[[Image:Splash-mom.jpg|right|720px]]<strong><font color="#06569f" size="4">3D Wire MoM And Surface MoM Solvers For Simulating Free-Space Structures</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Primer Tutorial Gateway]]'''Â [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== EM.Libera in a Nutshell ===
[[EM.Libera ]] is a full-wave 3D electromagnetic simulator based on the Method of Moments (MoM) for frequency domain modeling of free-space structure simulator for modeling metallic structures made up of metal and dielectric structuresregions or a combination of them. It features two full-wave Method of Moments (MoM) separate simulation engines, one based on a Wire Surface MoM formulation solver and the other based on a Surface MoM formulation. In general, a surface Wire MoM solver is used to simulate your physical structure, which may involve metallic that work independently and dielectric objects provide different types of arbitrary shapes as well as composite structures that contain joined solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric regions. If objects in your project workspace contains at least one line or curve object, EMphysical structure.Libera then invokes its The Wire MoM solver. In that case, can only handle metallic structure can be modeled, and all wireframe structures. [[EM.Libera]] selects the surface and solid PEC simulation engine automatically based on the types of objects are meshed as wireframespresent in your project workspace.
{{Note|You can use [[EM.Libera either for modeling metallic wire objects and wireframe structures ]] offers two distinct 3D MoM simulation engines. The Wire MoM solver is based on Pocklington's integral equation. The Surface MoM solver uses a number of surface integral equation formulations of Maxwell's equations. In particular, it uses an electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) for modeling metallicPEC regions. On the other hand, the so-called Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) technique is utilized for modeling dielectric ad composite structures that do not contain lines or curvesregions. Equivalent electric and magnetic currents are assumed on the surface of the dielectric objects to formulate their assocaited interior and exterior boundary value problems.}}
=== A Overview 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. {{Note|In a 3D MoM simulationgeneral, 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 equationsEM.Libera]] and relevant boundary conditions individually. The actual currents or fields on uses 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 solver to analyze your physical structure. EM.Libera offers two distinct 3D MoM simulation engines. The first If your project workspace contains at least one is a Wire MoM solverline or curve object, 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 equationsEM.Libera]]. 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 switches to formulate the interior and exterior boundary value problemsWire MoM solver.}} [[Image:MOREInfo_icon.png|40px30px]] Click here to learn more about the theory of the '''[[3D Basic Principles of The Method of Moments]]'''. == Constructing the Physical Structure & | 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 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 Method 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>r</sub> and electric conductivity s. Note that a PEC object is the limiting cases of a lossy dielectric material when σ → ∞. To define a new Dielectric group, follow these steps: * 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</sub>) and '''Electric Conductivity''' (s).* You may also choose from a list of preloaded material types. Click the button labeled '''Material''' to open [[EM.CubeMoments]]'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.
<table>
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<td> [[Image:wire_pic2Yagi Pattern.png|thumb|350px500px|EM.Libera's PEC dialog3D far-field radiation pattern of the expanded Yagi-Uda antenna array with 13 directors.]] </td><td> [[Image:wire_pic3.png|thumb|350px|EM.Libera's Dielectric dialog.]] </td>
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=== Moving Objects Between Groups & Modules EM.Libera as the MoM3D Module of EM.Cube ===
By default, the last object group that was defined n the navigation tree is active. The current active group is always listed in bold letters in the navigation tree. All the new objects are inserted under the current active group. A group can be activated by right-clicking on its entry in the navigation tree and then selecting the '''Active''' item of the contextual menu. You can move one or more selected objects to any desired PEC group. Right click on the highlighted selection and select '''Move To use [[File:larrow_tnEM.pngLibera]] MoM3D either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. [[File:larrow_tnEM.pngLibera]]''' from also serves as the contextual menu. This opens another subfrequency-menu with a list of all the available PEC groups already defined in the [[PO Module]]. Select the desired PEC groupdomain, 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 keyboardfull-wave 's ''MoM3D Module'Shift Key''of ' 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'', a comprehensive, integrated, modular electromagnetic modeling environment. In this case, the sub-[[menusEM.Libera]] of shares the''' Move To visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[File:larrow_tn.pngBuilding Geometrical Constructions in CubeCAD | CubeCAD]]''' item with all of the contextual menu will indicate all the [[EM.Cube|EM.CUBE]] 's other computational modules that have valid groups for transfer of the select objects.
== 3D Mesh Generation ==[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.
=== A Note on Advantages & Limitations of EM.Libera's Mesh Types Surface MoM & Wire MoM Solvers ===
EM.Libera features two simulation engines, Wire MoM and Surface MoM, The method of moments uses an open-boundary formulation of Maxwell's equations which does not require different mesh types. The Wire MoM simulator handles a discretization of the entire computational domain, but only wire the finite-sized objects and wireframe structureswithin it. These objects are discretized as elementary linear elements (filaments)As a result, [[EM. A wire Libera]]'s typical mesh size is simply subdivided into typically much smaller segments according to that that of a finite-domain technique like [[EM.Tempo]]'s FDTD. In addition, [[EM.Libera]]'s triangular surface mesh provides a more accurate representation of your physical structure than [[EM.Tempo]]'s staircase brick volume mesh, which often requires a fairly high mesh density criterionto capture the geometric details of curved surfaces. Curved wires are first converted These can be serious advantages when deciding on which solver to multi-segment polylines and then subdivided further if necessaryuse for analyzing highly resonant structures. At the connection points between two or more wiresIn that respect, junction basis functions [[EM.Libera]] and [[EM.Picasso]] are generated to ensure current continuitysimilar as both utilize MoM solvers and surface mesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.
On the other hands, [[EM.Libera]]'s Surface Wire MoM solver requires a triangular surface mesh of surface can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of the current limitations of [[Solid Objects|solid objectsEM.Libera]].The mesh generating algorithm tries , however, is its inability to generate regularized triangular cells mix wire structures with almost equal surface areas across the entire structuredielectric objects. You can control If your physical structure contains one ore more wire objects, then all the cell size using PEC surface and solid CAD objects of the "Mesh Density" parameterproject workspace are reduced to wireframe models in order to perform a Wire MoM simulation. By default, Also note that Surface MoM simulation of composite structures containing conjoined metal and dielectric parts may take long computation times due to the mesh density is expressed in terms slow convergence of the free-space wavelengthiterative linear solver for such types of numerical problems. The default mesh density is 10 cells per wavelengthSince [[EM. For meshing surfaces, Libera]] uses a mesh density surface integral equation formulation of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelengthdielectric objects, it can only handle homogeneous dielectric regions. AlternativelyFor structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you can base the definition of the mesh density on "Cell Edge Length" expressed in project unitsuse either [[EM.Tempo]] or [[EM.Picasso]] instead.
=== 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]]]]]]. 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 compositions.]] </td><td> [[Image:PO3Hemi current.png|thumb|450px500px|Trinagular The computed surface mesh of the two ellipsoidscurrent distribution on a metallic dome structure excited by a plane wave source.]] </td>
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=== Mesh of Connected Objects =EM.Libera Features at a Glance ==
All the [[Solid Objects|solid objects]] belonging to the same PEC group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping [[Solid Objects|solid objects]], their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the [[Surface Objects|surface objects]] belonging to the same PEC group are merged together before meshing. However, following [[EM.Cube|EM.CUBE]]'s union rules, a solid and a surface object cannot not be "unioned" together. Therefore, their meshes will not connect even if the two objects belong to the same PEC group.=== Physical Structure Definition ===
You can connect a line object to a touching surface. To connect lines to surfaces <ul> <li> Metal wires and allow for current continuity, you must make sure that the box labeled '''Connect Lines to Touching Surfaces''' is checked curves in the '''Mesh Settings Dialog'''. If the end of a line lies on a flat surface, [[EM.Cube|EM.CUBE]] will detect that free space</li> <li> Metal surfaces and create the connection automatically. However, this may not always be the case if the surface is not flat and has curvature. In such cases, you have to specifically instruct [[EM.Cube|EM.CUBE]] to enforce the connection. An example of this case is shown solids in free space</li> <li> Homogeneous dielectric solid objects in the figure below.free space</li> <li> Import STL CAD files as native polymesh structures</li> <li> Export wireframe structures as STL CAD files</li></ul>
[[File:wire_pic7_tn.png|260px]] [[File:wire_pic8_tn.png|260px]] [[File:wire_pic9_tn.png|260px]]=== Sources, Loads & Ports ===
The line object at the top of a PEC sphere <ul> <li> Gap sources on wires (for Wire MoM) and the structure's gap sources on long, narrow, metal strips (for Surface MoM)</li> <li> Gap arrays with amplitude distribution and phase progression</li> <li> Multi-port port definition for gap sources</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh without solution as collection of short dipoles</li> <li> RLC lumped elements on wires and narrow strips with proximity mesh connection enforcedseries-parallel combinations</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[EM.Terrano]] or external files)</li> <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>
== Excitation Sources = Mesh Generation ===
=== Gaps Sources On Wires === <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 is an infinitesimally narrow discontinuity that is placed on the path of the current. In [[EM.Cube]]'s [[MoM3D Module]], a gap is used to define an excitation source in the form of an ideal voltage source. Gap sources can be placed only on '''Line''' and '''Polyline''' objects. '''If you want to excite a curved wire antennas such as a circular loop or helix with a gap source, first you have to convert the curve object into a polyline using [[EM.Cube]]'s Polygonize Tool.''' The gap splits the wire into two segment with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. To define a new gap source, follow these steps:=== 3D Wire MoM & Surface MoM Simulations ===
* Right click on the '''Gap Sources''' item in the '''Sources''' section <ul> <li> 3D Pocklington integral equation formulation of the Navigation Tree wire structures</li> <li> 3D electric field integral equation (EFIE), magnetic field integral equation (MFIE) and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.combined field integral equation (CFIE) formulation of PEC structures</li>* In the '''Source Location''' section <li> PMCHWT formulation of the dialog, you will find a list homogeneous dielectric objects</li> <li> AIM acceleration of all the line Surface MoM solver</li> <li> Uniform and polyline objects in the Project Workspace. Select the desired line or polyline object. A gap symbol is immediately placed on the selected object.fast adaptive frequency sweep</li>* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected <li> Parametric sweep with variable object. You have the option to select either the positive properties or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.parameters</li>* In the case <li> Multi-variable and multi-goal optimization 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.scene</li>* 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 <li> Fully parallelized Surface MoM solver using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, MPI</li> <li> Both Windows and its side index and offset value are adjusted automatically.Linux versions of Wire MoM simulation engine available</li>* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.</ul>
[[File:wire_pic14_tn.png]]=== Data Generation & Visualization ===
A gap source placed on one <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]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of a polyline representing a polygonized circular loopan arbitrary array configuraition of the wire structure</li> <li> Bi-static and mono-static radar cross section: 3D visualization and 2D graphs</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
=== Modeling Lumped Circuits =Building the Physical Structure in EM.Libera ==
All the objects in your project workspace are organized into object groups based on their material composition and geometry type in the "Physical Structure" section of the navigation tree. In [[File:wire_pic15EM.png|thumb|300px|[[MoM3D Module]]'s lumped element dialogLibera]], you can create three different types of objects:
In {| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[EMFile:pec_group_icon.Cubepng]]'s | style="width:150px;" | [[MoM3D ModuleGlossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, you can define simple lumped elements in a similar manner as gap sourcessurface and curve objects| None|-| style="width:30px;" | [[File:thin_group_icon. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path png]]| style="width:150px;" | [[Glossary of the current, across which OhmEM.Cube'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 Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire structure and model a nonradiators| style="width:250px;" | Curve objects| Wire MoM solver only |-ideal voltage source with an internal resistance. Unlike the | style="width:30px;" | [[FDTD ModuleFile:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's single-device lumped loads that connect between two adjacent nodesMaterials, the 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;" | [[MoM3D ModuleFile:Virt_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's lumped circuit represent a series-parallel combination of resistorMaterials, inductor and capacitor elements. This is shown in the figure belowSources, 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 |}
Click on each category to learn more details about it in the [[File:image106Glossary of EM.pngCube's Materials, Sources, Devices & Other Physical Object Types]].
Both of [[File:wire_pic16_tnEM.png|thumb|200px|Active lumped element with 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 voltage gap radius parameters expressed in project units. All types of solid and surface CAD objects can be drawn in series with an RC circuit placed on a dipole wire]]PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.
To define a new lumped element, follow these steps<table><tr><td>[[Image:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] </td></tr></table>
* Right click Once a new object group node has been created on the '''Lumped Elements''' item in navigation tree, it becomes 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 " group of the dialogproject workspace, which is always listed in bold letters.* In the '''Source Location''' section of the dialog, When you will find draw a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline new CAD object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive such as a Box or negative direction for the source.* In the case of a gap on a line objectSphere, in it is inserted under the box labeled '''Offset''', enter the distance of the source from the start point of the linecurrently active group. This value by default There is initially set to the center of the line only one 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 group that side. By default, a gap source is placed active at the center of the first side of the polyline objectany time. You Any object type can also change be made active by right clicking on its name in the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, navigation tree and its side index and offset value are adjusted automatically.* In selecting the '''Load PropertiesActivate''' section, item of 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)contextual menu. The impedance of the circuit It is calculated at the operating frequency of the project. Only the elements recommended that have been checked are taken into account. By defaultyou first create object groups, only the series resistor has a value of 50Σ and all other circuit elements are initially grayed out.* If then draw new CAD objects under the lumped element is active and contains a gap sourceobject group. However, the '''Source Properties''' section of the dialog becomes enabled. Here if you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degreesstart a new [[EM.* If the workspace contains an array of line or polyline objectsLibera]] project from scratch, the array and start drawing a new object will be listed as an eligible without having previously defined any object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical directiongroups, offset, resistance, inductance a new default PEC object group is created and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution added to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need navigation tree to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression''' in degrees along all three principal axeshold your new CAD object.
=== Defining Ports === [[Image:Info_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]]'''.
Ports are used to order and index gap sources for S parameter calculation{{Note|In [[EM. They are defined in the '''Observables''' section of the Navigation Tree. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens upCube]], showing the total number of existing sources in the workspace. By default, as many ports as the total number of sources are created. You 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 import external CAD models (which contain gap sources). In the '''Port Association''' section of this dialogsuch as STEP, 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 caseIGES, STL models, you will have a coupled portetc. All the coupled sources are listed as associated with a single port) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. HoweverFrom [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you cannot associate can then move the same source with more than one portimported objects to [[EM. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50Σ. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedancesLibera]].}}
{{Note|In [[== EM.Cube]] you cannot assign ports to an array object, even if it contains sources on its elements. To calculate the S [[parameters]] of an antenna array, you have to construct it using individual elements, not as an array object.}}Libera's Excitation Sources ==
Your 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, electric surface currents on metal surface and both electric magnetic surface currents on the surface of dielectric objects. The excitation source you choose depends on the observables you seek in your project. [[File:port-definitionEM.pngLibera]]provides the following source types for exciting your physical structure:
The {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[MoM3D ModuleFile:gap_src_icon.png]]| [[Glossary of EM.Cube's port definition dialogMaterials, 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:gap_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Gap Circuit Source |Wire Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source| style="width:300px;" | Associated with an PEC or thin wire line or polyline, works only with WMOM solver|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}
=== Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources , Devices & Loads On Arrays Of Wire Radiators === Other Physical Object Types]].
If the workspace contains an array of line For antennas and planar circuits, where you typically define one or polyline objectsmore ports, the array object will be listed as an eligible object for you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap source placement. A gap source will be Gap is an infinitesimally narrow discontinuity that is placed on each element the path of the arraycurrent and is used to define an ideal voltage source. All the Wire gap sources will have identical direction and offset. However, you can prescribe certain amplitude and/or phase distributions. The available amplitude distributions include must be placed on '''Uniform''', '''BinomialThin Wire Line''' and '''ChebyshevThin Polyline'''objects to provide excitation for the Wire MoM solver. In The gap splits the last case, you need to set wire into two lines with a value for maximum side lobe level (an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''SLLPEC Rectangle Strip''') in dBobjects to provide excitation for the Surface MoM solver. You 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 also define '''Phase Progression''' in degrees along all three principal axesbe used to host a gap source.
{{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_pic12.pngCubeCAD]] [[File:wire_pic13_tn's Polygonize Tool.png]]}}
The A short dipole provides another simple way of exciting a 3D structure in [[MoM3D ModuleEM.Libera]]'s gap . A short dipole source dialog and gaps sources defined on acts like an array infinitesimally small ideal current source. You can also use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a plane wave source to compute the radar cross section of dipole wires 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 binomial weight distribution a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and 90° phase progressionmagnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.
=== Hertzian Dipole Sources === [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''.
<table><tr><td> [[FileImage:wire_pic17wire_pic14_tn.png|thumb|300pxleft|The short dipole 640px|A wire gap source dialogplaced on one side of a polyline representing a polygonized circular loop.]]</td></tr><tr></table>
A short dipole provides a simple way of exciting a structure in the <table><tr><td> [[MoM3D Module]]Image:po_phys16_tn. A short dipole source acts like png|thumb|left|420px|Illuminating a metallic sphere with an infinitesimally small ideal current obliquely incident plane wave source. To define a short dipole source, follow these steps:]] </td></tr></table>
* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' 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 to move the dipole around.* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' of the dipole in project units.* In the '''Direction Unit Vector''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitude.=== Modeling Lumped Circuits ===
When you simulate a wire structure in the In [[MoM3D ModuleEM.Libera]], you can define simple lumped elements in a '''Current Distribution Observable''' in your projectsimilar manner as gap sources. This In fact, a lumped element is used not only equivalent to visualize the current distribution an infinitesimally narrow gap that is placed in the project workspace but also to save path of the current solution into an ASCII data file. This data file , across which Ohm's law is called "MoMenforced as a boundary condition.IDI" by default and has You can define passive RLC lumped elements or active lumped elements containing a '''.IDI''' file extensionvoltage gap source. The current data are saved as line segments representing each of the wire cells together with the complex current at the center of each cell. In the [[MoM3D Module]], you latter case can import the current data from an existing '''.IDI''' file be used to serve as a set of short dipoles for excitation. To import excite a wire current solution, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree structure or metallic strip and select '''Import Dipole Sourcemodel a non-ideal voltage source with an internal resistance...''' from the contextual menu. This opens up the standard [[WindowsEM.Libera]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find its lumped circuit represent a series-parallel combination of resistor, select it inductor and click the '''Open''' button of the dialogcapacitor elements. This will create as many short dipole sources on the [[PO Module]]'s Navigation Tree as the total number of mesh cells is shown 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]].figure below:
=== Plane Wave Sources === [[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]]'''.
[[FileImage:po_phys15Info_icon.png|thumb40px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices |300px|plane wave dialogLinear Passive Devices]]'''.
The wire-frame structure in the [[MoM3D Module]] can be excited by an incident plane wave. In particular, a plane wave source can be used to compute the radar cross section of a metallic target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:=== Defining Ports ===
* TMz* TEz* Custom Linear* LCPz* RCPzPorts are used to order and index gap sources for S parameter calculation. They are defined in the '''Observables''' section of the navigation tree. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. All port impedances are 50Ω by default.
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 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 png|40px]] Click here 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 learn more general case of custom linear polarization, besides about the incidence angles, you have to enter the components of the unit electric '''Field Vector'''[[Glossary_of_EM. However, two requirements must be satisfied: Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''ê . ê''' = 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 <table><tr><td> [[Image:MOM7A.png|thumb|360px|Two metallic strips hosting a plane wave gap source follow these stepsand 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>
* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source..== EM.Libera''' The Plane wave Dialog opens up.* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selected, you also need to enter the X, Y, Z components of the '''E-Field Vector'''.s Simulation Data & Observables ==
At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: {{Note|In the spherical coordinate systemclass="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, normal 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 wave incidence from in the top 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 domain downward corresponds to 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 &thetaGraph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px; " | Computing the bistatic and monostatic RCS of 180a 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|}
Click on each category to learn more details about it in the [[File:po_phys16_tnGlossary of EM.pngCube's Simulation Observables & Graph Types]].
Figure: Illuminating Depending on the types of objects present in your project workspace, [[EM.Libera]] performs either a metallic sphere with an obliquely incident plane wave sourceSurface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted.
== Running Wire MoM Simulations ==<table><tr><td> [[Image:wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a PEC plate.]] </td><td> [[Image:wire_pic27_tn.png|thumb|360px|Current distribution plot of the monopole antenna connected above the PEC plate.]] </td></tr></table>
=== Running A Wire {{Note|Keep in mind that since [[EM.Libera]] uses MoM Analysis === solvers, the calculated field value at the source point is infinite. As a result, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}}
<table><tr><td> [[FileImage:wire_pic19wire_pic32_tn.png|thumb|300px360px|[[MoM3D ModuleElectric field plot of the circular loop antenna.]]'s run simulation dialog</td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]]</td></tr></table>
Once You need to define a far field observable if you have set up want to plot radiation patterns of your metal physical structure in [[EM.Cube|EM.CUBELibera]]'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 a simulation. To open the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Compute Toolbar''' or select Menu [[File:larrow_tn.png]] Compute [[File:larrow_tn.png]] Run...or use the keyboard shortcut '''Ctrl+R'''. To start the simulation click the '''Run''' button of this dialog. Once the Wire MoM simulation starts, After a new dialog called '''Output Window''' opens up that reports the various stages of Wire 3D MoM simulationis finished, displays three radiation patterns plots are added to the running time and shows far field entry in the percentage of completion for certain tasks during the Wire MoM simulation processNavigation Tree. A prompt announces These are the completion of the Wire MoM simulation. At this timefar field component in Theta direction, [[EM.Cube|EM.CUBE]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near far field data, component in Phi direction and the total 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.
You have the choice [[Image:Info_icon.png|30px]] Click here to run a '''Fixed Frequency''' simulation, which is learn more about the default choice, or run a theory of '''Frequency Sweep[[Defining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''. In the former case, the simulation will be carried out at the '''Center Frequency''' of the project. This frequency can be changed from the Frequency Dialog of the project or you can click the Frequency Settings button of the Run Dialog to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, too.
In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type<table><tr><td> [[Image: Adaptive''' or '''Uniform'''wire_pic38_tn. In a uniform sweep, equally spaced samples png|thumb|230px|The 3D radiation pattern of the frequency are used between the Start and End frequenciescircular loop antenna: Theta component. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog]] </td><td> [[Image:wire_pic39_tn. png|thumb|230px|The default '''Number 3D radiation pattern of Samples''' is 10.In the case of adaptive sweep, you have to specify the '''Maximum Number of Iterations''' as well as the '''Error'''circular loop antenna: Phi component. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is run]] </td><td> [[Image:wire_pic40_tn. Then, the intermediary samples are calculated in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation png|thumb|230px|The total radiation pattern of the S parameter response over the specified frequency range. The process stops when the error criterion is metcircular loop antenna.]] </td></tr></table>
When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[FileEM.Libera]] calculates the radar cross section (RCS) of a target. Three RCS quantities are computed:wire_pic20the θ and φ components of the radar cross section as well as the total radar cross section, which are dented by σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>.pngIn addition, [[EM.Libera]]calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub>; and φ<sub>0</sub>. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ and φ are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.
Figure: The output windowTo 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.
=== Setting Wire MoM Numerical Parameters === {{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}
A Wire MoM simulation involves a number of numerical [[parameters]] that normally take default values unless you change them. You can access these [[parameters]] and change their values by clicking on {{Note|Computing the '''Settings''' button next to the "Select Engine" drop3D mono-down list in the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialog. In the '''Solver''' section of the dialog, you can choose the type of linear solver. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the [[MoM3D Module]]. The BiCG solver is iterative. Once selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''. The Wire MoM simulator is based on Pocklington's integral equation method. In this method, the wires are assumed to have a very small radius. The basis functions are placed on the axis of the "wire cylinder", while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functions. In the "Source Singularity" section of the dialog, you can specify the '''Wire Radius''' . [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] assumes static RCS may take an identical wire radius for all wires and wireframe structures. This radius is expressed in free space wavelengths and its default value is 0.001λ<sub>0</sub>. The value enormous amount of the wire radius has a direct influence on the wire's computed reactancecomputation time.}}
<table><tr><td> [[FileImage:wire_pic21wire_pic51_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]]</td></tr></table>
The wire MoM engine settings dialog== 3D Mesh Generation in EM.Libera ==
=== 3D MoM Sweep Simulations A Note on EM.Libera's Mesh Types ===
You can run [[EM.Cube|EM.CUBELibera]]'s MoM3D features two simulation engine in the sweep modeengines, whereby a parameter like frequencyWire MoM and Surface MoM, plane wave angles of incidence or a user defined variable which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is varied over simply subdivided into smaller segments according to a specified range at predetermined samplesmesh density criterion. The output data Curved wires are saved into data file for visualization first converted to multi-segment polylines and plottingthen subdivided further if necessary. [[EMAt the connection points between two or more wires, junction basis functions are generated to ensure current continuity.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types of sweep:
# Frequency Sweep# Angular Sweep# Parametric SweepOn the other hands, [[EM.Libera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.
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[[Image:Info_icon. If you select either frequency or angular sweep, the png|30px]] Click here to learn more about '''Settings''' button located next to the simulation mode drop-down list becomes enabled[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectivelyCube. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project27s_Mesh_Generators | Working with Mesh Generator]]''s center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:
# Fix mesh at the highest frequency[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation# Fix mesh at the center frequencyThe_Triangular_Surface_Mesh_Generator | EM.# Re-mesh at each frequencyLibera's Triangular Surface Mesh Generator ]]'''.
The <table><tr><td> [[MoM3D Module]] offers two types of frequency sweepImage: adaptive or uniformMesh5. In a uniform sweep, equally spaced frequency samples are generated between the start and end frequenciespng|thumb|400px|EM. In the case of an adaptive sweep, you must specify the Libera'''Maximum Number of Iterations''' as well as s Mesh Settings dialog showing the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is initially run. Then, the intermediary frequency samples are calculated and inserted in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation parameters of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a mean-square sense. The adaptive sweep simulation results are always continuous and smooth. This is due to the fact that a rational function curve is fitted through the discrete frequency data points. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. However, you have to make sure that the process converges. Otherwise, you might get an entirely wrong, but still perfectly smooth, curve at the end of the simulationlinear wireframe mesh generator.]] </td></tr></table>
[[File:wire_pic22.png]] [[File:wire_pic24.png]]=== The Linear Wireframe Mesh Generator ===
The You can analyze metallic wire structures very accurately with utmost computational efficiency using [[MoM3D ModuleEM.Libera]]'s run simulation dialog with frequency sweep selected Wire 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 frequency settings dialogspecified 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.
In a parametric sweep, one or more user defined [[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. {{Note| The user defined [[variables]] are defined linear wireframe mesh generator discretizes rounded curves temporarily using [[EM.Cube|EM.CUBE]]CubeCAD's '''[[Variables]] Dialog'''Polygonize tool. For a description of [[EM.Cube|EM.CUBE]] [[variables]], please refer to the [[It also discretizes surface and solid CAD objects temporarily using CubeCAD|CUBECAD]] manual or the "Parametric Sweep" sections of the FDTD or [[Planar Module]] manuals's Polymesh tool.}}
== Working <table><tr><td> [[Image:Mesh6.png|thumb|200px|The geometry of an expanding helix with 3D MoM Simulation Data ==a circular ground.]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the helix with the default mesh density of 10 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 25 cells/λ<sub>0</sub>.]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/λ<sub>0</sub>.]] </td></tr></table>
=== Visualizing Wire Current Distributions Mesh of Connected Objects ===
[[File:wire_pic25All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains attached, interconnected or overlapping solid objects, their internal common faces are removed and only the surface of the external faces is meshed. Similarly, all the surface objects belonging to the same PEC group are merged together and their internal edges are removed before meshing. Note that a solid and a surface object belonging to the same PEC group might not always be merged properly.png|thumb|300px|[[MoM3D Module]]'s current distribution dialog]]
At the end of a MoM3D simulationWhen two objects belonging to two different material groups overlap or intersect each other, [[EM.Cube|EM.CUBELibera]]'s Wire MoM engine generates has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a number dielectric cylinder sitting on top of output data files that contain all the computed simulation dataa PEC plate. The main output data are two object share a circular area at the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots base of current distributions in the Project Workspacecylinder. Current distributions are visualized Are the cells on all this circle metallic or do they belong to the wires and dielectric material group? Note that the magnitude and phase cells of the electric currents junction are plotted for all the PEC objectsdisplayed in a different color then those of either groups. In order to view these currentsTo address problems of this kind, [[EM.Libera]] does provide a "Material Hierarchy" table, which you must first define current sensors before running the Wire MoM simulationcan modify. To do access thistable, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New ObservableMenu > Simulate > discretization > Mesh Hierarchy...'''. The Current Distribution Dialog opens up. Accept PEC groups by default have the default settings highest priority and close reside at the dialog. A new current distribution node is added to top of the Navigation Treetable. Unlike the [[Planar Module]], in the [[MoM3D Module]] you You can define only one current distribution node in select an group from the Navigation Tree, which covers all table and change its hierarchy using the PEC object in the Project Workspace. After a Wire MoM simulation is completed, new plots are added under the current distribution node {{key|Move Up}} or {{key|Move Down}} buttons of the Navigation Treedialog. Separate plots are produced for You can also change the magnitude and phase color of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -π and πjunction cells that belong to each group.
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 of the plot's legend box. Two '''scale''' options are available<table><tr><td> [[Image: '''Linear''' and '''dB'''MOM3. 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 valuespng|thumb|300px|EM. 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 plotLibera's property Mesh Hierarchy 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.]] </td></tr></table>
<table><tr><td> [[Image:MOREMOM1.png|40pxthumb|360px|A dielectric cylinder attached to a PEC plate.]] Click here to learn more about '''</td><td> [[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps Image:MOM2.png| Visualizing 3D Current Distribution Mapsthumb|360px|The surface mesh of the dielectric cylinder and PEC plate.]]'''.</td></tr></table>
[[File:wire_pic26_tn.png|400px]] [[File:wire_pic27_tn.png|400px]]=== Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===
Figure: A monopole antenna connected above 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 plate surface objects and its current distribution with 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 default plot settingslocation 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.
{{Note|In [[File:wire_pic28EM.png|360pxCube]] [[File:wire_pic29_tn, polymesh objects are regarded as already-meshed objects and are not re-meshed again during a simulation.png|440px]]}}
Figure: The output plot settings dialog, and the current distribution of the monopole-plate structure with You can convert any surface object or solid object to a user defined upper limitpolymesh using CubeCAD's '''Polymesh Tool'''.
=== Scattering Parameters and Port Characteristics === [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool | Converting Object to Polymesh]]''' in [[EM.Cube]].
If the project structure Once an object is excited by gap sourcesconverted to a polymesh, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) [[parameters]] you can place your wire at any of the selected ports, all based on the port impedances specified in the project's "Port Definition"its nodes. If more than one port has been defined in the projectIn that case, the scattering matrix of the multiport network is calculated. The S [[parameters]] are written into output ASCII data filesEM. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with "#". The admittance (Y) and impedance (Z) [[parametersLibera]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of s Wire MoM engine will sense the structure at the first port is also computed coincident nodes between line segments and saved will create a junction basis function to a real data '''.DAT''' fileensure current continuity.
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 <table><tr><td> [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''Image:MOM4. In the first three cases, another sub-menu gives png|thumb|360px|Geometry of 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 monopole wire connected to a list of all the port characteristics data files in [[EMPEC plate.Cube|EM.CUBE]]'s data manager. To open data manager, click the '''Data Manager''' </td><td> [[FileImage:data_manager_iconMOM5.png]] button of |thumb|360px|Placing the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click wire on the '''Data Manager''' item polymesh version of the Navigation Tree and select Open Data ManagerPEC plate... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You change the format of complex data plots. In general complex data can be plotted in three forms:</td></tr></table>
# Magnitude and Phase# Real and Imaginary Parts# Smith Chart== Running 3D MoM Simulations in EM.Libera ==
In particular, it may be useful to plot the S<sub>ii</sub> [[parameters]] on a Smith chart=== EM. To change the format of a data plot, go to the row in the '''Data Manager Dialog''' that contains a specific complex data fileLibera's name and click on the fourth column under the title '''Graph Type'''. The selected table cell turns into a dropdown list that contains the above three formats. Select the desired format and click the '''Plot''' button of the data manager dialog to plot the data in the new format.Simulation Modes ===
Once you have set up your structure in [[Image:MOREEM.png|40pxLibera]] Click here , have defined sources and observables and have examined the quality of the structure's mesh, you are ready to learn more about '''run a 3D MoM simulation. [[Data_Visualization_and_Processing#Graphing_Port_Characteristics | Graphing Port CharacteristicsEM.Libera]]'''.offers five simulation modes:
{| class="wikitable"|-! scope="col"| Simulation Mode! scope= "col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers Near Field Visualization | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style= "width:80px;" | None|}
You can set the simulation mode from [[File:wire_pic30EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s field sensor dialog]]"Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.
[[EM.Cube|EM.CUBE]] allows you to visualize the near fields at === Running a specific field sensor plane. Calculation of near fields is a postSingle-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps:Frequency MoM Analysis ===
* Right click on In a single-frequency analysis, the '''Field Sensors''' item in structure of your project workspace is meshed at the '''Observables''' section center frequency of the Navigation Tree project and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensorâs name. you can also change the color of the field sensor plane using the '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified analyzed by the normal vector one of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBELibera]] creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''s two MoM solvers. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only If your project contains at least one coordinate can effectively be changed. As you increment line or decrement this coordinatecurve object, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane Wire MoM solver is 100 Ã 100 project unitsautomatically selected. You can change Otherwise, the dimensions of the sensor plane Surface MoM solver will always be used to any desired sizesimulate your numerical problem. You can also In either case, the engine type is set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation timesautomatically.
After closing To open the Field Sensor Run Simulation Dialog, the a new field sensor item immediately appears under click the '''ObservablesRun''' section in the Navigation Tree and can be right clicked for additional editing[[File:run_icon. Once a Wire MoM simulation is finished, a total png]] button of 14 plots are added to every field sensor node in the Navigation Tree'''Simulate Toolbar''' or select '''Menu > Simulate > Run. These include ..''' or use the magnitude and phase of all three components of E and H fields and the total electric and magnetic field valueskeyboard shortcut {{key|Ctrl+R}}. Click on any of these items and a color-coded intensity plot of it will be visualized on By default, the Project WorkspaceSurface MoM solver is selected as your simulation engine. A legend box appears in To start the upper right corner of the field plotsimulation, which can be dragged around using click the left mouse {{key|Run}} button. The values of the magnitude plots are normalized between 0 and 1this dialog. The legend box contains Once the minimum field value corresponding to 0 3D MoM simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of the color mapMoM simulation, maximum field value corresponding to 1 of displays the color map, running time and shows the unit percentage of completion for certain tasks during the field quantity, which is V/m for E-field and MoM simulation process. A/m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change prompt announces the view completion of the field plot with the available view operations such as rotating, panning, zooming, etcMoM simulation.
<table><tr><td> [[Image:MORELibera L1 Fig13.png|40pxthumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] Click here to learn more about '''</td></tr><tr><td> [[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps Image:MOM3D MAN10.png| Visualizing 3D Near Field Maps]]''thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]] </td></tr></table>
[[File:wire_pic31_tn.png]]=== Setting MoM Numerical Parameters ===
Figure: A circular loop antenna fed by MoM simulations involve a gap sourcenumber 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_pic32_tnFirst we discuss the Wire MoM Engine Settings dialog.png|400px]] [[File:wire_pic33_tnIn the '''Solver''' section of this dialog, you can choose the type of '''Linear Solver'''. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''.png|400px]]
Electric and magnetic field plots of the circular loop antenna.<table>=== Visualizing 3D Radiation Patterns ===<tr><td> [[FileImage:wire_pic37MOM9B.png|thumb|300pxleft|480px|[[MoM3D Module]]'s radiation pattern dialog]] Unlike the FDTD method, the method of moments does not need a far field box to perform near-to-far-field transformations. But you still need to define a far field observable if you want to plot radiation patterns in EM.Libera. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output s Wire MoM Engine Settings section allows you to change the '''Angle Increment''' for both Theta and Phi observation angles in the degrees. These [[parameters]] indeed set the resolution of far field calculations. The default values are 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree and can be right clicked for further editing. After a 3D MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.  [[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field Computations]]'''.</td>[[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Using_Array_Factors_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]]'''.</tr> [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns | Visualizing 3D Radiation Patterns]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''. [[File:wire_pic38_tn.png|260px]] [[File:wire_pic39_tn.png|260px]] [[File:wire_pic40_tn.png|260px]] 3D radiation pattern of the circular loop antenna: (Left) Theta component, (Center) Phi components, and (Right) total far field.</table>
The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the dialog, you can choose among the three PEC formulations: EFIE, MFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is α === Modeling Antenna Arrays === 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 (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[EM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.
In view of far field characteristicsFor both Wire MoM and Surface MoM solvers, you can instruct [[EM.Cube|EM.CUBELibera]] can handle antenna arrays in two different ways. The first approach is full-wave and requires building an array to write the contents of radiating elements using the MoM matrix and excitation and solutions vectors into data files with '''Array Tool.DAT1''' and feeding individual array elements using some type of excitationfile extensions. This method is very accurate and takes into account all the inter-element coupling effects. At the end of the Wire MoM simulation of the array structure, you can plot the radiation patterns and other far field characteristics of the antenna array just like any other wire-frame structure. The second approach is based on the "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 These files 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 accessed from the '''Radiation Pattern DialogInput/Output Files''' tab of the projectData Manager. In the section titled '''Impose Array Factor'''both case, you will see a default value of 1 for have the '''Number of Elements''' along option to uncheck the three X, Y and Z directionscheck box labeled "Superpose Incident plane Wave Fields". This implies a single radiator, which is option applies when your structure in the project workspaceis excited by a plane wave source. There are also default zero values for When checked, the '''Element Spacing''' along field sensors plot the X, Y total electric and Z directions. You should change both magnetic field distributions including the number of elements and element spacing in the X, Y or Z directions to define any desired finite array latticeincident field. For exampleOtherwise, you can define a linear array by setting only the number of elements to 1 in two directions scattered electric and entering a larger value for the number of elements along the third directionmagnetic field distributions are visualized.
The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some <table><tr><td> [[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 [[EMImage:MOM9.Cubepng|thumb|left|640px|EM.CUBELibera's Surface MoM Engine Settings dialog.]] 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.</td></tr></table>
{{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.}}<br />
{{Note|Using an array factor for far field calculation, you cannot assign non-uniform amplitude or phase distribution to the array elements. For this purpose, you have to define an array object.}}<hr>
[[FileImage:wire_pic47Top_icon.png|30px]]'''[[EM.Libera#Product_Overview | Back to the Top of the Page]]'''
Defining a finite-sized 4-element array factor in the radiation pattern dialog. [[FileImage:wire_pic48_tnTutorial_icon.png|400px]] [[File:wire_pic46_tn.png|400px]] Radiation pattern of a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array object. === Computing Radar Cross Section ===  [[File:wire_pic49.png|thumb|300px|[[MoM3D Module30px]]'s RCS dialog]]  When your structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) of a target. Three RCS quantities are computed: the 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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