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The Method of Moments ([[Image:Splash-mom.jpg|right|720px]]<strong><font color="#06569f" size="4">3D Wire MoM) is a rigorous, fullAnd Surface MoM Solvers For Simulating Free-wave, numerical technique for solving open boundary electromagnetic problemsSpace 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=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. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resourcesCube#EM. The method of moments is an integral equation technique; it solves the integral form of Maxwell’s equations as opposed to their differential forms used in the finite element or finite difference time domain methodsLibera_Documentation | EM.Libera Tutorial Gateway]]'''

In a 3D MoM simulation, the currents or fields on the surface of a structure are the unknowns of the problem[[Image:Back_icon. The given structure is immersed in the free space. These 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 Maxwellpng|30px]] 's equations and relevant boundary conditions individually''[[EM. The actual currents or fields on the surface of the given structure (the solution of the problem) are expressed as a superposition of these elementary currents or fields with initially unknown amplitudes. Through the MoM solution, you find these unknown amplitudes, from which you can then calculate the currents or fields everywhere in the structureCube | Back to EM.Cube Main Page]]'''==Product Overview==

=== EM.Cube’s MoM3D module offers two distinct 3D MoM simulation engine. The first one is Libera in a Wire MoM solver that can be used to simulate wireframe models of metallic structures. This solver 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. In the case of solid dielectric objects, equivalent electric and magnetic currents are assumed on the surface of the dielectric object to formulate the interior and exterior boundary value problems.Nutshell ===

= A [[EM.Libera]] is a full-wave 3D electromagnetic simulator based on the Method Of of Moments Primer =(MoM) for frequency domain modeling of free-space structures made up of metal and dielectric regions or a combination of them. It features two separate simulation engines, a Surface MoM solver and a Wire MoM solver, that work independently and provide different types of solutions to your numerical problem. The Surface MoM solver utilizes a surface integration equation formulation of the metal and dielectric objects in your physical structure. The Wire MoM solver can only handle metallic wireframe structures. [[EM.Libera]] selects the simulation engine automatically based on the types of objects present in your project workspace.

The Green’s functions are the analytical solutions of boundary value problems when they are excited by an elementary source. This is usually an infinitesimally small vectorial point source. {{Note|In order for general, [[EM.Libera]] uses the Green’s functions surface MoM solver to be computationally useful, they must have analytical closed formsanalyze your physical structure. This can be a mathematical expression If your project workspace contains at least one line or a more complex recursive processcurve object, [[EM. It is no surprise that only very few electromagnetic boundary value problems have closed-form Green’s functionsLibera]] switches to the Wire MoM solver. The total electric (}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of the '''E[[Basic Principles of The Method of Moments | 3D Method of Moments]]''') field can be expressed in terms of the electric current in the following way:.

<table><tr><td>[[Image:/files/images/PMOM1(1)Yagi Pattern.png|thumb|500px|3D far-field radiation pattern of the expanded Yagi-Uda antenna array with 13 directors.]]</td></tr></table>

where is the dyadic Green’s functions for electric fields due to electric current sources and '''Eⁱ''' is the incident or impressed electric field=== EM. The incident or impressed field provides Libera as the excitation MoM3D Module of the structureEM. It may come from an incident plane wave or a gap source on a line, etc. The simplest background structure is the unbounded free space, which is represented by the following Green’s function:Cube ===

You can use [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/anEM.Libera]] either for simulating arbitrary 3D metallic, dielectric and composite surfaces and volumetric structures or for modeling wire objects and metallic wireframe structures. [[EM.Libera]] also serves as the frequency-overviewdomain, full-wave '''MoM3D Module''' of-3-d-method-'''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Libera]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of-moments/free-space-greens-function/03_freespace_tn[[EM.gifCube]]'s other computational modules.

where [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/free-space-greens-function/i_tnInfo_icon.gifpng|30px]] is the unit dyad, Click here to learn more about '''[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/free-space-greens-function/delta_tnGetting_Started_with_EM.gifCube | EM.Cube Modeling Environment]] is the gradient operator, '''r''' and '''r'''' are the position vectors of the observation and source points, respectively, and k₀ is the free-space propagation constant. This implies that electromagnetic waves propagate in free space in a spherical form away from the source. Note that the Green’s function has a singularity at the source, i.e. when '''r''' = '''r''''. This singularity must be removed when solving the integral equations.

== 3D Integral Equations = Advantages & Limitations of EM.Libera's Surface MoM & Wire MoM Solvers ===

In the more general The method of moments uses an open-boundary formulation of the field integration Maxwell's equationswhich does not require a discretization of the entire computational domain, both electric and magnetic currents are includedbut only the finite-sized objects within it. In As a result, [[EM.Libera]]'s typical mesh size is typically much smaller that casethat 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 to capture the total electric geometric details of curved surfaces. These can be serious advantages when deciding on which solver to use for analyzing highly resonant structures. In that respect, [[EM.Libera]] and magnetic fields [[EM.Picasso]] are given by the following equations:similar as both utilize MoM solvers and surface mesh generators. Whereas [[EM.Picasso]] is optimized for modeling multilayer planar structures, [[EM.Libera]] can handle arbitrarily complex 3D structures with high geometrical fidelity.

[[Image:/files/images/manuals/emagware/emcube/modules/planar/a-25-d-methodEM.Libera]]'s Wire MoM solver can be used to simulate thin wires and wireframe structures very fast and accurately. This is particularly useful for modeling wire-type antennas and arrays. One of-moments-primer/multilayer-greens-functions/image001_tnthe current limitations of [[EM.gifLibera]], however, is its inability to mix wire structures with dielectric objects. If your physical structure contains one ore more wire objects, then all the PEC surface and solid CAD objects of the project workspace are reduced to wireframe models in order to perform a Wire MoM simulation. Also note that Surface MoM simulation of composite structures containing conjoined metal and dielectric parts may take long computation times due to the slow convergence of the iterative linear solver for such types of numerical problems. Since [[EM.Libera]] uses a surface integral equation formulation of dielectric objects, it can only handle homogeneous dielectric regions. For structures that involve multiple interconnected dielectric and metal regions such as planar circuits, it is highly recommended that you use either [[EM.Tempo]] or [[EM.Picasso]] instead.

The above coupled equations involve four types of dyadic Green's functions that represent the electric and magnetic field radiated by an electric or a magnetic <table><tr><td>[[Image:Hemi current. png|thumb|500px|The incident or impressed electric and magnetic fields Ei and Hi exist independently of the given structures and are related to each other depending computed surface current distribution on the type of excitation a metallic dome structure excited by a plane wave source. ]] </td></tr></table>

Enforcing the boundary conditions on the integral definitions of the '''E''' and '''H''' fields results in == EM.Libera Features at a system of integral equations as follows:Glance ==

where [[Image:<ul> <li> Metal wires and curves in free space</filesli> <li> Metal surfaces and solids in free space</imagesli> <li> Homogeneous dielectric solid objects in free space</manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/3-d-integral-equations/05_3d-integrals_tn.gif]] is the boundary value operator for the electric field and [[Image:li> <li> Import STL CAD files as native polymesh structures</li> <li> Export wireframe structures as STL CAD files</imagesli></manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/3-d-integral-equations/05_3d-integrals_tn.gif]] is the boundary value operator for the magnetic field. For example, they may require that the tangential components the '''E'''field vanish on perfect electric conductors. Or they may require that the tangential components the '''E''' and '''H''' fields be continuous across an aperture in a perfect ground plane. Given the fact that the dyadic Green’s functions and the incident or impressed fields are all known, one can solve the above system of integral equations to find the unknown currents '''J''' and '''M'''. Therefore, through these relationships you can easily cast the above integral equations in terms of unknown '''E''' and '''H''' fields.ul>

== Galerkin Testing = Sources, Loads &amp; Ports ===

The integral equation derived in the previous section can be solved numerically by discretizing the computational domain using a proper meshing scheme. The original functional equation is reduced to a set of discretized linear algebraic equations over elementary cells. The unknown quantities are found by solving this system of linear equations<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 many other parameters can be computed thereafter. This method of numerical phase progression</li> <li> Multi-port port definition for gap sources</li> <li> Short dipole sources</li> <li> Import previously generated wire mesh solution of integral equations is known as the Method collection of Moments 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 (MoMray data imported from [[EM.Terrano]] or external files). In this method, the unknown electric current is represented by an expansion of basis functions as follows:</li> <li> Huygens sources imported from FDTD or other modules with arbitrary rotation and array configuration</li></ul>

where [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-<ul> <li> Polygonized mesh of-3-d-method-curves and wireframe mesh of-momentssurfaces and solids for Wire MoM simulation</numerical-solution-li> <li> User defined wire radius</li> <li> Connection of-3-d-integral-equationswires/08_numerical-solution_tn.gif]] are the generalized vector basis functions for the expansion of electric currents, lines to wireframe surfaces and [[Image:solids using polymesh objects</files/images/manuals/emagware/emcube/modules/mom3d/an-overview-li> <li> Surface triangular mesh of-3-d-method-of-momentssurfaces and solids for Surface MoM simulation</numerical-solution-li> <li> Local mesh editing of-3-d-integral-equationspolymesh objects</09_numerical-solution_tn.gif]] are the unknown complex amplitudes of these basis functions, which have to be determined. Substituting these expansions yields the following discretized integral equation:li></ul>

In order to solve the above <ul> <li> 3D Pocklington integral equationformulation of wire structures</li> <li> 3D electric field integral equation (EFIE), the method magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulation of moments uses Galerkin's technique to turn it into a set PEC structures</li> <li> PMCHWT formulation of linear algebraic equations. This is accomplished by testing the above equations homogeneous dielectric objects</li> <li> AIM acceleration of Surface MoM solver</li> <li> Uniform and fast adaptive frequency sweep</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Multi-variable and multi-goal optimization of scene</li> <li> Fully parallelized Surface MoM solver using the basis functions, leading to the following linear system:MPI</li> <li> Both Windows and Linux versions of Wire MoM simulation engine available</li></ul>

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/numerical-solution-of-3-d-integral-equations/12_numerical-solution_tn== Building the Physical Structure in EM.gif]]Libera ==

All the objects in your project workspace are organized into object groups based on their material composition andgeometry 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;" | [[ImageFile:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-pec_group_icon.png]]| style="width:150px;" | [[Glossary ofEM.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|-3-d-method-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary ofEM.Cube's Materials, Sources, Devices & Other Physical Object Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Curve objects| Wire MoM solver only |-moments/numerical-solution-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary ofEM.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 |-3-d-integral-equations/13_numerical-solution_tn| style="width:30px;" | [[File:Virt_group_icon.gifpng]]| 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 |}

Using a rooftop expansion of the currents Click on the wires, we can discretize the Pocklington integral equation. In order each category to convert learn more details about it in the discretized integral equation into a system [[Glossary of linear system of algebraic equations, we use Galerkin’s testing process, in which the testing functions are chosen to be identical to the expansion basis functionsEM. HoweverCube's Materials, to avoid the source singularity at r=r’Sources, the expansion functions are placed at the center of the wires, while the test functions are evaluated on the surface of the wires, assuming a finite non-zero radius for all wiresDevices & Other Physical Object Types]]. The solution vector [I] is then found as:

Both of [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/galerkin-testing-and-mom-solution/24_galerkin_tnEM.gifLibera]]'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'''.

where <table><tr><td>[Z]-1 is the inverse of the impedance matrix and [V] is the excitation vectorImage:wire_pic1.png|thumb|350px|EM.Libera's Navigation Tree.]] </td></tr></table>

Wire structures are made of linear PEC elements[[Image:Info_icon. These may consist of actual physical wires such as a dipole png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or loop antenna or a wireframe representation of a surface or solid objectModules | Moving Objects among Different Groups]]'''. In a wire structure, the unknown electric currents are one-dimensional. The integral equation is derived by forcing the tangential component of the electric field to vanish on the surface of the wire. This leads to the following simpler integral equation:

{{Note|In [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/14_pocklingtons_tnEM.gifCube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/14_pocklingtonsBuilding_Geometrical_Constructions_in_CubeCAD | CubeCAD]].gifFrom [[Building_Geometrical_Constructions_in_CubeCAD |files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/14_pocklingtonsCubeCAD]], you can then move the imported objects to [[EM.gifLibera]].}}

where [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons_tn== EM.gif]][[files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons.gif|files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons.gif]] is the free space Green’s function, I(l) is the unknown linear current in the wire and C is the contour of the wire. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/16_pocklingtons_tn.gif]][[files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/16_pocklingtons.gif|files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/16_pocklingtons.gif]] and [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/17_pocklingtons_tn.gif]][[files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/17_pocklingtons.gif|files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/17_pocklingtons.gif]] are the unit vectors along the wire contour. Note that [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons_tn.gif]][[files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons.gif|files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/pocklingtons-integral-equation-for-wire-structures/15_pocklingtons.gif]] has a singularity when r Libera's Excitation Sources == r’, which must be either removed or avoided as will be explained later.

The right choice {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of the basis functions that are used to represent the elementary currents is very importantEM. It will determine the accuracy and computational efficiency Cube's Materials, Sources, Devices & Other Physical Object Types#Strip Gap Circuit Source |Strip Gap Circuit Source]]| style="width:300px;" | General-purpose point voltage source | style="width:300px;" | Associated with a PEC rectangle strip, works only with SMOM solver|-| style="width:30px;" | [[File:gap_src_icon.png]]| [[Glossary of the resulting numerical solutionEM. Rooftop basis functions are one 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 the more popular types 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 basis functions used in a variety of MoM formulationsEM. The simplest rooftop function is the oneCube'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-dimensional triangular functions defined as in the figure belowalone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

Click on each category to learn more details about it in the [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-Glossary of-3-d-method-of-moments/meshing-and-discretization-of-wire-structures/18_meshing_tnEM.gifCube's Materials, Sources, Devices & Other Physical Object Types]].

This function provides a linear interpolation of the unknown currents or fields in For antennas and planar circuits, where you typically define one dimensionor more ports, you usually use lumped sources. Note that the function vanishes at it [[EM.Libera]] provides two endstypes of lumped sources: strip gap and wire gap. This A Gap is a desirable feature for basis functions an infinitesimally narrow discontinuity that represent electric currents is placed on metallic wires as the path of the current and is used to define an ideal voltage source. Wire gap sources must vanish at 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 ends of lines with a wirean infinitesimally small spacing between them, across which the ideal voltage source is connected. The total current Strip gap sources must be placed on long, narrow, '''PEC Rectangle Strip''' objects to provide excitation for the wire 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 approximated in a linear fashion by used to host a set of one-dimensional rooftop functions as shown in the figure below:gap source.

{{Note|If you want to excite a curved wire antenna such as a circular loop or helix with a wire gap source, first you have to convert the curve object into a polyline using [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/meshing-and-discretization-of-wire-structures/19_meshing_tn.gifCubeCAD]]'s Polygonize Tool.}}

This A short dipole provides another simple way of exciting a 3D structure in [[EM.Libera]]. A short dipole source acts like an infinitesimally small ideal current source. You can be written asalso use an incident plane wave to excite your physical structure in [[EM.Libera]]. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are &theta; = 180° and &phi; = 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.

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/meshing-and-discretization-of-wire-structures/20_meshing_tnInfo_icon.gifpng|40px]]Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays]]'''.

where l is the length coordinate along the wire with l=0 at its start point. <table><tr><td> [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/an-overview-wire_pic14_tn.png|thumb|left|640px|A wire gap source placed on one side of-3-d-method-of-moments/meshing-and-discretization-of-wire-structures/21_meshing_tna polyline representing a polygonized circular loop.gif]] is the scaled and translated version of the linear basis function f(l) shown in the previous figure. [[Image:</filestd></imagestr><tr></manuals/emagware/emcube/modules/mom3d/an-overview-of-3-d-method-of-moments/meshing-and-discretization-of-wire-structures/22_meshing_tn.gif]] is the unit vector along wire.table>

== Defining Groups Of PEC Objects = Modeling Lumped Circuits ===

In [[EM.Cube's MoM3D Module features two different simulation engines: Wire MoM and Surface MoM. Both simulation engines Libera]], you can handle metallic structures. The Wire MoM engine models metallic objects define simple lumped elements in a similar manner as wireframe structures, while the Surface MoM engine treats them as perfect electric conductor (PEC) surfacesgap sources. The PEC objects can be linesIn fact, curves, surfaces or solids. All the PEC objects are created under the '''PEC''' node a lumped element is equivalent to an infinitesimally narrow gap that is placed in the '''Physical Structure''' section path of the Navigation Tree. Objects are grouped together by their colorcurrent, across which Ohm's law is enforced as a boundary condition. You can insert different PEC groups with different colorsdefine passive RLC lumped elements or active lumped elements containing a voltage gap source. A new PEC group The latter case can be defined by simply right clicking on the '''PEC''' item in the Navigation Tree used to excite a wire structure or metallic strip and selecting '''Insert New PEC.model a non-ideal voltage source with an internal resistance.[[EM.Libera]]''' from the contextual menus lumped circuit represent a series-parallel combination of resistor, inductor and capacitor elements. A dialog for setting up This is shown in 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.figure below:

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/defining-groups-of-pec-objects/wire_pic1Info_icon.png|40px]] Click here to learn more about '''[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/defining-groups-of-pec-objects/wire_pic2.pngPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Lumped_Elements_in_the_MoM_Solvers | Defining Lumped Elements]]'''.

Figure 1[[Image: MoM3D ModuleInfo_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]]'''s Navigation Tree and its PEC dialog.

== = Defining Dielectric Objects Ports ===

Of the two simulation engines of EMPorts are used to order and index gap sources for S parameter calculation.Cube's MoM3D Module only the Surface MoM solver can handle dielectric objects as dielectric materials cannot be modeled by wireframe structures. Dielectric objects They are created under the '''Dielectric''' node defined in the '''Physical StructureObservables''' section of the Navigation Treenavigation tree. They By default, as many ports as the total number of sources are grouped together by their color and material propertiescreated. You can insert different dielectric groups with different colors and different permittivity ε_r and electric conductivity σ. Note that a PEC object is define any number of ports equal to or less than the limiting cases total number of a lossy dielectric material when σ → ∞sources. All port impedances are 50&Omega; by default.

To define a new Dielectric group, follow these steps[[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]]'''.

* Right click on the '''Dielectric''' item of the Navigation Tree and select '''Insert New Dielectric...''' from the contextual menu.<table>* Specify a '''Label''', '''Color''' (and optional Texture) and the electromagnetic properties of the dielectric material to be created: '''Relative Permittivity''' (ε<subtr>r</subtd>) and '''Electric Conductivity''' (σ)[[Image:MOM7A.* You may also choose from png|thumb|360px|Two metallic strips hosting a list of preloaded material types. Click the button labeled '''Material''' to open EM.Cube's Materials dialog. Select the desired material from the list or type the first letter of gap source and a material to find itlumped element. For example, typing '''V''' selects '''Vacuum''' in the list]] </td><td> [[Image:MOM7B. Once you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automatically.* Click the '''OK''' button png|thumb|360px|The surface mesh of the dielectric material dialog to accept the changes two strips with a gap source and close ita lumped element.]] </td></tr></table>

[[Image:/files/images/FDTD4== EM.png]]Libera's Simulation Data & Observables ==

Figure 1At the end of a 3D MoM simulation, [[EM.Libera]] generates a number of output data files that contain all the computed simulation data. The primary solution of the Wire MoM simulation engine consists of the linear electric currents on the wires and wireframe structures. The primary solution of the Surface MoM simulation engine consists of the electric and magnetic surface currents on the PEC and dielectric objects. [[EM.Libera]] currently offers the following types of observables: MoM3D Module {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Dielectric dialogSimulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on metal and dielectric objects, magnetic surface current distribution on dielectric objects and linear current distribution on wires| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port Definition |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}

Click on each category to learn more details about it in the [[Image:/files/images/FDTD5Glossary of EM.pngCube's Simulation Observables & Graph Types]] .

Figure 2: Depending on the types of objects present in your project workspace, [[EM.Cube's material listLibera]] 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.

By default, the last PEC group {{Note|Keep in mind that was defined 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 with a right click 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 since [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tnEM.pngLibera]] MoM3D [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/uses MoM solvers, the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]]''' from calculated field value at the contextual menusource point is infinite. This opens another sub-menu with As a list of all the available PEC groups already defined in the PO Module. Select the desired PEC groupresult, and all the selected objects will move to that group. The objects can field sensors must be selected either in the project workspace, or their names can be selected from the Navigation Tree. In the latter case, make sure that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a PEC group's name from the contextual menu. In a similar way, you can move placed at adequate distances (at least one or more objects few wavelengths) away from a Physical Optics PEC group to EM.CUBE's other modules. In this case, the sub-menus of the''' Move To [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-scatterers to-other-modules/larrow_tn.png]]''' item of the contextual menu will indicate all the EM.CUBE modules that have valid groups for transfer of the select objectsproduce acceptable results.}}

Coming SoonYou need to define a far field observable if you want to plot radiation patterns of your physical structure in [[EM.Libera]].After a 3D MoM simulation is finished, three radiation patterns plots are added to the far field entry in the Navigation Tree. These are the far field component in Theta direction, the far field component in Phi direction and the total far field.

<table><tr><td> [[Image:wire_pic38_tn.png|thumb|230px|The MoM3D Module's method 3D radiation pattern of moments solver assumes an infinite open boundary for your project's structure and uses the free space Green's functions for the background structurecircular loop antenna: Theta component. As a result, the extents ]] </td><td> [[Image:wire_pic39_tn.png|thumb|230px|The 3D radiation pattern of the computational domain are infinite in all directionscircular loop antenna: Phi component. ]] </td><td> [[Image:wire_pic40_tn.png|thumb|230px|The mesh generation process in EMtotal radiation pattern of the circular loop antenna.CUBE's MoM3D Module involves three steps:]] </td></tr></table>

# Setting When the mesh propertiesphysical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields.# Generating [[EM.Libera]] calculates the meshradar cross section (RCS) of a target.# Verifying Three RCS quantities are computed: the &theta; and &phi; components of the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. 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 &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta; and &phi; are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the meshbackscatter RCS is recorded.

The commercial release To calculate RCS, first you have to define an RCS observable instead of EM.CUBE's MoM3D Module provides a Wire MoM solverradiation pattern. In this simulation engine, all At the metallic objects are discretized as end of a wire-frame structure. WiresPO simulation, line and curves are discretized as polylines made up of small linear cells (segments).Surface and solid objects are discretized as a wire-frame mesh with triangular cells. The MoM3D mesh generator meshes the wires based on a specified mesh sampling rate expressed in cellsthee RCS plots &sigma;<sub>&theta;</?sub>, &sigma;_0&phi;. Curves are first polygonized and converted into '''Polyline''' Objects, whose edge lengths follow the specified mesh sampling rate. In the case of solid objects, only their surface and faces &sigma;_tot are discretized using a triangular wireframe mesh, which is regarded as a grid added under the far field section of interconnected wires. Two algorithms are offered for generation of a triangular wireframe mesh. The default algorithm is '''Regular Wireframe'''. This mesh generator creates wireframe elements that have almost equal edge lengths. The other algorithm is '''Structured Wireframe''', which usually creates a very structured wireframe with a large number of aligned wireframe elementsthe navigation tree.

To view {{Note| The 3D RCS plot is always displayed at the MoM3D Module's wire-frame mesh, click on the [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/creating-and-viewing-the-mesh/mesh_tool_tn.png]] button origin of the '''Compute Toolbar''' or select '''Menu [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Discretization [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Shoe Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the wire-frame mesh is displayed in the Project Workspacespherical coordinate system, EM.CUBE's mesh view mode is enabled. In this mode(0, you can perform view operations like rotate view0, pan0), zoom, etc. However, you cannot select or move or edit objects. While with respect to which the mesh view far radiation zone is enabled, the '''Show Mesh''' [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/creating-and-viewing-the-mesh/mesh_tooldefined.png]] button remains depressed. To get back to the Normal View modeOftentimes, click this button one more time, or deselect '''Menu [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/might not be the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Discretization [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Show Mesh''' to remove its check mark or simply click the '''Esc Key''' scattering center of the keyboard.&quot;Show Mesh&quot; 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 wire-frame mesh may take a long time depending on the complexity and size of objects. If you change the your physical 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 [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Discretization [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Regenerate Mesh''' or by right clicking on the '''3-D Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.}}

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/creating-and-viewing-{{Note|Computing the3D mono-mesh/wire_pic5_tnstatic RCS may take an enormous amount of computation time.png]]}}

<table><tr><td> [[Image:wire_pic51_tn.png|thumb|230px|The RCS of a metal plate structure: &sigma;_&theta;.]] </td><td> [[Image:wire_pic52_tn.png|thumb|230px|The RCS of a metal plate structure: &sigma;_&phi;.]] </td><td> [[Image:wire_pic53_tn.png|thumb|230px|The regular wireframe mesh total RCS of a PEC spheremetal plate structure: &sigma;_tot.]] </td></tr></table>

== Customizing the 3D Mesh Generation in EM.Libera ==

To set the wire-frame mesh properties, click === A Note on the [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/creating-and-viewing-the-mesh/mesh_tool_tnEM.png]] button of the Libera'''Compute Toolbar''' or select '''Menu [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Discretization [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] s Mesh Settings...'''or right click on the '''3-D Mesh''' item in the '''Discretization''' section or the Navigation Tree and select '''Mesh Settings...''' from the contextual menu. The MoM3D Mesh Settings Dialog opens up. You can change the mesh generation algorithm from the drop-down list labeled '''Mesh Type''' and select one of the two options: '''Regular Wireframe''' or '''Structured Wireframe'''. You can also set the '''Mesh Sampling Rate''', whose default value is 20 Cells/ ?₀.By default, surface objects or solids are wire-framed at the mesh cell size. Therefore, each wire segment of the wire-frame mesh contains one cell. Another parameter that can affect the shape of the mesh especially in the case of solid objects is the '''Curvature Angle Tolerance'''. This parameter expressed in degrees determines the apex angle of the triangular cells of the structured mesh. Lower values of the angle tolerance will results in more pointed triangular cells.Types ===

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/EM.Libera]] features two simulation engines, Wire MoM and Surface MoM, which require different meshtypes. 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-generation/customizing-segment polylines and then subdivided further if necessary. At the-mesh/wire_pic4connection points between two or more wires, junction basis functions are generated to ensure current continuity.png]]

The MoM3D ModuleOn the other hands, [[EM.Libera]]'s Surface MoM solver requires a triangular surface mesh of surface and solid objects.The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. For meshing surfaces, a mesh density of 7 cells per wavelength roughly translates to 100 triangular cells per squared wavelength. Alternatively, you can base the definition of the mesh settings dialogdensity on "Cell Edge Length" expressed in project units.

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/customizing-the-mesh/wire_pic6_tnInfo_icon.png|30px]]Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

Four-port view of the structured wireframe mesh of a PEC sphere[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.Libera's Triangular Surface Mesh Generator ]]'''.

== <table><tr><td> [[Image:Mesh5.png|thumb|400px|EM.Libera's Mesh Settings dialog showing the parameters of Connected Objects ==the linear wireframe mesh generator.]] </td></tr></table>

You can connect a analyze metallic wire structures very accurately with utmost computational efficiency using [[EM.Libera]]'s Wire MoM simulator. When you structure contains at least one PEC line , polyline or any curve CAD object to a touching surface, [[EM.Libera]] will automatically invoke its linear wireframe mesh generator. To connect This mesh generator subdivides straight lines to surfaces and allow for current continuity, you must make sure that the box labeled '''Connect Lines linear segments of polyline objects into or linear elements according to Touching Surfaces''' is checked in the '''Mesh Settings Dialog'''specified mesh density. If It also polygonizes rounded [[Curve Objects|curve objects]] into polylines with side lengths that are determined by the end of a line lies on a flat surface, EMspecified mesh density.CUBE will detect Note that polygonizing operation is temporary and create the connection automaticallysolely for he purpose of mesh generation. However, this may not always be the case if the As for surface is not flat and has curvature. In such casessolid CAD objects, you have to specifically instruct EM.CUBE to enforce the connection. An example a wireframe mesh of this case these objects is shown in the figure belowcreated which consists of a large number of interconnected linear (wire) elements.

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic7_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic7.png{{Note|files/images/manuals/emagware/emcube/modules/mom3d/The linear wireframe mesh-generation/mesh-of-connected-objects/wire_pic7generator discretizes rounded curves temporarily using CubeCAD's Polygonize tool.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic8_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic8.png|files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic8.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic9_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-objects/wire_pic9.png|files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/mesh-of-connected-It also discretizes surface and solid CAD objects/wire_pic9temporarily using CubeCAD's Polymesh tool.png]]}}

<table><tr><td> [[Image:Mesh6.png|thumb|200px|The line object at the top geometry of an expanding helix with a PEC sphere and circular ground.]] </td><td> [[Image:Mesh7.png|thumb|200px|Wireframe mesh of the structure's helix with the default mesh without and density of 10 cells/&lambda;₀.]] </td><td> [[Image:Mesh8.png|thumb|200px|Wireframe mesh of the helix with proximity a mesh connection enforceddensity of 25 cells/&lambda;₀.]] </td><td> [[Image:Mesh9.png|thumb|200px|Wireframe mesh of the helix with a mesh density of 50 cells/&lambda;₀.]] </td></tr></table>

== Local = Mesh Control of Connected Objects ===

EM.CUBE applies All the global mesh sampling rate objects belonging to discretize all the objects in the Project Workspace. However, you can lock the mesh sampling rate of any same PEC or dielectric group to a desired value different than are merged together using the global rateBoolean union operation before meshing. To do soIf your structure contains attached, open the property dialog of a PEC group by right clicking on its name in the Navigation Tree interconnected or overlapping solid objects, their internal common faces are removed and select '''Properties...''' from only the contextual menu. At the bottom surface of the dialog, check the box labeled '''Lock Mesh'''external faces is meshed. This will enable the '''Sampling Rate''' boxSimilarly, where you can set a desired value. The default value is equal to all the global mesh sampling rate. Keep in mind that surface objects that belong belonging to different the same PEC groups group are not merged during the mesh generation even if they overlap or together and their internal edges are intended removed before meshing. Note that a solid and a surface object belonging to the same PEC group might not always be connected to one anothermerged properly.<br />

When two objects belonging to two different material groups overlap or intersect each other, [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/mesh-generation/local-mesh-control/wire_pic10EM.pngLibera]]has to determine how to designate the overlap or common volume or surface. As an example, the figure below shows a dielectric cylinder sitting on top of a PEC plate. The two object share a circular area at the base of the cylinder. Are the cells on this circle metallic or do they belong to the dielectric material group? Note that the cells of the junction are displayed in a different color then those of either groups. To address problems of this kind, [[EM.Libera]] does provide a "Material Hierarchy" table, which you can modify. To access this table, select '''Menu > Simulate > discretization > Mesh Hierarchy...'''. The PEC groups by default have the highest priority and reside at the top of the table. You can select an group from the table and change its hierarchy using the {{key|Move Up}} or {{key|Move Down}} buttons of the dialog. You can also change the color of junction cells that belong to each group.

Locking the mesh sampling rate of a PEC group<table><tr><td> [[Image:MOM3.png|thumb|300px|EM.Libera's Mesh Hierarchy dialog.]] </td></tr></table>

== Gaps Sources On = Using Polymesh Objects to Connect Wires to Wireframe Surfaces ===

A Gap is an infinitesimally narrow discontinuity that is placed on If the path of project workspace contains a line object, the current. In EM.Cube's MoM3D Module, a gap wireframe mesh generator is used to define an excitation source in discretize your physical structure. From the form point of an ideal voltage source. Gap sources can be placed only on '''Line''' view of this mesh generator, all PEC surface objects and '''Polyline''' PEC solid objects are treated as wireframe objects. '''If you want to excite model a curved wire antennas such as radiator connected to a circular loop or helix with a gap sourcemetal surface, first you have to convert make sure that the curve object into resulting wireframe mesh of the surface has a polyline using node exactly at the location where you want to connect your wire. This is not guaranteed automatically. However, you can use [[EM.Cube]]'s Polygonize Toolpolymesh objects to accomplish this objective.''' 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:

* Right click on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source{{Note|In [[EM...''' from the contextual menu. The Gap Source Dialog opens up.* In the '''Source Location''' section of the dialogCube]], you will find a list of all the line and polyline polymesh objects are regarded as already-meshed 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 Degreesnot re-meshed again during a simulation.}}

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/gap-sources-on-wires/wire_pic14_tnYou can convert any surface object or solid object to a polymesh using CubeCAD's '''Polymesh Tool'''.png]]

A gap source placed on one side of a polyline representing a polygonized circular loop[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_CAD_Tools#Polymesh_Tool | Converting Object to Polymesh]]''' in [[EM.Cube]].

In EM<table><tr><td> [[Image:MOM4.Cube's MoM3D Module, you can define simple lumped elements in a similar manner as gap sources. In fact, a lumped element is equivalent to an infinitesimally narrow gap that is placed in the path png|thumb|360px|Geometry 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 monopole wire connected to excite a wire structure and model a non-ideal voltage source with an internal resistancePEC plate. Unlike the ]] </td><td> [[FDTD Module]]'s single-device lumped loads that connect between two adjacent nodes, Image:MOM5.png|thumb|360px|Placing the MoM3D Module's lumped circuit represent a series-parallel combination wire on the polymesh version of resistor, inductor and capacitor elementsthe PEC plate. This is shown in the figure below:]] </td></tr></table>

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/lumped-circuits/image106== Running 3D MoM Simulations in EM.png]]Libera ==

* 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: '''Passive RLC''' or '''Active with Gap Source'''. Choosing the latter option enables the '''Source Properties''' section of the dialog.* In the '''Source Location''' section of the dialog, Once 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 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 '''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, up your structure in the box labeled '''Offset''', enter the distance of the source from the start point of that side[[EM. 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 nextLibera]], have defined sources and its side index observables 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 examined the series resistor has a value quality of 50? and all other circuit elements are initially grayed out.* If the lumped element is active and contains a gap source, the structure'''Source Properties''' section of the dialog becomes enabled. Here you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of PMC traces) and the '''Phase''' in degrees.* If the workspace contains an array of line or polyline objectss mesh, 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 are ready to the gap sources. The available amplitude distributions include '''Uniform''', '''Binomial''' and '''Chebyshev'''. In the last case, you need to set run a value for minimum side lobe level ('''SLL''') in dB3D MoM simulation. You can also define '''Phase Progression''' in degrees along all three principal axes[[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:270px;" | Simulates the planar structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:/files/images/manuals/emagware/emcube/modules/mom3d/excitation80px;" | None|-sources/lumped| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the surface MoM or wire MoM solvers | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples or adds more frequency samples in an adaptive way| style="width:80px;" | None|-circuits/wire_pic15| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]] | style="width:270px;" | Varies the value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[ImageParametric_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:/files/images/manuals/emagware/emcube/modules/mom3d/excitation80px;" | None|-sources/lumped-circuits/wire_pic16_tn| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#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|}

The MoM3D ModuleYou can set the simulation mode from [[EM.Libera]]'s lumped element dialog and an active lumped element with "Simulation Run Dialog". A single-frequency analysis is a voltage gap single-run simulation. All the other simulation modes in series with an RC circuit placed on the above list are considered multi-run simulations. If you run a dipole wiresimulation 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.

== Defining Ports = Running a Single-Frequency MoM Analysis ===

Ports are used to order and index gap sources for S parameter calculation. They are defined in In a single-frequency analysis, the '''Observables''' section structure of your project workspace is meshed at the Navigation Tree. Right click on the '''Port Definition''' item center frequency of the Navigation Tree project and select '''Insert New Port Definition..analyzed by one of [[EM.Libera]]''' from the contextual menus two MoM solvers. The Port Definition Dialog opens upIf your project contains at least one line or curve object, showing the total number of existing sources in the workspaceWire MoM solver is automatically selected. By defaultOtherwise, as many ports as the total number of sources are created. You can define any number of ports equal Surface MoM solver will always be used to or less than the total number of sources. This includes both gap sources and active lumped elements (which contain gap sources)simulate your numerical problem. 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 either 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 50?. The table titled '''Port Configuration''' lists all the ports and their associated sources and port impedancesengine type is set automatically.

NOTETo open the Run Simulation Dialog, click the '''Run''' [[File: In EMrun_icon.CUBE you cannot assign ports to an array objectpng]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Run...''' or use the keyboard shortcut {{key|Ctrl+R}}. By default, even if it contains sources on its elementsthe Surface MoM solver is selected as your simulation engine. To calculate start the S parameters simulation, click the {{key|Run}} button of an antenna arraythis dialog. Once the 3D MoM simulation starts, you have to construct it using individual elementsa new dialog called '''Output Window''' opens up that reports the various stages of MoM simulation, not as an array objectdisplays the running time and shows the percentage of completion for certain tasks during the MoM simulation process. A prompt announces the completion of the MoM simulation.

<table><tr><td> [[Image:Libera L1 Fig13.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Wire MoM engine as the solver.]] </filestd></images/manuals/emagware/emcube/modules/mom3d/excitation-sources/defining-ports/port-definitiontr><tr><td> [[Image:MOM3D MAN10.png|thumb|left|480px|EM.Libera's Simulation Run dialog showing Surface MoM engine as the solver.]]</td></tr></table>

== Sources MoM simulations involve a number of numerical parameters that normally take default values unless you change them. You can access these parameters and change their values by clicking on the '''Settings''' button next to the &ampquot; Loads On Arrays Of Wire Radiators ==Select Engine&quot; 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.

If First we discuss the workspace contains an array of line or polyline objects, the array object will be listed as an eligible object for gap source placementWire MoM Engine Settings dialog. A gap source will be placed on each element of In the array. All the gap sources will have identical direction and offset. However'''Solver''' section of this dialog, you can prescribe certain amplitude and/or phase distributions. The available amplitude distributions include choose the type of '''UniformLinear Solver''', . The current options are '''BinomialLU''' and '''ChebyshevBi-Conjugate Gradient (BiCG)'''. In The LU solver is a direct solver and is the last casedefault option of the Wire MoM solver. The BiCG solver is iterative. If BiCG is selected, you need have to set a value for maximum side lobe level ('''SLLTolerance''') in dBfor its convergence. You can also define change the maximum number of BiCG iterations by setting a new value for '''Phase ProgressionMax. No. of Solver Iterations / System Size''' in degrees along all three principal axes.

<table><tr><td> [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/gap-sources-on-wires/wire_pic12MOM9B.png|thumb|left|480px|EM.Libera's Wire MoM Engine Settings dialog.]] [[Image:</filestd></imagestr></manuals/emagware/emcube/modules/mom3d/excitation-sources/gap-sources-on-wires/wire_pic13_tn.png]]table>

The MoM3D Module's gap source Surface MoM Engine Settings dialog is bit more extensive and gaps sources defined on an array provides more options. In the "Integral Equation" section of dipole wires with binomial weight distribution the dialog, you can choose among the three PEC formulations: EFIE, MFIE and 90° phase progressionCFIE. 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 &alpha; = 0.4. The Surface MoM solver provides two types of linear solver: iterative TFQMR and direct LU. The former is the default option and asks for additional parameters: '''Error Tolerance''' and '''Max. No. of Solver Iterations'''. When the system size is large, typically above 3000, [[EM.Libera]] uses an acceleration technique called the Adaptive Integral Method (AIM) to speed up the linear system inversion. You can set the "AIM Grid Spacing" parameter in wavelength, which has a default value of 0.05&lambda;₀. [[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.

A short dipole provides a simple way of exciting a structure in the MoM3D Module<table><tr><td> [[Image:MOM9. A short dipole source acts like an infinitesimally small ideal current sourcepng|thumb|left|640px|EM. To define a short dipole source, follow these steps:Libera's Surface MoM Engine Settings dialog.]] </td></tr></table>

[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/short-dipole-sources/wire_pic17Top_icon.png|30px]] '''[[EM.Libera#Product_Overview | Back to the Top of the Page]]'''

The short dipole source dialog and a short dipole placed in front of a PEC sphere[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Libera_Documentation | EM.Libera Tutorial Gateway]]'''

== Plane Wave Sources == The wire-frame structure in the MoM3D Module can be excited by an incident plane wave. In particular, a plane wave source can be used to compute the radar cross section of a metallic target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. EM.CUBE's MoM3D Module provides the following polarization options: # TMz# TEz# Custom Linear# LCPz# RCPz The direction of incidence is defined through the ? and ? angles of the unit propagation vector in the spherical coordinate system. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi'''. The default values are ? = 180° and ? = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM_z and TE_z 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 × 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 (? = 180°). To define a plane wave source follow these steps: * Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' The Plane wave Dialog opens up.* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selected, you also need to enter the X, Y, Z components of the '''E-Field Vector'''. NOTE: In the spherical coordinate system, normal plane wave incidence from the top of the domain downward corresponds to ? = 180^o. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/plane-waves/po_phys15Back_icon.png|30px]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/excitation-sources/plane-waves/po_phys16_tn.png]] The plane wave dialog and illuminating a metallic sphere with an obliquely incident plane wave source. = Running Wire MoM Simulations = == Running A Wire MoM Analysis == Once you have set up your metal structure in EM.CUBE's MoM3D Module, have defined sources and observables and have examined the quality of the structure's wire-frame mesh, you are ready to run a simulation. To open the Run Simulation Dialog, click the '''Run''' [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/running-a-wire-mom-analysis/run_icon.png]] button of the '''Compute Toolbar''' or select Menu [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/larrow_tn.png]] Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/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 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'''. In the former case, the simulation will be carried out at the '''Center Frequency''' of the project. This frequency can be changed from the Frequency Dialog of the project or you can click the Frequency Settings button of the Run Dialog to open up the Frequency Settings dialog. You can change the value of Center Frequency from this dialog, too. In case you choose Frequency Sweep, the Frequency Settings dialog gives two options for '''Sweep Type: Adaptive''' or '''Uniform'''. In a uniform sweep, equally spaced samples of the frequency are used between the Start and End frequencies. These are initially set by the project Bandwidth, but you can change their values from the Frequency Settings dialog. The default '''Number of Samples''' is 10.In the case of adaptive sweep, you have to specify the '''Maximum Number of Iterations''' as well as the '''Error'''. An adaptive sweep simulation starts with a few initial frequency samples, where the Wire MoM engine is run. Then, the intermediary samples are calculated in a progressive manner. At each iteration, the frequency samples are used to calculate a rational approximation of the S parameter response over the specified frequency range. The process stops when the error criterion is met. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/running-a-wire-mom-analysis/wire_pic19.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/running-a-wire-mom-analysis/wire_pic20.png]] The MoM3D Module's run simulation dialog and output window. == Setting Wire MoM Numerical Parameters == A Wire MoM simulation involves a number of numerical parameters that normally take default values unless you change them. You can access these parameters and change their values by clicking on the '''Settings''' button next to the &quot;Select Engine&quot; 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)'''. The LU solver is a direct solver and is the default option of the MoM3D Module. The BiCG solver is iterative. Once selected, you have to set a '''Tolerance''' for its convergence. You can also change the maximum number of BiCG iterations by setting a new value for '''Max. No. of Solver Iterations / System Size'''. The Wire MoM simulator is based on Pocklington's integral equation method. In this method, the wires are assumed to have a very small radius. The basis functions are placed on the axis of the &quot;wire cylinder&quot;, while the Galerkin testing is carried out on its surface to avoid the singularity of the Green's functions. In the &quot;Source Singularity&quot; section of the dialog, you can specify the '''Wire Radius''' . EM.CUBE's MoM3D Module assumes an identical wire radius for all wires and wireframe structures. This radius is expressed in free space wavelengths and its default value is 0.001?₀. The value of the wire radius has a direct influence on the wire's computed reactance. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/setting-the-numerical-parameters/wire_pic21.png]] The wire MoM engine settings dialog. == Visualizing Wire Current Distributions == At the end of a MoM3D simulation, EM.CUBE's Wire MoM engine generates a number of output data files that contain all the computed simulation data. The main output data are the current distributions and far fields. You can easily examine the 3-D color-coded intensity plots of current distributions in the Project Workspace. Current distributions are visualized on all the wires and the magnitude and phase of the electric currents are plotted for all the PEC objects. In order to view these currents, you must first define current sensors before running the Wire MoM simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the MoM3D Module you can define only one current distribution node in the Navigation Tree, which covers all the PEC object in the Project Workspace. After a Wire MoM simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of the linear wire currents. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -? and ?. 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: '''Linear''' and '''dB'''. With the '''Linear''' (default) option selected, the current value is always normalized to the maximum total current in that plane, and the normalized scale is mapped between the minimum and maximum values. If the '''dB''' option is selected, the normalized current is converted to dB scale. The plot limits (bounds) can be set individually for every current distribution plot. In the '''Limits''' section of the plot's property dialog, you see four options: '''Default''', '''User Defined''', '''95% Conf.''' and '''95% Conf.'''. Select the user defined option and enter new values for the '''Lower''' and '''Upper''' limits. The last two options are used to remove the outlier data within the 95% and 99% confidence intervals, respectively. In other words, the lower and upper limits are set to ? ± 1.96? and ? ± 2.79? , respectively, assuming a normal distribution of the data. Three color maps are offered: '''Default''', '''Rainbow''' and '''Grayscale'''. You can hide the legend box by deselecting the box labeled '''Show Legend Box'''. You can also change the foreground and background colors of the legend box. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-current-distributions/wire_pic25.png]] The MoM3D Module's current distribution dialog. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-current-distributions/wire_pic26_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-current-distributions/wire_pic27_tn.png]] A monopole antenna connected above a PEC plate and its current distribution with the default plot settings. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-current-distributions/wire_pic28.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-current-distributions/wire_pic29_tn.png]] The output plot settings dialog, and the current distribution of the monopole-plate structure with a user defined upper limit. == Scattering Parameters and Port Characteristics == 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) parameters of the selected ports, all based on the port impedances specified in the project's &quot;Port Definition&quot;. If more than one port has been defined in the project, the scattering matrix of the multiport network is calculated. 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 &quot;#&quot;. The admittance (Y) and impedance (Z) parameters are also calculated and saved in complex data files with '''.CPX''' file extensions. The voltage standing wave ratio of the structure at the first port is also computed and saved to a real data '''.DAT''' file. You can plot the port characteristics from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S Parameters''', '''Plot Y Parameters''', '''Plot Z Parameters''', or '''Plot VSWR'''. 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's data manager. To open data manager, click the '''Data Manager''' [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/scattering-parameters-and-port-characteristics/data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/scattering-parameters-and-port-characteristics/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: # Magnitude and Phase# Real and Imaginary Parts# Smith Chart In particular, it may be useful to plot the S_ii parameters 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 and click on the fourth column under the title '''Graph Type'''. The selected table cell turns into a dropdown list that contains the above three formats. Select the desired format and click the '''Plot''' button of the data manager dialog to plot the data in the new format. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/scattering-parameters-and-port-characteristics/wire_pic56.png]] EM.CUBE's data manager showing the port characteristics data files for a two-port structure consisting of two adjacent dipoles. The magnitude and phase graphs of the S₁₁ parameter. The real and imaginary part graphs of the Z₂₁ parameter. The Smith chart. = Running Surface MoM Simulations = == Running A Surface MoM Analysis == Coming Soon... == Setting Surface MoM Numerical Parameters == Coming Soon... == Visualizing Surface Current Distributions == Coming Soon... == Visualizing Near &amp; Far Fields In MoM3D Module == == Near Field Visualization == EM.CUBE allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify. To define a new Field Sensor, follow these steps: * Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''* The '''Label''' box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default EM.CUBE creates a field sensor plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also changes these coordinates using the spin buttons. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe the sensor plane moving along that direction in the Project Workspace.* The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These determine the resolution of near field calculations. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once a Wire MoM simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the Project Workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -? and ?.You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/near-field-visualization/wire_pic30.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/near-field-visualization/wire_pic31_tn.png]] The MoM3D Module's field sensor dialog and a circular loop antenna fed by a gap source. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/near-field-visualization/wire_pic32_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/near-field-visualization/wire_pic33_tn.png]] Electric and magnetic field plots of the circular loop antenna. = Visualizing 3D Radiation Patterns = Unlike the FDTD method, in the MoM3D Module you do not need a far field box to perform near-to-far-field transformations. Nonetheless, you still need to define a far field observable if you want to plot radiation patterns. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the '''Angle Increment''' in the degrees, which indeed sets the resolution of far field calculations. The default value is 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 Wire 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. The 3-D plots can be viewed by clicking on their name in the navigation tree. They are displayed in the Project Workspace and overlaid on the project's structure. The view of a 3-D radiation pattern plot can be changed with the available view operations such as rotate view, pan, zoom, etc. If the structure blocks the view of the pattern, you can simply hide the whole structure or parts of it. The fields are always normalized to the maximum of the total far field:<br />[[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-3-d-radiation-patterns/farfieldformula.gif]] A legend box appears in the upper right corner of the 3-D radiation plot, which can be moved around by clicking and dragging with the left mouse button. The calculated Directivity of the (antenna) structure is displayed at the bottom of the legend box. It is important to note that if the wire-frame structure is excited by an incident plane wave, the radiation patterns indeed represent the far-zone scattered field data. NOTE: If you do not define a far field observable in your project, no radiation patterns will be calculated at the end of a wire MoM simulation. NOTE: Every time you change the angle increment of the far field, you have to start a new simulation, even if your structure has not changed. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-3-d-radiation-patterns/wire_pic37.png]] The MoM3D Module's radiation pattern dialog. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-3-d-radiation-patterns/wire_pic38_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-3-d-radiation-patterns/wire_pic39_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/visualizing-3-d-radiation-patterns/wire_pic40_tn.png]] 3-D radiation pattern of the circular loop antenna: (Left) Theta component, (Center) Phi components, and (Right) total far field. == Modeling Antenna Arrays == In view of far field characteristics, 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 '''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 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 &quot;Array Factor&quot; 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 direction. 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 calculate all such parameters if you check the relevant boxes in the &quot;Additional Radiation Characteristics&quot; 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. 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. NOTE: Using an array factor for far field calculation, you cannot assign non-uniform amplitude or phase distribution to the array elements. For this purpose, you have to define an array object. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/handling-antenna-arrays/wire_pic47.png]] Defining a finite-sized 4-element array factor in the radiation pattern dialog. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/handling-antenna-arrays/wire_pic48_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/handling-antenna-arrays/wire_pic46_tn.png]] Radiation pattern of a 4-element dipole array: (Left) computed using array factor and (Right) computed by simulating an array object. == Radar Cross Section == When the wire-frame structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. EM.CUBE calculates the radar cross section (RCS) of a target, which is defined in the following manner: [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/rcs_equation.png]] EM.CUBE calculates three RCS quantities: the ? and ? components of the radar cross section as well as the total radar cross section: ?_?, ?_?, and ?_tot. In addition, EM.CUBE MoM3D Module 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 ?₀ and ?₀ and the RCS is measured and plotted at all ? and ? angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles ?₀ and ?₀ and the RCS is measured and plotted at the echo angles 180°-?₀; and ?₀.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 ?₀ and ?₀ are varied over the intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded. To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' 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 ? and ? 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 ?-cut. This latter cut is at ?=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 ?_?, ?_?, and ?_totare added under the far field section of the Navigation Tree. These plots are very similar to the three 3-D radiation pattern plots. You can view them by clicking on their names in the navigation tree. The RCS values are expressed in m². For visualization purposes, the 3-D plots are normalized to the maximum RCS value, which is also displayed in the legend box. The 2-D RCS graphs can be plotted from EM.CUBE's data manager exactly in the same way that you plot 2-D radiation pattern graphs. A total of eight 2-D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. At the end of a sweep simulation, EM.CUBE 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 &amp; Elevation''' in the &quot;Output Settings&quot; 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 3-D mono-static RCS may take an enormous amount of computation time. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic49.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic50_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic50.pngCube |files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic50.png]] The MoM3D Module's RCS dialog and a half-wave wire connected to a metal plate illuminated by an obliquely incident plane wave. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic51_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic51.png|files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic51.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic52_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic52.png|files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic52.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic53_tn.png]][[files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic53.png|files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/radar-cross-section/wire_pic53.png]] The RCS of the wire-plate structure: (Left) ?_?, (Center) ?_? and (Right) total RCS.. == Customizing 3D Plots == Similar Back to the current distribution and field sensor plots, EM.CUBE's 3-D radiation pattern plots are interactive. When you move the mouse over a pattern plot, tiny dots appear on its surface. These dots correspond to the theta-phi angle pairs on the surface of the unit sphere where the far field data have been calculated. Upon mouse-over, you can highlight one of these points. A small tooltip appears on the plot that shows the normalized far field value in that direction. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/customizing-3-d-pattern-plots/wire_pic41_tn.pngCube Main Page]] Reading far field values from a 3-D radiation pattern plot by mouse-over. You can change the type of the 3-D radiation pattern plot through the '''Radiation Pattern Dialog'''. The plot type change applies to all the three nodes: theta component, phi component and total field patterns. In the 3D Display Type section of this dialog you can choose from three options: '''3D Polar''', which is the default choice, '''Spherical Map''' and '''Cone'''. In the last two cases, the far field values are plotted on the surface of the unit sphere, where each point correspond to a (? , ?) pair. In the spherical map, the curved cells of the unit sphere are colored based on their field value. In the cone-type plot, a vectorial visualization of the far fields is generated. In the last case, you can also set the size of the cones that represent the far field vectors. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/customizing-3-d-pattern-plots/wire_pic42_tn.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/customizing-3-d-pattern-plots/wire_pic43_tn.png]] The spherical map and cone (vectorial) versions of the radiation pattern show in the previous figure. Just like current distribution and field sensor plots, each individual 3-D radiation pattern plots has an '''Output Settings Dialog''', from which you can further customize the plot's scale (linear vs. dB), lower and upper limits and color map type. == 2D Radiation Graphs == At the end of a Wire MoM simulation, the radiation pattern data E_?, E_?, and E_tot in the three principal XY, YZ and ZX planes as well as an additional user defined phi plane cut are available for plotting on 2-D graphs. There are a total of eight 2D pattern graphs in the data manager: 4 polar graphs and 4 Cartesian graphs of the same pattern data. To open data manager, click the '''Data Manager''' [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/scattering-parameters-and-port-characteristics/data_manager_icon.png]] button of the '''Compute Toolbar''' or select '''Compute [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/the-metal-structure/moving-objects-between-pec-groups-or-transferring-to-other-modules/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'''. In the Data manager Dialog, you will see a list of all the data files available for plotting. These include the four polar pattern data files with a '''.ANG''' file extension and the four Cartesian pattern data file with a '''.DAT''' file extension. Select any data file by clicking and highlighting its '''ID''' in the table and then click the '''Plot''' button to plot the graph. At the end of a Wire MoM sweep simulation, other radiation characteristics are also computed as a function of the sweep variable (frequency, angle, or any other user defined variable). These include the '''Directivity (D0)''', '''Total Radiated Power (PRAD)''' and '''Directive Gain (DG)''' as a function of the theta and phi angles. Another radiation characteristic of interest especially in circularly polarized scenarios is the Axial Ratio. In EM.CUBE, the axial ratio is always defined in the LCPz or RCPz sense based on the X- and Y-components of the electric field. In order to calculate the directive gain or axial ratio, you have to check the boxes labeled '''Axial Ratio (AR)''' or '''Directive Gain (DG)''' in the &quot;Additional Radiation Characteristics&quot; section of the '''Radiation Pattern Dialog'''. Four 2-D Cartesian graphs of the axial ratio as functions of the theta angle a generated in the three principal XY, YZ and ZX planes as well as the additional user defined phi plane cut. At the end of a Wire MoM sweep simulation, the directive gain and axial ratio can also be plotted as functions of the sweep variable. In this case, either quantity needs to be computed at a fixed pair of phi and theta angles. These angles are specified in degrees as '''User Defined Azimuth &amp; Elevation''' in the &quot;Output Settings&quot; section of the '''Radiation Pattern Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/2-d-radiation-graphs/wire_pic44.png]] The data manager dialog showing a list of 2-D polar and Cartesian radiation pattern graphs. = More 3D MoM Simulation Types = == 3D MoM Sweep Simulations == You can run EM.CUBE's MoM3D simulation engine in the sweep mode, whereby a parameter like frequency, plane wave angles of incidence or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data file for visualization and plotting. EM.CUBE's MoM3D Module currently offers three types of sweep: # Frequency Sweep# Angular Sweep# Parametric Sweep To run a MoM3D sweep, open the '''Run Simulation Dialog''' and select one of the above sweep types from the '''Simulation Mode''' drop-down list in this dialog. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode drop-down list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based 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.# Fix mesh at the center frequency.# Re-mesh at each frequency. 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. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/wire-mom-sweep-simulations/wire_pic22.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/wire-mom-sweep-simulations/wire_pic24.png]] The MoM3D Module's run simulation dialog with frequency sweep selected and the frequency settings dialog. You can run an angular sweep only if your project has a plane wave excitation. In this case, you have to define a plane wave source with the default settings. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range. The other angle remains fixed at the value that is specified in the '''Plane Wave Dialog'''. You have to select either '''Theta''' or '''Phi''' as the '''Sweep Angle''' in the Angle Settings Dialog. Then you can set the start and end angles as well as the number of angle samples. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/wire-mom-sweep-simulations/wire_pic23.png]] [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/running-wire-mom-simulations/wire-mom-sweep-simulations/po_phys54.png]] The PO Module's run simulation dialog with angular sweep selected and the angle settings dialog. In a parametric sweep, one or more user defined variables are varied at the same time over their specified ranges. This creates a parametric space with the total number of samples equal to the product of the number of samples for each variable. The user defined variables are defined using EM.CUBE's '''Variables Dialog'''. For a description of EM.CUBE variables, please refer to the CUBECAD manual or the &quot;Parametric Sweep&quot; sections of the FDTD or [[Planar Module]] manuals. == Animation of MoM3D Data == At the end of a frequency, angular or parametric sweep simulation in EM.CUBE's MoM3D Module, the output data are saved for visualization and plotting. In particular, if you have defined current distribution, field sensor or far field observables in your project, multiple 3-D plots as many as the total number of sweep samples are added to the Navigation Tree. In a single simulation run, a total of 7 current distribution plots, 14 field sensor plot and 3 radiation pattern plots or 3 RCS plots are generated under every observable node defined in the navigation tree. However, after a sweep simulation, only one plot is saved for each sweep sample. This is done to keep the resulting plots manageable. Thus, only the magnitude of the total wire currents '''|J_L|''' and the total radiation pattern or total RCS are saved for each sweep sample. In the case of a field sensor observable, you have the choice to save either the total E-field magnitude plot or the total H-field magnitude plot. To change this, open the '''Field Sensor Dialog''' by right clicking on a field sensor's name in the Navigation Tree and selecting '''Properties...''' from the contextual menu. In the '''Field Display - Multiple Plots''' section of this dialog, select one of the radio sensors labeled '''E-Field''' or '''H-Field''' From this dialog, you can also choose the type of 3-D field plot for animation. The options are '''Confetti''' or '''Cone'''. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/animation-of-mom3d-data/wire_pic60.png]] Selecting control-type H-Field plot for sweep data visualization in the field sensor dialog. Once the sweep simulation is finished, you can click any of the field plots and visualize it in the main window. You can also animate these field plots. Animation in EM.CUBE consists of consecutive display of the plots in the main window at a preset speed. To animate the field sensor plots, right click on the field sensor's name in the Navigation Tree and select '''Animation''' from the contextual menu. The field plots start to animate beginning with the first sample, going through all the plots one by one until the last one and repeating the loop all over again. While the animation proceeds in the main window, a dialog titled '''Animation Controls''' pops up at the lower right corner of the screen. You can drag this dialog anywhere in the project workspace from its title bar. The controls dialog shows the title of each graph as it is reviewed. You can set the speed of animation by typing in a value for '''Rate''', which is indeed the frame duration expressed in multiples of 100 milliseconds. The default frame duration is 300 msec. You can pause the animation and resume at any time. You can rewind to the first sample or skip to the last sample. You can also step through the samples one at a time using the increment (forward) or decrement (backward) buttons. To stop animation at any time, use the keyboard's '''Esc Key''' or click the '''Close (X)''' button of the animation controls dialog. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/animation-of-mom3d-data/wire_pic61_tn.png]] The animation controls dialog and animation of the H-field plots of a two adjacent dipoles after a frequency sweep. [[Image:/files/images/manuals/emagware/emcube/modules/mom3d/visualizing-simulation-data/animation-of-mom3d-data/wire_pic62_tn.png]] Animation of the wire current plots of a two adjacent dipoles after a frequency sweep.