== An EM.Libera Primer == === EM.Libera in a Nutshell === EM.Libera is a 3D free-space structure simulator for modeling metallic and dielectric structures. It features two full-wave Method of Moments (MoM) simulation engines, one based on a Wire MoM formulation and the other based on a Surface MoM formulation. In general, a surface MoM solver is used to simulate your physical structure, which may involve metallic and dielectric objects of arbitrary shapes as well as composite structures that contain joined metal and dielectric regions. If your project workspace contains at least one line or curve object, EM.Libera then invokes its Wire MoM solver. In that case, only metallic structure can be modeled, and all the surface and solid PEC objects are meshed as wireframes.  {{Note|You can use EM.Libera either for modeling metallic wire objects and wireframe structures or for modeling metallic, dielectric ad composite structures that do not contain lines or curves.}}  === A Overview of 3D Method Of Moments === The Method of Moments (MoM) is a rigorous, full-wave, numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwellâs equations as opposed to their differential forms used in the finite element or finite difference time domain methods. In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem. The given structure is immersed in the free space. The unknown currents or fields are discretized as a collection of elementary currents or fields with small finite spatial extents. Such elementary currents or fields are called basis functions. They obviously have a vectorial nature and must satisfy [[Maxwell's Equations|Maxwell's equations]] and relevant boundary conditions individually. The actual currents or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudes. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structure. EM.Libera offers two distinct 3D MoM simulation engines. The first one is a Wire MoM solver, which is based on Pocklington's integral equation. This solver can be used to simulate wireframe models of metallic structures and is particularly useful for modeling wire-type antennas and arrays. The second engine features a powerful Surface MoM solver. It can model metallic surfaces and solids as well as solid dielectric objects. The Surface MoM solver uses a surface integral equation formulation of [[Maxwell's Equations|Maxwell's equations]]. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. For the modeling of the dielectric regions of the physical structure , the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized, in which equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problems. [[Image:MORESplash-mom.pngjpg|40pxright|720px]] Click here to learn more about the theory of '''[[3D Method of Moments]]'''. <strong><font color="#06569f" size= Constructing the Physical Structure & "4">3D Mesh Generation == === Defining Groups Of PEC Objects ===  [[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] EM.Libera features two different simulation engines: Wire MoM and And Surface MoM. Both simulation engines can handle metallic structures. The Wire MoM engine models metallic objects as perfect electric conductor (PEC) wireframe structures, while the Surface MoM engine treats them as PEC surfaces. The PEC objects can be lines, curves, surfaces or solids. All the PEC objects are created under the '''PEC''' node in the '''Physical Structure''' section of the Navigation Tree. Objects are grouped together by their color. You can insert different PEC groups with different colors. A new PEC group can be defined by simply right clicking on the '''PEC''' item in the Navigation Tree and selecting '''Insert New PEC...''' from the contextual menu. A dialog for setting up the PEC properties opens up. From this dialog you can change the name of the group or its color. Note that PEC object do not have any material properties that can be edited. === Defining Dielectric Objects ===  Of EM.Libera's two simulation engines, only the Surface MoM solver can handle dielectric objects. Dielectric objects are created under the '''Dielectric''' node in the '''Physical Structure''' section of the Navigation Tree. They are grouped together by their color and material properties. You can insert different dielectric groups with different colors and different permittivity e<sub>rSolvers For Simulating Free-Space Structures</subfont> and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when σ → ∞. To define a new Dielectric group, follow these steps: * Right click on the '''Dielectric''' item of the Navigation Tree and select '''Insert New Dielectric...''' from the contextual menu.* Specify a '''Label''', '''Color''' (and optional Texture) and the electromagnetic properties of the dielectric material to be created: '''Relative Permittivity''' (e<sub>r</substrong>) and '''Electric Conductivity''' (s).* You may also choose from a list of preloaded material types. Click the button labeled '''Material''' to open [[EM.Cube]]'s Materials dialog. Select the desired material from the list or type the first letter of a material to find it. For example, typing '''V''' selects '''Vacuum''' in the list. Once you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automatically.* Click the '''OK''' button of the dielectric material dialog to accept the changes and close it.Â
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<td> [[Imageimage:wire_pic2Cube-icon.png|thumblink=Getting_Started_with_EM.Cube]] [[image:cad-ico.png |350pxlink=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png |link=EM.Libera's PEC dialogTempo]] [[image:prop-ico.png | link=EM.Terrano]] </td><td> [[Imageimage:wire_pic3static-ico.png|thumb|350pxlink=EM.Ferma]] [[image:planar-ico.png |link=EM.Libera's Dielectric dialogPicasso]] [[image:po-ico.png | link=EM.Illumina]] </td></tr>
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[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''
[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''=== Moving Objects Between Groups & Modules =Product Overview==
By default, the last object group that was defined n the navigation tree is active=== EM. The current active group is always listed Libera in bold letters in the navigation tree. All the new objects are inserted under the current active group. A group can be activated by right-clicking on its entry in the navigation tree and then selecting the '''Active''' item of the contextual menu. You can move one or more selected objects to any desired PEC group. Right click on the highlighted selection and select '''Move To [[File:larrow_tn.png]] MoM3D [[File:larrow_tn.png]]''' from the contextual menu. This opens another sub-menu with a list of all the available PEC groups already defined in the [[PO Module]]. Select the desired PEC group, and all the selected objects will move to that group. The objects can be selected either in the project workspace, or their names can be selected from the Navigation Tree. In the latter case, make sure that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a PEC group's name from the contextual menu. In a similar way, you can move one or more objects from a Physical Optics PEC group to [[EM.Cube|EM.CUBE]]'s other modules. In this case, the sub-[[menus]] of the''' Move To [[File:larrow_tn.png]]''' item of the contextual menu will indicate all the [[EM.Cube|EM.CUBE]] modules that have valid groups for transfer of the select objects.Nutshell ===
== [[EM.Libera]] is a full-wave 3D Mesh Generation ==electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structures made up of metal and dielectric regions or a combination of them. It features two separate simulation engines, a Surface MoM solver and a Wire MoM solver, that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric objects in your physical structure. The Wire MoM solver can only handle metallic wireframe structures. [[EM.Libera]] selects the simulation engine automatically based on the types of objects present in your project workspace.
=== A Note on [[EM.Libera]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's Mesh Types ===integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling PEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric regions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.
{{Note|In general, [[EM.Libera features two simulation engines, Wire MoM and Surface ]] uses the surface MoMsolver to analyze your physical structure. If your project workspace contains at least one line or curve object, which require different mesh types[[EM. The Libera]] switches to the Wire MoM simulator handles only wire objects and wireframe structuressolver. These objects are discretized as elementary linear elements (filaments)}} [[Image:Info_icon. A wire is simply subdivided into smaller segments according png|30px]] Click here 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 learn more wires, junction basis functions are generated to ensure current continuityabout the theory of the '''[[Basic Principles of The Method of Moments | 3D Method of Moments]]'''.
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.
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=== Creating & Viewing the Mesh ===
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The mesh generation process in EM.Libera involves three steps:
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# Setting the mesh properties.
# Generating the mesh.
# Verifying the mesh.
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The objects of your physical structure are meshed based on a specified mesh density expressed in cells/λ<sub>0</sub>. The default mesh density is 10 cells/λ<sub>0</sub>. To view the PO mesh, click on the [[File:mesh_tool_tn.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the PO mesh is displayed in the 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.
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"Show Mesh" generates a new mesh and displays it if there is none in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating a PO mesh may take a long time depending on the complexity and size of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory and force [[EM.Cube]] to generate a mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.
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To set the PO mesh properties, click on the [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Mesh Settings... '''or right click on the '''3-D Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the value of '''Mesh Density''' to generate a triangular mesh with a higher or lower resolutions. Some additional mesh [[parameters]] can be access by clicking the {{key|Tessellation Options}} button of the dialog. In the Tessellation Options dialog, you can change '''Curvature Angle Tolerance''' expressed in degrees, which as a default value of 15°. This parameter can affect the shape of the mesh especially in the case of [[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|[[Solid Objects|solid objects]]]]]]]]]]. 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.
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<td> [[Image:PO2.png|thumb|450px|Two ellipsoids of different (PEC and dielectric) compositions.]] </td><td> [[Image:PO3Yagi Pattern.png|thumb|450px500px|Trinagular surface mesh 3D far-field radiation pattern of the two ellipsoidsexpanded Yagi-Uda antenna array with 13 directors.]] </td>
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=== Mesh EM.Libera as the MoM3D Module of Connected Objects EM.Cube ===
You can use [[Image:MOM3.png|thumb|350px|EM.Libera's Mesh Hierarchy dialog.]] All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attachedeither for simulating arbitrary 3D metallic, interconnected dielectric and composite surfaces and volumetric structures or overlapping for modeling wire objects and metallic wireframe structures. [[Solid Objects|solid objectsEM.Libera]], their internal common faces are removed and only also serves as the surface frequency-domain, full-wave '''MoM3D Module''' of the external faces is meshed'''[[EM. SimilarlyCube]]''', all the a comprehensive, integrated, modular electromagnetic modeling environment. [[Surface Objects|surface objectsEM.Libera]] belonging to shares the same PEC group are merged together visual interface, 3D parametric CAD modeler, data visualization tools, and their internal edges are removed before meshing. Note that a solid many more utilities and a surface object belonging to the same PEC group might not always be merged properlyfeatures collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.
When two objects belonging to two different material groups overlap or intersect each other, EM[[Image:Info_icon.Libera has png|30px]] Click here 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 learn more about '''Menu > Simulate < discretization < Mesh Hierarchy.[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''. 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 group.
You can connect === Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===Â The method of moments uses an open-boundary formulation of Maxwell's equations which does not require a line object to a touching surfacediscretization of the entire computational domain, but only the finite-sized objects within it. To connect lines to surfaces and allow for current continuityAs a result, you must make sure [[EM.Libera]]'s typical mesh size is typically much smaller that the box labeled that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]'s triangular surface mesh provides a more accurate representation of your physical structure than [[EM.Tempo]]'Connect Lines s staircase brick volume mesh, which often requires a fairly high mesh density to Touching Surfaces''' is checked in capture the '''Mesh Settings Dialog'''. If the end geometric details of a line lies curved surfaces. These can be serious advantages when deciding on a flat which solver to use for analyzing highly resonant structures. In that respect, [[EM.Libera]] and [[EM.Picasso]] are similar as both utilize MoM solvers and surfacemesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Cube|Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity. Â [[EM.CUBELibera]] will detect that 's Wire MoM solver can be used to simulate thin wires and create wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the connection automaticallycurrent limitations of [[EM. HoweverLibera]], this 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 not always be take long computation times due to the case if slow convergence of the iterative linear solver for such types of numerical problems. Since [[EM.Libera]] uses a surface is not flat and has curvatureintegral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. In For structures that involve multiple interconnected dielectric and metal regions such casesas planar circuits, it is highly recommended that you have to specifically instruct use either [[EM.Cube|Tempo]] or [[EM.CUBEPicasso]] to enforce the connection. An example of this case is shown in the figure belowinstead.
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<td> [[Image:MOM1.png|thumb|450px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM2Hemi current.png|thumb|450px500px|The computed surface mesh of the dielectric cylinder and PEC platecurrent distribution on a metallic dome structure excited by a plane wave source.]] </td>
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[[File:wire_pic7_tn== EM.png|260px]] [[File:wire_pic8_tn.png|260px]] [[File:wire_pic9_tn.png|260px]]Libera Features at a Glance ==
The line object at the top of a PEC sphere and the structure's mesh without and with proximity mesh connection enforced.=== Physical Structure Definition ===
== Excitation Sources ==<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>
=== Gaps Sources On Wires , Loads & Ports ===
A <ul> <li> Gap is an infinitesimally narrow discontinuity that is placed sources on the path of the current. In [[EM.Cube]]'s [[MoM3D Module]], a wires (for Wire MoM) and gap is used to define an excitation source in the form of an ideal voltage source. Gap sources can be placed only on '''Line''' long, narrow, metal strips (for Surface MoM)</li> <li> Gap arrays with amplitude distribution and '''Polyline''' objects. '''If you want to excite a curved phase progression</li> <li> Multi-port port definition for gap sources</li> <li> Short dipole sources</li> <li> Import previously generated wire antennas such mesh solution as a collection of short dipoles</li> <li> RLC lumped elements on wires and narrow strips with series-parallel combinations</li> <li> Plane wave excitation with linear and circular loop or helix with a gap source, first you have to convert the curve object into a polyline using polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM.CubeTerrano]]'s Polygonize Tool.''' The gap splits the wire into two segment or external files)</li> <li> Huygens sources imported from FDTD or other modules with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. To define a new gap source, follow these steps:arbitrary rotation and array configuration</li></ul>
* Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A gap symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.=== Mesh Generation ===
[[File:wire_pic14_tn.png]]<ul> <li> Polygonized mesh of curves and wireframe mesh of surfaces and solids for Wire MoM simulation</li> <li> User defined wire radius</li> <li> Connection of wires/lines to wireframe surfaces and solids using polymesh objects</li> <li> Surface triangular mesh of surfaces and solids for Surface MoM simulation</li> <li> Local mesh editing of polymesh objects</li></ul>
A gap source placed on one side of a polyline representing a polygonized circular loop.=== 3D Wire MoM & Surface MoM Simulations ===
=== Modeling Lumped Circuits === <ul> <li> 3D Pocklington integral equation formulation of wire structures</li> <li> 3D electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of PEC structures</li> <li> PMCHWT formulation of homogeneous dielectric objects</li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Multi-variable and multi-goal optimization of scene</li> <li> Fully parallelized Surface MoM solver using MPI</li> <li> Both Windows and Linux versions of Wire MoM simulation engine available</li></ul>
[[File:wire_pic15.png|thumb|300px|[[MoM3D Module]]'s lumped element dialog]]=== Data Generation & Visualization ===
In <ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude & phase)</li> <li> Huygens surface data generation for use in MoM3D or other [[EM.Cube]]'s [[MoM3D Module]]modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, you can define simple lumped elements in a similar manner as gap sourcesbeam width, axial ratio, side lobe levels and null parameters, etc. In fact, a lumped element is equivalent to </li> <li> Radiation pattern of an infinitesimally narrow gap that is placed in the path arbitrary array configuraition of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure </li> <li> Bi-static and model a nonmono-ideal voltage source with an internal resistance. Unlike the [[FDTD Module]]'s single-device lumped loads that connect between two adjacent nodesstatic radar cross section: 3D visualization and 2D graphs</li> <li> Port characteristics: S/Y/Z parameters, the [[MoM3D Module]]'s lumped circuit represent a seriesVSWR and Smith chart</li> <li> Touchstone-parallel combination 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 resistor, inductor and capacitor elements. This is shown in the figure below:standard outputs</li></ul>
[[File:image106== Building the Physical Structure in EM.png]]Libera ==
All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of the navigation tree. In [[File:wire_pic16_tnEM.png|thumb|200px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wireLibera]], you can create three different types of objects:
To define a new lumped element{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, follow these stepsSources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects| None|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects| None |}
* Right click 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: '''Passive RLC''' or '''Active with Gap Source'''. 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 each category to select either the positive or negative direction for the source.* In the case of a gap on a line object, learn more details about it in the box labeled '''Offset''', enter the distance [[Glossary of the source from the start point of the lineEM. 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 Cube'''Side''' of the polyline where you want to place the source. Thens Materials, in the box labeled '''Offset'''Sources, 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 50Devices Σ 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 Progression''' in degrees along all three principal axesOther Physical Object Types]].
=== Defining Ports === Both of [[EM.Libera]]'s two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and volumetric metal objects under '''PEC Objects'''. In other words, you can draw lines, polylines and other curve objects as thin wires, which have a radius parameters expressed in project units. All types of solid and surface CAD objects can be drawn in a PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.
Ports are used to order and index gap sources for S parameter calculation<table><tr><td>[[Image:wire_pic1. They are defined in the '''Observables''' section of the Navigation Treepng|thumb|350px|EM. Right click on the Libera'''Port Definition''' item of the s Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the total number of existing sources in the workspace. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. This includes both gap sources and active lumped elements (which contain gap sources). In the '''Port Association''' section of this dialog, you can go over each one of the sources and associate them with a desired port. Note that you can associate more than one source with same given port. In this case, you will have a coupled port. All the coupled sources are listed as associated with a single port. However, you cannot associate the same source with more than one port. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50Σ. The ]] </td></tr></table titled '''Port Configuration''' lists all the ports and their associated sources and port impedances.>
{{Note|In [[EMOnce 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.Cube]] When you cannot assign ports to an array draw a new CAD objectsuch as a Box or a Sphere, even if it contains sources 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 elementsname in the navigation tree and selecting the '''Activate''' item of the contextual menu. To calculate It is recommended that you first create object groups, and then draw new CAD objects under the S active object group. However, if you start a new [[parametersEM.Libera]] of an antenna arrayproject from scratch, you have to construct it using individual elementsand start drawing a new object without having previously defined any object groups, not as an array a new default PEC object group is created and added to the navigation tree to hold your new CAD object.}}
[[FileImage:port-definitionInfo_icon.png|30px]]Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.
The {{Note|In [[MoM3D ModuleEM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. From [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you can then move the imported objects to [[EM.Libera]]'s port definition dialog.}}
=== EM.Libera's Excitation Sources & Loads On Arrays Of Wire Radiators ===
If Your 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, electric surface currents on metal surface and both electric magnetic surface currents on the workspace contains an array surface of line or polyline dielectric objects, the array object will be listed as an eligible object for gap source placement. A gap The excitation source will be placed you choose depends on each element of the array. All the gap sources will have identical direction and offset. However, observables you can prescribe certain amplitude and/or phase distributionsseek in your project. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''[[EM. In Libera]] provides the last case, you need to set a value following source types for maximum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression''' in degrees along all three principal axes.exciting your physical structure:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:wire_pic12gap_src_icon.png]] | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source | style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:wire_pic13_tngap_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source| style="width:300px;" | Associated with an PEC or thin wire line or polyline, works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}
The Click on each category to learn more details about it in the [[MoM3D Module]]Glossary of EM.Cube's gap source dialog and gaps sources defined on an array of dipole wires with binomial weight distribution and 90° phase progressionMaterials, Sources, Devices & Other Physical Object Types]].
=== For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current and is used to define an ideal voltage source. Wire gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''PEC 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. Hertzian Dipole Sources ===
{{Note|If you want to excite a curved wire antenna such as a circular loop or helix with a wire gap source, first you have to convert the curve object into a polyline using [[File:wire_pic17.png|thumb|300px|The short dipole source dialogCubeCAD]]'s Polygonize Tool.}}
A short dipole provides a another simple way of exciting a 3D structure in the [[MoM3D ModuleEM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. To define You can also use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a short dipole plane wave source, follow these steps:to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.
* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source[[Image:Info_icon...''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialog, you can set the coordinate of the center of the short dipole. By default, the source is placed at the origin of the world coordinate system at (0,0,0).You can type in new coordinates or use the spin buttons png|40px]] Click here to move the dipole around.* In the learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Properties''' section, you can specify the '''Amplitude''' Arrays in Volts, the Antenna Arrays]]'''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 magnitude.
When you simulate a wire structure in the <table><tr><td> [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your projectImage:wire_pic14_tn. This is used not only to visualize the current distribution in the project workspace but also to save the current solution into an ASCII data file. This data file is called "MoM.IDI" by default and has a '''.IDI''' file extension. The current data are saved as line segments representing each of the png|thumb|left|640px|A wire cells together with the complex current at the center gap source placed on one side of each cell. In the [[MoM3D Module]], you can import the current data from an existing '''.IDI''' file to serve as a set of short dipoles for excitation. To import polyline representing a wire current solution, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Sourcepolygonized circular loop...''' from the contextual menu. This opens up the standard [[Windows]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find it, select it and click the '''Open''' button of the dialog. This will create as many short dipole sources on the [[PO Module]]'s Navigation Tree as the total number of mesh cells in the Wire MoM solution. From this point on, each of the imported dipoles behave like a regular short dipole source. You can open the property dialog of each individual source and modify its [[parameters]].</td></tr><tr></table>
=== Plane Wave Sources === <table><tr><td> [[Image:po_phys16_tn.png|thumb|left|420px|Illuminating a metallic sphere with an obliquely incident plane wave source.]] </td></tr></table>
[[File:po_phys15.png|thumb|300px|plane wave dialog]]=== Modeling Lumped Circuits ===
The wire-frame structure in the In [[MoM3D ModuleEM.Libera]] , you can be excited by an incident plane wavedefine simple lumped elements in a similar manner as gap sources. In particularfact, a plane wave lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source . The latter case can be used to compute the radar cross section of excite a wire structure or metallic target. A plane wave is defined by its propagation vector indicating the direction of incidence strip and its polarizationmodel a non-ideal voltage source with an internal resistance. [[EM.Cube|EM.CUBELibera]]'s [[MoM3D Module]] provides lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the following polarization optionsfigure below:
* TMz* TEz* Custom Linear* LCPz* RCPz[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.
The direction of incidence is defined through the θ and φ angles of the unit propagation vector in the spherical coordinate system[[Image:Info_icon. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi'''. The default values are θ = 180° and φ = 0° representing png|40px]] Click here for a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM<sub>z</sub> and TE<sub>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case discussion of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_. However, two requirements must be satisfied: '''ê 26_Nonlinear_Passive_. ê26_Active_Devices | Linear Passive Devices]]''' = 1 and '''ê à k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (θ = 180°).
To define a plane wave source follow these steps:=== Defining Ports ===
* Right click on the '''Plane Waves''' item Ports are used to order and index gap sources for S parameter calculation. They are defined in the '''SourcesObservables''' section of the Navigation Tree and select '''Insert New Sourcenavigation tree...''' The Plane wave Dialog opens up.* In the Field Definition section of the dialogBy default, you can enter as many ports as the '''Amplitude''' total number of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degreessources are created. You can also set the '''Polarization''' define any number of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selected, you also need ports equal to enter or less than the X, Y, Z components total number of the '''E-Field Vector'''sources. All port impedances are 50Ω by default.
{{Note[[Image:Info_icon.png|In the spherical coordinate system, normal plane wave incidence from the top of the domain downward corresponds 40px]] Click here to θ of 180°learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''. }}
<table><tr><td> [[FileImage:po_phys16_tnMOM7A.png|thumb|360px|Two metallic strips hosting a gap source and a lumped element.]] </td><td> [[Image:MOM7B.png|thumb|360px|The surface mesh of the two strips with a gap source and a lumped element.]]</td></tr></table>
Figure: Illuminating a metallic sphere with an obliquely incident plane wave source== EM.Libera's Simulation Data & Observables ==
== Running At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM Simulations simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}
=== Running A Wire MoM Analysis === Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]].
Depending on the types of objects present in your project workspace, [[File:wire_pic19EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s run performs either a Surface MoM simulation dialog]]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.
Once you have set up your metal structure in <table><tr><td> [[EMImage:wire_pic26_tn.Cubepng|EM.CUBE]]'s [[MoM3D Module]], have defined sources and observables and have examined the quality of the structure's wire-frame mesh, you are ready to run thumb|360px|A monopole antenna connected above a simulationPEC plate. To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Compute Toolbar''' or select Menu </td><td> [[FileImage:larrow_tnwire_pic27_tn.png]] Compute [[File:larrow_tn.png]] Run...or use the keyboard shortcut '''Ctrl+R'''. To start the simulation click the '''Run''' button |thumb|360px|Current distribution plot of this dialog. Once the Wire MoM simulation starts, a new dialog called '''Output Window''' opens up that reports monopole antenna connected above the various stages of Wire MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the Wire MoM simulation processPEC plate. A prompt announces the completion of the Wire MoM simulation. At this time, [[EM.Cube|EM.CUBE]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.</td></tr></table>
You have {{Note|Keep in mind that since [[EM.Libera]] uses MoM solvers, the choice to run a '''Fixed Frequency''' simulation, which calculated field value at the source point is the default choice, or run infinite. As a '''Frequency Sweep'''. In the former caseresult, the simulation will field sensors must be carried out placed at the '''Center Frequency''' of the project. This frequency can be changed adequate distances (at least one or few wavelengths) away from the Frequency Dialog of the project or you can click the Frequency Settings button of the Run Dialog scatterers to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, tooproduce acceptable results.}}
In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type<table><tr><td> [[Image: Adaptive''' or '''Uniform'''wire_pic32_tn. In a uniform sweep, equally spaced samples png|thumb|360px|Electric field plot of the frequency are used between the Start and End frequenciescircular loop antenna. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog]] </td><td> [[Image:wire_pic33_tn. The default '''Number png|thumb|360px|Magnetic field plot of Samples''' is 10.In the case of adaptive sweep, you have to 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 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 metcircular loop antenna.]] </td></tr></table>
You need to define a far field observable if you want to plot radiation patterns of your physical structure in [[File:wire_pic20EM.pngLibera]]. 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.
Figure[[Image: The output windowInfo_icon.png|30px]] Click here to learn more about the theory of '''[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.
=== <table><tr><td> [[Image:wire_pic38_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Theta component.]] </td><td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the circular loop antenna: Phi component.]] Setting Wire MoM Numerical Parameters === </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the circular loop antenna.]] </td></tr></table>
A Wire MoM simulation involves When the physical structure is excited by a number of numerical plane wave source, the calculated far field data indeed represent the scattered fields. [[parameters]] that normally take default values unless you change themEM. You can access these [[parametersLibera]] and change their values by clicking on calculates the '''Settings''' button next to radar cross section (RCS) of a target. Three RCS quantities are computed: the "theta;Select Engineand "phi; drop-down list in components of the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialog. In the '''Solver''' radar cross section of as well as the dialogtotal radar cross section, you can choose the type of linear solver. The current options which are '''LU''' dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and '''Bi-Conjugate Gradient (BiCG)'''σ<sub>tot</sub>. The LU solver is a direct solver and is the default option of the In addition, [[MoM3D ModuleEM.Libera]]. The BiCG solver is iterative. Once selected, you have to set a calculates two types of RCS for each structure: '''ToleranceBi-Static RCS''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for and '''Max. No. of Solver Iterations / System SizeMono-Static RCS'''. The Wire MoM simulator is based on Pocklington's integral equation method. In this methodbi-static RCS, the wires are assumed to have structure is illuminated by a very small radius. The basis functions are placed on the axis of the plane wave at incidence angles "theta;wire cylinder<sub>0</sub> and "phi;<sub>0</sub>, while and the Galerkin testing RCS is carried out on its surface to avoid the singularity of the Green's functionsmeasured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles "theta;Source Singularity<sub>0</sub> and "phi; section of the dialog<sub>0</sub>, 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 the RCS is expressed in free space wavelengths measured and its default value is plotted at the echo angles 180°-θ<sub>0.001</sub>; and &lambdaphi;<sub>0</sub>. The value It is clear that in the case of mono-static RCS, the wire radius has a direct influence on PO simulation engine runs an internal angular sweep, whereby the wire's computed reactancevalues 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.
[[File:wire_pic21To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree.png]]
{{Note| The wire MoM engine settings dialog3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined.Oftentimes, this might not be the scattering center of your physical structure.}}
=== {{Note|Computing the 3D MoM Sweep Simulations === mono-static RCS may take an enormous amount of computation time.}}
You can run <table><tr><td> [[EMImage:wire_pic51_tn.Cubepng|EM.CUBE]]'s MoM3D simulation engine in the sweep mode, whereby a parameter like frequency, plane wave angles thumb|230px|The RCS of incidence or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data file for visualization and plottingmetal plate structure: σ<sub>θ</sub>. ]] </td><td> [[EMImage:wire_pic52_tn.Cubepng|EMthumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>.CUBE]]'s </td><td> [[MoM3D Module]] currently offers three types Image:wire_pic53_tn.png|thumb|230px|The total RCS of sweepa metal plate structure:σ<sub>tot</sub>.]] </td></tr></table>
# Frequency Sweep# Angular Sweep# Parametric Sweep== 3D Mesh Generation in EM.Libera ==
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. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based === A Note on the project's center frequency and bandwidthEM. During a frequency sweep, as the projectLibera'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:Mesh Types ===
# Fix [[EM.Libera]] features two simulation engines, Wire MoM and Surface MoM, which require different mesh at the highest frequencytypes.# Fix 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 at the center frequencydensity criterion.# ReCurved wires are first converted to multi-mesh at each frequencysegment 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.
The On the other hands, [[MoM3D ModuleEM.Libera]] offers two types 's Surface MoM solver requires a triangular surface mesh of frequency sweep: adaptive or uniformsurface and solid objects. In a uniform sweep, equally spaced frequency samples are generated between The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the start and end frequenciesentire structure. In You can control the case of an adaptive sweep, you must specify cell size using the '''Maximum Number of Iterations''' as well as the '''Error'''"Mesh Density" parameter. An adaptive sweep simulation starts with a few initial frequency samplesBy default, where the Wire MoM engine mesh density is initially run. Then, the intermediary frequency samples are calculated and inserted expressed in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation terms of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a meanfree-square sensespace wavelength. The adaptive sweep simulation results are always continuous and smooth. This default mesh density is due to the fact that a rational function curve is fitted through the discrete frequency data points10 cells per wavelength. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. HoweverFor meshing surfaces, you have a mesh density of 7 cells per wavelength roughly translates to make sure that the process converges100 triangular cells per squared wavelength. OtherwiseAlternatively, you might get an entirely wrong, but still perfectly smooth, curve at can base the end definition of the simulationmesh density on "Cell Edge Length" expressed in project units.
[[FileImage:wire_pic22Info_icon.png|30px]] Click here to learn more about '''[[File:wire_pic24Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.pngCube.27s_Mesh_Generators | Working with Mesh Generator]]'''.
The [[MoM3D ModuleImage:Info_icon.png|30px]]Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera's run simulation dialog with frequency sweep selected and the frequency settings dialogTriangular Surface Mesh Generator ]]'''.
In a parametric sweep, one or more user defined <table><tr><td> [[variables]] are varied at the same time over their specified ranges. This creates 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 using [[EMImage:Mesh5.Cubepng|thumb|400px|EM.CUBE]]Libera's '''[[Variables]] Dialog'''. For a description of [[EM.Cube|EM.CUBE]] [[variables]], please refer to Mesh Settings dialog showing the [[CubeCAD|CUBECAD]] manual or the "Parametric Sweep" sections parameters of the FDTD or [[Planar Modulelinear wireframe mesh generator.]] manuals.</td></tr></table>
== Working with 3D MoM Simulation Data = The Linear Wireframe Mesh Generator ===
=== Visualizing You can analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Libera]]'s Wire Current Distributions === MoM simulator. When you structure contains at least one PEC line, polyline or any curve CAD object, [[EM.Libera]] 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.
[[File:wire_pic25.png{{Note|thumb|300px|[[MoM3D Module]]The linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's current distribution dialog]]Polygonize tool. It also discretizes surface and solid CAD objects temporarily using CubeCAD's Polymesh tool.}}
At the end of a MoM3D simulation, <table><tr><td> [[EMImage:Mesh6.Cubepng|EMthumb|200px|The geometry of an expanding helix with a circular ground.CUBE]]'s Wire MoM engine generates a number of output data files that contain all the computed simulation data</td><td> [[Image:Mesh7. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots png|thumb|200px|Wireframe mesh of current distributions in the Project Workspace. Current distributions are visualized on all helix with the wires and the magnitude and phase default mesh density of the electric currents are plotted for all the PEC objects10 cells/λ<sub>0</sub>. In order to view these currents, you must first define current sensors before running the Wire MoM simulation]] </td><td> [[Image:Mesh8. To do this, right click on png|thumb|200px|Wireframe mesh of the '''Current Distributions''' item in the '''Observables''' section helix with a mesh density of the Navigation Tree and select '''Insert New Observable25 cells/λ<sub>0</sub>...'''. 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 </td><td> [[MoM3D Module]] you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project WorkspaceImage:Mesh9. After a Wire MoM simulation is completed, new plots are added under the current distribution node png|thumb|200px|Wireframe mesh of the Navigation Tree. Separate plots are produced for the magnitude and phase helix with a mesh density 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 -50 cells/π and &pilambda;<sub>0</sub>.]] </td></tr></table>
Current distribution maps are displayed with some default settings and options. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface === Mesh of the plot'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.Connected Objects ===
[[Image:MOREAll the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the surface objects belonging to the same PEC group are merged together and their internal edges are removed before meshing.png|40px]] Click here Note that a solid and a surface object belonging to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''the same PEC group might not always be merged properly.
When two objects belonging to two different material groups overlap or intersect each other, [[File:wire_pic26_tnEM.png|400pxLibera]] 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, [[File:wire_pic27_tnEM.png|400pxLibera]]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.
Figure<table><tr><td> [[Image: A monopole antenna connected above a PEC plate and its current distribution with the default plot settingsMOM3.png|thumb|300px|EM.Libera's Mesh Hierarchy dialog.]] </td></tr></table>
<table><tr><td> [[FileImage:wire_pic28MOM1.png|thumb|360px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[FileImage:wire_pic29_tnMOM2.png|440pxthumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]]</td></tr></table>
Figure: The output plot settings dialog, and the current distribution of the monopole-plate structure with a user defined upper limit.=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===
=== Scattering Parameters 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 objects and Port Characteristics === 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 [[EM.Cube]]'s polymesh objects to accomplish this objective.
If the project structure is excited by gap sources, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) {{Note|In [[parameters]] of the selected ports, all based on the port impedances specified in the project's "Port Definition"EM. If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. The S [[parametersCube]] are written into output ASCII data files. Since these data are complex, they polymesh objects are stored regarded as '''.CPX''' files. Every file begins with a header starting with "#". The admittance (Y) already-meshed objects 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 not re-meshed again during a real data '''.DAT''' filesimulation.}}
You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', convert any surface object or '''Plot VSWR'''. In the first three cases, another sub-menu gives solid object to a list of individual port [[parameters]]. Keep in mind that in multi-port structures, each individual port parameter has its own graph. You can also see a list of all the port characteristics data files in [[EM.Cube|EM.CUBE]]polymesh using CubeCAD's data manager. To open data manager, click the '''Data ManagerPolymesh Tool''' [[File:data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You change the format of complex data plots. In general complex data can be plotted in three forms:
[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools# Magnitude and Phase# Real and Imaginary Parts# Smith ChartPolymesh_Tool | Converting Object to Polymesh]]''' in [[EM.Cube]].
Once an object is converted to a polymesh, you can place your wire at any of its nodes. In particularthat case, it may be useful to plot the S<sub>ii</sub> [[parametersEM.Libera]] on a Smith chart. To change the format of a data plot, go to the row in the '''Data Manager Dialog''' that contains a specific complex data file's name Wire MoM engine will sense the coincident nodes between line segments and click on the fourth column under the title '''Graph Type'''. The selected table cell turns into will create a dropdown list that contains the above three formats. Select the desired format and click the '''Plot''' button of the data manager dialog junction basis function to plot the data in the new formatensure current continuity.
<table><tr><td> [[Image:MOREMOM4.png|40pxthumb|360px|Geometry of a monopole wire connected to a PEC plate.]] Click here to learn more about '''</td><td> [[Data_Visualization_and_Processing#Graphing_Port_Characteristics Image:MOM5.png| Graphing Port Characteristicsthumb|360px|Placing the wire on the polymesh version of the PEC plate.]]'''.</td></tr></table>
=== Near Field Visualization =Running 3D MoM Simulations in EM.Libera ==
[[File:wire_pic30=== EM.png|thumb|300px|[[MoM3D Module]]Libera's field sensor dialog]]Simulation Modes ===
Once you have set up your structure in [[EM.Cube|EM.CUBELibera]] allows you to visualize , have defined sources and observables and have examined the near fields at a specific field sensor plane. Calculation quality of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that structure's mesh, you specify. To define are ready to run a new Field Sensor, follow these steps3D MoM simulation. [[EM.Libera]] offers five simulation modes:
* Right click on the '''Field Sensors''' item in the '''Observables''' section {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:270px;" | Simulates the Navigation Tree and select '''Insert New Observable...'''planar structure "As Is"* The '''Label''' box allows you to change | style="width:80px;" | Single run| style="width:250px;" | Runs at the sensorâs namecenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. you can also change the color of the field sensor plane using the '''Color''' buttonCube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]* Set | style="width:270px;" | Varies the '''Direction''' operating frequency of the field sensor. This is surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified by the normal vector set of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.frequency samples or adds more frequency samples in an adaptive way* By default | style="width:80px;" | None|-| style="width:120px;" | [[EMParametric_Modeling_%26_Simulation_Modes_in_EM.Cube|EM#Running_Parametric_Sweep_Simulations_in_EM.CUBECube | Parametric Sweep]] creates a field sensor plane passing through | style="width:270px;" | Varies the origin of coordinates value(0,0,0s) and coinciding with the XY plane. You can change the location of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. You can also changes these coordinates using the spin buttonsCube#Performing_Optimization_in_EM. Keep in mind that you can move a sensor plane only along Cube | Optimization]]| style="width:270px;" | Optimizes the specified direction value(s) of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the sensor plane moving along that direction in the Project Workspacecenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]* The initial size of | style="width:270px;" | Varies the sensor plane is 100 Ã 100 project units. You can change the dimensions value(s) of the sensor plane one or more project variables to any desired size. You can also set generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at 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.center frequency fc| style="width:80px;" | None|}
After closing You can set the Field Sensor simulation mode from [[EM.Libera]]'s "Simulation Run Dialog, the ". A single-frequency analysis is a new field sensor item immediately appears under single-run simulation. All the '''Observables''' section other simulation modes in the Navigation Tree and can be right clicked for additional editingabove list are considered multi-run simulations. Once If you run a Wire MoM simulation is finishedwithout having defined any observables, a total of 14 plots are added to every field sensor node in no data will be generated at the Navigation Tree. These include the magnitude and phase end of all three components of E and H fields and the total electric and magnetic field valuessimulation. Click on any of these items In multi-run simulation modes, certain parameters are varied and a color-coded intensity plot collection of it will be visualized on the Project Workspacesimulation data files are generated. A legend box appears in At the upper right corner end of the field plota sweep simulation, which you can be dragged around using graph 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 simulation results in Radians between -π and πEM. You Grid or you can change animate the view of 3D simulation data from the field plot with the available view operations such as rotating, panning, zooming, etcnavigation tree.
[[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near=== Running a Single-Field_Maps | Visualizing 3D Near Field Maps]]'''.Frequency MoM Analysis ===
In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed by one of [[File:wire_pic31_tnEM.pngLibera]]'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.
FigureTo open the Run Simulation Dialog, click the '''Run''' [[File: A circular loop antenna fed by 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 gap sourcenew dialog called '''Output Window''' opens up that reports the various stages of MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the MoM simulation process. A prompt announces the completion of the MoM simulation.
<table><tr><td> [[FileImage:wire_pic32_tnLibera L1 Fig13.png|400pxthumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] </td></tr><tr><td> [[FileImage:wire_pic33_tnMOM3D MAN10.png|400pxthumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]]</td></tr></table>
Electric and magnetic field plots of the circular loop antenna.=== Setting MoM Numerical Parameters ===
=== Visualizing 3D Radiation Patterns ===MoM simulations involve 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" dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.
[[File:wire_pic37First we discuss the Wire MoM Engine Settings dialog.png|thumb|300px|[[MoM3D Module]]In the 's radiation pattern ''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'''.
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. <table><tr><td> [[Image:MOREMOM9B.png|40px]] Click here to learn more about the theory of '''[[Computing_the_Far_Fields_%26_Radiation_Characteristicsthumb| Far Field Computations]]'''. [[Image:MORE.pngleft|40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays 480px| Using Array Factors to Model Antenna Arrays ]]''EM.Libera's Wire MoM Engine Settings dialog. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]'''.</td>[[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''.</tr> [[File:wire_pic38_tn.png|260px]] [[File:wire_pic39_tn.png|260px]] [[File:wire_pic40_tn.png|260px]]</table>
3D radiation pattern The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the circular loop antennadialog, you can choose among the three PEC formulations: (Left) Theta componentEFIE, (Center) Phi componentsMFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is α = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (RightAIM) total far fieldto speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[EM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.
=== 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. Modeling Antenna Arrays ===
In view of far field characteristics, <table><tr><td> [[EMImage:MOM9.Cubepng|thumb|left|640px|EM.CUBE]] can handle antenna arrays in two different ways. The first approach is full-wave and requires building an array of radiating elements using the Libera'''Array Tool''' and feeding individual array elements using some type of excitation. This method is very accurate and takes into account all the inter-element coupling effects. At the end of the Wire s Surface MoM simulation of the array structure, you can plot the radiation patterns and other far field characteristics of the antenna array just like any other wire-frame structure. The second approach is based on the "Array Factor" concept and ignores any inter-element coupling effects. In this approach, you can regard the structure in the project workspace as a single radiating element. A specified array factor can be calculated and multiplied by the element pattern to estimate the radiation pattern of the overall radiating array. To define an array factor, open the '''Radiation Pattern Dialog''' of the project. In the section titled '''Impose Array Factor''', you will see a default value of 1 for the '''Number of Elements''' along the three X, Y and Z directions. This implies a single radiator, which is your structure in the project workspace. There are also default zero values for the '''Element Spacing''' along the X, Y and Z directions. You should change both the number of elements and element spacing in the X, Y or Z directions to define any desired finite array lattice. For example, you can define a linear array by setting the number of elements to 1 in two directions and entering a larger value for the number of elements along the third directionEngine Settings dialog.]] </td></tr></table>
The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some [[parameters]] of interest in such structures include the '''Half Power Beam Width (HPBW)''', '''Maximum Side Lobe Level (SLL)''' and '''First Null [[Parameters]]''' such as first null level and first null beam width. You can have [[EM.Cube|EM.CUBE]] calculate all such [[parameters]] if you check the relevant boxes in the "Additional Radiation Characteristics" section of the '''Radiation Pattern Dialog'''. These quantities are saved into ASCII data files of similar names with '''.DAT''' file extensions. In particular, you can plot such data files at the end of a sweep simulation.<br />
{{Note|Defining an array factor in the radiation pattern dialog simply performs a post-processing calculation. The resulting far field obviously do not take into account any inter-element coupling effects as [[EM.Cube]] does not construct a real physical array in the project workspace.}}<hr>
{{Note[[Image:Top_icon.png|Using an array factor for far field calculation, you cannot assign non-uniform amplitude or phase distribution to the array elements30px]] '''[[EM. For this purpose, you have Libera#Product_Overview | Back to define an array object.}}the Top of the Page]]'''
[[FileImage:wire_pic47.png]] Defining a finite-sized 4-element array factor in the radiation pattern dialog. [[File:wire_pic48_tnTutorial_icon.png|400px]] [[File:wire_pic46_tn.png|400px]] Radiation pattern of a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array object. === Computing Radar Cross Section ===  [[File:wire_pic49.png|thumb|300px|[[MoM3D Module30px]]'s RCS dialog]]  When your structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) of a target. Three RCS quantities are computed: the 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°] and [0°, 360°], respectively, and the backscatter RCS is recordedEM. To calculate RCS, first you have to define an RCS observable instead of a radiation patternCube#EM. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the 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, Libera_Documentation | EM.Libera calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, the RCS needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth & 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|40pxTutorial Gateway]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]'''. <table><tr><td> [[Image:wire_pic51_tn.png|thumb|300px|The RCS of a metal plate structure: 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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