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[[EM.Tempo ]] is a powerful 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 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 ]] has undergone several evolutionary development cycles since its initial release inception in 2004. The original simulation engine utilized an FDTD formulation based on the uniaxial perfectly matched layer (UPML) boundary termination. Subsequently, a more advanced boundary termination based on the convolutional perfectly matched layer (CPML) was implemented 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 using CPML walls that touch material media. A novel formulation of periodic boundary conditions was 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 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:Info_icon.png|30px]] Click here for an overview of the '''[[Basic Principles of The Finite Difference Time Domain Method | Basic FDTD Theory]]'''.

[[Image:ART GOLF Fig title.png|thumb|left|400px| The 3D far-field radiation pattern of the a vehicle-mounted antenna structuresimulated by EM.Tempo.]]

[[EM.Tempo ]] is a general-purpose EM simulator than can 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 [[EM.Cube]] simulation environment as its full-wave "FDTD Module" of . [[EM.CubeTempo]]. 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.

=== 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. [[Image:Info_iconEM.png|30pxTempo]] Click here uses a staircase "Yee" mesh to learn more about discretize the basic functionality 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. [[Building_Geometrical_Constructions_in_CubeCAD | CubeCADEM.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 your physical structure. <table><tr><td>[[Image:Airplane Mesh.png|thumb|left|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>

Generalized uniaxial metamaterial and doubly negative refractive index metamaterials with arbitrary numbers of both electric and magnetic poles</li>

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

Passive RLC lumped loads and nonliear diode elementselement</li> <li> Active and pssive one-port and two-port networks with arbitrary Netlist definitions</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 structure</li> <li> Remote simulation capabilitystructures</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>

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> Electric and magnetic energies&nbsp;</li>

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

Your physical structure in [[EM.Tempo ]] can be made up of several geometric objects with different material compositions. In other words, the geometric objects you draw or import from external files are grouped together based on a common material composition. [[EM.Tempo]]'s material types are divided into seven categories:

| style="width:150px;" | [[Glossary of EM.Cube's Materials & Physical Object Types#Voxel Database |Voxel DatabasesDatabase]]

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

[[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.

Once a new material node has been created on the navigation tree, it becomes the "Active" material group of the project workspace, which is always listed in bold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active material type. There is only one material group that is active at any time. Any material can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create 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 object.

{{Note|You can import external objects only to CubeCAD. You can then move the imported objects form CubeCAD to [[EM.Tempo]].}}

[[Image:Info_icon.png|30px]] Click here to access the '''[[Glossary of EM.Cube's Materials , Sources, Devices & Other Physical Object Types]]'''.

[[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.

[[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.

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.}}

<td> [[Image:FDTD MAN10.png|thumb|left|550px360px|The boundary CPML cells placed outside the visible domain box.]] </td></tr></table><table><tr><td> [[Image:FDTD15.png|thumb|left|480px360px|CPML Settings dialog.]] </td>

You can use [[EM.Tempo ]] to model planar structures of infinite extents. A planar substrate usually consists of one or more dielectric layers, possibly with a PEC ground plane at its bottom. To model a laterally infinite dielectric substrate, you must assign a PML boundary condition to the four lateral sides of the domain box and set the lateral domain offset values along the ±X and ±Y directions all equal to zero. If the planar structure ends in an infinite dielectric half-space from the bottom, you must assign a PML boundary condition to the bottom side of the domain box and set the -Z offset equal to zero. This leaves only the +Z offset with a nonzero value.

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 layers of laterally infinite extents. In other words, your anisotropic or dispersive material objects must not touch the CPML domain boundaries.}}

<td> [[Image:FDTD MAN8.png|thumb|left|550px360px|The domain box of a patch antenna with a finite-sized substrate and ground.]] </td></tr><tr><td> [[Image:FDTD MAN9.png|thumb|left|550px360px|The domain box of a laterally infinite patch antenna with zero ±X, ±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>

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:

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

| 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: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 specified 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: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:150px;" | [[Glossary of EMGlossary_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: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:150px;" | [[Glossary of EMGlossary_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:150px;" | [[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Plane Wave |Plane Wave Source]]| style="width:300px250px;" | Used for modeling electromagnetic scattering & computation of reflection/transmission characteristics of periodic surfaces | style="width:250px200px;" | StandNone (stand-alone source)| style="width:200px;" | Surface of a cube enclosing the physical structure| style="width:200px;" | None

| style="width:150px;" | [[Glossary of EMGlossary_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:250px200px;" | StandNone (stand-alone source)| style="width:200px;" | Surface of a cube enclosing the physical structure| style="width:200px;" | None

Click on each category to learn more details about it in the [[Glossary of EM.Cube's Excitation Sources]]each source type and how to define one.

A lumped source is [[Image:Info_icon.png|30px]] More information about all the most commonly used way of exciting a structure in EM.Tempo. A lumped source is an ideal source that must types can be placed on a line object that is parallel to one of found in the three principal axes and shows up 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 '''[[Glossary of transmission line structures in EM.Tempo including filtersCube's Materials, 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 casesSources, 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 portsDevices & Other Physical Object Types]]'''.

[[ImageIn the most general sense, one can consider two fundamental types of excitation sources for an FDTD simulation:Info_icona lumped source and a distributed source.png|30px]] Click here to learn more about '''[[Glossary of EM.Cube's Excitation Sources#Modeling Finite-Sized Source Arrays | Using Source Arrays A lumped sources is localized at a single mesh point in Antenna Arrays]]'''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 MAN11.png|thumb|550px360px|A plane wave box enclosing a PEC cylinder at oblique incidence: &theta; = 105&deg; and &phi; = 315&deg;.]] </td></tr><tr><td> [[Image:FDTD MAN12.png|thumb|550px360px|A Gaussian beam box enclosing a PEC cylinder at oblique incidence: &theta; = 105&deg; and &phi; = 315&deg;. The concentric circles represent the beam's focus point and radius.]] </td>

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 Excitation Materials, Sources, Devices & Other Physical Object Types#Lumped Source |Lumped sources]]*[[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Distributed Source |Distributed sources]]*[[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Microstrip Port |Microstrip port sources]]*[[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Coplanar Waveguide (CPW) Port |CPW port sources]]*[[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Coaxial Port |Coaxial port sources]]*[[Glossary of EM.Cube's Excitation Materials, Sources, Devices & Other Physical Object Types#Waveguide Port |Waveguide port sources]]

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:

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]].}}

A sinusoidal waveform is single-tone and periodic. Its spectrum is concentrated around a single frequency, which is equal to your project's center frequency. A Gaussian pulse decays exponentially as t &rarr; &infin;, but it has a lowpass frequency spectrum which is concentrated around f = 0. A modulated Gaussian pulse decays exponentially as t &rarr; &infin;, and it has a bandpass frequency spectrum concentrated around your project's center frequency. For most practical problems, a modulated Gaussian pulse waveform with [[EM.Tempo]]'s default parameters provides an adequate performance.

The accuracy of the FDTD simulation results depends on the right choice of temporal waveform. [[EM.Tempo]]'s default waveform choice is a modulated Gaussian pulse. At the end of an FDTD simulation, the time domain field data are transformed into the frequency domain at your specified frequency or bandwidth to produce the desired observables.

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

[[Image:Info_icon.png|30px]] Click here to learn more about [[EM.Tempo]]'s '''[[Basic FDTD Theory#The Relationship Between Excitation Waveform and Frequency-Domain Characteristics | Standard & Custom Waveforms and Discrete Fourier Transforms]]'''.

== = Defining Lumped Devices === In [[EM.Tempo]], you can define four types of lumped devices: # '''[[Glossary of EM.Cube's Simulation Data Lumped Devices & Circuits#Lumped Resistor | Resistor]]''' # '''[[Glossary of EM.Cube's Lumped Devices & Circuits#Lumped Capacitor | Capacitor]]''' # '''[[Glossary of EM.Cube's Lumped Devices & Circuits#Lumped Inductor | Inductor]]'''# '''[[Glossary of EM.Cube's Lumped Devices & Circuits#Lumped Nonlinear Diode | Nonlinear Diode]]'''  Although lumped devices are not sources and do not excite a structure, their properties are similar to lumped sources. 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 source, lumped devices have a '''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|30px]] Click here for a general discussion of '''[[Glossary of EM.Cube's Lumped Devices & Circuits#A Review of Linear & Nonlinear Passive & Active Devices | Linear & Nonlinear Passive & Active Devices]]'''. {{Note|Small values of inductance may result in the divergence of the FDTD numerical scheme. To avoid this problem, you need to increase the mesh resolution and adopt a higher mesh density. This, of course, may lead to a much longer computation time.}} <table><tr><td> [[Image:FDTD MAN17.png|thumb|left|480px|EM.Tempo's lumped device dialog.]] </td></tr></table> == EM.Tempo's Observables & Simulation Data Types==

[[EM.Tempo]]'s FDTD simulation engine calculates all the six electric and magnetic field components (E_x, E_y, E_z, H_x, H_y and H_z) at every mesh grid node at all time steps from t = 0 until the end of the time marching loop. However, in order to save memory usage, the engine discards the temporal field data from each time step to the next. Storage, manipulation and visualization of 3D data can become overwhelming for complex structures and larger computational domains. Furthermore, calculation of some field characteristics such as radiation patterns or radar cross section (RCS) can be sizable, time-consuming, post-processing tasks. That is why [[EM.Tempo ]] asks you to define project observables to instruct what types of output data you want in each simulation process.

[[EM.Tempo ]] offers the following types of output simulation data:

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.

[[EM.Tempo]]'s FDTD time marching loop computes all the six electric and magnetic field components at every Yee cell of your structure's mesh at every time step. This amounts to a formidable amount of data that is computationally very inefficient to store. Instead, you can instruct [[EM.Tempo ]] to save a small potion of these data for visualization and plotting purposes. Using a '''Field Probe''' at a specified point, you can record the a time-domain field component over the entire FDTD loop. The time-domain results are also transformed to the frequency domain within the specified bandwidth using a discrete Fourier transform (DFT).

In [[EM.Tempo]], you can visualize the near fields at a specific frequency in a specific plane of the computational domain. To do so, you need to define a '''Field Sensor''' observable. [[EM.Tempo]]'s field sensor defines a plane across the entire computational domain parallel to one of the three principal planes. The magnitude and phase of all the six components of the electric and magnetic fields on the mesh grid points on the sensor plane are computed and displayed.

In the FDTD method, the far fields are calculated using a near-field-to-far-field transformation of the field quantities on a given closed surface. [[EM.Tempo ]] uses rectangular boxes to define these closed surfaces. You can use [[EM.Tempo]]'s default radiation box or define your own custom box. Normally, the radiation box must enclose the entire FDTD structure. In this case, the calculated radiation pattern corresponds to the entire radiating structure. Alternatively, you can define a custom radiation box that may contain only parts of a structure, which results in a partial radiation pattern.

The default radiation box is placed at an offset of 0.1&lambda;₀ from the largest bounding box of your physical structure. You can change the offset value from the "Far Field Acceleration" dialog, which can be accessed by clicking the {{key|Acceleration...}} button of [[EM.Tempo]]'s Radiation Pattern dialog. Calculation of far-field characteristics at high angular resolutions can be a very time consuming computational task. You can accelerate this process by setting a lower '''Max. Far Field Sampling Rate''' from the same dialog. The default sampling rate is 30 samples per wavelength. A low sampling rate will under-sample the mesh grid points on the radiation box.

In [[EM.Tempo]], you can use CPML boundary conditions with zero offsets to model a structure with infinite lateral extents. The calculation of the far fields using the near-field-to-far-field transformation requires the dyadic Green's function of the background structure. By default, the FDTD engine uses the free space dyadic Green's function for the far field calculation. In general, the [[EM.Tempo ]] provides the dyadic Green's functions for four scenarios:

In other words, [[EM.Tempo ]] lets you calculate the far field radiation pattern of a structure in the presence of any of the above four background structure types. You can set these choices in [[EM.Tempo]]'s "Far Field Background Medium" dialog. To access this dialog, open the Radiation Pattern dialog and click the button labeled {{key|Background...}}. From this dialog, you can also set the Z-coordinate of the top of the terminating half-space medium. If you set the -Z boundary condition of your computational domain to PEC or PMC types, the cases of infinite PEC or PMC ground planes from the above list are automatically selected, respectively, and the Z-coordinates of the ground plane and the bottom face of the computational domain will be identical.

The fourth case applies when your computational domain ends from the bottom in a dielectric layer with a CPML -Z boundary along with a -Z domain offset equal to zero. If you set the lateral domain offset values along the ±X and ±Y directions equal to zero, too, , then your structure is, in effect, terminated at an infinite half-space dielectric medium. In that case, you have to specify the permittivity &epsilon;_r and electric conductivity &sigma; of the terminating medium in the Background Medium dialog. You may additionally want to set the Z-coordinate of the top of that dielectric layer as the position of the interface between the free space and the lower dielectric half-space. Note that the current version of [[EM.Tempo ]] does not calculate the far-field Green's function of a conductor-backed, dielectric substrate with a finite layer thickness. To use the background medium feature of [[EM.Tempo]], your structure can have either an infinite PEC/PMC ground or a dielectric half-space termination.

[[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 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.

In [[EM.Tempo]], you can choose one of the three FDTD mesh types:

[[EM.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 '''Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. 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 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 ]] also offers a uniform, frequency-independent, '''Fixed-Cell''' FDTD mesh generator. The fixed-cell mesh consists of three uniform grids in the XY, YZ and ZX principal planes. However, the uniform mesh cell dimensions along the three direction, i.e. &Delta;x, &Delta;y and &Delta;z 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.

[[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.

[[Image:FDTD MAN18.png|thumb|left|550px360px|The top view of the adaptive FDTD mesh of the dielectric ellipsoid.]]

[[Image:FDTD MAN19.png|thumb|left|550px360px|The top view of the regular FDTD mesh of the dielectric ellipsoid with the same mesh density.]]

[[Image:FDTD MAN20A.png|thumb|left|550px360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the larger cell size inside the air region.]]

[[Image:FDTD MAN20.png|thumb|left|550px360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the smaller cell size inside the dielectric region.]]

[[Image:FDTD MAN24.png|thumb|left|450px360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]]

[[Image:FDTD MAN27.png|thumb|left|450px360px|The high-resolution adaptive mesh of the PEC parabolic reflector.]]

[[Image:FDTD MAN26.png|thumb|left|550px360px|The top (XY) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]

[[Image:FDTD MAN25.png|thumb|left|550px360px|The right (YZ) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]

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:

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 '''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.

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.

The '''Dispersion Sweep '''option of the Simulation Mode 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.Tempo ]] 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 [[EM.Tempo]]'s Plane Wave Dialog.

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