[[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>
</tr>
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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|solid objects]]]]]]]]. It determines the apex angle of the triangular cells of the primary tessellation mesh which is generated initially before cell regularization. Lower values of the angle tolerance result in a less smooth and more pointed mesh of curved surface like a sphere.
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<td> [[Image:PO2.png|thumb|450px|Two ellipsoids of different (PEC and dielectric) compositions.]] </td><td> [[Image: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>
<table><tr><td> [[Image:MOM1.png|thumb|450px|A dielectric cylinder attached to a PEC plate.]] </td><td> [[Image:MOM2.png|thumb|450px|The surface mesh of the dielectric cylinder and PEC plate.]] </td></tr></table>=== Sources, Loads & Ports ===
<ul> <li> Gap sources on wires (for Wire MoM) and 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 solution as collection of short dipoles</li> <li> RLC lumped elements on wires and narrow strips with series-parallel combinations</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-Ray excitation capability (ray data imported from [[File:wire_pic7_tnEM.png|260px]] [[File:wire_pic8_tn.png|260px]] [[File:wire_pic9_tn.png|260pxTerrano]]or external files)</li> <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>
The line object at the top of a PEC sphere and the structure's mesh without and with proximity mesh connection enforced.=== Mesh Generation ===
== Excitation Sources ==<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>
=== Gaps Sources On Wires 3D Wire MoM & Surface MoM Simulations ===
A Gap is an infinitesimally narrow discontinuity that is placed on the path <ul> <li> 3D Pocklington integral equation formulation of the current. In [[EM.Cube]]'s [[MoM3D Module]]wire structures</li> <li> 3D electric field integral equation (EFIE), a gap is used to define an excitation source in the form magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of PEC structures</li> <li> PMCHWT formulation of an ideal voltage source. Gap sources can be placed only on '''Line''' homogeneous dielectric objects</li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and '''Polyline''' objects. '''If you want to excite a curved wire antennas such as a circular loop fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or helix with a gap source, first you have to convert the curve object into a polyline parameters</li> <li> Multi-variable and multi-goal optimization of scene</li> <li> Fully parallelized Surface MoM solver 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:MPI</li> <li> Both Windows and Linux versions of Wire MoM simulation engine available</li></ul>
* Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Gap Source Dialog opens up.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A gap symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option to select either the positive or negative direction for the source. This parameter is obviously relevant only for lumped elements of active type.* In the case of a gap on a line object, in the box labeled '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.=== Data Generation & Visualization ===
<ul> <li> Wireframe and electric and magnetic current distributions</li> <li> Near Field intensity plots (vectorial - amplitude & phase)</li> <li> Huygens surface data generation for use in MoM3D or other [[File:wire_pic14_tnEM.pngCube]]modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2D Cartesian and polar graphs</li> <li> Far field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of an arbitrary array configuraition of the wire structure</li> <li> Bi-static and mono-static radar cross section: 3D visualization and 2D graphs</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Touchstone-style S parameter text files for direct export to RF.Spice or its Device Editor</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
A gap source placed on one side of a polyline representing a polygonized circular loop== Building the Physical Structure in EM.Libera ==
=== Modeling Lumped Circuits === 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 [[EM.Libera]], you can create three different types of objects:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Restrictions|-| style="width:30px;" | [[File:wire_pic15pec_group_icon.png]]|thumbstyle="width:150px;" |[[Glossary 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, surface and curve objects| None|-| style="width:30px;" |[[MoM3D ModuleFile:thin_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's lumped element dialogMaterials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects| Surface MoM solver only |-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects| None |}
In Click on each category to learn more details about it in the [[Glossary of EM.Cube]]'s [[MoM3D Module]]Materials, you can define simple lumped elements in a similar manner as gap sources. In factSources, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path of the current, across which Ohm's law is enforced as a boundary condition. You can define passive RLC lumped elements or active lumped elements containing a voltage gap source. The latter case can be used to excite a wire structure and model a non-ideal voltage source with an internal resistance. Unlike the [[FDTD ModuleDevices & Other Physical Object Types]]'s single-device lumped loads that connect between two adjacent nodes, the [[MoM3D Module]]'s lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. This is shown in the figure below:
Both of [[File:image106EM.pngLibera]]'s two simulation engines, Wire MoM and Surface MoM, can handle metallic structures. You define wires under '''Thin Wire''' groups and surface and volumetric metal objects under '''PEC Objects'''. In other words, you can draw lines, polylines and other curve objects as thin wires, which have a radius parameters expressed in project units. All types of solid and surface CAD objects can be drawn in a PEC group. Only solid CAD objects can be drawn under '''Dielectric Objects'''.
<table><tr><td>[[FileImage:wire_pic16_tnwire_pic1.png|thumb|200px350px|Active lumped element with a voltage gap in series with an RC circuit placed on a dipole wireEM.Libera's Navigation Tree.]] </td></tr></table>
To define Once a new lumped elementobject group node has been created on the navigation tree, follow these steps:it becomes the "Active" group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active group. There is only one object group that is active at any time. Any object type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create object groups, and then draw new CAD objects under the active object group. However, if you start a new [[EM.Libera]] project from scratch, and start drawing a new object without having previously defined any object groups, a new default PEC object group is created and added to the navigation tree to hold your new CAD object.
* Right click on the '''Lumped Elements''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. The Lumped Element Dialog opens up.* In the '''Lumped Circuit Type''' select one of the two options[[Image: '''Passive RLC''' or '''Active with Gap Source'''Info_icon. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, you will find a list of all the line and polyline objects in the Project Workspace. Select the desired line or polyline object. A lumped element symbol is immediately placed on the selected object.* The box labeled '''Direction''' shows the polarity of the voltage source placed on the selected object. You have the option png|30px]] Click here to select either the positive or negative direction for the source.* In the case of a gap on a line object, in the box labeled learn more about '''Offset''', enter the distance of the source from the start point of the line. This value by default is initially set to the center of the line object.* In the case of a gap on a polyline object, first choose the '''Side''' of the polyline where you want to place the source. Then, [[Building Geometrical Constructions in the box labeled '''Offset''', enter the distance of the source from the start point of that side. By default, a gap source is placed at the center of the first side of the polyline object. You can also change the offset value using the spin buttons. If you keep pushing the spin buttons, the gap source moves from one side to the next, and its side index and offset value are adjusted automatically.* In the '''Load Properties''' section, the series and shunt resistance values Rs and Rp are specified in Ohms, the series and shunt inductance values Ls and Lp are specified in nH (nanohenry), and the series and shunt capacitance values Cs and Cp are specified in pF (picofarad). The impedance of the circuit is calculated at the operating frequency of the project. Only the elements that have been checked are taken into account. By default, only the series resistor has a value of 50Σ and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the '''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (CubeCAD#Transferring Objects Among Different Groups or in Amperes in the case of PMC traces) and the Modules | Moving Objects among Different Groups]]'''Phase''' in degrees.* If the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placement. A lumped element will be placed on each element of the array. All the lumped elements will have identical direction, offset, resistance, inductance and capacitance values. If you define an active lumped element, you can prescribe certain amplitude and/or phase distribution to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set a value for minimum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression''' in degrees along all three principal axes.
=== Defining Ports === {{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]. From [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]], you can then move the imported objects to [[EM.Libera]].}}
Ports are used to order and index gap sources for S parameter calculation== EM. They are defined in the Libera'''Observables''' section of the Navigation Tree. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the total number of existing sources in the workspace. By default, as many ports as the total number of sources are created. You can define any number of ports equal to or less than the total number of sources. This includes both gap sources and active lumped elements (which contain gap sources). In the '''Port Association''' section of this dialog, you can go over each one of the sources and associate them with a desired port. Note that you can associate more than one source with same given port. In this case, you will have a coupled port. All the coupled sources are listed as associated with a single port. However, you cannot associate the same source with more than one port. Finally, you can assign '''Port Impedance''' in Ohms. By default, all port impedances are 50Σ. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedances.s Excitation Sources ==
{{Note|In [[EM.Cube]] you cannot assign ports to an array objectYour 3D physical structure must be excited by some sort of signal source that induces electric linear currents on thin wires, even if it contains sources electric surface currents on its elementsmetal surface and both electric magnetic surface currents on the surface of dielectric objects. To calculate The excitation source you choose depends on the S observables you seek in your project. [[parametersEM.Libera]] of an antenna array, you have to construct it using individual elements, not as an array object.}}provides the following source types for exciting your physical structure:
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:portgap_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-definitionpurpose 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|}
The Click on each category to learn more details about it in the [[MoM3D Module]]Glossary of EM.Cube's port definition dialogMaterials, Sources, Devices & Other Physical Object Types]].
=== Sources & Loads On Arrays Of For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. [[EM.Libera]] provides two types of lumped sources: strip gap and wire gap. A Gap is an infinitesimally narrow discontinuity that is placed on the path of the current and is used to define an ideal voltage source. Wire Radiators === gap sources must be placed on '''Thin Wire Line''' and '''Thin Polyline''' objects to provide excitation for the Wire MoM solver. The gap splits the wire into two lines with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the Surface MoM solver. The gap splits the strip into two strips with a an infinitesimally small spacing between them, across which the ideal voltage source is connected. Only narrow rectangle strip object that have a single mesh cell across their width can be used to host a gap source.
{{Note|If the workspace contains an array of line you want to excite a curved wire antenna such as a circular loop or polyline objects, the array object will be listed as an eligible object for helix with a wire gap source placement. A gap source will be placed on each element of the array. All the gap sources will have identical direction and offset. However, first you can prescribe certain amplitude and/or phase distributions. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In have to convert the last case, you need to set curve object into a value for maximum side lobe level ('''SLL''') in dB. You can also define '''Phase Progression''polyline using [[CubeCAD]]' in degrees along all three principal axess Polygonize Tool.}}
A short dipole provides another simple way of exciting a 3D structure in [[File:wire_pic12EM.pngLibera]] . A short dipole source acts like an infinitesimally small ideal current source. You can also use an incident plane wave to excite your physical structure in [[File:wire_pic13_tnEM.pngLibera]]. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the θ and φ angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are θ = 180° and φ = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.
The [[MoM3D ModuleImage: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]]'''s gap source dialog and gaps sources defined on an array of dipole wires with binomial weight distribution and 90° phase progression.
=== Hertzian Dipole Sources === <table><tr><td> [[Image:wire_pic14_tn.png|thumb|left|640px|A wire gap source placed on one side of a polyline representing a polygonized circular loop.]] </td></tr><tr></table>
<table><tr><td> [[FileImage:wire_pic17po_phys16_tn.png|thumb|300pxleft|The short dipole 420px|Illuminating a metallic sphere with an obliquely incident plane wave source dialog.]]</td></tr></table>
A short dipole provides a simple way of exciting a structure in the [[MoM3D Module]]. A short dipole source acts like an infinitesimally small ideal current source. To define a short dipole source, follow these steps:=== Modeling Lumped Circuits ===
* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New SourceIn [[EM...''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialogLibera]], you can set the coordinate of the center of the short dipoledefine simple lumped elements in a similar manner as gap sources. By defaultIn fact, the source a lumped element is equivalent to an infinitesimally narrow gap that is placed at in the origin path of the world coordinate system at (0current,0,0)across which Ohm's law is enforced as a boundary condition.You can type in new coordinates define passive RLC lumped elements or use the spin buttons to move the dipole aroundactive lumped elements containing a voltage gap source.* In the '''Source Properties''' section, you The latter case can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' of the dipole in project unitsbe used to excite a wire structure or metallic strip and model a non-ideal voltage source with an internal resistance.* In the [[EM.Libera]]'''Direction Unit Vector''' section, you can specify the orientation s lumped circuit represent a series-parallel combination of the short dipole by setting values for the components '''uX''', '''uY'''resistor, inductor and '''uZ''' of the dipole's unit vectorcapacitor elements. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes This is shown in the vector components upon closure even if your component values do not satisfy a unit magnitude.figure below:
When you simulate a wire structure in the [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your projectImage:Info_icon. This is used not only to visualize the current distribution in the project workspace but also to save the current solution into an ASCII data file. This data file is called "MoM.IDI" by default and has a '''.IDI''' file extension. The current data are saved as line segments representing each of the wire cells together with the complex current at the center of each cell. In the [[MoM3D Modulepng|40px]], you can import the current data from an existing '''.IDI''' file Click here to serve as a set of short dipoles for excitation. To import a wire current solution, right click on learn more about '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Source...''' from the contextual menu. This opens up the standard [[WindowsPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find it, select it and click the '''Open''' button of the dialog. This will create as many short dipole sources on the [[PO Module]]'s Navigation Tree as the total number of mesh cells in the Wire MoM solution. From this point on, each of the imported dipoles behave like a regular short dipole source. You can open the property dialog of each individual source and modify its [[parameters]].
=== Plane Wave Sources === [[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_Active_Devices | Linear Passive Devices]]'''.
[[File:po_phys15.png|thumb|300px|plane wave dialog]]=== Defining Ports ===
The wire-frame structure Ports are used to order and index gap sources for S parameter calculation. They are defined in the [[MoM3D Module]] can be excited by an incident plane wave'''Observables''' section of the navigation tree. In particularBy default, a plane wave source as many ports as the total number of sources are created. You can be used define any number of ports equal to compute or less than the radar cross section total number of a metallic targetsources. A plane wave is defined All port impedances are 50Ω by its propagation vector indicating the direction of incidence and its polarizationdefault. [[EM.Cube|EM.CUBE]]'s [[MoM3D Module]] provides the following polarization options:
* TMz* TEz* Custom Linear* LCPz* RCPz[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''.
The direction of incidence is defined through the θ <table><tr><td> [[Image:MOM7A.png|thumb|360px|Two metallic strips hosting a gap source and φ angles of the unit propagation vector in the spherical coordinate systema lumped element. ]] </td><td> [[Image:MOM7B.png|thumb|360px|The values surface mesh of these angles are set in degrees in the boxes labeled '''Theta''' two strips with a gap source 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-vectorlumped element. In the TM]] <sub/td>z</subtr> and TE<sub>z</subtable> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfied: '''ê . ê''' = 1 and '''ê à k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (θ = 180°).
To define a plane wave source follow these steps:== EM.Libera's Simulation Data & Observables ==
* Right click 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 '''Plane Waves''' item in wires and wireframe structures. The primary solution of the '''Sources''' section Surface MoM simulation engine consists of the Navigation Tree electric and select '''Insert New Sourcemagnetic surface currents on the PEC and dielectric objects.[[EM.Libera]] currently offers the following types of observables: {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube''' The Plane wave Dialog opens ups Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]* In the | style="width:150px;" | Near-Field Definition section Distribution Maps| style="width:150px;" | [[Glossary of the dialog, you can enter the EM.Cube'''Amplitude''' of the incident s Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric field in V/m and its '''Phase''' in degrees. The default magnetic field Amplitude is 1 V/m with components on a zero Phasespecified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]* The direction | style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of the Plane Wave is determined by the incident '''Theta''EM.Cube' s Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and '''Phi''' angles in degreesadditional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. You can also set the '''Polarization''' | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave and choose from the five options described earliersource|-| style="width:30px;" | [[File:port_icon. When the 'png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube''Custom Linear''' option is selected, you also need to enter s Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the X, S/Y, /Z components parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of the '''Ethese source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-Field Vector''| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}
{{Note|In Click on each category to learn more details about it in the spherical coordinate system, normal plane wave incidence from the top [[Glossary of the domain downward corresponds to θ of 180EM.Cube's Simulation Observables °Graph Types]]. }}
Depending on the types of objects present in your project workspace, [[File:po_phys16_tnEM.pngLibera]]performs either a Surface MoM simulation or a Wire MoM simulation. In the former case, the electric and magnetic surface current distributions on the surface of PEC and dielectric objects can be visualized. In the latter case, the linear electric currents on all the wires and wireframe objects can be plotted.
Figure<table><tr><td> [[Image: Illuminating wire_pic26_tn.png|thumb|360px|A monopole antenna connected above a metallic sphere with an obliquely incident plane wave sourcePEC 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 Wire {{Note|Keep in mind that since [[EM.Libera]] uses MoM Simulations ==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.}}
=== Running A Wire MoM Analysis === <table><tr><td> [[Image:wire_pic32_tn.png|thumb|360px|Electric field plot of the circular loop antenna.]] </td><td> [[Image:wire_pic33_tn.png|thumb|360px|Magnetic field plot of the circular loop antenna.]] </td></tr></table>
You need to define a far field observable if you want to plot radiation patterns of your physical structure in [[File:wire_pic19EM.png|thumb|300px|[[MoM3D ModuleLibera]]'s run . After a 3D MoM simulation dialog]]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.
Once you have set up your metal structure in [[EMImage:Info_icon.Cubepng|EM.CUBE30px]]'s [[MoM3D Module]], have defined sources and observables and have examined the quality of the structure's wire-frame mesh, you are ready Click here to run a simulation. To open learn more about the Run Simulation Dialog, click the '''Run''' [[File:run_icon.png]] button theory of the '''Compute Toolbar''' or select Menu [[File:larrow_tn.pngDefining_Project_Observables_%26_Visualizing_Output_Data#Using_Array_Factor_to_Model_Antenna_Arrays | Using Array Factors to Model Antenna Arrays ]] 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, a new dialog called '''Output Window''' opens up that reports the various stages of Wire MoM simulation, displays the running time and shows the percentage of completion for certain tasks during the Wire MoM simulation process. A prompt announces the completion of the Wire MoM simulation. At this time, [[EM.Cube|EM.CUBE]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.
You have the choice to run a '''Fixed Frequency''' simulation, which is the default choice, or run a '''Frequency Sweep'''<table><tr><td> [[Image:wire_pic38_tn. In the former case, the simulation will be carried out at the '''Center Frequency''' png|thumb|230px|The 3D radiation pattern of the projectcircular loop antenna: Theta component. This frequency can be changed from the Frequency Dialog ]] </td><td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the project or you can click the Frequency Settings button circular loop antenna: Phi component.]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The total radiation pattern of the Run Dialog to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, toocircular loop antenna.]] </td></tr></table>
In case you choose Frequency Sweep, When the Frequency Settings dialog gives two options for '''Sweep Type: Adaptive''' or '''Uniform'''. In physical structure is excited by a uniform sweepplane wave source, equally spaced samples of the frequency calculated far field data indeed represent the scattered fields. [[EM.Libera]] calculates the radar cross section (RCS) of a target. Three RCS quantities are used between computed: the Start θ and End frequencies. These φ components of the radar cross section as well as the total radar cross section, which are initially set dented by the project Bandwidthσ<sub>θ</sub>, but you can change their values from the Frequency Settings dialog. The default '''Number of Samples''' is 10σ<sub>φ</sub>, and σ<sub>tot</sub>.In the case of adaptive sweepaddition, you have to specify the [[EM.Libera]] calculates two types of RCS for each structure: '''Maximum Number of IterationsBi-Static RCS''' as well as the and '''ErrorMono-Static RCS'''. An adaptive sweep simulation starts with In bi-static RCS, the structure is illuminated by a few initial frequency samplesplane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub>, where and the Wire MoM engine RCS is runmeasured and plotted at all θ and φ angles. ThenIn mono-static RCS, the intermediary samples are calculated in structure is illuminated by a progressive mannerplane 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>. At each iterationIt is clear that in the case of mono-static RCS, the frequency samples are used to calculate a rational approximation PO simulation engine runs an internal angular sweep, whereby the values of the S parameter response plane wave incidence angles θ and φ are varied over the specified frequency range. The process stops when entire intervals [0°, 180°] and [0°, 360°], respectively, and the error criterion backscatter RCS is metrecorded.
[[File:wire_pic20To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub> are added under the far field section of the navigation tree.png]]
Figure: {{Note| The output window3D 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.}}
=== Setting Wire MoM Numerical Parameters === {{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}}
A Wire MoM simulation involves a number of numerical <table><tr><td> [[parameters]] that normally take default values unless you change themImage:wire_pic51_tn. You can access these [[parameters]] and change their values by clicking on the '''Settings''' button next to the png|thumb|230px|The RCS of a metal plate structure: "sigma;Select Engine<sub>"theta; drop-down list in the '''Run Dialog'''. This opens up the Wire MoM Engine Settings Dialog. In the '''Solver''' section of the dialog, you can choose the type of linear solver. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''</sub>. 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'''td><td> [[Image:wire_pic52_tn. png|thumb|230px|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 RCS of the a metal plate structure: "sigma;wire cylinder<sub>"phi;, while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functions</sub>. In the "Source Singularity" section of the dialog, you can specify the '''Wire Radius''' . [[EM.Cube|EM.CUBE]]'s </td><td> [[MoM3D Module]] assumes an identical wire radius for all wires and wireframe structuresImage:wire_pic53_tn. This radius is expressed in free space wavelengths and its default value is 0.001png|thumb|230px|The total RCS of a metal plate structure: &lambdasigma;<sub>0tot</sub>. The value of the wire radius has a direct influence on the wire's computed reactance.]] </td></tr></table>
[[File:wire_pic21== 3D Mesh Generation in EM.png]]Libera ==
The wire MoM engine settings dialog=== A Note on EM.Libera's Mesh Types ===
=== 3D [[EM.Libera]] features two simulation engines, Wire MoM Sweep Simulations === and Surface MoM, which require different mesh types. The Wire MoM simulator handles only wire objects and wireframe structures. These objects are discretized as elementary linear elements (filaments). A wire is simply subdivided into smaller segments according to a mesh density criterion. Curved wires are first converted to multi-segment polylines and then subdivided further if necessary. At the connection points between two or more wires, junction basis functions are generated to ensure current continuity.
You can run On the other hands, [[EM.Cube|EM.CUBELibera]]'s MoM3D simulation engine in the sweep mode, whereby 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 like frequency. By default, plane wave angles of incidence or a user defined variable the mesh density is varied over a specified range at predetermined samplesexpressed in terms of the free-space wavelength. The output data are saved into data file for visualization and plottingdefault mesh density is 10 cells per wavelength. [[EMFor meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength.Cube|EM.CUBE]]'s [[MoM3D Module]] currently offers three types Alternatively, you can base the definition of sweep:the mesh density on "Cell Edge Length" expressed in project units.
[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation# Frequency Sweep# Angular Sweep# Parametric SweepWorking_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.
To run a MoM3D sweep, open the [[Image:Info_icon.png|30px]] Click here to learn more about '''Run Simulation Dialog''' and select one of the above sweep types from the '''Simulation Mode''' drop-down list in this dialog[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM. If you select either frequency or angular sweep, the Libera's Triangular Surface Mesh Generator ]]''Settings''' button located next to the simulation mode drop-down list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:
# Fix mesh at the highest frequency.<table># Fix mesh at the center frequency.<tr># Re-<td> [[Image:Mesh5.png|thumb|400px|EM.Libera's Mesh Settings dialog showing the parameters of the linear wireframe mesh at each frequencygenerator.]] </td></tr></table>
=== The [[MoM3D Module]] offers two types of frequency sweep: adaptive or uniform. In a uniform sweep, equally spaced frequency samples are generated between the start and end frequencies. In the case of an adaptive sweep, you must specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is initially run. Then, the intermediary frequency samples are calculated and inserted in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation of the scattering parameter response over the specified frequency range. The process stops when the specified error criterion is met in a mean-square sense. The adaptive sweep simulation results are always continuous and smooth. This is due to the fact that a rational function curve is fitted through the discrete frequency data points. This usually captures frequency response characteristics such as resonances with much fewer calculated data points. However, you have to make sure that the process converges. Otherwise, you might get an entirely wrong, but still perfectly smooth, curve at the end of the simulation.Linear Wireframe Mesh Generator ===
You can analyze metallic wire structures very accurately with utmost computational efficiency using [[File:wire_pic22EM.pngLibera]] 's Wire MoM simulator. When you structure contains at least one PEC line, polyline or any curve CAD object, [[File:wire_pic24EM.pngLibera]]will automatically invoke its linear wireframe mesh generator. This mesh generator subdivides straight lines and linear segments of polyline objects into or linear elements according to the specified mesh density. It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are determined by the specified mesh density. Note that polygonizing operation is temporary and solely for he purpose of mesh generation. As for surface and solid CAD objects, a wireframe mesh of these objects is created which consists of a large number of interconnected linear (wire) elements.
{{Note| The [[MoM3D Module]]linear wireframe mesh generator discretizes rounded curves temporarily using CubeCAD's run simulation dialog with frequency sweep selected Polygonize tool. It also discretizes surface and the frequency settings dialogsolid CAD objects temporarily using CubeCAD's Polymesh tool.}}
In a parametric sweep, one or more user defined <table><tr><td> [[variables]] are varied at the same time over their specified rangesImage:Mesh6. This creates png|thumb|200px|The geometry of an expanding helix with a parametric space with the total number of samples equal to the product of the number of samples for each variablecircular ground. The user defined [[variables]] are defined using </td><td> [[EMImage:Mesh7.Cubepng|EMthumb|200px|Wireframe mesh of the helix with the default mesh density of 10 cells/λ<sub>0</sub>.CUBE]]'s '''</td><td> [[Variables]] Dialog'''Image:Mesh8. For png|thumb|200px|Wireframe mesh of the helix with a description mesh density of [[EM.Cube|EM25 cells/λ<sub>0</sub>.CUBE]] </td><td> [[variables]], please refer to the [[CubeCADImage:Mesh9.png|CUBECAD]] manual or thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/"lambda;Parametric Sweep" sections of the FDTD or [[Planar Module<sub>0</sub>.]] manuals.</td></tr></table>
== Working with 3D MoM Simulation Data = Mesh of Connected Objects ===
=== Visualizing Wire Current Distributions === All the objects belonging to the same PEC or dielectric group are merged together using the Boolean union operation before meshing. If your structure contains 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.
When two objects belonging to two different material groups overlap or intersect each other, [[File:wire_pic25EM.png|thumb|300px|Libera]] has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top of a PEC plate. The two object share a circular area at the base of the cylinder. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, [[MoM3D ModuleEM.Libera]]does provide a "Material Hierarchy" table, which you can modify. To access this table, select 's current distribution ''Menu > Simulate > discretization > Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the top of the table. You can select an group from the table and change its hierarchy using the {{key|Move Up}} or {{key|Move Down}} buttons of the dialog]]. You can also change the color of junction cells that belong to each group.
At the end of a MoM3D simulation, <table><tr><td> [[EMImage:MOM3.Cubepng|thumb|300px|EM.CUBE]]Libera's Wire MoM engine generates a number of output data files that contain all the computed simulation data. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currents, you must first define current sensors before running the Wire MoM simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the Mesh Hierarchy dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[MoM3D Module]] you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire MoM simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -π and π. </td></tr></table>
Current distribution maps are displayed with some default settings and options. You can customize the individual maps (total, magnitude, phase, etc.). To do so, open the '''Output Plot Settings Dialog''' by right clicking on the specific plot entry in the Navigation Tree and selecting '''Properties...''' or by double clicking on the surface of the plot's legend box. Two '''scale''' options are available<table><tr><td> [[Image: '''Linear''' and '''dB'''MOM1. With the '''Linear''' (default) option selected, the current value is always normalized png|thumb|360px|A dielectric cylinder attached to the maximum total current in that plane, and the normalized scale is mapped between the minimum and maximum valuesa PEC plate. If the '''dB''' option is selected, the normalized current is converted to dB scale. The plot limits (bounds) can be set individually for every current distribution plot. In the '''Limits''' section of the plot's property dialog, you see four options]] </td><td> [[Image: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select the user defined option and enter new values for the '''Lower''' and '''Upper''' limitsMOM2. png|thumb|360px|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 surface mesh of the data. Three color maps are offered: '''Default''', '''Rainbow''' dielectric cylinder 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 boxPEC plate.]] </td></tr></table>
[[Image:MORE.png|40px]] Click here === Using Polymesh Objects to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''.Connect Wires to Wireframe Surfaces ===
[[File:wire_pic26_tnIf the project workspace contains a line object, the wireframe mesh generator is used to discretize your physical structure.png|400px]] From the point of view of this mesh generator, all PEC surface objects and PEC solid objects are treated as wireframe objects. If you want to model a wire radiator connected to a metal surface, you have to make sure that the resulting wireframe mesh of the surface has a node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[File:wire_pic27_tnEM.png|400pxCube]]'s polymesh objects to accomplish this objective.
Figure: A monopole antenna connected above a PEC plate {{Note|In [[EM.Cube]], polymesh objects are regarded as already-meshed objects and its current distribution with the default plot settingsare not re-meshed again during a simulation.}}
[[File:wire_pic28You can convert any surface object or solid object to a polymesh using CubeCAD's '''Polymesh Tool'''.png|360px]] [[File:wire_pic29_tn.png|440px]]
Figure[[Image: The output plot settings dialog, and the current distribution of the monopole-plate structure with a user defined upper limitInfo_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]].
=== Scattering Parameters Once an object is converted to a polymesh, you can place your wire at any of its nodes. In that case, [[EM.Libera]]'s Wire MoM engine will sense the coincident nodes between line segments and Port Characteristics === will create a junction basis function to ensure current continuity.
If the project structure is excited by gap sources, and one or more ports have been defined, the Wire MoM engine calculates the scattering (S) <table><tr><td> [[parameters]] of the selected ports, all based on the port impedances specified in the project's "Port Definition"Image:MOM4. If more than one port has been defined in the project, the scattering matrix png|thumb|360px|Geometry of the multiport network is calculateda monopole wire connected to a PEC plate. The S [[parameters]] are written into output ASCII data files. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with "#". The admittance (Y) and impedance (Z) </td><td> [[parameters]] are also calculated and saved in complex data files with '''Image:MOM5.CPX''' file extensions. The voltage standing wave ratio png|thumb|360px|Placing the wire on the polymesh version of the structure at the first port is also computed and saved to a real data '''.DAT''' filePEC plate.]] </td></tr></table>
You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item == Running 3D MoM Simulations in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]]. Keep in mind that in multi-port structures, each individual port parameter has its own graph. You can also see a list of all the port characteristics data files in [[EM.Cube|EM.CUBE]]'s data manager. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[File:larrow_tn.png]]Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You change the format of complex data plots. In general complex data can be plotted in three forms:Libera ==
# Magnitude and Phase# Real and Imaginary Parts# Smith Chart=== EM.Libera's Simulation Modes ===
In particular, it may be useful to plot the S<sub>ii</sub> Once you have set up your structure in [[parametersEM.Libera]] on a Smith chart. To change the format of a data plot, go to the row in the '''Data Manager Dialog''' that contains a specific complex data file's name have defined sources 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 observables and click have examined the '''Plot''' button quality of the data manager dialog structure's mesh, you are ready to plot the data in the new formatrun a 3D MoM simulation.[[EM.Libera]] offers five simulation modes:
{| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[Image#Running a Single-Frequency MoM Analysis| Single-Frequency Analysis]]| style="width:MORE270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube |40pxFrequency Sweep]] Click here to learn | style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more about '''frequency samples in an adaptive way| style="width:80px;" | None|-| style="width:120px;" | [[Data_Visualization_and_ProcessingParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Graphing_Port_Characteristics Running_Parametric_Sweep_Simulations_in_EM.Cube | Graphing Port CharacteristicsParametric 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|}
=== Near Field Visualization === You can set the simulation mode from [[EM.Libera]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and 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.
[[File:wire_pic30.png|thumb|300px|[[MoM3D Module]]'s field sensor dialog]]=== Running a Single-Frequency MoM Analysis ===
In a single-frequency analysis, the structure of your project workspace is meshed at the center frequency of the project and analyzed by one of [[EM.Cube|EM.CUBELibera]] allows you to visualize the near fields at a specific field sensor plane's two MoM solvers. Calculation of near fields If your project contains at least one line or curve object, the Wire MoM solver is a post-processing process and may take a considerable amount of time depending on automatically selected. Otherwise, the resolution that you specifySurface MoM solver will always be used to simulate your numerical problem. To define a new Field SensorIn either case, follow these steps:the engine type is set automatically.
* Right To open the Run Simulation Dialog, click on the '''Field SensorsRun''' item in [[File:run_icon.png]] button of the '''ObservablesSimulate Toolbar''' section of the Navigation Tree and or select '''Insert New ObservableMenu > Simulate > Run...'''* The '''Label''' box allows you to change or use the sensorâs namekeyboard shortcut {{key|Ctrl+R}}. you can also change By default, the color of Surface MoM solver is selected as your simulation engine. To start the field sensor plane using simulation, click the '''Color''' {{key|Run}} button.* Set the '''Direction''' of the field sensorthis dialog. This is specified by Once the normal vector of the sensor plane. The available options are '''X'''3D MoM simulation starts, '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube|EM.CUBE]] creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z dialog called '''Center CoordinatesOutput Window'''. You can also changes these coordinates using the spin buttons. Keep in mind opens up that you can move a sensor plane only along reports the specified direction various stages of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinateMoM simulation, you can observe displays the sensor plane moving along that direction in running time and shows the Project Workspace.* The initial size percentage of completion for certain tasks during the sensor plane is 100 Ã 100 project unitsMoM simulation process. You can change A prompt announces the dimensions completion of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation timesMoM simulation.
After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the <table><tr><td> [[Image:Libera L1 Fig13.png|thumb|left|480px|EM.Libera'''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a s Simulation Run dialog showing Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in engine as the Navigation Treesolver. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values]] </td></tr><tr><td> [[Image:MOM3D MAN10. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the png|thumb|left mouse button|480px|EM. The values of Libera's Simulation Run dialog showing Surface MoM engine as the magnitude plots are normalized between 0 and 1solver. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V]] </m for E-field and Atd></m for H-field. The values of phase plots are always shown in Radians between -π and π. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc.tr></table>
[[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near Field Maps]]'''.=== Setting MoM Numerical Parameters ===
[[File:wire_pic31_tnMoM simulations involve a number of numerical parameters that normally take default values unless you change them. You can access these parameters and change their values by clicking on the '''Settings''' button next to the "Select Engine" dropdown list in the '''Run Dialog'''. Depending on which MoM solver has been chosen for solving your problem, the corresponding Engine Settings dialog opens up.png]]
Figure: A circular loop antenna fed First we discuss the Wire MoM Engine Settings dialog. In the '''Solver''' section of this dialog, you can choose the type of '''Linear Solver'''. The current options are '''LU''' and '''Bi-Conjugate Gradient (BiCG)'''. The LU solver is a direct solver and is the default option of the Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a gap sourcenew value for '''Max. No. of Solver Iterations / System Size'''.
[[File:wire_pic32_tn.png|400px]] [[File:wire_pic33_tn.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]]</table>
3D radiation pattern The Surface MoM Engine Settings dialog is bit more extensive and provides more options. In the "Integral Equation" section of the circular loop antennadialog, you can choose among the three PEC formulations: (Left) Theta componentEFIE, (Center) Phi componentsMFIE and CFIE. The EFIE formulation is the default option. In the case of the CFIE formulation, you can set a value for the "Alpha" parameter, which determines the weights for the EFIE and MFIE terms of the combine field formulation. The default value of this parameter is α = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (RightAIM) total far fieldto speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05λ<sub>0</sub>. [[EM.Libera]]'s Surface MoM solver has been highly parallelized using MPI framework. When you install [[EM.Cube]] on your computer, the installer program also installs the Windows MPI package on your computer. If you are using a multicore CPU, taking advantage of the MPI-parallelized solver can speed up your simulations significantly. In the "MPI Settings" of the dialog, you can set the "Number of CPU's Used", which has a default value of 4 cores.
=== For both Wire MoM and Surface MoM solvers, you can instruct [[EM.Libera]] to write the contents of the MoM matrix and excitation and solutions vectors into data files with '''.DAT1''' file extensions. These files can be accessed from the '''Input/Output Files''' tab of the Data Manager. In both case, you have the option to uncheck the check box labeled "Superpose Incident plane Wave Fields". This option applies when your structure is excited by a plane wave source. When checked, the field sensors plot the total electric and magnetic field distributions including the incident field. Otherwise, only the scattered electric and magnetic field distributions are visualized. Modeling Antenna Arrays ===
In view of far field characteristics, <table><tr><td> [[EMImage:MOM9.Cubepng|thumb|left|640px|EM.CUBE]] can handle antenna arrays in two different ways. The first approach is full-wave and requires building an array of radiating elements using the Libera'''Array Tool''' and feeding individual array elements using some type of excitation. This method is very accurate and takes into account all the inter-element coupling effects. At the end of the Wire s Surface MoM simulation of the array structure, you can plot the radiation patterns and other far field characteristics of the antenna array just like any other wire-frame structure. The second approach is based on the "Array Factor" concept and ignores any inter-element coupling effects. In this approach, you can regard the structure in the project workspace as a single radiating element. A specified array factor can be calculated and multiplied by the element pattern to estimate the radiation pattern of the overall radiating array. To define an array factor, open the '''Radiation Pattern Dialog''' of the project. In the section titled '''Impose Array Factor''', you will see a default value of 1 for the '''Number of Elements''' along the three X, Y and Z directions. This implies a single radiator, which is your structure in the project workspace. There are also default zero values for the '''Element Spacing''' along the X, Y and Z directions. You should change both the number of elements and element spacing in the X, Y or Z directions to define any desired finite array lattice. For example, you can define a linear array by setting the number of elements to 1 in two directions and entering a larger value for the number of elements along the third directionEngine Settings dialog.]] </td></tr></table>
The radiation patterns of antenna arrays usually have a main beam and several side lobes. Some [[parameters]] of interest in such structures include the '''Half Power Beam Width (HPBW)''', '''Maximum Side Lobe Level (SLL)''' and '''First Null [[Parameters]]''' such as first null level and first null beam width. You can have [[EM.Cube|EM.CUBE]] calculate all such [[parameters]] if you check the relevant boxes in the "Additional Radiation Characteristics" section of the '''Radiation Pattern Dialog'''. These quantities are saved into ASCII data files of similar names with '''.DAT''' file extensions. In particular, you can plot such data files at the end of a sweep simulation.<br />
{{Note|Defining an array factor in the radiation pattern dialog simply performs a post-processing calculation. The resulting far field obviously do not take into account any inter-element coupling effects as [[EM.Cube]] does not construct a real physical array in the project workspace.}}<hr>
{{Note[[Image:Top_icon.png|Using an array factor for far field calculation, you cannot assign non-uniform amplitude or phase distribution to the array elements30px]] '''[[EM. For this purpose, you have Libera#Product_Overview | Back to define an array object.}}the Top of the Page]]'''
[[FileImage:wire_pic47.png]] Defining a finite-sized 4-element array factor in the radiation pattern dialog. [[File:wire_pic48_tnTutorial_icon.png|400px]] [[File:wire_pic46_tn.png|400px]] Radiation pattern of a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array object. === Computing Radar Cross Section ===  [[File:wire_pic49.png|thumb|300px|[[MoM3D Module30px]]'s RCS dialog]]  When your structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.Libera can calculate the radar cross section (RCS) of a target. Three RCS quantities are computed: the φ and θ components of the radar cross section as well as the total radar cross section: σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. In addition, EM.Libera calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub> and the RCS is measured and plotted at all θ and φ angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles θ<sub>0</sub> and φ<sub>0</sub> and the RCS is measured and plotted at the echo angles 180°-θ<sub>0</sub> and φ<sub>0</sub>.It is clear that in the case of mono-static RCS, the Wire MoM simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles θ<sub>0</sub> and φ<sub>0</sub> are varied over the intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recordedEM. To calculate RCS, first you have to define an RCS observable instead of a radiation patternCube#EM. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the θ and φ angles are incremented by 5 degrees. At the end of a Wire MoM simulation, besides calculating the RCS data over the entire (spherical) 3-D space, a number of 2-D RCS graphs are also generated. These are RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant φ-cut. This latter cut is at φ=45° by default. You can assign another phi angle in degrees in the box labeled '''Non-Principal Phi Plane'''. At the end of a Wire MoM simulation, the thee RCS plots σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>are added under the far field section of the navigation tree. The 2D RCS graphs can be plotted from the data manager exactly in the same way that you plot 2D radiation pattern graphs. A total of eight 2D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, Libera_Documentation | EM.Libera calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, the RCS needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the '''Radar Cross Section Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith. {{Note|Computing the 3D mono-static RCS may take an enormous amount of computation time.}} [[Image:MORE.png|40pxTutorial Gateway]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]'''. [[Image:MORE.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]'''. <table><tr><td> [[Image:wire_pic51_tn.png|thumb|300px|The RCS of a metal plate structure: σ<sub>θ</sub>.]] </td><td> [[Image:wire_pic52_tn.png|thumb|300px|The RCS of a metal plate structure: σ<sub>φ</sub>.]] </td><td> [[Image:wire_pic53_tn.png|thumb|300px|The total RCS of a metal plate structure: σ<sub>tot</sub>.]] </td></tr></table>
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