[[Image:Splash-mom.jpg|right|720px]]<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Primer Tutorial Gateway]]'''Â [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== EM.Libera in a Nutshell ===
[[EM.Libera ]] is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structure simulator for modeling metallic structures made up of metal and dielectric structuresregions or a combination of them. It features two full-wave Method of Moments (MoM) separate simulation engines, one based on a Wire Surface MoM formulation solver and the other based on a Surface MoM formulation. In general, a surface Wire MoM solver is used to simulate your physical structure, which may involve metallic that work independently and dielectric objects provide different types of arbitrary shapes as well as composite structures that contain joined solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric regions. If objects in your project workspace contains at least one line or curve object, EMphysical structure.Libera then invokes its The Wire MoM solver. In that case, can only handle metallic structure can be modeled, and all wireframe structures. [[EM.Libera]] selects the surface and solid PEC simulation engine automatically based on the types of objects are meshed as wireframespresent in your project workspace.
{{Note|You can use [[EM.Libera either for modeling metallic wire objects and wireframe structures ]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling metallicPEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric ad composite structures that do not contain lines or curvesregions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.}}
=== A Overview {{Note|In general, [[EM.Libera]] uses the surface MoM solver to analyze your physical structure. If your project workspace contains at least one line or curve object, [[EM.Libera]] switches to the Wire MoM solver.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of the '''[[Basic Principles of The Method of Moments | 3D Method Of of Moments ===]]'''.
The Method of Moments (MoM) is a rigorous, full-wave, numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwellâs equations as opposed to their differential forms used in the finite element or finite difference time domain methods.<table><tr><td>In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem. The given structure is immersed in the free space. The unknown currents or fields are discretized as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields are called basis functions. They obviously have a vectorial nature and must satisfy [[Maxwell's EquationsImage:Yagi Pattern.png|thumb|500px|Maxwell's equations]] and relevant boundary conditions individually. The actual currents or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudes. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structure. EM.Libera offers two distinct 3D MoM simulation engines. The first one is a Wire MoM solver, which is based on Pocklington's integral equation. This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wirefar-type antennas and arrays. The second engine features a powerful Surface MoM solver. It can model metallic surfaces and solids as well as solid dielectric objects. The Surface MoM solver uses a surface integral equation formulation of [[Maxwell's Equations|Maxwell's equations]]. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. For the modeling radiation pattern of the dielectric regions of the physical structure , the soexpanded Yagi-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problemsUda antenna array with 13 directors. [[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[3D Method of Moments]]'''.</td>== Constructing the Physical Structure & 3D Mesh Generation ==</tr>=== Defining Groups Of PEC Objects === </table>
[[Image:wire_pic1.png|thumb|350px|=== EM.Libera's Navigation Tree.]] EM.Libera features two different simulation engines: Wire MoM 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 MoM3D Module 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 editedEM.Cube ===
=== Defining Dielectric Objects === 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.
Of EM[[Image:Info_icon.Liberapng|30px]] Click here to learn more about 's two simulation engines, only the Surface MoM solver can handle dielectric objects. Dielectric objects are created under the ''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'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>r</sub> 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:=== Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===
* Right click on the The method of moments uses an open-boundary formulation of Maxwell'''Dielectric''' item s equations which does not require a discretization of the Navigation Tree and select '''Insert New Dielectric...''' from entire computational domain, but only the contextual menufinite-sized objects within it.* Specify As a '''Label'''result, [[EM.Libera]]'''Color''' (and optional Texture) and the electromagnetic properties s typical mesh size is typically much smaller that that of the dielectric material to be created: a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]''Relative Permittivity''' (e<sub>r</sub>) and '''Electric Conductivity''' (s).* You may also choose from triangular surface mesh provides a list more accurate representation of preloaded material types. Click the button labeled '''Material''' to open your physical structure than [[EM.CubeTempo]]'s Materials dialog. Select the desired material from the list or type staircase brick volume mesh, which often requires a fairly high mesh density to capture the first letter geometric details of a material curved surfaces. These can be serious advantages when deciding on which solver to find ituse for analyzing highly resonant structures. For exampleIn that respect, typing '''V''' selects '''Vacuum''' in the list[[EM. Once you close the dialog by clicking '''OK'''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, the selected material properties fill the parameter fields automatically[[EM.* Click the '''OK''' button of the dielectric material dialog to accept the changes and close itLibera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.
{{Note|Under dielectric material groups, you cannot draw [[Surface Objects|surface objectsEM.Libera]] or '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 [[Curve Objects|EM.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 [[Curve Objects|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 [[Curve Objects|EM.Tempo]] or [[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|[[Curve Objects|curve objects]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]EM.Picasso]]instead.}}
<table>
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<td> [[Image:wire_pic2Hemi current.png|thumb|350px500px|EM.Libera's PEC dialogThe computed surface current distribution on a metallic dome structure excited by a plane wave source.]] </td><td> [[Image:wire_pic3.png|thumb|350px|EM.Libera's Dielectric dialog.]] </td>
</tr>
</table>
=== Moving Objects Between Groups & Modules =EM.Libera Features at a Glance ==
By default, the last object group that was defined n the navigation tree is active. The current active group is always listed in bold letters in the navigation tree. All the new objects are inserted under the current active group. A group can be activated by right-clicking on its entry in the navigation tree and then selecting the '''Active''' item of the contextual menu. You can move one or more selected objects to any desired PEC group. Right click on the highlighted selection and select '''Move To [[File:larrow_tn.png]] MoM3D [[File:larrow_tn.png]]''' from the contextual menu. This opens another sub-menu with a list of all the available PEC groups already defined in the [[PO Module]]. Select the desired PEC group, and all the selected objects will move to that group. The objects can be selected either in the project workspace, or their names can be selected from the Navigation Tree. In the latter case, make sure that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a PEC group's name from the contextual menu. In a similar way, you can move one or more objects from a === Physical Optics PEC group to [[EM.Cube|EM.CUBE]]'s other modules. In this case, the sub-[[menus]] of the''' Move To [[File:larrow_tn.png]]''' item of the contextual menu will indicate all the [[EM.Cube|EM.CUBE]] modules that have valid groups for transfer of the select objects.Structure Definition ===
== 3D Mesh Generation ==<ul> <li> Metal wires and curves in free space</li> <li> Metal surfaces and solids in free space</li> <li> Homogeneous dielectric solid objects in free space</li> <li> Import STL CAD files as native polymesh structures</li> <li> Export wireframe structures as STL CAD files</li></ul>
=== A Note on EM.Libera's Mesh Types Sources, Loads & Ports ===
EM.Libera features two simulation engines, <ul> <li> Gap sources on wires (for Wire MoM ) and gap sources on long, narrow, metal strips (for Surface MoM, which require different )</li> <li> Gap arrays with amplitude distribution and phase progression</li> <li> Multi-port port definition for gap sources</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized solution as elementary linear collection of short dipoles</li> <li> RLC lumped elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved on wires are first converted to multiand narrow strips with series-segment polylines parallel combinations</li> <li> Plane wave excitation with linear and then subdivided further if necessarycircular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM. At the connection points between two Terrano]] or more wires, junction basis functions are generated to ensure current continuity. external files)</li> <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>
On the other hands, 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 surface areas across the entire structure. You can control the cell size using the "=== Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.Generation ===
=== Creating & Viewing the Mesh === <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>
The mesh generation process in EM.Libera involves three steps:=== 3D Wire MoM & Surface MoM Simulations ===
# Setting the mesh <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># Generating the mesh. Both Windows and Linux versions of Wire MoM simulation engine available</li># Verifying the mesh.</ul>
The objects of your physical structure are meshed based on a specified mesh density expressed in cells/=== Data Generation &lambdaamp;<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 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 one more time, or deselect '''Menu > Simulate > Discretization > Show Mesh''' to remove its check mark or simply click the '''Esc Key''' of the keyboard.Visualization ===
<ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude "amp;Show Mesh" generates a new mesh and displays it if there is none phase)</li> <li> Huygens surface data generation for use in the memory, MoM3D 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 other [[EM.Cube]] to generate a mesh from the ground up by selecting '''Menu modules</li> Simulate <li> Discretization Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item <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 Navigation Tree wire structure</li> <li> Bi-static and selecting '''Regenerate''' from the contextual menumono-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>
To set == Building 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 Physical Structure 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|[[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|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:PO2.png|thumb|450px|Two ellipsoids of different (PEC and dielectric) compositions.]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoidsEM.]] </td></tr></table>Libera ==
=== Mesh 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 Connected Objects === the navigation tree. In [[EM.Libera]], 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;" | [[ImageFile:MOM3pec_group_icon.png]]|thumb|350pxstyle="width:150px;" |[[Glossary of EM.LiberaCube's Mesh Hierarchy dialog.Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]] All the | style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing| None|-| style="width:30px;" | [[File:thin_group_icon. If your structure contains attached, interconnected or overlapping png]]| style="width:150px;" | [[Solid ObjectsGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |solid objectsThin Wire]], their internal common faces are removed and | style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only the surface of the external faces is meshed|-| style="width:30px;" | [[File:diel_group_icon. Similarly, all the png]]| style="width:150px;" | [[Surface ObjectsGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |surface 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]] 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| 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 |}
When two objects belonging to two different material groups overlap or intersect Click on each other, EM.Libera has category to determine how to designate learn more details about it in the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top [[Glossary of a PEC plate. The two 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" tableCube's Materials, which you can modify. To access this tableSources, 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 {{key|Move Down}} buttons of the dialog. You can also change the color of junction cells that belong to each groupDevices & Other Physical Object Types]].
You can connect a line object to a touching surfaceBoth of [[EM. To connect lines to surfaces Libera]]'s two simulation engines, Wire MoM and allow for current continuitySurface MoM, you must make sure that the box labeled can handle metallic structures. You define wires under '''Connect Lines to Touching SurfacesThin Wire''' is checked in the groups and surface and volumetric metal objects under '''Mesh Settings DialogPEC Objects'''. If the end of a line lies on a flat surfaceIn other words, [[EM.Cube|EM.CUBE]] will detect that and create the connection automatically. Howeveryou can draw lines, this may not always be the case if the surface is not flat polylines and has curvature. In such casesother curve objects as thin wires, you which have to specifically instruct [[EMa radius parameters expressed in project units.Cube|EM.CUBE]] to enforce the connection. An example All types of this case is shown solid and surface CAD objects can be drawn in the figure belowa PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.
<table>
<tr>
<td> [[Image:MOM1wire_pic1.png|thumb|450px350px|A dielectric cylinder attached to a PEC plateEM.Libera's Navigation Tree.]] </td> <td> [[Image:MOM2.png|thumb|450px|The surface mesh of the dielectric cylinder and PEC plate.]] </td>
</tr>
</table>
=== Using Polymesh Objects Once a new object group node has been created on the navigation tree, it becomes the "Active" group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active group. There is only one object group that is active at any time. Any object type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create object groups, and then draw new CAD objects under the active object group. However, if you start a new [[EM.Libera]] project from scratch, and start drawing a new object without having previously defined any object groups, a new default PEC object group is created and added to Connect Wires the navigation tree to Wireframe Surfaces === hold your new CAD object.
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 Building Geometrical Constructions in CubeCAD#Transferring ObjectsAmong Different Groups or Modules |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.CubeMoving Objects among Different Groups]]'s polymesh objects to accomplish this objective''.
{{Note|In [[EM.Cube]], polymesh objects are regards you can import external CAD models (such as already-meshed 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 and are not re-meshed again during a simulationto [[EM.Libera]].}}
You can convert any surface object or solid object to a polymesh using [[CubeCAD]]== EM.Libera's '''Polymesh Tool'''. Excitation Sources ==
[[Image:MOREYour 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.png|40px]] Click here to learn more about '''[[Discretizing_Objects#Converting_Objects_to_Polymesh | Converting Object to Polymesh]]''' The excitation source you choose depends on the observables you seek in your project. [[EM.CubeLibera]].provides the following source types for exciting your physical structure:
<table>{| class="wikitable"<tr>|-<td> ! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[ImageFile:MOM4gap_src_icon.png]]|thumb[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |450pxStrip Gap Circuit Source]]|Geometry of a monopole wire connected to style="width:300px;" | General-purpose point voltage source | style="width:300px;" | Associated with a PEC platerectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:gap_src_icon.png]] </td><td> | [[ImageGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]| style="width:MOM5300px;" | 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]]|thumb[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |450pxHertzian Short Dipole Source]]|Placing the wire on the polymesh version style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of the PEC plateEM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]] </td></tr>| style="width:300px;" | Used for modeling scattering </table>| 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|}
== Excitation Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources ==, Devices & Other Physical Object Types]].
=== Gaps Sources For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on PEC Wires the path of the current and Strips === is used to define an ideal voltage source. Wire gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source.
A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current. In EM.Libera, {{Note|If you want to excite a curved wire antenna such as a circular loop or helix with a wire gap is used to define an excitation source in the form of an ideal voltage source. Gap sources can be placed on PEC '''Line''' and '''Polyline''' objects , first you have to provide excitation for convert the Wire MoM solver. The gap splits the wire curve object into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connectedpolyline using [[CubeCAD]]'s Polygonize Tool. }}
{{Note|If you want to excite A short dipole provides another simple way of exciting a curved wire antennas such as a circular loop or helix with a gap 3D structure in [[EM.Libera]]. A short dipole sourceacts 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, first you have need a plane wave source to convert compute the curve object into radar cross section of a polyline using 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 = 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 [[CubeCADEM.Cube]]'s Polygonize Toolcomputational module.}}
Gap sources can also be placed on long, narrow, PEC '''Rectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source. To define a new gap source, follow these steps[[Image:Â * Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New SourceInfo_icon...''' 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 png|40px]] Click here 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 learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Properties''' section, you can specify the '''Source Amplitude''' Arrays in Volts and the Antenna Arrays]]'''Phase''' in Degrees.
<table>
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<td> [[Image:MOM6wire_pic14_tn.png|thumb|360pxleft|EM.Libera's Wire Gap Source dialog.]] </td><td> [[Image:MOM6B.png640px|thumb|360px|EM.Libera's Strip Gap Source dialogA wire gap source placed on one side of a polyline representing a polygonized circular loop.]] </td>
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<tr>
</table>
[[File:wire_pic14_tn.png]]Â A gap source placed on one side of a polyline representing a polygonized circular loop.<table><tr><td> [[Image:MOREpo_phys16_tn.png|40pxthumb|left|420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]] Click here to learn more about '''[[Using Sources & Loads in Antenna Arrays]]'''.</td></tr></table>
=== Modeling Lumped Circuits ===
In [[File:wire_pic15EM.png|thumb|300px|[[MoM3D ModuleLibera]], you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped element dialogelements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. [[EM.Libera]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
In EM[[Image:Info_icon.Libera, you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent png|40px]] Click here to an infinitesimally narrow gap that is placed in the path of the current, across which Ohmlearn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]''s law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance. EM.Libera's lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
[[FileImage:image106Info_icon.png|40px]]Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.
[[File:wire_pic16_tn.png|thumb|200px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wire]]=== Defining Ports ===
To define a new lumped elementPorts 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, follow these steps: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.
* Right click on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the two options[[Image: '''Passive RLC''' or '''Active with Gap Source'''Info_icon. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option png|40px]] Click here to select either learn more about the positive or negative direction for the source.* 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[[Glossary_of_EM. 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 '''Load Properties''' section, the series and shunt resistance values Rs and Rp are specified in Ohms, the series and shunt inductance values Ls and Lp are specified in nH (nanohenry), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad). The impedance of the circuit is calculated at the operating frequency of the project. Only the elements that have been checked are taken into account. By default, only the series resistor has a value of 50Σ and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the '''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees.* If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical direction, offset, resistance, inductance and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase ProgressionCube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]''' in degrees along all three principal axes.
<table>
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<td> [[Image:MOM6AMOM7A.png|thumb|480px360px|EM.Libera's Wire Lumped Element dialogTwo metallic strips hosting a gap source and a lumped element.]] </td><td> [[Image:MOM6CMOM7B.png|thumb|480px360px|EM.Libera's Strip Lumped Element dialogThe surface mesh of the two strips with a gap source and a lumped element.]] </td>
</tr>
</table>
[[Image:port-definition.png|thumb|450px|== EM.Libera's Port Definition dialog.]]=== Defining Ports =Simulation Data & Observables ==
Ports are used to order and index gap sources for S parameter calculation. They are defined in At the '''Observables''' section end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the Navigation Treecomputed simulation data. Right click on The primary solution of the '''Port Definition''' item Wire MoM simulation engine consists of the Navigation Tree linear electric currents on the wires and select '''Insert New Port Definition...''' from the contextual menuwireframe structures. The Port Definition Dialog opens up, showing primary solution of the total number Surface MoM simulation engine consists of existing sources in the workspaceelectric and magnetic surface currents on the PEC and dielectric objects. By default, as many ports as [[EM.Libera]] currently offers the total number following types of sources are createdobservables: {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon. You can define any number png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of ports equal to or less than the total number of sourcesEM. This includes both gap sources and active lumped elements (which contain gap sources). In the Cube'''Port Association''' section of this dialogs Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal and dielectric objects, you can go over each one of the sources magnetic surface current distribution on dielectric objects and associate them with a desired portlinear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. Note that you can associate more than one source with same given portpng]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM. In this case, you will have Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a coupled portspecified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon. All png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the coupled sources are listed radiation pattern and additional radiation characteristics such as associated with a single port. Howeverdirectivity, you cannot associate axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the same bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source with more than one port|-| style="width:30px;" | [[File:port_icon. Finally, you can assign '''png]]| style="width:150px;" | Port Impedance''' in Ohms. By default, all port impedances are 50&SigmaCharacteristics| style="width:150px;" | [[Glossary of EM. The table titled ''Cube's Simulation Observables & Graph Types#Port Configuration''' lists all Definition |Port Definition]] | style="width:300px;" | Computing the ports and their associated sources S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port impedances|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}
{{Note|In Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]] you cannot assign ports to an array object, even if it contains sources on its elements. To calculate the S [[parameters]] of an antenna array, you have to construct it using individual elements, not as an array object.}}
Depending on the types of objects present in your project workspace, [[Image:MOM7.png|thumb|360px|EM.Libera's short dipole source dialog.]]=== Hertzian Dipole Sources === performs either a Surface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted.
<table><tr><td> [[Image:wire_pic26_tn.png|thumb|360px|A short dipole provides monopole antenna connected above a simple way of exciting a structure in EMPEC plate.Libera]] </td><td> [[Image:wire_pic27_tn. A short dipole source acts like an infinitesimally small ideal current sourcepng|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate. To define a short dipole source, follow these steps:]] </td></tr></table>
* Right click on the '''Short Dipoles''' item {{Note|Keep in the '''Sources''' section of the Navigation Tree and select '''Insert New Sourcemind that since [[EM...''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialogLibera]] uses MoM solvers, you can set the coordinate of calculated field value at the center of the short dipolesource point is infinite. By defaultAs a result, the source is field sensors must be placed at the origin of the world coordinate system adequate distances (at (0,0,0least one or few wavelengths).You can type in new coordinates or use away from the spin buttons scatterers to move the dipole around.* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' of the dipole in project units.* In the '''Direction Unit Vector''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitudeproduce acceptable results.}}
<table><tr><td> [[Image:MOM8wire_pic32_tn.png|thumb|360px|EMElectric field plot of the circular loop antenna.Libera's Plane Wave dialog]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]]</td></tr>=== Plane Wave Sources === </table>
The wire-frame You need to define a far field observable if you want to plot radiation patterns of your physical structure in the [[MoM3D ModuleEM.Libera]] can be excited by an incident plane wave. In particularAfter a 3D MoM simulation is finished, a plane wave source can be used three radiation patterns plots are added to compute the radar cross section of a metallic targetfar field entry in the Navigation Tree. A plane wave is defined by its propagation vector indicating These are the far field component in Theta direction, the far field component in Phi direction of incidence and its polarizationthe total far field. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:
* TMz* TEz* Custom Linear* LCPz* RCPz[[Image:Info_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 ]]'''.
The direction of incidence is defined through the θ and φ angles of the unit propagation vector in the spherical coordinate system<table><tr><td> [[Image:wire_pic38_tn. png|thumb|230px|The values 3D radiation pattern of these angles are set in degrees in the boxes labeled '''circular loop antenna: Theta''' and '''Phi'''component. 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]] </subtd> and TE<subtd>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively[[Image:wire_pic39_tn. png|thumb|230px|The components 3D radiation pattern of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialogcircular loop antenna: Phi component. 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]] </td><td> [[Image: '''ê wire_pic40_tn. ê''' = 1 and '''ê à k''' = 0 . This can be enforced using the '''Validate''' button at the bottom png|thumb|230px|The total radiation pattern 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°)loop antenna.]] </td></tr></table>
To define When the physical structure is excited by a plane wave source follow these steps, 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.
* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' The Plane wave Dialog opens up.* In the Field Definition section of the dialogTo calculate RCS, first you can enter the '''Amplitude''' have to define an RCS observable instead of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phaseradiation pattern.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set At the '''Polarization''' end of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selecteda PO simulation, you also need to enter the Xthee RCS plots σ<sub>θ</sub>, Yσ<sub>φ</sub>, Z components and σ<sub>tot</sub> are added under the far field section of the '''E-Field Vector'''navigation tree.
{{Note|In The 3D RCS plot is always displayed at the origin of the spherical coordinate system, normal plane wave incidence from (0,0,0), with respect to which the top of far radiation zone is defined. Oftentimes, this might not be the domain downward corresponds to θ scattering center of 180°your physical structure. }}
[[File:po_phys16_tn{{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.png]]}}
Figure<table><tr><td> [[Image: Illuminating wire_pic51_tn.png|thumb|230px|The RCS of a metallic sphere with an obliquely incident plane wave sourcemetal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]] </td></tr></table>
== Running 3D MoM Simulations Mesh Generation in EM.Libera ==
=== Running A Wire MoM Analysis Note on EM.Libera's Mesh Types ===
[[Image:MOM9A.png|thumb|450px|EM.Libera's Simulation Run dialog.]]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.
Once you have set up your metal structure in On the other hands, [[EM.Cube|EM.CUBELibera]]'s [[MoM3D Module]], have defined sources Surface MoM solver requires a triangular surface mesh of surface and observables and have examined the quality of the structure's wire-frame solid objects.The mesh, you are ready generating algorithm tries to run a simulation. To open generate regularized triangular cells with almost equal surface areas across the Run Simulation Dialog, click the '''Run''' [[File:run_iconentire structure.png]] button of You can control the '''Compute Toolbar''' or select Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Run...or use cell size using the keyboard shortcut '''Ctrl+R'''"Mesh Density" parameter. To start the simulation click the '''Run''' button of this dialog. Once the Wire MoM simulation startsBy default, a new dialog called '''Output Window''' opens up that reports the various stages mesh density is expressed in terms of Wire MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the Wire MoM simulation processfree-space wavelength. A prompt announces the completion of the Wire MoM simulationThe default mesh density is 10 cells per wavelength. At this timeFor meshing surfaces, [[EM.Cube|EM.CUBE]] generates a number mesh density of output data files that contain all the computed simulation data7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. These include current distributionsAlternatively, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if you can base the structure is excited by a plane wave sourcedefinition of the mesh density on "Cell Edge Length" expressed in project units.
You have the choice [[Image:Info_icon.png|30px]] Click here to run a '''Fixed Frequency''' simulation, which is the default choice, or run a '''Frequency Sweeplearn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube. In the former case, the simulation will be carried out at the 27s_Mesh_Generators | Working with Mesh Generator]]'''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, too.
In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type[[Image: Adaptive''' or '''Uniform'''Info_icon. In a uniform sweep, equally spaced samples of the frequency are used between the Start and End frequencies. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog. The default png|30px]] Click here to learn more about '''Number of Samples''' is 10[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.In the case of adaptive sweep, you have to specify the Libera's Triangular Surface Mesh Generator ]]''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 run. Then, the intermediary samples are calculated in a progressive manner. At each iteration, 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 met.
<table><tr><td> [[FileImage:wire_pic20Mesh5.png|thumb|400px|EM.Libera's Mesh Settings dialog showing the parameters of the linear wireframe mesh generator.]]</td></tr></table>
Figure: === The output window.Linear Wireframe Mesh Generator ===
You can analyze metallic wire structures very accurately with utmost computational efficiency using [[Image:wire_pic21.png|thumb|450px|EM.Libera]]'s Wire MoM Engine Settings dialogsimulator.]]When you structure contains at least one PEC line, polyline or any curve CAD object, [[Image:MOM9.png|thumb|450px|EM.Libera's Surface MoM Engine Settings dialog]] will automatically invoke its linear wireframe mesh generator.This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the specified mesh density. It also polygonizes rounded [[Curve Objects|curve objects]]=== into polylines with side lengths that are determined by the specified mesh density. Note that polygonizing operation is temporary and solely for he purpose of mesh generation. As for surface and solid CAD objects, a wireframe mesh of these objects is created which consists of a large number of interconnected linear (wire) elements. Setting Wire MoM Numerical Parameters ===
A Wire MoM simulation involves a number of numerical [[parameters]] that normally take default values unless you change them. You can access these [[parameters]] and change their values by clicking on the '''Settings''' button next to the "Select Engine" drop-down list 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 {{Note| The linear solver. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)''wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool. The LU solver is a direct solver and is the default option of the [[MoM3D Module]]. The BiCG solver is iterative. Once selected, you have to set a '''Tolerance''' for its convergence. You can It also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''. The Wire MoM simulator is based on Pocklington's integral equation method. In this method, the wires are assumed to have a very small radius. The basis functions are placed on the axis of the "wire cylinder", while the Galerkin testing is carried out on its discretizes surface to avoid the singularity of the Green's functions. In the "Source Singularity" section of the dialog, you can specify the '''Wire Radius''' . [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] assumes an identical wire radius for all wires and wireframe structures. This radius is expressed in free space wavelengths and its default value is 0.001λ<sub>0</sub>. The value of the wire radius has a direct influence on the wiresolid CAD objects temporarily using CubeCAD's computed reactancePolymesh tool.}}
<table>
<tr>
<td> [[Image:Mesh6.png|thumb|200px|The geometry of an expanding helix with a circular ground.]] </td>
<td> [[Image:Mesh7.png|thumb|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>
=== 3D MoM Sweep Simulations Mesh of Connected Objects ===
You can run [[EM.Cube|EM.CUBE]]'s MoM3D simulation engine in All the sweep modeobjects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, whereby a parameter like frequencyinterconnected or overlapping solid objects, plane wave angles their internal common faces are removed and only the surface of incidence or a user defined variable the external faces is varied over a specified range at predetermined samplesmeshed. The output data Similarly, all the surface objects belonging to the same PEC group are saved into data file for visualization merged together and plottingtheir internal edges are removed before meshing. [[EMNote that a solid and a surface object belonging to the same PEC group might not always be merged properly.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types of sweep:
# Frequency Sweep# Angular Sweep# Parametric SweepWhen 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 two 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 top of the table. 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.
To run a MoM3D sweep, open the '''Run Simulation Dialog''' and select one of the above sweep types from the '''Simulation Mode''' drop-down list in this dialog<table><tr><td> [[Image:MOM3. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabledpng|thumb|300px|EM. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the projectLibera's center frequency and bandwidthMesh Hierarchy dialog. 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:]] </td></tr></table>
# Fix mesh at the highest frequency<table><tr><td> [[Image:MOM1.png|thumb|360px|A dielectric cylinder attached to a PEC plate.]] </td># Fix <td> [[Image:MOM2.png|thumb|360px|The surface mesh at of the center frequencydielectric cylinder and PEC plate.]] </td># Re-mesh at each frequency.</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 in a progressive manner. At each iteration, the frequency samples are used === Using Polymesh Objects 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 Connect Wires 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 simulation.Wireframe Surfaces ===
[[File:wire_pic22If the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure.png]] 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 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 [[File:wire_pic24EM.pngCube]]'s polymesh objects to accomplish this objective.
The {{Note|In [[MoM3D ModuleEM.Cube]]'s run simulation dialog with frequency sweep selected , polymesh objects are regarded as already-meshed objects and the frequency settings dialogare not re-meshed again during a simulation.}}
In a parametric sweep, one You can convert any surface object or more user defined [[variables]] are varied at the same time over their specified ranges. This creates solid object to a parametric space with the total number of samples equal to the product of the number of samples for each variable. The user defined [[variables]] are defined polymesh using [[EM.Cube|EM.CUBE]]CubeCAD's '''[[Variables]] DialogPolymesh Tool'''. For a description of [[EM.Cube|EM.CUBE]] [[variables]], please refer to the [[CubeCAD|CUBECAD]] manual or the "Parametric Sweep" sections of the FDTD or [[Planar Module]] manuals.
== Working with 3D MoM Simulation Data ==[[Image: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.Cube]].
=== Visualizing Once an object is converted to a polymesh, you can place your wire at any of its nodes. In that case, [[EM.Libera]]'s Wire Current Distributions === MoM engine will sense the coincident nodes between line segments and will create a junction basis function to ensure current continuity.
<table><tr><td> [[FileImage:wire_pic25MOM4.png|thumb|300px360px|[[MoM3D ModuleGeometry of a monopole wire connected to a PEC plate.]]'s current distribution dialog</td><td> [[Image:MOM5.png|thumb|360px|Placing the wire on the polymesh version of the PEC plate.]]</td></tr></table>
At the end of a MoM3D simulation, [[EM.Cube|EM.CUBE]]'s Wire == Running 3D 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 Simulations 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 πEM.Libera ==
Current distribution maps are displayed with some default settings and options=== EM. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface of the plotLibera's legend box. Two '''scale''' options are available: '''Linear''' and '''dB'''. With the '''Linear''' (default) option selected, the current value is always normalized to the maximum total current in that plane, and the normalized scale is mapped between the minimum 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 for every current distribution plot. In the '''Limits''' section of the plot's property dialog, you see four options: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select the user defined option and enter new values for the '''Lower''' and '''Upper''' limits. The last two options are used to remove the outlier data within the 95% and 99% confidence intervals, respectively. In other words, the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution 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 of the legend box.Simulation Modes ===
Once you have set up your structure in [[Image:MOREEM.png|40pxLibera]] Click here , have defined sources and observables and have examined the quality of the structure's mesh, you are ready to learn more about '''run a 3D MoM simulation. [[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution MapsEM.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_pic26_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_pic27_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|}
Figure: You can set the simulation mode from [[EM.Libera]]'s "Simulation Run Dialog". A monopole antenna connected 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 PEC plate 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 its current distribution with 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 default plot settingsnavigation tree.
[[File:wire_pic28.png|360px]] [[File:wire_pic29_tn.png|440px]]=== Running a Single-Frequency MoM Analysis ===
Figure: The output plot settings dialogIn a single-frequency analysis, and the current distribution structure of your project workspace is meshed at the monopole-plate structure with a user defined upper limitcenter frequency of the project and analyzed by one of [[EM.Libera]]'s 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.
=== Scattering Parameters To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, the Surface MoM solver is selected as your simulation engine. To start the simulation, click the {{key|Run}} button of this dialog. Once the 3D MoM simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of MoM simulation, displays the running time and Port Characteristics === shows the percentage of completion for certain tasks during the MoM simulation process. A prompt announces the completion of the MoM simulation.
If the project structure is excited by gap sources, and one or more ports have been defined, the <table><tr><td> [[Image:Libera L1 Fig13.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine calculates as the scattering (S) [[parameterssolver.]] of the selected ports, all based on the port impedances specified in the project's "Port Definition". If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. The S </td></tr><tr><td> [[parameters]] are written into output ASCII data filesImage:MOM3D MAN10. Since these data are complex, they are stored as '''png|thumb|left|480px|EM.CPXLibera''' filess Simulation Run dialog showing Surface MoM engine as the solver. Every file begins with a header starting with "#". The admittance (Y) and impedance (Z) [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of the structure at the first port is also computed and saved to a real data '''.DAT''' file.</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 [[=== Setting MoM Numerical Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. ===
[[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#Graphing_Port_Characteristics | Graphing Port Characteristics]]Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.
=== Near Field Visualization === First we discuss the Wire MoM Engine Settings dialog. 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 set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.
<table><tr><td> [[FileImage:wire_pic30MOM9B.png|thumb|300pxleft|[[MoM3D Module]]'s field sensor dialog]] [[EM.Cube480px|EM.CUBE]] allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps: * Right click on the Libera'''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensorâs name. you can also change the color of the field sensor plane using the '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBE]] creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane is 100 à 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a s Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation TreeEngine Settings dialog. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field Maps]]'''.</td>[[File:wire_pic31_tn.png]]</tr> Figure: A circular loop antenna fed by a gap source. [[File:wire_pic32_tn.png|400px]] [[File:wire_pic33_tn.png|400px]]</table>
Electric The Surface MoM Engine Settings dialog is bit more extensive and magnetic provides more options. In the "Integral Equation" section of the dialog, you can choose among the three PEC formulations: EFIE, MFIE 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 plots 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 circular loop antennadefault 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 (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<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.
=== Visualizing 3D Radiation Patterns ===For both Wire MoM and Surface MoM solvers, you can instruct [[EM.Libera]] to write the contents of the MoM matrix and excitation and solutions vectors into data files with '''.DAT1''' file extensions. These files can be accessed from the '''Input/Output Files''' tab of the Data Manager. In both case, you have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your structure is excited by a plane wave source. When checked, the field sensors plot the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualized.
<table><tr><td> [[FileImage:wire_pic37MOM9.png|thumb|300pxleft|[[MoM3D Module]]640px|EM.Libera's radiation pattern Surface MoM Engine Settings dialog.]]</td></tr></table>
Unlike the FDTD method, the method of moments does not need a far field box to perform near-to-far-field transformations. But you still need to define a far field observable if you want to plot radiation patterns in EM.Libera. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the '''Angle Increment''' for both Theta and Phi observation angles in the degrees. These [[parameters]] indeed set the resolution of far field calculations. The default values are 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked for further editing. After a 3D MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field. <br />
[[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field Computations]]'''.<hr>
[[Image:MORETop_icon.png|40px30px]] Click here to learn more about the theory of '''[[Data_Visualization_and_ProcessingEM.Libera#Using_Array_Factors_to_Model_Antenna_Arrays Product_Overview | Using Array Factors Back to Model Antenna Arrays the Top of the Page]]'''.
[[Image:MORETutorial_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]'''EM. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingCube#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''EM. [[File:wire_pic38_tn.pngLibera_Documentation |260px]] [[File:wire_pic39_tn.png|260px]] [[File:wire_pic40_tn.png|260px]] 3D radiation pattern of the circular loop antenna: (Left) Theta component, (Center) Phi components, and (Right) total far field. === Computing Radar Cross Section ===  [[File:wire_pic49.png|thumb|300px|[[MoM3D Module]]'s RCS dialog]]  When your structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) of a target. Three RCS quantities are computed: the φ and θ components of the radar cross section as well as the total radar cross section: 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 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°Tutorial Gateway] 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...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the 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 generated. These are RCS cuts at certain planes, 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 the navigation tree. The 2D RCS graphs can be plotted from the data manager exactly in the same way that you plot 2D radiation pattern graphs. A total of eight 2D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, EM.Libera calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, the RCS needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth & 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]]'''. <table><tr><td> [[Image:wire_pic51_tn.png|thumb|300px|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png|thumb|300px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td><td> [[Image:wire_pic53_tn.png|thumb|300px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]] </td></tr></table>
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