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

=== 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 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.

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.

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.Cube]]'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. [[FDTD Module]]'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.

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.Cube]] automatically chooses a time step that satisfies the CFL condition.

=== A Note on Pros and Cons of FDTD Simulation ===

Under each material node, you can create new material groups of the same type/category but with different properties (color, texture, or electric and magnetic constitutive [[parameters]]). These material groups are used to organize the CAD objects you draw in the project workspace or import from external model files. When you create a new geometrical object such as a Box or a Sphere, it is inserted under the currently active material type. There is only one material group that is active at any time. It is recommended that you first create material groups, and then draw new objects under the active material group. However, if you start a new EM.Tempo project from scratch, and start drawing a new object without having previously defined any material groups, a new default PEC group is created and added to the navigation tree to hold your new CAD object.

===Defining a New Material Group===

In many 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. The boundary CPML cells in the project workspace are transparent 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.

===Modeling Planar Structures of Infinite Extents===

Occasionally, you may prefer a more regular FDTD mesh with almost equal grid line spacing everywhere, but still with a frequency-dependent cell size. In that case, you can select the "<u>'''Regular'''</u>" option of the '''Mesh Type '''dropdown list in the FDTD Mesh Settings dialog. The regular FDTD mesh enforces only two of the above [[parameters]]: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''. Or you may opt for an absolutely "<u>'''Uniform'''</u>" mesh type, for which you need to specify the '''Cell Size '''along the X, Y, Z directions in project units.

==Setting Up an Excitation Source==

# '''[[FDTD_Source_Types#Gaussian_Beam_Source|Gaussian Beam Source]]''': A distributed source with a complex-valued focused Gaussian beam profile defined using a virtual box object enclosing the entire physical structure.

===Defining a New Source===

{{Note|All of EM.Tempo's excitation sources have a default modulated Gaussian pulse waveform unless you change them.}}

===Defining Ports===

Using simple lumped sources, you can simulate a variety of transmission line structures in [[EM.Tempo]] including filters, couplers or antenna feeds and you can calculate their scattering [[parameters]]. 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.

[[File:FDTD56.png|thumb|300px|EM.Tempo's Lumped Load dialog.]]

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]], VSWR and periodic characteristics like reflection and transmission coefficients, are calculated over the entire specified bandwidth of your project.

===Defining a New Observable===

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{{FDTD Details}}