_tnleft|480px|EM.Libera's Wire MoM Engine Settings dialog.png|260px]]</td></tr></table>
3D radiation pattern The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the circular loop antennadialog, you can choose among the three PEC formulations: (Left) Theta componentEFIE, (Center) Phi componentsMFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is α = 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: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (RightAIM) total far fieldto speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[EM.Libera]]'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 MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.
=== Computing Radar Cross Section ===  For both Wire MoM and Surface MoM solvers, you can instruct [[File:wire_pic49EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s RCS dialog]]  When your structure is excited by a plane wave source, to write the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) contents of a target. Three RCS quantities are computed: the φ MoM matrix and θ components of the radar cross section as well as the total radar cross section: σ<sub>θ</sub>, σ<sub>φ</sub>, excitation and σ<sub>tot</sub>. In addition, EM.Libera calculates two types of RCS for each structure: solutions vectors into data files with '''Bi-Static RCS.DAT1''' and file extensions. These files can be accessed from the '''Mono-Static RCSInput/Output Files'''. In bi-static RCS, tab of the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub> and the RCS is measured and plotted at all θ and φ anglesData Manager. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub> and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub> and φ<sub>0</sub>.It is clear that in the both case of mono-static RCS, the Wire MoM simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ<sub>0</sub> and φ<sub>0</sub> are varied over the intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded. To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' option to open uncheck the Radar Cross Section Dialog. Use the '''Label''' check 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'''"Superpose Incident plane Wave Fields". The former This option applies when your structure is the default choice. The resolution of RCS calculation is specified excited by '''Angle Increment''' expressed in degrees. By default, the θ and φ 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 generatedplane wave source. These are RCS cuts at certain planesWhen checked, which include the three principal XY, YZ and ZX planes plus one additional constant φ-cut. This latter cut is at φ=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 σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>are added under the far field section of sensors plot 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 electric and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, EM.Libera calculates some other quantities magnetic field distributions 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)incident field. In this caseOtherwise, only the RCS needs to be computed at a fixed pair of phi scattered electric and theta angles. These angles magnetic field distributions are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" 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|40px]] 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]]'''visualized.
<table>
<tr>
<td> [[Image:wire_pic51_tnMOM9.png|thumb|300pxleft|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png640px|thumb|300px|The RCS of a metal plate structure: σ<sub>φ</sub>EM.]] </td><td> [[Image:wire_pic53_tn.png|thumb|300px|The total RCS of a metal plate structure: σ<sub>tot</sub>Libera's Surface MoM Engine Settings dialog.]] </td>
</tr>
</table>
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