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[[Image:Splash-fdtd.jpg|right|800px720px]]<strong><font color="#961717" size="4">Fast Multi-Core And Multicore & GPU-Accelerated FDTD Solvers For Tackling The for Simulating the Most Complex Electromagnetic Modeling Problems</font></strong>

<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:prop-ico.png | link=EM.Terrano]] [[image:postatic-ico.png | link=EM.IlluminaFerma]] [[image:staticplanar-ico.png | link=EM.FermaPicasso]] [[image:planarmetal-ico.png | link=EM.PicassoLibera]] [[image:metalpo-ico.png | link=EM.LiberaIllumina]] </td>

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EM.Tempo is a powerful time-domain electromagnetic simulator for full-wave modeling of 3D radiation, scattering and propagation problems. It features a highly efficient Finite Difference Time Domain (FDTD) simulation engine that has been optimized for speed and memory usage. EM.Tempo brings to your desktop the ultimate in computational power. Its FDTD solver has been parallelized to take full advantage of multi-core processor architectures. With a large variety of geometrical, material and excitation features including open-boundary and periodic structures, you can use EM.Tempo as a general purpose 3D field simulator for most of your electromagnetic modeling needs. EM.Tempo's new advanced simulation capabilities are your the key to the a thorough understanding of wave the interaction in of electromagnetic waves with complex media such as anisotropic composites, metamaterials or biological environmentsor with passive and active devices and nonlinear circuits.

EM.Tempo is the outcome of evolution of our older FDTD simulation tool, EM.Lounge, first introduced has undergone several evolutionary development cycles since its inception in 2004. The original simulation code engine utilized an FDTD formulation based on the uniaxial perfectly matched layer (UPML) boundary termination. Through subsequent expansionsSubsequently, a far superior more advanced boundary termination based on the convolutional perfectly matched layer (CPML) was implemented, which performs impeccably with a far superior performance for all oblique wave incidences in different types of media. EM.Tempo now has the ability to model laterally infinite layered structures as well as using CPML walls that touch material media. A novel formulation of periodic boundary conditions with oblique plane wave incidenceswas implemented based on the constant transverse wavenumber method (or direct spectral FDTD). In 2013 we introduced an Open-MP optimized multi-core version of the FDTD engine as well as a hardware-accelerated versions solver that runs on CUDA-enabled graphical processing unit (GPU) platforms. Both of these fast solvers are now a standard part of the EM.Tempo Pro package.

[[Image:Tutorial_iconInfo_icon.png|40px30px]] Click here to access for an overview of the '''[[EM.Cube#EM.Tempo_Tutorial_Lessons Basic Principles of The Finite Difference Time Domain Method | EM.Tempo Tutorial GatewayBasic FDTD Theory]]'''.

[[Image:ship_image1ART GOLF Fig title.png|thumb|left|600px400px|Analyzing an imported battleship model with The 3D far-field radiation pattern of a vehicle-mounted antenna structure simulated by EM.Tempo.]]

[[EM.Tempo]] is a general-purpose EM simulator than can handle solve most types of electromagnetic modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains. It has also serves as been integrated within the full-wave '''FDTD Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling simulation environmentas its full-wave "FDTD Module". EM.Tempo shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

=== The Advantages & Limitations of EM.Tempo's FDTD Simulator === A time domain simulation like FDTD offers several advantages over frequency domain simulations. In certain applications, the time domain signature or behavior of a system, e.g. the transient response of a circuit or an antenna, is sought. In other applications, you may need to determine the wideband frequency response of a system. In such cases, using a frequency domain technique, you have to run the simulation engine many times to adequately sample the specified frequency range. In contrast, using the FDTD method requires a single-run simulation. The temporal field data are transformed into the Fourier domain to obtain the wideband frequency response of the simulated system. Among other advantages of the FDTD method are its versatility in handling complex material compositions as well as its superb numerical stability. It is worth noting that unlike most frequency domain methods, the FDTD technique does not involve numerical solution of large ill-conditioned matrix equations that are often very sensitive to the mesh quality. Like every numerical technique, the FDTD method has disadvantages, too. Adding the fourth dimension, time, to the computations increases the size of the numerical problem significantly. Unfortunately, this translates to both larger memory usage and longer computation times. Note that the field data are generated in both the 3D space and time. EM.Tempo uses a staircase "Yee" mesh to discretize the physical structure. This works perfectly fine for rectangular objects that are oriented along the three principal axes. In the case of highly curved structures or slanted surfaces and lines, however, this may compromise the geometrical fidelity of your structure. EM.Tempo provides a default adaptive FDTD mesher that can capture the fine details of geometric contours, slanted thin layers, surfaces, etc. to arbitrary precision. However, with smaller mesh cells, the stability criterion leads to smaller time steps; hence, longer computation times. Another disadvantage of the FDTD technique compared to naturally open-boundary methods like the method of moments (MoM) is its finite-extent computational domain. This means that to model open boundary problems like radiation or scattering, absorbing boundary conditions are needed to dissipate the incident waves at the walls of the computational domain and prevent them from reflecting back into the domain. The accuracy of the FDTD simulation results depends on the quality of these absorbers and their distance from the actual physical structure. EM.Tempo provides high quality perfectly matched layer (PML) terminations at the boundaries, which can be placed fairly close to your physical structure to reduce the total size of the computational domain. <table><tr><td>[[Image:Info_iconAirplane Mesh.png|40px]] Click here to learn more about the basic functionality of '''[[Building_Geometrical_Constructions_in_CubeCAD thumb| CubeCADleft|480px|The Yee mesh of an imported aircraft CAD model.]]'''.</td></tr></table>

Anisotropic Uniaxial and fully anisotropic materials with four complete constitutive tensors</li>

Dispersive materials of Debye, Drude and Lorentz types with arbitrary number of poles and generalized metamaterials</li>

Voxel databases for pointwise grid definition Generalized uniaxial and doubly negative refractive index metamaterials with arbitrary numbers of inhomogeneous both electric and magnetic poles</li> <li> Two types of gyrotropic materials: ferrites and magnetoplasmas</li>

=== Sources, Ports & Lumped Devices ===

Lumped voltage sources with internal resistanceplaced on a PEC line or thin wire object with an arbitrary orientation</li>

Passive RLC lumped loads and nonliear diode elementsHuygens sources</li>

Fast generation of Yee grid approximation mesh of solids, surfaces and curves</li>

Geometry-aware and material-aware adaptive mesh generator with gradual grid transitions</li>

Fixed-cell uniform mesh generator with three unequal cell dimensions</li> <li> Mesh view with mesh three principal grid profilerprofilers</li>

FullWideband full-wave simulation of 3D structures</li> <li> Transient analysis with arbitrary user defined excitation waveforms</li> <li> Multi-frequency computation of frequency domain quantities in a single FDTD simulation run</li>

Multi-variable and multi-goal optimization of structurestructures</li>

Remote simulation capability</li> <li> Both Windows and Linux versions Automated generation of the FDTD compact reduced order surrogate models from full-wave simulation engine availabledata</li>

Near -field intensity (colorgrid), contour and surface plots (vectorial - amplitude &amp; phase)</li>

Near -field probes for monitoring fields field components in both time &amp; frequency domains</li>

Far -field radiation patterns: 3-D 3D pattern visualization and 2-D 2D polar and Cartesian graphs</li>

Far -field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li>

Huygens surface data generation for use in other [[EM.Cube]] modules</li> <li> Periodic reflection/transmission coefficients and k-&szligbeta; diagrams</li>

Touchstone-style S parameter text files for direct export to RF.Spice or its Device EditorTime and frequency domain port voltages, currents and powers</li>

Electric Touchstone-style S-parameter text files for direct export to [[RF.Spice A/D]]</li> <li> Interanl node voltages and currents of Netlist-based one-port and two-port networks</li> <li> Computation of electric, magnetic energies&nbsp;and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes</li>

Custom output parameters defined as mathematical expressions or Python functions of standard outputs</li>

==An FDTD Simulation Primer Building the Physical Structure in EM.Tempo ==

=== An Overview of FDTD Modeling === In the Finite Difference Time Domain (FDTD) method, a discretized form of Maxwell’s equations is solved numerically and simultaneously Material Variety in both the 3D space and time. During this process, the electric and magnetic fields are computed everywhere in the computational domain and as a function of time starting at t = 0. From knowledge of the primary fields in space and time, one can compute other secondary quantities including frequency domain characteristics like scattering parameters, input impedance, far field radiation patterns, radar cross section, etc. [[Image:Info_icon.png|40px]] Click here for an overview of '''[[Basic_FDTD_Theory | Basic FDTD Theory]]'''. Since FDTD is a finite domain numerical technique, the computational domain of the problem must be truncated. At the boundaries of the computational domain, proper boundary conditions must be enforced. In a shielded structure, all objects are enclosed within a perfect electric (or magnetic) conductor box. In an open boundary problem like an antenna, some kind of absorbing boundary conditions such as a perfectly matched layer (PML) must be used to emulate the free space. The absorbing boundaries should act such that the field propagates through them without any back reflection. The FDTD simulation time depends directly on the size of the computational domain and on how close you can place the PML walls to the enclosed objects.  [[Image:Info_icon.png|40px]] Click here to learn more about EM.Tempo's '''[[Basic_FDTD_Theory#Why_Does_FDTD_Need_Domain_Termination.3F | Perfectly Matched Layer Termination]]'''. The FDTD computational domain must be discretized using an appropriate meshing scheme. EM.Tempo uses a non-uniform, variable, staircase (pixelated) Yee mesh with a mesh density that you can customize. A fixed-cell mesh generator is also available, where you can set constant cell dimensions along the three principal axes for the entire computational domain. The variable mesh density is specified in terms of the effective wavelength inside material media. As a result, the mesh resolution and average mesh cell size differ in regions that are filled with different types of material. EM.Tempo's non-uniform mesher generates more cells in the areas that are occupied by dielectric materials, fewer cells in the free-space regions and no cells inside (impenetrable) PEC regions. EM.Tempo's default "adaptive" mesh generator also refines the mesh around curved segments of lines, surface or solids to produce a far more accurate representation of your geometry. The example on the right illustrates a metal ellipsoid and a 3D view of its Yee mesh. <table><tr><td>[[Image:FDTD93.png|thumb|left|480px|Geometry of an imported aircraft CAD model...]]</td></tr><tr><td>[[Image:FDTD94.png|thumb|left|480px|...and its Yee mesh.]]</td></tr></table> The FDTD method provides a wideband simulation of your physical structure. In order to produce sufficient spectral information, an appropriate wideband temporal waveform is needed to excite the physical structure. The choice of the waveform, its bandwidth and time delay all affect the convergence behavior of the FDTD time marching loop. By default, EM.Tempo uses a modulated Gaussian waveform with optimal [[parameters]]. Another issue of concern is the numerical stability of the time marching scheme. You might expect to get better and more accurate results if you keep increasing the FDTD mesh resolution. However, in order to satisfy the Courant-Friedrichs-Levy (CFL) stability condition, the time step must be inversely proportional to the maximum grid cell size . A high resolution mesh requires a smaller time step. To let the fields in the computational domain fully evolve over time, a smaller time step will require a larger number of time steps to converge. EM.Tempo automatically chooses a time step that satisfies the CFL condition. [[Image:Info_icon.png|40px]] For more detailed information about the stability of the FDTD algorithm, see '''[[Basic_FDTD_Theory#Waveform.2C_Bandwidth.2C_Stability| Waveform, Bandwidth, Stability]]'''. === The Advantages & Limitations of EM.Tempo's FDTD Simulator === A time domain simulation like FDTD offers several advantages over a frequency domain simulation. In certain applications, the time domain signature or behavior of a system, e.g. the transient response of a circuit or an antenna, is sought. In other applications, you may need to determine the wideband frequency response of a system. In such cases, using a frequency domain technique, you have to run the simulation engine many times to adequately sample the specified frequency range. In contrast, using the FDTD method requires a single-run simulation. The temporal field data are transformed into the Fourier domain to obtain the wideband frequency response of the simulated system. Among other advantages of the FDTD method are its versatility in handling complex material compositions as well as its superb numerical stability. It is worth noting that unlike frequency domain methods like the finite element method (FEM) or method of moments (MoM), the FDTD technique does not involve numerical solution of large ill-conditioned matrix equations that are often very sensitive to the mesh quality. Like every numerical technique, the FDTD method has disadvantages, too. Adding the fourth dimension, time, to the computations increases the size of the numerical problem significantly. Unfortunately, this translates to both larger memory usage and longer computation times. Note that the field data are generated in both the 3D space and time. EM.Tempo uses a staircase "Yee" mesh to discretize the physical structure. This works perfectly fine for rectangular objects that are oriented along the three principal axes. In the case of highly curved structures or slanted surfaces and lines, however, this may compromise the geometrical fidelity of your structure. EM.Tempo provides a default adaptive FDTD mesher that can capture the fine details of geometric contours, slanted thin layers, surfaces, etc. to arbitrary precision. However, with smaller mesh cells, the stability criterion leads to smaller time steps; hence, longer computation times. Another disadvantage of the FDTD technique compared to naturally open-boundary methods like MoM is its finite-extent computational domain. This means that to model open boundary problems like radiation or scattering, absorbing boundary conditions are needed to dissipate the incident waves at the walls of the computational domain and prevent them from reflecting back into the domain. The accuracy of the FDTD simulation results depends on the quality of these absorbers and their distance from the actual physical structure. EM.Tempo provides high quality perfectly match layer (PML) terminations at the boundaries which can be placed fairly close your physical structure. == Building the Physical Structure in EM.Tempo ==

Your physical structure in EM.Tempo can be made up of several geometric objects with different material compositions. EM.Tempo groups your In other words, the geometric objects in the project workspace you draw or import from external files are grouped together based on their material type. All the objects belonging to the same material group share the same color and same a common material propertiescomposition. EM.Tempo's material types are divided into seven categories:

| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]'''

| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Thin Wire |Thin Wire]]'''

| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC)]]'''

| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dielectric Material |Dielectric Material]]'''

| style="width:30px;" | [[File:aniso_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Anisotropic Material |Anisotropic Material]]'''

| style="width:30px;" | [[File:disp_group_icon.png]]| style="width:150px;" | '''[[Glossary of EMGlossary_of_EM.Cube's Materials & Physical Object Types%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dispersive Material |Dispersive Material]]'''

| style="width:30px;" | [[File:voxel_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gyrotropic_Material |Gyrotropic Material]]| style="width:300px;" | Modeling ferrites and magnetoplasmas| style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:150px;" | '''[[Glossary of EM.Cube's Materials , Sources, Devices & Other Physical Object Types#Voxel Database Virtual_Object_Group |Voxel DatabasesVirtual Object]]'''| style="width:300px;" | Modeling general inhomogeneous materials defined pointwise using a voxel databaseUsed for representing non-physical items | style="width:250px;" | Must import ".CAR" type data fileAll types of objects

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials , Sources, Devices & Other Physical Object Types]]. === Organizing the Physical Structure by Material Groups ===

EM.Tempo groups your geometric objects in the project workspace based on their material type. All the objects belonging to the same material group share the same color and same material properties. Under each material node in the navigation tree, you can create new material groups of the same type but with different properties such as color, texture, or electric and magnetic constitutive parameters. These material groups are used to organize both the geometric objects you draw in the project workspace and those you import from external CAD model files.

[[Image:Info_icon.png|40px30px]] Click here to access the '''[[Glossary of EM.Cube's Materials , Sources, Devices & Other Physical Object Types]]'''.

[[Image:FDTD_MAN1Tempo NavTree.png|thumb|left|300px400px|EM.Tempo's navigation tree.]]

[[EM.Tempo ]] allows overlapping objects although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same material type and group overlap, they are merged using the Boolean union operation during the mesh generation process. If two overlapping objects belong to two different material categories, then the material properties of the FDTD cells in the overlap region will follow the [[EM.Tempo]]'s material hierarchy rule. In that case, the overlap area cells will always be regarded as having the material type of the higher priority. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner:

If planned carefully, taking advantage of [[EM.Tempo]]'s material hierarchy rule would make the construction of complex objects easier. For example, a dielectric coated metallic cylinder can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in the illustration below. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinder.

In [[EM.Tempo]], you can define two types of domain box. A "'''Default'''" -type domain is a box that is placed at a specified offset distance from the largest extents of your physical structure (global bounding box). The offset is specified in free-space wavelengths. A "'''Custom'''" -type domain, on the other hand, is defined as a fixed-size and fixed-location box in the World Coordinate System (WCS). In this case, you have to specify the coordinates of the lower left front corner (Corner 1) and upper right back corner (Corner 2) of the domain box.

When you start a new project in [[EM.Tempo]], a default-type domain is automatically created with a default offset value set equal to a quarter free-space wavelength (0.25&lambda;₀). As soon as you draw your first object, a blue domain box shows up in the project workspace and encloses your object. As you add more objects and increase the overall size of your structure, the domain box grows accordingly to encompass your entire physical structure. When you delete objects from the project workspace, the domain box also shrinks accordingly.

* Click the '''Domain''' [[Image:domain_icon.png]] button of the '''Simulate ''' Toolbar or select the menu item '''Menu > Simulate > &rarr; Computational Domain > &rarr; Domain Settings...''' or right click on the '''FDTD Domain''' item of the Navigation Tree and select '''Domain Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+A'''. The Domain Settings Dialog opens up, showing the current domain type selection.

[[Image:FDTD13EM.png|thumb|300px|[[FDTD ModuleTempo]]'s Boundary Conditions dialog]]EM.Tempo supports four types of domain boundary conditions: PEC, PMC, Convolutional Perfectly Matched Layers (CPML) and Periodic Boundary Conditions (PBC). By default, all the six sides of the computational domain box are set to CPML, representing a completely open-boundary structure. Different boundary conditions can be assigned to each of the six walls of the domain box. The periodic boundary conditions are special ones that are assigned through [[EM.Tempo]]'s Periodicity Dialog and will be discussed later under modeling of periodic structures. The current release of [[EM.Cube]] allows periodic boundary conditions only on the side walls of the computational domain, and not on the top or bottom walls.

* Select the menu item '''Menu > Simulate > &rarr; Computational Domain > &rarr; Boundary Conditions''' or right click on the '''Boundary Conditions''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Boundary Conditions...''' from the contextual menu. The Boundary Conditions Dialog opens.

<table><tr><td> [[Image:FDTD13.png|thumb|left|480px|EM.Tempo's boundary conditions dialog.]]</td></tr></table> === Advanced CMPL CPML Setup ===

In many open-boundary electromagnetic modeling problems , you need a boundary condition that simply absorbs all the incoming radiation. For problems of this nature, an absorbing boundary condition (ABC) is often chosen that effectively minimizes wave reflections at the boundary. [[EM.Tempo ]] uses Convolutional Perfectly Matched Layers (CPML) for absorbing boundary conditions. Usually two or more ABC layers must be placed at the boundaries of the physical structure to maximize wave absorption. The boundary CPML cells in the project workspace are transparent not visible to the user. But, in effect, multiple rows of CPML cells are placed on the exterior side of each face of the visible domain box.

You can set the number of CPML layers as well as their order. This is done through the CPML Settings Dialog, which can be accessed by right clicking on the '''CPML''' item in the '''Computational Domain''' section of the navigation tree and selecting '''CPML Settings...''' from the contextual menu. By default, four eight CPML layers of the third order are placed outside the FDTD problem domain. It is recommended that you always try a four-layer CPML first to assess the computational efficiency. The number of CPML layers may be increased only if a very low reflection is required (<-40dB).

{{Note|[[EM.Tempo]]'s default quarter wavelength offset for the domain box is a and its 8-layer CPML walls are very conservative choice choices and can be reduced further relaxed in many cases. A An offset equal to eight free-space grid cells beyond the largest bounding box usually give gives a more compact, but still valid, domain box.}}

[[Image:Info_icon.png|40px30px]] Click here to learn more about the theory of '''[[Basic_FDTD_TheoryBasic_Principles_of_The_Finite_Difference_Time_Domain_Method#Why_Does_FDTD_Need_Domain_TerminationCPML_vs.3F _PML | Perfectly Matched Layer Termination]]'''.

<td> [[Image:fdtd_manual-11FDTD MAN10.png|thumb|400pxleft|360px|The boundary ABC CPML cells placed outside the visible domain box.]] </td><td> [[Image:FDTD15.png|thumb|left|400px|CPML Settings dialog.]] </td>

When a domain boundary wall is designated as CPML and its has a zero domain offset, meaning it touches a material block, the CPML cells outside the domain wall are reflected back inside the computational domain. In other words, the effective number of CPML layers will be twice the one specified in the CPML Settings dialog. This will effectively extend the material block infinitely beyond the boundary wall and will create an open boundary effect in the specified direction. It goes without saying that only "substrate" objects are supposed to touch the boundary walls in such a scenario. Because of the rolled-back CPML cells inside the domain, it is very important to make sure that other finite-sized parts and objects stay clear from the domain walls as well as from the invisible "interior" CPML cells.  {{Note|The current release of [[EM.Tempo]] does not support full-anisotropic or dispersive or gyrotropic layers of laterally infinite extents. In other words, your anisotropic or dispersive or gyrotropic material objects must not touch the CPML domain boundaries.}}

<td> [[Image:FDTD24AFDTD MAN8.png|thumb|left|360px|The domain box of a patch antenna with a finite-sized substrateand ground.]] </td><td> [[Image:FDTD24FDTD MAN9.png|thumb|left|360px|The domain box of a laterally infinite patch antenna with a PEC ground and zero ±X and , ±Y and -Z domain offsets. Note that the bottom PEC plate can be replaced with a PEC boundary condition at the -Z domain wall.]] </td>

=== Source Variety in EM.Tempo === Before you can run an FDTD simulation, you have to define a source to excite your project’s physical structure. EM.Tempo offers a variety of excitation mechanisms for your physical structure depending on your particular type of modeling problem or application (click on each type to learn more about it):

! scope="col"| Host Object! scope="col"| Spatial Domain! scope="col"| Restrictions/ Additional Requirements

| '''style="width:30px;" | [[File:lumped_src_icon.png]]| style="width:150px;" | [[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Lumped Source |Lumped Source]]'''| style="width:300px250px;" | General-purpose point voltage source| style="width:250px200px;" | Associated with a PEC or thin wire lineparallel to a principal axis| style="width:200px;" | A single point| style="width:200px;" | None

| '''style="width:30px;" | [[File:distrb_src_icon.png]]| style="width:150px;" | [[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Distributed Source |Distributed Source]]'''| style="width:300px250px;" | General-purpose distributed voltage planar sourcewith a uniform, edge-singular or sinusoidal impressed field profile| style="width:250px200px;" | Associated with a virtual Virtual rectangle stripparallel to a principal plane| style="width:200px;" | A rectangular area| style="width:200px;" | None

| '''style="width:30px;" | [[File:mstrip_icon.png]]| style="width:150px;" | [[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Microstrip Port |Microstrip Port Source]]'''| style="width:300px250px;" | Used for S-parameter computationsin microstrip-type structures| style="width:250px200px;" | Associated with a PEC rectangle strip parallel to a principal plane| style="width:200px;" | A vertical rectangular area underneath the host strip| style="width:200px;" | Requires a PEC ground plane strip underneath the host strip

| '''style="width:30px;" | [[Glossary of EMFile:cpw_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Coplanar Waveguide (CPW) Port |Coplanar Waveguide (CPW) Port Source]]'''| style="width:300px250px;" | Used for S-parameter computationsin CPW-type structures| style="width:250px200px;" | Associated with a PEC rectangle strip parallel to a principal plane| style="width:200px;" | Two parallel horizontal rectangular areas attached to the opposite lateral edges the host center strip| style="width:200px;" | Requires two parallel PEC ground strips on the two sides of the host center strip

| '''style="width:30px;" | [[File:coax_icon.png]]| style="width:150px;" | [[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Coaxial Port |Coaxial Port Source]]'''| style="width:300px250px;" | Used for S-parameter computationsin coaxial-type structures| style="width:250px200px;" | Associated with a PEC Cylinderoriented along a principal axis| style="width:200px;" | A circular ring area enveloping the host inner conductor cylinder| style="width:200px;" | Requires a concentric hollow outer conductor cylinder

| '''style="width:30px;" | [[Glossary of EMFile:wg_src_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Waveguide Port |Waveguide Port Source]]'''| style="width:300px250px;" | Used for S-parameter computationsin waveguide structures| style="width:250px200px;" | Associated with Hollow PEC box oriented along a principal axis| style="width:200px;" | A rectangular area at the cross section of the host hollow PEC box| style="width:200px;" | The host box object can have one capped end at most.

| '''style="width:30px;" | [[Glossary of EMFile:hertz_src_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Plane Wave Filamentary_Current_Source |Plane Wave Filamentary Current Source]]'''| style="width:300px250px;" | Used for scattering computationsGeneral-purpose wire current source of two types: Hertzian short dipole radiator and long wire current source with a uniform, triangular or sinusoidal current distribution profile| style="width:250px200px;" | StandNone (stand-alone source)| style="width:200px;" | A line| style="width:200px;" | Hertzian short dipole radiators can have an arbitrary orientation, but long wire current sources must be aligned along one of the principal axes

| '''style="width:30px;" | [[Glossary File:plane_wave_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Plane Wave |Plane Wave Source]]| style="width:250px;" | Used for modeling electromagnetic scattering & computation of EMreflection/transmission characteristics of periodic surfaces | style="width:200px;" | None (stand-alone source)| style="width:200px;" | Surface of a cube enclosing the physical structure| style="width:200px;" | None|-| style="width:30px;" | [[File:gauss_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gaussian Beam |Gaussian Beam Source]]'''| style="width:300px250px;" | Used for modeling focused beams | style="width:200px;" | None (stand-alone source)| style="width:200px;" | Surface of a cube enclosing the physical structure| style="width:200px;" | None|-| style="width:30px;" | [[File:huyg_src_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:250px;" | StandUsed for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:200px;" | None (stand-alone source)| style="width:200px;" | Surface of a cube | style="width:200px;" | Imported from a Huygens surface data file

A lumped source is the most commonly used way of exciting a structure in EM.Tempo. A lumped source is an ideal source that must be placed Click on a line object that is parallel each category to one of the three principal axes learn more details about each source type and shows up as a small red arrow on the host line. Lumped sources are typically used how to define ports and compute the port characteristics like S/Y/Z parameters. Using simple lumped sources, you can simulate a variety of transmission line structures in EM.Tempo including filters, couplers or antenna feeds. This approach may become less accurate at very high frequencies when the details of the feed structures become important and can no longer be modeled with highly localized lumped ports. In such cases, it is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the ports for calculation of the incident and reflected waves. Waveguide source is used to excite the dominant TE₁₀ mode of a hollow rectangular waveguide. Waveguide sources typically provide more accurate results for scattering parameters of waveguide structures compared to lumped sources as they represent the actual dominant propagating modes at the transmission line portsone.

[[Image:Info_icon.png|40px30px]] Click here to learn more More information about all the source types can be found in the '''[[Common_Excitation_Source_Types_in_EMGlossary of EM.Cube#Defining_Finite-Sized_Source_Arrays | Using Source Arrays in Antenna Arrays's Materials, Sources, Devices & Other Physical Object Types]]'''.

In the most general sense, one can consider two fundamental types of excitation sources for an FDTD simulation: a lumped source and a distributed source. A lumped sources is localized at a single mesh point in the computational domain, while a distributed source is spread over several mesh cells. Among the source types of the above list, the microstrip port, CPW port, coaxial port, waveguide port, plane wave and Gaussian beam sources are indeed special cases of a distributed source for specific applications.  A lumped source is the most commonly used way of exciting a structure in EM.Tempo. A lumped source is a voltage source with a series internal resistor that must be placed on a PEC or thin wire line object that is parallel to one of the three principal axes. A lumped source is displayed as a small red arrow on the host line. Lumped sources are typically used to define ports and compute the port characteristics like S/Y/Z parameters. Using simple lumped sources, you can simulate a variety of transmission line structures including filters, couplers or antenna feeds. This approach may become less accurate at higher frequencies when the details of the feed structure become important and can no longer be modeled with highly localized lumped ports. In such cases, it is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the ports for calculation of the incident and reflected waves. Waveguide source is used to excite the dominant TE₁₀ mode of a hollow rectangular waveguide. Other special types of distributed sources are microstrip port, CPW port and coaxial ports that can be used effectively to excite their respective transmission line structures.  When you create an array of an object type that can host one of the above source types, you can also associate a source array with that array object.  [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Modeling Finite-Sized Source Arrays]]'''. A plane wave source is a popular excitation method that is used for calculation of the radar cross section of targets or reflection and transmission characteristics of periodic surfaces. A Gaussian beam source is another source type that is highly localized as opposed to the uniform plane wave. For both plane wave and Gaussian beam sources, [EM.Tempo requires a finite incidence surface to calculate the excitation. When you create either of these sources, a plane wave box or a Gaussian beam box is created as part of their definition. A trident symbol on the box shows the propagation vector as well as the E-field and H-field polarization vectors. The time domain plane wave or Gaussian beam excitation is calculated on the surface of this box and injected into the computational domain. The plane wave box is displayed in the project workspace as a purple wireframe box enclosing the structure, while the Gaussian beam box appears as a green wireframe box. Both boxes have an initial default size with an offset of 0.2&lambda;₀ from the largest bounding box enclosing your entire physical structure. In both source dialogs, the radio button '''Size: Default''' is selected by default. The radio button '''Size: Custom''' allows you to set the excitation box manually. The values for the coordinates of '''Corner 1''' and '''Corner 2''' can now be changed. Corner 1 is the front lower left corner and Corner 2 is the rear upper right corner of the box. The corner coordinates are defined in the world coordinate system (WCS).

<td> [[Image:FDTD_FF5FDTD MAN11.png|thumb|360px|A plane wave box enveloping enclosing a PEC plate cylinder at normal oblique incidence: &theta; = 105&deg; and &phi; = 0315&deg;.]] </td><td> [[Image:FDTD_FF5AFDTD MAN12.png|thumb|360px|A Gaussian beam source illuming box enclosing a PEC plate cylinder at oblique incidence: &theta; = 135105&deg;, and &phi; = 225315&deg;. The concentric circles represent the beam's focus point and radius.]] </td></tr></table> === Simulating a Multiport Structure in EM.Tempo === Ports are used to order and index sources for circuit parameter calculations like S/Y/Z parameters. In EM.Tempo, you can define ports at the location of the following types of sources:  *[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Lumped Source |Lumped sources]]*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Distributed Source |Distributed sources]]*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Microstrip Port |Microstrip port sources]]*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Coplanar Waveguide (CPW) Port |CPW port sources]]*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Coaxial Port |Coaxial port sources]]*[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Waveguide Port |Waveguide port sources]] Every time you create a new source with one of the above types, the program asks if you want to initiate a new port and associate it with the newly created source. If the physical structure of your project workspace has N sources, then N default ports are defined, with one port assigned to each source according to their order in the navigation tree. You can define any number of ports equal to or less than the total number of sources in your project.  If your physical structure has two or more sources, but you have not defined any ports, all the sources will excite the structure simultaneously during the simulation. However, when you assign N ports to the sources, then you have a multiport structure that is characterized by an N×N scattering matrix, an N×N impedance matrix, and an N×N admittance matrix. To calculate these matrices, EM.Tempo uses a binary excitation scheme in conjunction with the principle of linear superposition. In this binary scheme, the structure is analyzed a total of N times. Each time one of the N port-assigned sources is excited, and all the other port-assigned sources are turned off. In other words, the FDTD solver runs a "port sweep" internally. When the ''j''th port is excited, all the S_ij parameters are calculated together based on the following definition: :<math> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math> where V_i is the voltage across Port i, I_i is the current flowing into Port i and Z_i is the characteristic impedance of Port i. The sweep loop then moves to the next port until all ports have been excited.  In summary, to analyze an N-port structure, EM.Tempo runs N separate FDTD time marching loops. The S/Z/Y parameters are frequency-domain quantities. The port voltages and currents are Fourier-transformed to the frequency domain over the frequency range [fc-bw/2, fc+bw/2], where fc is the center frequency and bw is the bandwidth of your project. You can reduce the frequency range of the Fourier transform by settings new values for '''Start''' and '''End''' frequencies in the "Port Definition" dialog as long as these are within the range [fc-bw/2, fc+bw/2]. By default, 200 frequency samples are taken over the specified frequency range. This number can be modified from the FDTD simulation engine settings dialog.  {{Note|In order to obtain correct results, the port impedance must equal the characteristic impedance of the transmission line on which the port is established. This is not automatically taken care of by EM.Tempo.}} [[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Glossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.26_Ports | Modeling Coupled Sources & Ports]]'''. <table><tr><td> [[Image:FDTD MAN15.png|thumb|left|640px|A two-port CWP transmission line segment.]] </td></tr><tr><td> [[Image:FDTD MAN16.png|thumb|left|480px|EM.Tempo's port definition dialog.]] </td>

When an FDTD simulation starts, your project's source starts pumping energy into the computational domain at t > 0. Maxwell's equations are solved in all cells at every time step until the solution converges, or the maximum number of time steps is reached. A physical source has a zero value at t = 0, but it rises from zero at t > 0 according to a specified waveform. [[EM.Tempo]] currently offers four types of temporal waveform:

[[Image:Info_icon.png|40px30px]] Click here to learn more about EM.Tempo's '''[[Waveforms and Discrete Fourier Transforms Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#The_Relationship_Between_Excitation_Waveform_and_Frequency-Domain_Characteristics | Standard & Custom Waveforms and Discrete Fourier Transforms]]'''.

===Defining Ports & Modeling Feeds Custom Waveforms in Practical ApplicationsEM.Tempo ===

[[Image:FDTD48.png|thumb|450px|EM.Tempo's Port Definition dialog.]]Ports are used to order and index sources for circuit parameter calculations like S/Y/Z parameters. In EM.Temposome time-domain applications, you can define ports at may want to simulate the location propagation of the types a certain kind of sources: lumped, distributed, microstrip, CPW, coaxial and waveguidewaveform in a circuit or structure. If In addition to the physical structure in your project workspace has N sources, then N default ports are definedwaveforms, with one port assigned EM.Tempo allows you to define custom waveforms by either time or frequency specifications for each individual source according to their order in the navigation treeyour project. You can define any number of ports equal to or less than If you open up the total number property dialog of sources any source type in EM.Tempo, you will see an {{key|Excitation Waveform...}} button located in the "Source Properties" section of the dialog. Clicking this button opens up EM.Tempo's Excitation Waveform dialog. From this dialog, you can override EM.Tempo's default waveform and customize your projectown temporal waveform. The Excitation Waveform dialog offers three different options for defining the waveform:

[[Image:Info_icon.png|40px]] Click here to learn more about The first option, which is also the default option, constructs an optimal modulated Gaussian pulse waveform based on your project'''[[Common_Excitation_Source_Types_in_EMs specified center frequency and bandwidth. This optimal waveform guarantees the most accurate frequency domain computations for your simulation.Cube#The_Port_Definition_Observable | The Port Definition Observable]]'''second option gives you a choice of the three standard waveforms and lets you define their waveform parameters in terms of frequency domain characteristics like center frequency and bandwidth and spectral contents. The third option lets you define a completely arbitrary temporal waveform for your source.

Select the third option of waveform definition and then choose the '''Custom''' option from the '''Waveform Type''' dropdown list. Enter a mathematical expression for your custom waveform a function of the time variable "T" or "t" in the box labeled '''Expression'''. You can use arithmetic operations, standard and library functions as well as user-defined Python functions. [[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubeUsing Python to Create Functions, Models & Scripts#Exciting_Multiport_Structures_Using_Linear_Superposition Creating Custom Python Functions | Exciting Multiport Structures Using Linear SuperpositionCreating Custom Python Functions]]'''.

<table><tr><td> [[Image:Info_iconFDTD MAN13.png|40px]] Click here to learn more about thumb|left|720px|EM.Tempo'''[[Common_Excitation_Source_Types_in_EMs excitation waveform dialog showing the default standard modulated Gaussian pulse temporal waveform.Cube#Modeling_Coupled_Ports | Modeling Coupled Ports]]'''.</td></tr></table>

[[File:FDTD56.pngWhen you define a custom waveform in the Excitation Waveform dialog, make sure to click the {{key|thumb|380px|EMAccept}} button of the dialog to make your changes effective.TempoA graph of your custom waveform is plotted in the right panel of the dialog for your review. It is important to keep in mind that typical time scales in the FDTD simulation of RF structures are on the order of nanosecond or smaller. Using the variable "fc" in the expression of your waveform definition usually takes care of this required scaling. Otherwise, you need to use scaling factors like 1e-9 explicitly in your expression. For example, in the figure below, we have defined a modulated Bessel waveform in the form of "sp.j0(t/2e-9)*sin(2*pi*fc*t)", where sp.j0(x) denotes the zeroth-order Bessel function of the first kind burrowed from Python's Lumped Load dialogspecial functions module.]]

In EM.Tempo, {{Note| If you can define four types a custom excitation waveform for your source, none of lumped devices:the standard frequency domain output data and parameters will be computed at the end of your FDTD simulation.}}

# '''<table><tr><td> [[Glossary of EMImage:FDTD MAN14.Cube's Lumped Devices & Circuits#Lumped Resistor png|thumb|left|720px| Resistor]]''' # '''[[Glossary of EM.CubeTempo's Lumped Devices & Circuits#Lumped Capacitor | Capacitor]]''' # '''[[Glossary of EMexcitation waveform dialog showing a custom modulated Bessel temporal waveform defined using the Python function sp.j0(x).Cube's Lumped Devices & Circuits#Lumped Inductor | Inductor]]'''# '''[[Glossary of EM.Cube's Lumped Devices & Circuits#Lumped Nonlinear Diode | Nonlinear Diode]]''' </td></tr></table>

Although lumped loads are not sources and do not excite a structure, their properties are similar to lumped sources== EM. Lumped Loads are incorporated into the FDTD grid across two adjacent nodes in a similar manner to lumped sources. Likewise, lumped loads are defined on Line objects. Tempo's Active & Passive Devices ==

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.Cube#Defining_Lumped_Loads_in_EM.Tempo | === Defining Lumped Loads in EM.Tempo]]'''.Devices ===

In [[EM.Tempo]], you can define eigth types of lumped devices: # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Resistor | Resistor]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Inductor | Inductor]]'''# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Capacitor | Capacitor]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Series_RL_Device | Series RL Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Parallel_RC_Device | Parallel RC Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Diode | Nonlinear Diode]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_One-Port_Device | Active Lumped One-Port Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_Two-Port_Device | Active Lumped Two-Port Device]]'''  Lumped devices are connected between two adjacent FDTD mesh nodes. Although lumped devices are not sources and the passive types do not excite a structure, their properties are similar to lumped sources. That is why they are listed under the '''Sources''' section of the navigation tree. A lumped device has to be associated with a PEC line object that is parallel to one of the three principal axes. Similar to lumped sources, lumped devices have an '''Offset''' parameter that is equal to the distance between their location on the host line and its start point.  A lumped device is characterized by a v-i equation of the form: :<math>i(t) = L \{ v(t) \} </math> where V(t) is the voltage across the device, i(t) is the current flowing through it and ''L'' is an operator function, which may involve differential or integral operators. Lumped devices are incorporated into the FDTD grid across two adjacent nodes in a similar manner to lumped sources. At the location of a lumped device, the FDTD solver enforces the device's governing equation by relating the device voltage and current to the electric and magnetic field components and updating the fields accordingly at every time step. [[Image:Info_icon.png|40px30px]] Click here for a general discussion of '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.Cube26_Nonlinear_Passive_.26_Active_Devices | Linear Passive & Nonlinear Passive & Active Devices]]'''.

<table><tr><td> [[Image:FDTD MAN17.png|thumb|left|480px|EM.Tempo's lumped device dialog for nonlinear diode.]] </td></tr><tr><td> [[Image:FDTD MAN17A.png|thumb|left|480px|EM.Tempo's lumped device dialog for active lumped two-port device.]] </td></tr></table> == Working = Defining Active Distributed Multiport Networks === EM.Tempo also provides two types of active distributed multiport network devices: # '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_One-Port_Device | Active Distributed One-Port Device/Circuit]]''' # '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_Two-Port_Device | Active Distributed Two-Port Device/Circuit]]'''  Unlike the active lumped devices, these devices are rather distributed and their behavior is similar to a microstrip port source. In other words, the active distributed one-port device requires a rectangle strip object as a host, while the active distributed two-port device requires two rectangle strip objects for its definition. You can choose one of the edges of the strip object for establishing the circuit port. In the case of a two-port device, you need two parallel and end-to-end aligned strip objects.  The circuit behavior of these devices is defined by a Netlist file. Their property dialog provides a text editor for simply writing the Netlist description of the device. You can also import an existing external Netlist file with a ".CIR" or ".TXT" file extension using the button labeled {{key|Load Netlist}}..  {{Note|[[RF.Spice A/D]] can generate a Netlist file corresponding to an existing circuit project, which can then be saved to a text file with a ".TXT" file extension. }} <table><tr><td> [[Image:ActiveOnePort.png|thumb|left|480px|EM.Tempo's active one-port device/circuit dialog.]] </td></tr></table> <table><tr><td> [[Image:ActiveTwoPort.png|thumb|left|720px|EM.Tempo's active two-port device/circuit dialog.]] </td></tr></table> === A Note on Using Active Devices === When your physical structure contains an active device, EM.Tempo performs an EM-circuit co-simulation that involves both the full-wave FDTD EM solver and the SPICE circuit solver. In a global self-consistent co-simulation, at each time step of the FDTD time marching loop, the electric and magnetic fields at the location of the device ports are used to compute the port voltages and currents. These quantities are then used in the SPCIE circuit solver to update all the voltages and currents at the internal nodes of the active device. The updated port voltages and currents are finally used to update the electric and magnetic fields in the physical mesh cells and the time marching loop proceeds to the next time step.  EM.Tempo can handle several active one-ports and two-ports simultaneously. In that case, all the devices are automatically compiled into a single Netlist that serves as the input of the SPICE solver. The individual internal nodes of each device need to be renamed for the global Netlist. Besides the main circuit, the Netlist of each device may contain several "subcircuits". Note that the subcircuit nodes are not re-indexed for the global Netlist as is expected.  {{Note|If you want to use a B-type nonlinear dependent source in the Netlist definition of an active one-port or two-port, it must be contained in a subcircuit definition rather than in the main circuit.}} The figure below shows the geometry of a two-port amplifier device with microstrip input and output transmission lines. The Netlist of the two-port device is given below: ---- C1 1 0 1p R1 1 0 50 E1 2 0 1 0 20 RS 2 3 10 R2 3 0 50 C2 3 0 1p ---- In this case, a linear voltage-controlled voltage source (E1) with a voltage gain of 20 has been used. The input and output nodes are 1 and 3, respectively.  <table><tr><td> [[Image:Amp circ.png|thumb|left|420px|The schematic of the amplifier circuit in RF.Spice A/D.]] </td></tr></table> The same Netlist can be written using a B-type nonlinear dependent source as follows: ---- C1 1 0 1p X1 1 0 2 0 amp_dev .subckt amp_dev 1 2 3 4  R1 1 2 50 B1 3 4 v = 20*v(1,2) .ends RS 2 3 10 R2 3 0 50 C2 3 0 1p ---- {{Note|You can use active one-ports to define custom voltage or current sources for your entire physical structure rather than using one of the physical excitation source types of the navigation tree.}} <table><tr><td> [[Image:Amp ex.png|thumb|left|550px|The geometry of a microstrip-based amplifier with an active two-port device.]] </td></tr></table> == EM.Tempo's Observables & Simulation Data Types==

! scope="col"| Associated Observable Type

| style="width:150px30px;" | '''[[Glossary of EMFile:fieldprobe_icon.Cube's Simulation Observables#Temporal Field Probe |Point Fieldspng]]'''| style="width:150px;" | '''Temporal Waveforms| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Temporal Field Probe Temporal_Field_Probe_Observable |Temporal Field Probe]]'''| style="width:300px;" | Computing E- electric and H-magnetic field components at a fixed location in both the time and frequency domainsdomain

| style="width:150px30px;" | '''[[Glossary of EMFile:fieldprobe_icon.Cube's Simulation Observables#Near-Field Sensor |Near-Field Distributionpng]]'''| style="width:150px;" | '''Point Fields| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Near-Field Sensor Temporal_Field_Probe_Observable |Near-Temporal Field SensorProbe]]''' | style="width:300px;" | Computing E- the amplitude and H-phase of electric and magnetic field components on at a planar cross section of fixed location in the computational frequency domain in both time and frequency domains

| style="width:150px30px;" | '''[[Glossary of EMFile:fieldsensor_icon.Cube's Simulation Observables#Far-Field Radiation Pattern png]]|Farstyle="width:150px;" | Near-Field Radiation Characteristics]]'''Distribution Maps| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#FarNear-Field Radiation Pattern Field_Sensor_Observable |FarNear-Field Radiation PatternSensor]]'''| style="width:300px;" | Computing the radiation pattern amplitude and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. phase of electric and magnetic field components on a planar cross section of the computational domain in the frequency domain

| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Time-Domain Near-Field Animation| style="width:150px;" | [[Glossary of EM.Cube'''s Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:300px;" | Computing either total electric or total magnetic field distribution on a planar cross section of the computational domain in the time domain| style="width:250px;" | The field maps are generated at certain specified time intervals|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Patterns| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Radar Cross Section (RCS) Far-Field_Radiation_Pattern_Observable |Far-Field Scattering CharacteristicsRadiation Pattern]]| style="width:300px;" | Computing the 3D radiation pattern in spherical coordinates | style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| 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_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Scattering Patterns| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the 3D scattering pattern in spherical coordinates | style="width:250px;" | Requires a plane wave or Gaussian beam source|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Radar Cross Section | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS) _Observable |Radar Cross Section (RCS)]]'''

| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Polarimetric Scattering Matrix Data| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Port Definition Radar_Cross_Section_(RCS)_Observable |Port CharacteristicsRCS]] | style="width:300px;" | Computing the scattering matrix of a target for various plane wave source incident angles| 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_Observable |Port Definition]]'''

| style="width:150px30px;" | '''[[Glossary of EMFile:port_icon.Cube's Simulation Observables#Port Definition png]]| style="width:150px;" |Port VoltageVoltages, Current Currents & Powers]]'''| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Port Definition Port_Definition_Observable |Port Definition]]'''

| style="width:30px;" | [[File:period_icon.png]]| style="width:150px;" | Periodic Reflection & Transmission Coefficients| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Periodic Characteristics |Periodic Characteristics]]'''| style="width:150px;" | (No observable definition required )

| style="width:150px30px;" | '''[[Glossary of EMFile:energy_icon.Cube's Simulation Observables#Domain Energy |Domain Energypng]]'''| style="width:150px;" | '''Electric and Magnetic Energy| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Domain Energy -Power_Observable |Domain Energy-Power]]'''| style="width:300px;" | Computing the total electric and , magnetic and total energy in inside the entire computational domain in the time domain

| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power| style="width:150px;" | '''[[Glossary of EM.Cube's Simulation Observables& Graph Types#Huygens Surface Energy-Power_Observable |Huygens SurfaceEnergy-Power]]| style="width:300px;" | Computing the total dissipated power inside the entire computational domain in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Electric and Magnetic Energy Density| style="width:150px;" | [[Glossary of EM.Cube'''s Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the electric, magnetic and total energy density on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power (Ohmic Loss) Density and Specific Absorption Rate (SAR) Density| style="width:150px;" | [[Glossary of EM.Cube'''s Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the dissipated power density and SAR density on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Poynting Vector| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables& Graph Types#Huygens Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the complex Poynting vector on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent Electric and Magnetic Surface Currents| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens_Surface_Observable |Huygens Surface]]'''

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]]. Of EM.Tempo's frequency domain observables, the near fields, far fields and all of their associated [[parameters]] like directivity, RCS, etc., are calculated at a certain single frequency that is specified as part of the definition of the observable. To compute those frequency domain data at several frequencies, you need to define multiple observables, one for each frequency. On the other hand, port characteristics like S/Y/Z [[parameters]] and VSWR are calculated over the entire specified bandwidth of your project. Of EM.Tempo's source types, lumped sources, waveguide sources and distributed sources let you define one or more ports for your physical structure and compute its port characteristics. One of EM.Tempo's real advantages over frequency-domain solvers is its ability of generate wideband S/Z/Y parameter data in a single simulation run.

<td> [[Image:FDTD_FS2.png|thumb|360pxleft|420px|EM.Tempo's Field Sensor dialog.]] </td></tr><tr><td> [[Image:FDTD_FS1FDTD_FS1_new.png|thumb|360pxleft|480px|Three field sensor planes defined around a PEC ellipsoid illuminated by a plane wave source.]] </td>

<td> [[Image:FDTD_FS3FDTD_FS3_new.png|thumb|left|360px|Electric field distribution above the PEC plate.]] </td><td> [[Image:FDTD_FS4FDTD_FS4_new.png|thumb|left|360px|Magnetic field distribution above the PEC plate.]] </td>

<td> [[Image:FDTD_FF1.png|thumb|360pxleft|720px|EM.Tempo's Radiation Pattern dialog.]] </td></tr><tr><td> [[Image:FDTD_FF3.png|thumb|360pxleft|600px|EM.Tempo's Radar Cross Section dialog.]] </td>

<table><tr><td> [[Image:FDTD133FDTD_FF2.png|thumb|350pxleft|Far Field Background Medium 480px|EM.Tempo's far field acceleration dialog.]]</td></tr></table>

<td> [[Image:fdtd_out36_tn.png|thumb|300pxleft|360px|Radiation pattern of a vertical dipole above PEC ground.]] </td><td> [[Image:fdtd_out37_tn.png|thumb|300pxleft|360px|Radiation pattern of a vertical dipole above PMC ground.]] </td>

<td> [[Image:fdtd_out38_tn.png|thumb|300pxleft|360px|Radiation pattern of a horizontal dipole above PEC ground.]] </td><td> [[Image:fdtd_out39_tn.png|thumb|300pxleft|360px|Radiation pattern of a horizontal dipole above PMC ground.]] </td>

=== Generating the FDTD Mesh and Working with Multi-Frequency Simulation Data ===

One of the primary advantages of the FDTD method is its ability to run wideband EM simulations. The frequency domain data are computed by transforming the time-domain data to the Fourier domain. This is done automatically when EM.Tempo computes the port characteristics such as S/Z/Y parameters. The following frequency-domain observables are defined at a single frequency: * Near-Field Sensor* Far-field Radiation Pattern* RCS* Huygens Surface The default computation frequency of the above observables is the project's center frequency (fc). You can change the observable frequency from the observable's property dialog and enter any frequency in Hz. The reason these types of simulation data are computed at a single frequency is their typically very large size. However, you can define as many instances of these observables and set different frequency values for each one. In the case of radiation pattern and RCS, there are two dialogs that can be accessed from the navigation tree. Right-click on the "Fer-Field Radiation Patterns" or "Radar Cross Sections" items of the navigation tree and select '''Insert Multi-Frequency Radiation Pattern...''' or '''Insert Multi-Frequency RCS...''' from the contextual menu.  <table><tr><td> [[Image:RadPattern multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radiation Pattern dialog.]] </td><td> [[Image:RCS multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radar Cross Section dialog.]] </td></tr></table> Using the multi-frequency dialogs, you can set the value of Start Frequency, Stop Frequency and Step Frequency in Hz. You can also set the values of Theta Angle Increment and Phi Angle Increment in degrees. The default values of both quantities are 5&deg;. In the case of RCS, you have choose one of the two options: '''Bistatic RCS''' or '''Monostatic RCS'''.  To facilitate the process of all the defining multi-frequency observables in EM.Tempo, you can also use the following Python functions at the command line: ---- emag_field_sensor_multi_freq(f1,f2,df,dir_coordinate,x0,y0,z0) emag_farfield_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_rcs_bistatic_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_rcs_monostatic_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_huygens_surface_multi_freq(f1,f2,df,x1,y1,z1,x2,y2,z2) ---- In the above Python functions, f1 and f2 are the start and stop frequencies, respectively, and df is the frequency increment, all expressed in Hz. Note that the above commands simply create and insert the specified observables in the navigation tree. They do not run perform a simulation. The created observables have the same "base name" with ordered numeric indices. For example, far-field radiation patterns are names as Multi_FF_1, Multi_FF_2, ... EM.Tempo also provides some additional Python functions for the far-field radiation patterns and RCS observables.  ---- emag_farfield_consolidate(x1,x2,dx,base_name) emag_rcs_consolidate(x1,x2,dx,base_name) emag_farfield_explode(base_name) emag_rcs_explode(base_name) emag_farfield_average(n,base_name) emag_rcs_average(n,base_name) ---- The two "consolidate" Python functions take the results of multi-frequency simulation observables and merge them into a single data file. The base name in the case of far-field radiation patterns is "Multi_FF" as pointed out earlier. The name of the resulting consolidated data file is the same as the base name with a "_All" suffix and a ".DAT" file extension. In the case of far-field radiation patterns, it is "Multi_FF_All.DAT". The two "explode" Python functions take a consolidated data file names as "base_name_All.DAT" and break it up into several single-frequency ".RAD" or ".RCS" data files. Finally, the two "average" Python functions take several radiation pattern or RCS files with a common base name in the current project folder, compute their average and save the results to a new data file named "base_name_ave" with a ".RAD" or ".RCS" file extensions, respectively. == Generating the FDTD Mesh in EM.Tempo == === EM.Tempo's Mesh Types === EM.Tempo generates a brick volume mesh for FDTD simulation. The FDTD mesh is a rectangular Yee mesh that extends to the entire computational domain. It is primarily constructed from three mesh grid profiles along in the XY, YZ and ZX principal planes. These projections together create a 3D mesh space consisting of a large number of cubic volume cells (voxels) carefully assembled in a way that approximates the shape of the original structure.

[[Image:Info_iconEM.png|40px]] Click here to learn more about Tempo's default mesh generator produces an adaptive brick mesh of your physical structure, whose mesh resolution varies with the frequency. As the operating frequency of your project increases, the default ''[[Mesh_Generation_Schemes_in_EM'Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure.Cube#Working_with_Mesh_Generator | Working The adaptive mesh is optimized in such a way as to capture all the geometric details, curvatures and thin slanted plates or sheets, which often pose a challenge to staircase meshing. It usually provides a reasonably accurate discretization of most complex structures. Occasionally, you may opt for a more regularized FDTD mesh with Mesh Generator ]]almost equal grid line spacings everywhere, but still with a frequency-dependent cell size. In that case, you can use EM.Tempo's '''Regular''' FDTD mesh generator, which is indeed a simplified version of its adaptive mesh generator. The regular FDTD mesh enforces only two criteria: minimum mesh density and absolute minimum grid spacing. The grid cell sizes in this mesh are almost uniform in objects of the same material composition or in free-space regions.

EM.Tempo's default mesh generator creates an adaptive brick volume mesh that uses also offers a variable staircase profileuniform, where the grid line spacings vary with the curvature (derivative) of the edge or face. As a resultfrequency-independent, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh DensityFixed-Cell''', expressed in cells per effective wavelengthFDTD mesh generator. Since FDTD is a timeThe fixed-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency cell mesh consists of three uniform grids in the project: f_max = f₀ + &Delta;f/2XY, where f₀ is your project's center frequency YZ and &Delta;f (or BW) is its specified bandwidthZX principal planes. In other wordsHowever, the effective wavelength in uniform mesh cell dimensions along the free space is &lambda;_{0three direction,eff} = c / f_max, c being the speed of light in the free spacei. The effective wavelength in a dielectric material with relative permittivity e_r and permeability µ_r is given by . &lambdaDelta;_dx,eff = &lambdaDelta;_0,eff / y and &radicDelta;&epsilon;_r&mu;_rz do not have to be equal. The fixed-cell mesh generator tries to fit your physical structure to the mesh grid rather than adapting the mesh to your physical structure.

{{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed and independent of your project's frequency settings.}} [[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Adaptive_Yee_Mesh | EM.Tempo's Adaptive Brick Mesh Generator]]'''.27s_Adaptive_Brick_Mesh_Generator  [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Tempo's Adaptive Fixed-Cell Brick Mesh Generator]]'''. <table><tr><td> [[Image:Tempo L11 Fig5.png|thumb|left|550px|A human head model and a cellular phone handset on its side.]] </td></tr><tr><td> [[Image:Tempo L11 Fig7.png|thumb|left|550px|The FDTD mesh of the human head model and the cellular phone handset.]] </td></tr><tr><td> [[Image:Tempo L11 Fig8.png|thumb|left|550px|Another view of the FDTD mesh of the human head model and the cellular phone handset.]] </td></tr></table> === Discretizing the Physical Structure Using the Adaptive Yee Mesh === EM.Tempo's default mesh generator creates an adaptive brick volume mesh that uses a variable staircase profile, where the grid line spacings vary with the curvature (derivative) of the object edges or faces. As a result, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed in cells per effective wavelength. Since FDTD is a time-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency of the project: f_max = f₀ + &Delta;f/2, where f₀ (or fc) is your project's center frequency and &Delta;f (or bw) is its specified bandwidth. In other words, the effective wavelength in the free space is &lambda;_0,eff = c / f_max, c being the speed of light in the free space. The effective wavelength in a dielectric material with relative permittivity &epsilon;_r and permeability &mu;_r is given by &lambda;_d,eff = &lambda;_0,eff / &radic;&epsilon;_r&mu;_r.  The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e_r and permeability µ_r is given by &lambda;_d,eff = &lambda;_0,eff / &radic;&epsilon;_r&mu;_r. Therefore, the average ratio of the cell size in a dielectric region to the cell size in the free space is 1/&radic;(&epsilon;_r&mu;_r). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is more visible in the case of curved solids, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using a staircase profile. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best way. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regions. For example, this often happens around the interface between the free space and high permittivity dielectric objects. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structures. A carefully calculated, "<u>'''Adaptive'''</u>" mesh of your physical structure is generated in order to satisfy the following criteria: * Optimize the number of mesh cells in each dimension. The product of the number of cells in all the three dimension determines the total mesh size. The larger the mesh size, the longer the simulation time, especially with the CPU version of the FDTD engine. Also, a very large mesh size requires more RAM, which may exceed your GPU memory capacity. Set the '''Minimum Mesh Density''' to a moderately low value to keep the mesh size manageable, but be careful not to set it too low (see the next item below).* Ensure simulation accuracy by requiring an acceptable minimum number of cells per wavelength through each object and in the empty (free) space between them and the computational domain boundaries. An effective wavelength is defined for each material at the highest frequency of the project's specified spectrum. We recommend a '''Minimum Mesh Density '''of at least 15-20 cells/ wavelength. But for some resonant structures, 25 or even 30 cells per wavelength may be required to achieve acceptable accuracy. As you reduce the mesh density, the simulation accuracy decreases.* Accurately represent and approximate the boundaries of edges or surfaces that are not grid-aligned by closely adhering to their geometric contours. This is controlled by the '''Minimum Grid Spacing Over Geometric Contours''', which can be specified either as a fraction of the free space grid spacing or as an absolute length value in project units.* Maximize the minimum grid spacing in any dimension inside the computational domain and thus maximize the simulation time step. The time step size is dictated by the CFL stability criterion and is driven by the smallest grid spacing in each dimension. The smaller the time step, the larger the number of time steps required for convergence. This is controlled using the '''Absolute Minimum Grid Spacing''', which can be specified either as a fraction of the free space grid spacing or as an absolute value. It is critical to accurately represent and precisely maintain the object edge/surface boundaries in certain structures like resonant antennas and filters, as the phase of the reflected fields/waves is affected by the object boundary positions. When object boundaries are very close to each other, the mesh needs to represent them by two separate, but very closely spaced, grid lines. To control the minimum allowed grid spacing, use the '''Absolute Minimum Grid Spacing '''settings,* Maintain a smooth grid with no abrupt jumps from low-density to high-density regions. This feature is enabled with the '''Create Gradual Grid Transitions '''check box (always checked by default). When [[EM.Cube]] generates an FDTD mesh, a large number of geometrical considerations are taken into account. These include the bounding box of each object and its corners, the ends of a line, the apex of a cone or pyramid, or the locations of lumped sources, field probes and sensors, vertices of plane wave or far field boxes, to name a few examples. These points are “locked” as fixed grid nodes in the FDTD mesh. [[EM.Cube]] determines these points internally to generate a mesh that best approximates the original structure. As you saw earlier, you can use the FDTD mesh settings to control the shape and resolution of the mesh, for example, around the curved portions of your structure, or on slanted lines or faces, etc. These settings are global and apply to all the objects making up your physical structure. You can control the global mesh more selectively using the Advanced FDTD Mesh Settings Dialog. To open this dialog, click the '''Advanced '''button at the bottom of the FDTD Mesh Settings dialog. For example, you can control the quality of the gradual grid transitions by setting the value of '''Max Adjacent Cell Size Ratio'''. The default value of this parameter is 1.3, which maintains a smooth grid line spacing scheme with no more than 1:1.3 ratio for adjacent cells. By default, grid lines are enforced at all source and observable locations. You have the option to disable this feature and round up source locations to their closest grid lines. You may also uncheck the box labeled "Adapt mesh resolution to material properties". In that case, the same effective wavelength will be used to determine the mesh resolution inside all materials as well as the free-space regions.

EM.Tempo also offers a uniform, frequency-independent, fixed-cell FDTD mesh generator. The fixed-cell mesh consists figures below compare the three types of three uniform grids along the XY, YZ and ZX principal planesFDTD mesh for a dielectric ellipsoid with &epsilon;_r = 4. In Note that case, the fixed-cell mesh generator tries to fit your physical structure to size inside the mesh grid rather than adapting dielectric region is half the mesh to your physical structurecell size in the air region.

<table><tr><td> [[Image:Info_iconFDTD MAN21.png|40pxthumb|left|360px|The geometry of a dielectric ellipsoid with &epsilon;_r = 4.]] Click here to learn more about '''</td><td> [[Mesh_Generation_Schemes_in_EMImage:FDTD MAN22.Cube#The_Fixed-Cell_Brick_Mesh_Generator png|thumb|left|360px| The Fixed-Cell Brick Mesh Generator adaptive mesh of the dielectric ellipsoid.]]'''.</td></tr></table>

Occasionally, you may opt for a more regularized <table><tr><td> [[Image:FDTD MAN18.png|thumb|left|360px|The top view of the adaptive FDTD mesh with almost equal grid line spacings everywhere, but still with a frequency-dependent cell sizeof the dielectric ellipsoid. For that purpose, EM]]</td><td> [[Image:FDTD MAN19.Tempo offers png|thumb|left|360px|The top view of the '''Regular''' regular FDTD mesh generator, which is a simplified version of its adaptive the dielectric ellipsoid with the same mesh generatordensity. ]]</td></tr><tr><td> [[Image:FDTD MAN20A.png|thumb|left|360px|The regular top view of the fixed-cell FDTD mesh enforces only two criteriaof the dielectric ellipsoid using the larger cell size inside the air region.]]</td><td> [[Image: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''FDTD MAN20. png|thumb|left|360px|The grid top view of the fixed-cell sizes in this FDTD mesh are almost I=uniform in objects of the same material composition or in free-space regionsdielectric ellipsoid using the smaller cell size inside the dielectric region.]]</td></tr></table>

{{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with The figures below compare the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed low resolution and independent high resolution adaptive FDTD meshes of your project's frequency settingsa PEC parabolic reflector. This structure involves both a curved surface and a very thin surface.}}

<td> [[Image:FDTD34FDTD MAN23.png|thumb|left|450px|The geometry of a PEC parabolic reflector.]]</td></tr></table> <table><tr><td> [[Image:FDTD MAN24.png|thumb|left|360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN27.png|thumb|left|360px|The high-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr><tr><td> [[Image:FDTD MAN26.png|thumb|left|360px|The top (XY) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN25.png|thumb|left|360px|The right (YZ) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr></table> === Adding Fixed Grid Points to the Adaptive Yee Mesh === Adding fixed grid points to an FDTD mesh increases its resolution locally. Each fixed grid point adds three grid lines along the three principal axes passing through that point. You can add as many fixed grid points as you desire and create dense meshes at certain regions. Fixed grid points appear as grey points in the project workspace. To insert a new fixed grid point, follow these steps: * Open the Fixed Grid Points Dialog by selecting '''Menu > Simulate > Discretization > Fixed Grid Points...''' or by right-clicking on the '''FDTD''' '''Mesh''' item of the navigation tree and selecting '''Fixed Grid Points Settings...'''* Click the {{key|Add/Edit}} button to open the "Add Fixed Grid Point" dialog.* Enter the (X, Y, Z) coordinates of the new fixed point in the coordinate boxes and click the {{key|OK}} button.* To modify the coordinates of an existing fixed grid point, select it from the table and click the {{key|Add/Edit}} button.* You can also remove a fix grid point from the FDTD mesh using the {{key|Delete}} button. <table><tr><td> [[Image:FDTD36.png|thumb|left|480px|A human head model user-defined fixed grid point in an FDTD mesh.]] </td></tr><tr><td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.Tempo's fixed grid points settings dialog.]] </td></tr><tr><td> [[Image:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]] </td></tr></table> According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, EM.Tempo's adaptive mesh generator may create extremely tiny grid cells that would result in extremely small time steps. This would then translate into a very long computation time. [[EM.Cube]] offers the "Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. In a regular FDTD mesh, the grid cell sizes stay rather the same in objects of the same material composition. The mesh resolution increases in materials of higher permittivity and /or permeability based on the effective wavelength in exactly the same way as the adaptive mesh. === Profiling the Brick Mesh === A volumetric brick mesh is overwhelming for visualization in the 3D space. For this reason, [[EM.Cube]]'s mesh view shows only the outline of the cells on exterior surface of the (staircased) meshed objects. The mesh grid planes provide a cellular phone handset 2D profile of the mesh cells along the principal coordinate planes. To display a mesh grid plane, select '''Menu > Simulate > Discretization > Grid Planes >''' and pick one of the three options: '''XY Plane''', '''YZ Plane''' or '''ZX Plane'''. You may also right click on its sideone of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and select '''Show''' from the contextual menu. While a mesh grid plane is visible, you can move it back and forth between the two boundary planes at the two opposite sides of the computational domain. You can do this in one of the following four ways: * Using the keyboard's Page Up {{key|PgUp}} key and Page Down {{key|PgDn}} key.* By selecting '''Menu > Simulate > Discretization > Grid Planes > Increment Grid''' or ''' Decrement Grid'''.* By right clicking on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and selecting '''Increment Grid''' or ''' Decrement Grid''' from the contextual menu.* Using the keyboard shortcut {{key|>}} or {{key|<}}. As you “step through” or profile the mesh grid, you can see how the structure is discretized along internal planes of the computational domain. <table><tr><td> [[Image:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]] </td><td> [[Image:FDTD33Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td></tr></table> === The FDTD Grid Coordinate System (GCS) === When your physical structure is discretized using the brick mesh generator, a second coordinate system becomes available to you. The mesh grid coordinate system allows you to specify any location in the computational domain in terms of node indices on the human head model mesh grid. [[EM.Cube]] displays the total number of mesh grid lines of the simulation domain (N_x × N_y × N_z) along the three principal axes on the '''Status Bar'''. Therefore, the number of cells in each direction is one less than the number of grid lines, i.e. (N_x-1)× (N_y-1) × (N_z-1). The lower left front corner of the domain box (Xmin, Ymin, Zmin) becomes the origin of the mesh grid coordinate system (I = 0, J = 0, K = 0). The upper right back corner of the domain box (Xmax, Ymax, Zmax) therefore becomes (I = N_x-1, J = N_y-1, K = N_z-1). [[EM.Cube]] allows you to navigate through the mesh grid and evaluate the cellular phone handsetgrid points individually.Every time you display one of the three mesh grid planes, the "'''Grid Coordinate System (GCS)'''" is automatically activated. On the Status Bar, you will see [[Image:statusgrid.png]] instead of the default [[Image:statusworld.png]]. This means that the current coordinates reported on Status Bar are now expressed in grid coordinate system. The current grid point is displayed by a small white circle on the current mesh grid plane, and it always starts from (I = 0, J = 0, K = 0). Using the keyboard's '''Arrow Keys''', you can move the white circle through the mesh grid plane and read the current node's (I, J, K) indices on the status bar. You can switch back to the "'''World Coordinate System (WCS)'''" or change to the "'''Domain Coordinate System'''" by double-clicking the status bar box that shows the current coordinate system and cycling through the three options. The domain coordinate system is one that establishes its origin at the lower left front corner of the computational domain and measure distances in project unit just like the WCS. <table><tr><td> [[Image:FDTD35(1).png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.]]</td>

== Running FDTD Simulations Using in EM.Tempo ==

[[Image:FDTD57.png|thumb|390px|EM.Tempo's Run dialog.]][[Image:FDTD66.png|thumb|480px|EM.Tempo's output window.]]Once you build your physical structure in the project workspace and define an excitation source, you are ready to run an FDTD simulation. The simulation engine will run even if you have not defined any observables. Obviously, no simulation data will be generated in that case. [[EM.Tempo ]] currently offers several different simulation modes as follows:

| style="width:120px;" | [[#Running a Wideband FDTD Analysis| Wideband Analysis]]

| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]

| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]

| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]

| style="width:120px;" | [[#Running a Dispersion Sweepin EM.Tempo | Dispersion Sweep]]

The FDTD method is one of the most versatile numerical techniques for solving electromagnetic modeling problems. Choosing the right settings and optimal values for certain numerical [[parameters]] will have a significant impact on both accuracy and computational efficiency of an FDTD simulation. Below are a number of steps that you should typically follow by order when planning your FDTD simulation:

Wideband analysis is [[EM.Tempo]]'s simplest and most straightforward simulation mode. It runs the FDTD time marching loop once. At the end of the simulation, the time-domain field data are transformed into the frequency domain using a discrete Fourier transform (DFT). As a result, you can generate wideband frequency data from a single time-domain simulation run. The other simulation modes will be explained later in this manual.

To open the Simulation Run Dialog, click the '''Run''' [[Image:run_icon.png]] button of the '''Simulate Toolbar''' or select the menu item '''Menu > Simulate > &rarr; Run...''' from the menu bar or use the keyboard shortcut {{key|Ctrl+R}}. To start the FDTD simulation, click the {{key|Run}} button at the bottom of this dialog. Once the simulation starts, the "'''Output Message Window'''" pops up and reports messages during the different stages of the FDTD simulation. During the FDTD time marching loop, after every 10th time step, the output window updates the values of the time step, elapsed time, the engine performance in Mega-cells per seconds, and the value of the convergence ratio U_n/U_max in dB. An [[EM.Tempo ]] simulation is terminated when the ratio U_n/U_max falls below the specified power threshold or when the maximum number of time steps is reached. You can, however, terminate the FDTD engine earlier by clicking the '''Abort Simulation''' button. <table><tr><td> [[Image:Tempo L1 Fig13.png|thumb|left|480px|EM.Tempo's simulation run dialog.]]</td></tr><tr><td> [[Image:Tempo L1 Fig15.png|thumb|left|550px|EM.Tempo's output message window.]]</td></tr></table>

In the " '''Convergence''' " section of the dialog, you can set the '''Termination Criterion''' for the FDTD time loop. The time loop must stop after a certain point in time. If you use a decaying waveform like a Gaussian pulse or a Modulated Gaussian pulse, after certain number of time steps, the total energy of the computational domain drops to very negligible values, and continuing the time loop thereafter would not generate any new information about your physical structure. By contrast, a sinusoidal waveform will keep pumping energy into the computational domain forever, and you have to force the simulation engine to exit the time loop. [[EM.Tempo ]] provides two mechanism to terminated the time loop. In the first approach, an energy-like quantity defined as U_n = &Sigma; [ &epsilon;₀|'''E_i,n'''|² + &mu;₀|'''H_i,n'''|² ].&Delta;V_i is calculated and recorded at a large random set of points in the computational domain. Here i is the space index and n is the time index. The quantity U_n has a zero value at t = 0 (i.e. n = 0), and its value starts to build up over time. With a Gaussian or Modulated Gaussian pulse waveform, U_n reach a maximum value U_max at some time step and starts to decline thereafter. The ratio 10.log( U_n/ U_max) expressed in dB is used as the convergence criterion. When its value drops below certain '''Power Threshold''', the time loop is exited. The default value of Power Threshold is -30dB, meaning that the FDTD engine will exit the time loop if the quantity U_n drops to 1/1000 of its maximum value ever. The second termination criterion is simply reaching a '''Maximum Number of Time Steps''' , whose default value set to 10,000. A third option, which is [[EM.Tempo]]'s default setting (labeled "'''Both'''"), terminates the simulation as soon as either of the first two criteria is met first.

The serial CPU solver is [[EM.Tempo]]'s basic FDTD kernel that run the time marching loop on a single central processing unit (CPU) of your computer. The default option is the multi-core CPU solver. This is a highly parallelized version of the FDTD kernel based on the Open-MP framework. It takes full advantage of a multi-core, multi-CPU architecture, if your computer does have one. The GPU solver is a hardware-accelerated FDTD kernel optimized for CUDA-enabled graphical processing unit (GPU) cards. If your computer has a fast NVIDIA GPU card with enough onboard RAM, the GPU kernel can speed up your FDTD simulations up to 50 times or more over the single CPU solver.

[[Image:Info_icon.png|40px30px]] Click here to learn more about the theory of '''[[Basic_FDTD_TheoryBasic_Principles_of_The_Finite_Difference_Time_Domain_Method#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]]'''.

</tr></tr></table> <table><tr><tr><td> [[Image:Period2.png|thumb|350px720px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td>

[[Image:FDTD144.png|thumb|250px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]The '''Dispersion Sweep '''option of the Simulation Mode dropdown drop-down list performs a sweep of constant k_l wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.Cube]]'s [[FDTD ModuleTempo]] uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k_li, you can find the reflection and transmission coefficients for all combinations of frequency f_j and incident angle &theta;_j such that (2&pi;/c) . f_j. sin &theta;_j = k_li. This provides a complete picture of the dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the eigenvalues of the periodic structure. The horizontal axis represents the constant transverse wavenumber k_l (or beta). The vertical axis represents frequency. Sometimes, the free space wave number k₀ = (2&pi;/c).f is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] plots frequency vs. wavenumber. Both the horizontal and vertical axes start from 0 and extend to f_max and k_l,max, respectively, where f_max = f₀ + &Delta;f/2, and &Delta;f is the specified bandwidth of the project. For this sweep option you have to specify the number of wavenumber samples. Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle &phi; as specified in [[FDTD ModuleEM.Tempo]]'s Plane Wave Dialog.

[[Image:FDTD148KBT Settings.png|leftthumb|450px360px|A typical dispersion diagram of a periodic structure[[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]

<ptable>&nbsp;<tr><td>[[Image:KBT R.png|thumb|360px|A typical reflection coefficient dispersion diagram of a periodic structure.]]</ptd><td>[[Image:KBT T.png|thumb|360px|A typical transmission coefficient dispersion diagram of a periodic structure.]]</td></tr></table> <br /> <hr> [[Image:Top_icon.png|48px30px]] '''[[EM.Tempo#Product_Overview | Back to the Top of the Page]]'''

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