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[[Image:Splash-fdtd.jpg|right|720px]]<strong><font color="#961717" size="4">Fast Multicore & GPU-Accelerated FDTD Solvers for Simulating the Most Complex Electromagnetic Modeling Problems</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:prop-ico.png | link=An EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Tempo_Documentation | EM.Tempo Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

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 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.

=== Pros and Cons EM.Tempo has undergone several evolutionary development cycles since its 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 Simulation ===). 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.

A time domain simulation like FDTD offers several advantages over a frequency domain simulation[[Image:Info_icon. In certain applications, the time domain signature or behavior png|30px]] Click here for an overview of a system, e.g. the transient response '''[[Basic Principles 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 Finite Difference Time Domain Method | Basic 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 qualityTheory]]'''.

Like every numerical technique, the FDTD method has disadvantages, too<table><tr><td>[[Image:ART GOLF Fig title. 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 png|thumb|left|400px| The 3D far-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 radiation pattern 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 openvehicle-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 mounted antenna structure. simulated by EM.Tempo provides high quality perfectly match layer (PML) terminations at the boundaries which can be placed fairly close your physical structure.]]</td></tr></table>

=== An Overview of EM.Tempo as the FDTD Modeling Module of EM.Cube ===

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 been integrated within the [[Image:FDTD93.png|thumb|300px|A metal ellipsoid object..EM.Cube]][[Image:FDTD94simulation environment as its full-wave "FDTD Module".png|thumb|300px|EM...and its Yee mesh.]]In Tempo shares the Finite Difference Time Domain (FDTD) methodvisual interface, a discretized form of Maxwell’s equations is solved numerically and simultaneously in both the 3D space and time. During this processparametric CAD modeler, data visualization tools, the electric and magnetic fields are computed everywhere in the computational domain many more utilities and features collectively known as a function [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all 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 [[parametersEM.Cube]], input impedance, far field radiation patterns, radar cross section, etc's other computational modules.

[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Differential Form of Maxwell's EquationsGetting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

Since FDTD is a finite domain numerical technique, the computational domain === The Advantages & Limitations of the problem must be truncatedEM. 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 Tempo's 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. Simulator ===

Click here 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 learn more about EMdetermine the wideband frequency response of a system.Tempo's [[Perfectly Matched Layer Termination]]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.

The Like every numerical technique, the FDTD computational domain must be discretized using an appropriate meshing schememethod 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 non-uniform, variable, staircase (pixelated) "Yee " mesh with a mesh density that you can customizeto discretize the physical structure. A fixed-cell mesh generator is also available, where you can set constant cell dimensions This works perfectly fine for rectangular objects that are oriented along the three principal axes for the entire computational domain. The variable mesh density is specified in terms In the case of the effective wavelength inside material media. As a resulthighly curved structures or slanted surfaces and lines, however, this may compromise the mesh resolution and average mesh cell size differ in regions that are filled with different types geometrical fidelity of materialyour structure. [[EM.Cube]]'s non-uniform Tempo provides a default adaptive FDTD mesher generates more cells in the areas that are occupied by dielectric materialscan capture the fine details of geometric contours, fewer slanted thin layers, surfaces, etc. to arbitrary precision. However, with smaller mesh cells in , the free space regions and no cells inside (impenetrable) PEC regionsstability criterion leads to smaller time steps; hence, longer computation times. [[Another disadvantage of the FDTD Module]]'s default "adaptive" mesh generator also refines technique compared to naturally open-boundary methods like the mesh around curved segments method of lines, surface moments (MoM) is its finite-extent computational domain. This means that to model open boundary problems like radiation or solids scattering, absorbing boundary conditions are needed to produce a far more accurate representation dissipate the incident waves at the walls of your geometrythe computational domain and prevent them from reflecting back into the domain. The example accuracy of the FDTD simulation results depends on the right illustrates a metal ellipsoid quality of these absorbers and a 3D view 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 its Yee meshthe computational domain.

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 <table><tr><td>[[parameters]]Image:Airplane Mesh. 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 png|thumb|left|480px|The Yee 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 convergean imported aircraft CAD model. [[EM.Cube]] automatically chooses a time step that satisfies the CFL condition.</td></tr></table>

For more detailed information, see [[Waveform, Bandwidth, Stability]]== EM.Tempo Features at a Glance ==

==Building the = Physical StructureDefinition ===

[[Image:FDTD1.png|thumb|200px|[[FDTD Module]]'s Navigation Tree.]]<ul>In [[EM.Tempo]] <li> PEC, a physical structure consists PMC and dielectric materials and thin wires</li> <li> Uniaxial and fully anisotropic materials with four complete constitutive tensors</li> <li> Dispersive materials of sets of objects that are grouped together Debye, Drude and identified by their material Lorentz types. All the objects belonging to the same material group share the same color with arbitrary number of poles</li> <li> Generalized uniaxial and same material properties. Materials are divided into seven categories that are listed under the '''Physical Structure''' node at the top doubly negative refractive index metamaterials with arbitrary numbers of the navigation treeboth electric and magnetic poles</li> <li> Two types of gyrotropic materials:ferrites and magnetoplasmas</li> <li> PEC, PMC and convolutional perfectly match layer (CPML) boundary conditions</li> <li> Doubly periodic structures</li></ul>

Under each material node<ul> <li> Lumped voltage sources with internal resistance placed on a PEC line or thin wire object with an arbitrary orientation</li> <li> Distributed sources with uniform, you can create new material groups of sinusoidal and edge-singular profiles</li> <li> Microstrip, coplanar Waveguide (CPW) and coaxial ports</li> <li> Waveguide sources with the same typedominant TE<sub>10</category but sub> modal profile</li> <li> Multi-port and coupled port definitions</li> <li> Two types of filamentary current sources: Hertzian short dipole radiators with different properties (color, texturearbitrary orientation and long wire current sources aligned along one of the principal axes with a uniform, triangular or electric sinusoidal current distribution profile</li> <li> Plane wave excitation with linear and magnetic constitutive circular polarizations</li> <li> Multi-ray excitation capability (ray data imported from [[parametersEM.Terrano]]). 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)</li> <li> Gaussian beam excitation</li> <li> Huygens sources</li> <li> Source arrays with weight distribution &amp; phase progression</li> <li> Periodic sources with user defined beam scan angles</li> <li> Standard excitation waveforms (Gaussian pulse, modulated Gaussian and then draw new objects as part of the active material group. Howeversinusoidal) for optimal frequency&nbsp;domain computations&nbsp;</li> <li> Arbitrary user-defined temporal excitation waveforms using mathematical expressions and Python functions</li> <li> Passive lumped devices: R, if you start a new EM.Tempo project from scratchL, and start drawing a new object without having previously defined any material groupsC, a new default PEC group is created series RL and added to parallel RC and nonlinear diode device</li> <li> Active lumped one-port and two-port devices placed on PEC lines aligned along one of the navigation tree to hold your new CAD object.principal axes with arbitrary Netlist definitions</li> <li> Active distributed one-port and two-port devices placed under microstrip lines with arbitrary Netlist definitions</li></ul>

===Defining a New Material GroupMesh Generation ===

To define a new material group<ul> <li> Fast generation of Yee grid mesh of solids, follow these steps:surfaces and curves</li> <li> Geometry-aware and material-aware adaptive mesh generator with gradual grid transitions</li> <li> Fixed-cell uniform mesh generator with three unequal cell dimensions</li> <li> Mesh view with three principal grid profilers</li> <li> Manual control of mesh parameters and fixed grid points</li></ul>

Once <ul> <li> Wideband 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 new material node has been created single FDTD simulation run</li> <li> OpenMP-parallelized multi-core and multi-thread FDTD simulation engine</li> <li> GPU-accelerated FDTD simulation engine based on NVIDIA CUDA platforms</li> <li> Total-field-scattered-field analysis of plane wave and Gaussian beam excitation</li> <li> Full-wave analysis of periodic structures with arbitrary plane wave incidence angles using the navigation tree, it becomes the "Active" Direct Spectral FDTD method</li> <li> Infinite material group half-space Green&#39;s functions for calculation of the project workspace, which is always listed far fields in bold letters. Then you can start drawing new objects under that node. Any material can be made active by right clicking presence of a lossy ground</li> <li> Accelerated computation of S-parameters of resonant structures based on its name in the Navigation Tree and selecting the Prony'''Activate''' item s method of the contextual menu.exponential interpolation</li> <li> Parametric sweeps of variable object properties or source parameters including frequency and angular sweeps</li> <li> Multi-variable and multi-goal optimization of structures</li> <li> Automated generation of compact reduced order surrogate models from full-wave simulation data</li></ul>

===Understanding the FDTD Material TypesData Generation &amp; Visualization ===

Click here to learn more about <ul> <li> Near-field intensity (colorgrid), contour and surface plots (vectorial - amplitude &amp; phase)</li> <li> Near-field probes for monitoring field components in both time &amp; frequency domains</li> <li> Far-field radiation patterns: 3D pattern visualization and 2D polar and Cartesian graphs</li> <li> Far-field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li> <li> Radiation pattern of arbitrary array configurations of the various FDTD structure or periodic unit cell</li> <li> Bistatic and monostatic radar cross section</li> <li> Huygens surface data generation for use in other [[FDTD Material TypesEM.Cube]]modules</li> <li> Periodic reflection/transmission coefficients and k-&beta; diagrams</li> <li> Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li> <li> Time and frequency domain port voltages, currents and powers</li> <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> Computation of electric, magnetic and total energy densities, dissipated power density (Ohmic loss), specific absorption rate (SAR) density and complex Poynting vector on field sensor planes</li> <li> Animation of temporal evolution of fields</li> <li> Custom output parameters defined as mathematical expressions or Python functions of standard outputs</li></ul>

===Moving Objects among Material Groups=Building the Physical Structure in EM.Tempo ==

[[Image:FDTD21(1).png|thumb|325px|Moving objects from one FDTD material group to another.]]You can move one or more selected objects at a time among different material groups. The objects can be selected either === Material Variety in the project workspace, or their names can be selected from the navigation tree. Right click on the highlighted selection and select '''Move To > FDTD >''' from the contextual menu. This opens up another sub-menu with a list of all the available material groups already defined in your EM.Tempo project. Select the desired material node, and all the selected objects will move to that material group. In the case of a multiple selection from the navigation tree using the keyboard's '''Shift Key''' or '''Ctrl Key''', make sure that you continue to hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting the destination material group's name from the contextual menu.===

In a similar way, you Your physical structure in EM.Tempo can move one or more be made up of several geometric objects from an FDTD with different material group to one of [[EMcompositions.Cube]]'s In other modules. In this casewords, the sub-[[menus]] of the '''Move To >''' item of the contextual menu will indicate all the [[EM.Cube]] modules that have valid groups for transfer of the selected geometric objects. You can also move one you draw or more objects import from [[external files are grouped together based on a common material composition. EM.Cube]]Tempo's other modules to a material group in EM.Tempo. types are divided into seven categories:

{{Note|You can import external class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects only |-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Lines parallel to '''one of the three principal axes|-| style="width:30px;" | [[CubeCADFile:pmc_group_icon.png]]'''| style="width:150px;" | [[Glossary_of_EM. You need Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC)]]| style="width:300px;" | Modeling perfect magnetic sheets | style="width:250px;" | Rectangle strips parallel to move one of the imported three principal planes|-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects form |-| style="width:30px;" | [[CubeCADFile:aniso_group_icon.png]] to EM| style="width:150px;" | [[Glossary_of_EM.Tempo as described aboveCube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Anisotropic Material |Anisotropic Material]]| style="width:300px;" | Modeling unaxial or generalized anisotriopic materials| style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:disp_group_icon.}png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dispersive Material |Dispersive Material]]| style="width:300px;" | Modeling Debye, Drude and Lorentz materials and generalized metamaterials | style="width:250px;" | Solid objects|-| 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#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects|}

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

[[Image:fdtd14_tn.png|thumb|400px|Geometric construction of a dielectric-coated metallic cylinder.]]The following rules apply to === Organizing the definition of materials and objects in [[EM.Tempo]]:Physical Structure by Material Groups ===

* Under EM.Tempo groups your geometric objects in the [[#Perfect Conductors|PEC]] category, you can define all types of solid, and surface and [[Curve Objects|curve objects]]project workspace based on their material type.* Under All the [[#Perfect Conductors|PMC]] category, you can define only define rectangle strip objects parallel belonging to the principal planes. * Under same material group share the [[#Dielectric Materials|Dielectric]], [[#Anisotropic Materials|Anisotropic]] same color and [[#Dispersive Materials|Dispersive]] same material categories, you can define only [[Solid Objects|solid objects]]properties.* Under each material node in the Inhomogeneous Material categorynavigation tree, you can only import a Cartesian ".CAR" data file.* Under create new material groups of the Thin Wire categorysame type but with different properties such as color, you can only define line objects parallel to the principal axestexture, or electric and magnetic constitutive parameters.

[[EM.Tempo]] allows overlapping objectsOnce a new material node has been created on the navigation tree, although it becomes the "Active" material group of the project workspace, which is generally recommended that object overlaps be avoided always listed in favor of clearly defined geometries and bold letters. When you draw a new geometric object boundaries. If two such as a box or more objects of a sphere, its name is added under the same currently active material type and . There is only one material group overlap, they are merged using that is active at any time. Any material can be made active by right clicking on its name in the Boolean union operation during navigation tree and selecting the mesh generation process'''Activate''' item of the contextual menu. If two overlapping objects belong to two different It is recommended that you first create material categoriesgroups, and then draw new objects under the active material properties of the FDTD cells in the overlap region will follow the group. However, if you start a new EM.Tempo's material hierarchy rule. In that caseproject from scratch, the overlap area cells will always be regarded as and start drawing a new object without having the previously defined any material type of the higher priority. According to this rulegroups, the material types are ordered from the highest priority a new default PEC group is created and added to the lowest in the following manner:navigation tree to hold your new object.

# [[#Perfect Conductors{{Note|PEC]]# [[#Perfect Conductors|PMC]]# [[#Dispersive Materials|Dispersive]]# General [[#Anisotropic Materials|Anisotropic]]# Uniaxial [[#Anisotropic Materials|Anisotropic]]# [[#Dielectric Materials|Dielectric]]You can import external objects only to CubeCAD. You can then move the imported objects form CubeCAD to EM.Tempo.}}

If planned carefully, taking advantage [[Image:Info_icon.png|30px]] Click here to access the '''[[Glossary of EM.TempoCube's material hierarchy rule would make the construction of complex objects easier. For exampleMaterials, 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. AlternativelySources, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinderDevices & Other Physical Object Types]]'''.

==Setting EM.Tempo's Computational Domain & Boundary Conditions==

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.

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<table><tr><td> [[Image:FDTD13. png|thumb|left|480px|EM.Tempo uses Convolutional Perfectly Matched Layers (CPML) for absorbing 's boundary conditionsdialog. 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.]]</td></tr></table>

Click here to learn more about In 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. [[Advanced CPML SetupEM.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 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, 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 if a very low reflection is required (<-40dB).  {{Note|[[EM.Tempo]]'s default quarter wavelength offset for the domain box and its 8-layer CPML walls are very conservative choices and can be relaxed in many cases. An offset equal to eight free-space grid cells beyond the largest bounding box usually gives a more compact, but still valid, domain box.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#CPML_vs._PML | Perfectly Matched Layer Termination]]'''. <table><tr><td> [[Image:FDTD MAN10.png|thumb|left|360px|The boundary CPML cells placed outside the visible domain box.]] </td><td> [[Image:FDTD15.png|thumb|left|400px|CPML Settings dialog.]] </td></tr></table> ===Modeling Planar Using CPML to Model Structures of Infinite Extents===

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:FDTD22(1)FDTD MAN8.png|thumb|300pxleft|360px|The computational domain box of a metallic sphere patch antenna with nonzero offset in all directionsa finite-sized substrate and ground.]] </td><td> [[Image:FDTD24FDTD MAN9.png|thumb|400pxleft|360px|The computational domain box of a laterally infinite planar structure 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>

== Generating the FDTD Mesh = Source Variety in EM.Tempo ===

=== The Before you can run an FDTD Mesh Types ===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:

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Host Object! scope="col"| Spatial Domain! scope="col"| Restrictions / Additional Requirements|-| style="width:30px;" | [[ImageFile:FDTD28lumped_src_icon.png]]|thumb|350pxstyle="width:150px;" |The adaptive FDTD meshes of a metallic sphere[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Lumped Source |Lumped Source]]| style="width:250px;" | General-purpose point voltage source| style="width:200px;" | PEC or thin wire line parallel to a principal axis| style="width:200px;" | A single point| style="width:200px;" | None|-| style="width:30px;" | [[ImageFile:FDTD34distrb_src_icon.png]]|thumbstyle="width:150px;" |350px|A human head model and a cellular phone handset on its side[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Distributed Source |Distributed Source]]| style="width:250px;" | General-purpose distributed planar source with a uniform, edge-singular or sinusoidal impressed field profile| style="width:200px;" | Virtual rectangle strip parallel to a principal plane| style="width:200px;" | A rectangular area| style="width:200px;" | None|-| style="width:30px;" | [[ImageFile:FDTD33mstrip_icon.png]]|thumbstyle="width:150px;" |350px[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Microstrip Port |The FDTD mesh of Microstrip Port Source]]| style="width:250px;" | Used for S-parameter computations in microstrip-type structures| style="width:200px;" | PEC rectangle strip parallel to a principal plane| style="width:200px;" | A vertical rectangular area underneath the human head model and host strip| style="width:200px;" | Requires a PEC ground plane strip underneath the cellular phone handsethost strip|-| style="width:30px;" | [[File:cpw_icon.png]]| style="width:150px;" | [[EMGlossary_of_EM.TempoCube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Coplanar Waveguide (CPW) Port |Coplanar Waveguide (CPW) Port Source]]'s FDTD mesh is | style="width:250px;" | Used for S-parameter computations in CPW-type structures| style="width:200px;" | PEC rectangle strip parallel to a principal plane| style="width:200px;" | Two parallel horizontal rectangular Yee mesh that extends areas attached to the entire computational domain. It is primarily constructed from three mesh grid profiles along opposite lateral edges the XYhost 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_EM.Cube%27s_Materials, YZ and ZX _Sources,_Devices_%26_Other_Physical_Object_Types#Coaxial Port |Coaxial Port Source]]| style="width:250px;" | Used for S-parameter computations in coaxial-type structures| style="width:200px;" | PEC Cylinder oriented along a principal planes. These projections together create axis| style="width:200px;" | A circular ring area enveloping the host inner conductor cylinder| style="width:200px;" | Requires a 3D rectangular (voxel) mesh spaceconcentric hollow outer conductor cylinder|-| style="width:30px;" | [[File:wg_src_icon. Straight linespng]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials, boxes and _Sources,_Devices_%26_Other_Physical_Object_Types#Waveguide Port |Waveguide Port Source]]| style="width:250px;" | Used for S-parameter computations in waveguide structures| style="width:200px;" | Hollow PEC box oriented along a principal axis| style="width:200px;" | A rectangular plates whose edges are aligned with area at the three principal axes are cross section of the simplest objects to mesh in EMhost hollow box| style="width:200px;" | The host box object can have one capped end at most.Tempo|-| style="width:30px;" | [[File:hertz_src_icon. Such objects preserve their exact shapes after discretizationpng]]| style="width:150px;" | [[Glossary_of_EM. All the objects with curved edges Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Filamentary_Current_Source |Filamentary Current Source]]| style="width:250px;" | General-purpose wire current source of two types: Hertzian short dipole radiator and curved surfaces or objects long wire current source with straight edges and flat faces that are not parallel to a uniform, triangular or sinusoidal current distribution profile| style="width:200px;" | None (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 or principal planes |-| style="width:30px;" | [[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 reflection/transmission characteristics of periodic surfaces | style="width:200px;" | None (such as oblique lines and slanted lateral faces stand-alone source)| style="width:200px;" | Surface of a pyramidcube enclosing the physical structure| style="width:200px;" | None|-| style="width:30px;" | [[File:gauss_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gaussian Beam |Gaussian Beam Source]]| style="width:250px;" | Used for modeling focused beams | style="width:200px;" | None (stand-alone source) are discretized using | style="width:200px;" | Surface of a staircase 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;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:200px;" | None (Yeestand-alone source) profile.| style="width:200px;" | Surface of a cube | style="width:200px;" | Imported from a Huygens surface data file|}

EM.Tempo's adaptive mesh generator uses a variable staircase profile, where the cell sizes of grid line spacing vary with the curvature (derivative) of the edge or face. As a result, a higher mesh resolution is achieved at "more curvy" areas Click on each category to better capture the geometrical learn more detailsabout each source type and how to define one.

[[Image:Info_icon.png|30px]] More information about all the source types can be found in the '''[[Glossary of EM.Cube'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). <table><tr><td> [[Image:FDTD MAN11.png|thumb|360px|A plane wave box enclosing a PEC cylinder at oblique incidence: &theta; = 105&deg; and &phi; = 315&deg;.]] </td><td> [[Image:FDTD MAN12.png|thumb|360px|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></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></tr></table> === Excitation Waveform & Frequency Domain Computations === 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: # Sinusoidal# Gaussian Pulse# Modulated Gaussian Pulse# Arbitrary User-Defined Function 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_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 Custom Waveforms in EM.Tempo === In some time-domain applications, you may want to simulate the propagation of a certain kind of waveform in a circuit or structure. In addition to the default waveforms, EM.Tempo allows you to define custom waveforms by either time or frequency specifications for each individual source in your project. If you open up the property dialog of 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 own temporal waveform. The Excitation Waveform dialog offers three different options for defining the waveform: * Automatically Generate Optimal Waveform* Use Custom Frequency Domain Specifications* Use Custom Time Domain Specifications The first option , which is also the default option, constructs an optimal modulated Gaussian pulse waveform based on your project's specified center frequency and bandwidth. This optimal waveform guarantees the most accurate frequency domain computations for your simulation. The 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|30px]] Click here to learn more about '''[[Using Python to Create Functions, Models & Scripts#Creating Custom Python Functions | Creating Custom Python Functions]]'''. <table><tr><td> [[Image:FDTD MAN13.png|thumb|left|720px|EM.Tempo's excitation waveform dialog showing the default standard modulated Gaussian pulse temporal waveform.]]</td></tr></table> When you define a custom waveform in the Excitation Waveform dialog, make sure to click the {{key|Accept}} button of the dialog to make your changes effective. A 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 special functions module. [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary of EM.Cube's Python Functions#Standard Python Functions | Python's Standard & Advanced Mathematical Functions]]'''. {{Note| If you define a custom excitation waveform for your source, none of the standard frequency domain output data and parameters will be computed at the end of your FDTD simulation.}} <table><tr><td> [[Image:FDTD MAN14.png|thumb|left|720px|EM.Tempo's excitation waveform dialog showing a custom modulated Bessel temporal waveform defined using the Python function sp.j0(x).]]</td></tr></table> == EM.Tempo's Active & Passive Devices == === Defining Lumped 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|30px]] Click here for a general discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.26_Nonlinear_Passive_.26_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 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> === 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== === Understanding the FDTD Observable 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:  {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Associated Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:fieldprobe_icon.png]]| style="width:150px;" | Temporal Waveforms| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]| style="width:300px;" | Computing electric and magnetic field components at a fixed location in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldprobe_icon.png]]| style="width:150px;" | Point Fields| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]| style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components at a fixed location in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components on a planar cross section of the computational domain in the frequency domain| style="width:250px;" | None|-| 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#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation 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 | RCS]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Polarimetric Scattering Matrix Data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS)_Observable | RCS]] | 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_Observable |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Voltages, Currents & Powers| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]] | style="width:300px;" | Computing the port voltages, port currents and total port powers in both time and frequency domains| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| 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]] (No observable definition required) | style="width:300px;" | Computing the reflection and transmission coefficients of a periodic surface| style="width:250px;" | Requires a plane wave source and periodic boundary conditions |-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Electric and Magnetic Energy| 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 inside the entire computational domain in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-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#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]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|-| style="width:30px;" | [[File:CartData_icon.png]]| style="width:150px;" | Generic 3D Cartesian Spatial Data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#3D_Cartesian_Data_Observable | 3D Cartesian Data]]| style="width:300px;" | Visualizing the contents of generic 3D Cartesian spatial data files overlaid on the project workspace | style="width:250px;" | Requires import of an existing ".CAR" data file|} 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. === Examining the Near Fields in Time and Frequency Domains === 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). <table><tr><td> [[Image:FDTD77.png|thumb|left|480px|Time-domain evolution of the electric field at a given point.]]</td></tr></table> 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. <table><tr><td> [[Image:FDTD_FS2.png|thumb|left|420px|EM.Tempo's Field Sensor dialog.]] </td></tr><tr><td> [[Image:FDTD_FS1_new.png|thumb|left|480px|Three field sensor planes defined around a PEC ellipsoid illuminated by a plane wave source.]] </td></tr></table><table><tr><td> [[Image:FDTD_FS3_new.png|thumb|left|360px|Electric field distribution above the PEC plate.]] </td><td> [[Image:FDTD_FS4_new.png|thumb|left|360px|Magnetic field distribution above the PEC plate.]] </td></tr></table> === Computing Far-Field Characteristics in FDTD === Far fields are the asymptotic form the fields when r &rarr; &infin; or k₀r >> 1. Under these assumptions, the fields propagate outward as transverse electromagnetic (TEM) waves: <math> \mathbf{H^{ff}(r)} = \frac{1}{\eta_0} \mathbf{ \hat{k} \times E^{ff}(r)} </math>  Far fields are typically computed in the spherical coordinate system as functions of the elevation and azimuth observation angles &theta; and &phi;. Only far-zone electric fields are normally considered. When your physical structure is excited using a lumped source, a waveguide source, a distributed source, a short dipole source, or an array of such sources, the far fields represent the radiation pattern of your source(s) in the far zone. In that case, you need to define a '''Radiation Pattern - Far Field Observable''' for your project. When your physical structure is illuminated by a plane wave source or a Gaussian beam source, the far fields represent the scattered fields. In the case of a plane source, you can compute the radar cross section (RCS) of your target structure. In that case, you need to define an '''RCS - Far Field Observable''' for your project. 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.  <table><tr><td> [[Image:FDTD_FF1.png|thumb|left|720px|EM.Tempo's Radiation Pattern dialog.]] </td></tr><tr><td> [[Image:FDTD_FF3.png|thumb|left|600px|EM.Tempo's Radar Cross Section dialog.]] </td></tr></table> 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.  <table><tr><td> [[Image:FDTD_FF2.png|thumb|left|480px|EM.Tempo's far field acceleration dialog.]] </td></tr></table> === Radiation Pattern Above a Half-Space Medium === 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: # Free space background# Free space background terminated in an infinite PEC ground plane at the bottom# Free space background terminated in an infinite PMC ground plane at the bottom# Free space background terminated in an infinite dielectric half-space medium <table><tr><td> [[Image:FDTD133.png|thumb|left|480px|EM.Tempo's far field background medium dialog.]] </td></tr></table> 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. <table><tr><td> [[Image:fdtd_out36_tn.png|thumb|left|360px|Radiation pattern of a vertical dipole above PEC ground.]] </td><td> [[Image:fdtd_out37_tn.png|thumb|left|360px|Radiation pattern of a vertical dipole above PMC ground.]] </td></tr><tr><td> [[Image:fdtd_out38_tn.png|thumb|left|360px|Radiation pattern of a horizontal dipole above PEC ground.]] </td><td> [[Image:fdtd_out39_tn.png|thumb|left|360px|Radiation pattern of a horizontal dipole above PMC ground.]] </td></tr></table> === Generating 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 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:

The EM.Tempo's default choice is the mesh generator produces an adaptive brick meshof your physical structure, which is a quite sophisticated whose mesh. The resolution of varies with the adaptive FDTD mesh is driven by frequency. As the operating frequency of your project increases, the default '''Mesh DensityAdaptive''', expressed in cells per effective wavelength. Since FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. The adaptive mesh is optimized in such a time-domain method and way as to capture all the excitation waveform 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 have opt for a wideband spectral contentmore regularized FDTD mesh with almost equal grid line spacings everywhere, the effective wavelength is calculated based on the highest but still with a frequency of the project: f_max = f₀ + &Delta;f/2-dependent cell size. In that case, where f₀ is your projectyou can use EM.Tempo's center frequency and &Delta;f (or BW) '''Regular''' FDTD mesh generator, which is indeed a simplified version of its specified bandwidthadaptive mesh generator. In other words, the effective wavelength 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 free space is &lambda;_0,eff = c / f_max, c being the speed of light same material composition or in the free -spaceregions.

The adaptive FDTD mesh, however, produces different grid cell sizes in the free space regions and inside dielectric regionsEM. 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 Tempo 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 offers 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 exampleuniform, 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. According to the Courantfrequency-Friedrichs-Levy (CFL) stability criterionindependent, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, [[FDTD Module]]'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. Finally, [[EM.Cube]]'s FDTD Modules offers a "Uniform" 'Fixed-Cell''' FDTD mesh generator. The uniform fixed-cell mesh consists of three uniform grids along in the XY, YZ and ZX principal planes. In other wordsHowever, the grid uniform mesh cell sizes dimensions along the three direction, i.e. &Delta;x, &Delta;y and &Delta;z are fixed throughout the entire computational domaindo not have to be equal. In this case, the uniform The fixed-cell mesh generator has tries to fit your physical structure to the fixed mesh, grid rather than adapting the mesh to your physical structure.

===Viewing [[Image:Info_icon.png|30px]] Click here to learn more about the FDTD properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Adaptive_Yee_Mesh | EM.Tempo's Adaptive Brick Mesh===Generator]]'''.

To generate an FDTD mesh and view it the project workspace, follow these steps[[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 Fixed-Cell Brick Mesh Generator]]'''.

* First, click the '''Mesh Settings''' <table><tr><td> [[Image:mesh_settingsTempo L11 Fig5.png|thumb|left|550px|A human head model and a cellular phone handset on its side.]] button of the '''Simulate Toolbar''' or select '''Menu </td> Simulate </tr> Discretization <tr> Mesh Settings...''', or right click on the '''Yee Mesh''' item of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. The Mesh Settings Dialog opens up, where you can set the values of the various mesh <td> [[parameters]] including the '''Mesh Density'''.* After specifying the desired mesh density, you can examine the mesh grid planeImage:Tempo L11 Fig7. png|thumb|left|550px|The XY, YZ, and ZX FDTD mesh grid planes can be displayed through '''Menu > Simulate > Discretization > Grid Planes > XY Plane''', '''YZ Plane''' or '''ZX Plane''' or by right clicking on one of the three '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the Navigation Tree human head model and selecting '''Show''' from the contextual menucellular phone handset. The mesh grid planes give you a good idea of what the mesh will look like once it is generated and its resolution along different planes. To remove a mesh grid plane from the project workspace, select '''Menu ]] </td> Simulate </tr> Discretization <tr> Grid Planes <td>''' one more time and remove the check mark in front of the name of the currently displayed mesh grid plane, or right click on the name of the currently displayed mesh grid plane in the Navigation Tree and select '''Hide''' from the contextual menu.* To display the FDTD mesh, click the '''Show Mesh''' [[Image:mesh_toolTempo L11 Fig8.png]] button |thumb|left|550px|Another view of the '''Simulate''' '''Toolbar '''or select '''Menu > Simulate > Discretization > Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. This takes [[EM.Cube]] into its "Mesh View" mode, and the Yee FDTD mesh of the whole structure is displayed in human head model and the project workspacecellular phone handset. While the mesh view is enabled, the '''Show Mesh''' [[Image:mesh_tool.png]] button remains depressed. To get back to [[EM.Cube]]'s "Normal View" mode, click this button one more time, or deselect '''Menu </td> Simulate </tr> Discretization </table> Show Mesh''' to remove its check mark or simply hit the '''Esc Key''' of the keyboard.

In [[EM.Cube]]'s "Mesh View" mode, you can rotate or pan === Discretizing the view of Physical Structure Using the project workspace, but you cannot edit the objects. '''"Show Mesh"''' generates a new mesh and displays it if there is none in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating an FDTD mesh may take a long time depending on the complexity of structure and the total size of the computational domain. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore any mesh in the memory and force [[EM.Cube]] to generate a fresh FDTD mesh from the ground up by selecting '''Menu > Simulate >Discretization > Regenerate Mesh''' or by right clicking on the '''Adaptive Yee Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.===

=== Changing 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 Settings 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:FDTD80The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions.png|thumb|600px|EMThe 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.Tempo's Mesh Settings dialog]]

[[EM.Cube]]'s [[FDTD Module|FDTD module]] discretizes objects using what is often referred to as the “staircase approximation”. In this mesh generation scheme, the structure is recreated using a large number of cubic cells carefully assembled in a way that approximates the shape of the original structure. By default, a 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 each 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).

Occasionally, you may prefer a more regular When [[EM.Cube]] generates an FDTD mesh with almost equal grid line spacing everywhere, but still with a frequency-dependent cell sizelarge number of geometrical considerations are taken into account. In that caseThese include the bounding box of each object and its corners, you can select the "<u>'''Regular'''</u>" option ends of a line, the '''Mesh Type '''dropdown list in apex of a cone or pyramid, or the FDTD Mesh Settings dialoglocations of lumped sources, field probes and sensors, vertices of plane wave or far field boxes, to name a few examples. The regular These points are “locked” as fixed grid nodes in the FDTD mesh enforces only two of the above . [[parametersEM.Cube]]: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''determines these points internally to generate a mesh that best approximates the original structure. Or As you may opt for an absolutely "<u>'''Uniform'''</u>" mesh typesaw earlier, for which you need can use the FDTD mesh settings to specify control the '''Cell Size '''along shape and resolution of the Xmesh, Yfor example, Z directions in project unitsaround 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.

Click here to learn You can control the global mesh more about [[selectively using the Advanced Meshing in EMFDTD Mesh Settings Dialog.Tempo]]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.

Before you can run an The figures below compare the three types of the FDTD simulation, you have to define mesh for a source to excite your project’s physical structuredielectric ellipsoid with &epsilon;_r = 4. EMNote that the cell size inside the dielectric region is half the cell size in the air region.Tempo offers a variety of excitation mechanisms for your physical structure depending on your particular type of modeling problem or application:

# '''Ideal Source''': A stand-alone localized voltage source with an internal resistance.<table><tr><td> # '''Lumped Source'''[[Image: An ideal source that must be place on a wire (a PEC line object)FDTD MAN21.# '''Distributed Source''': A source with a prescribed impressed field component that is defined on a rectangular region png|thumb|left|360px|The geometry of space parallel to a principal planedielectric ellipsoid with &epsilon;_r = 4.]]# '''Waveguide Source''': A distributed source that must be placed across a hollow PEC box object.</td><td> # '''Plane Wave Source'''[[Image: A distributed source with a plane wave profile defined using a virtual box object enclosing the entire physical structureFDTD MAN22. # '''Gaussian Beam Source''': A distributed source with a complex-valued focused Gaussian beam profile defined using a virtual box object enclosing png|thumb|left|360px|The adaptive mesh of the entire physical structuredielectric ellipsoid. ]]# '''Huygens Source''': A distributed source defined based on know tangential electric and magnetic field components on the surface of a virtual box object.</td></tr></table>

<table><tr><td> [[Image:FDTD48FDTD MAN18.png|thumb|300pxleft|360px|The Port Definition dialogtop view of the adaptive FDTD mesh of the dielectric ellipsoid.]]</td><td> [[Image:FDTD49FDTD MAN19.png|thumb|300pxleft|Reassigning sources to ports and defining coupled ports360px|The top view of the regular FDTD mesh of the dielectric ellipsoid with the same mesh density.]]===Defining a New Source===</td></tr><tr><td> [[Image:FDTD MAN20A.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the larger cell size inside the air region.]]</td><td> [[Image:FDTD MAN20.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the smaller cell size inside the dielectric region.]]</td></tr></table>

To create The figures below compare the low resolution and high resolution adaptive FDTD meshes of a new source, follow these steps:PEC parabolic reflector. This structure involves both a curved surface and a very thin surface.

* Right click on the name of the source type in the '''Sources''' section of the navigation tree and select '''Insert New Source...''' from the contextual menu. This opens up the respective Source Dialog.<table>* You can change the default name of the source as well as its color.<tr>* Change the location of the source, if necessary, by the changing the values of the supplied coordinate fields<td> [[Image:FDTD MAN23. * Change the polarization png|thumb|left|450px|The geometry of the source, if necessarya PEC parabolic reflector. ]]* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.</td>* To change the amplitude and</or phase of a source, click the button labeled '''Excitation Waveform''' to open the Waveform Dialog.tr>* From the waveform dialog, you can also change the waveform type, if necessary.</table>

Once you define a source, you can always changes its <table><tr><td> [[parametersImage:FDTD MAN24.png|thumb|left|360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]] later from its property dialog, which can be accessed from its right</td><td> [[Image:FDTD MAN27.png|thumb|left|360px|The high-click contextual menuresolution adaptive mesh of the PEC parabolic reflector. You can also delete sources]]</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>

===Understanding Adding Fixed Grid Points to the FDTD Source TypesAdaptive Yee Mesh ===

Click here Adding fixed grid points to learn more about the various [[an FDTD Source Types]]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:

Ports are used to order and index sources for circuit parameter calculations like S/Y/Z <table><tr><td> [[parameters]]Image:FDTD36. That is why they are png|thumb|left|480px|A user-defined fixed grid point in the '''Observables''' section of Navigation Treean FDTD mesh. In ]] </td></tr><tr><td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.CubeTempo's fixed grid points settings dialog.]]'s </td></tr><tr><td> [[FDTD ModuleImage:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]], you can define ports at the location of '''Lumped Sources''', '''Waveguide Sources''' and '''Distributed Sources'''. In other words, ideal sources or other types of sources cannot be used to define ports or calculate port characteristics.</td></tr></table>

Ports are defined in According to the '''Observables''' section of Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the Navigation Treesmallest cell size in your FDTD mesh. Right click on the Occasionally, EM.Tempo'''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definitions 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.''' from Cube]] offers the contextual menu"Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. The Port Definition Dialog opens upIn a regular FDTD mesh, showing the default port assignmentsgrid cell sizes stay rather the same in objects of the same material composition. If you have N sources The mesh resolution increases in your physical structure, then N default ports are defined, with one port assigned to each source according to their order materials of higher permittivity and/or permeability based on the Navigation Treeeffective wavelength in exactly the same way as the adaptive mesh.

You can define any number of ports equal to or less than === Profiling the total number of sources in your project. The Port List of the dialog shows a list of all the ports in ascending order, with their associated sources and the port's characteristic impedance, which is 50O by default. You can delete any port by selecting it from the Port List and clicking the '''Delete '''button of the dialog. Keep in mind that after deleting a port, you will have a source in your project without any port assignment. Make sure that is what you intend. When you delete one or more ports in your project, their associated sources become free and "available" for either defining new ports or reassignment to the other ports. To define a new port, click the '''Add '''button of the Port Definition dialog to open the "Add Port" dialog. On the left side of this dialog, you will see a table containing all the available sources. Select one or more ports and use the right arrow ('''--->''') button to move them to the table on the right side, labeled "Associated". These ports are now associated with the new port being defined. You can move sources from the "Associated" table back to the "Available" table on the left using the left arrow ('''<---''') button of the dialog. You can associate more than one source with the same port. In that case, you will have coupled sources, collectively representing a coupled port.Brick Mesh ===

{{Note|In order to obtain correct results, the port impedance must equal the characteristic impedance of the transmission line on which the port A volumetric brick mesh is established. This is not done automatically 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 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 one 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.}}

You While a mesh grid plane is visible, you can change the characteristic impedance of a port by selecting move it from the Port List back and clicking forth between the '''Edit '''button two boundary planes at the two opposite sides of the dialogcomputational domain. This opens up the Edit Port dialog, where you You can enter a new value do this in one of the box labeled '''Impedance'''.following four ways:

===Modeling Feeds * 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 Practical Applications===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|<}}.

Using simple lumped sources, As you can simulate a variety of transmission line structures in [[EM.Tempo]] including filters“step through” or profile the mesh grid, couplers or antenna feeds and you can calculate their scattering [[parameters]]. This approach may become less accurate at very high frequencies when see how the details of the feed structures become important and can no longer be modeled with highly localized lumped ports. In such cases, it structure is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the ports for calculation discretized along internal planes of the incident and reflected wavescomputational domain.

Click here to learn more about <table><tr><td> [[Using Lumped Sources to Model Transmission Line FeedsImage:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]]</td><td> [[Image:Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td></tr></table>

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 mesh grid. [[File:FDTD56.png|thumb|300px|EM.Tempo's Lumped Load dialog.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 =Defining Lumped Loads0). 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).

In [[EM.TempoCube]] allows you can define four lumped load typesto navigate through the mesh grid and evaluate the grid 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.

# '''Resistor''' with a Resistance value (R) in Ohms.<table># '''Capacitor''' with a Capacitance value <tr><td> [[Image:FDTD35(C1) in pF.# '''Inductor''' with an Inductance value png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (LI, J, K) in nHdisplayed on the status bar. ]]# '''Nonlinear Diode''' with a Saturation Current (I<sub/td>s</subtr></table>)in fA, ambient temperature (T) in degree Kelvin, and a dimensionless ideality factor (n). The default values of these [[parameters]] are 100fA, 300&deg;K and 1, respectively.

Although lumped loads are not sources and do not excite a structure, their properties are similar to lumped sources. Lumped Loads are incorporated into the == Running FDTD grid across two adjacent nodes Simulations in a similar manner to lumped sources. Likewise, lumped loads are defined on Line objects. In order to create a lumped load, you must have at least one line object in your project. Lumped loads show up as small yellow arrows on their host line object. Similar to lumped a source, a lumped load has an offset parameter that determines its location on the host lineEM. Tempo ==

{{Note|Small values of inductance may result in the divergence of the FDTD numerical scheme=== EM. 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.}}Tempo's Simulation Modes ===

==Running Once you build your physical structure in the project workspace and define an excitation source, you are ready to run an FDTD Simulations==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:

{| class="wikitable"|-! scope="col"| Simulation Mode! scope=Strategy For An Accurate & Efficient "col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Wideband FDTD SimulationAnalysis | Wideband Analysis]]| style="width:270px;" | Simulates the physical structure "As Is"| style="width:100px;" | Single run| style="width:200px;" | Generates data for many frequency samples| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:100px;" | Multiple runs| style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:100px;" | Multiple runs | style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:100px;" | Multiple runs | style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[#Running a Dispersion Sweep in EM.Tempo | Dispersion Sweep]]| style="width:270px;" | Varies the value of wavenumber in a periodic structure | style="width:100px;" | Multiple runs | style="width:200px;" | Runs at multiple frequency points corresponding to constant wavenumber values| style="width:150px;" | Only for periodic structures excited by a plane wave source|}

=== Running a Wideband FDTD Analysis === 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:

For certain problems, more than one combination or choice of settings and [[parameters]] may still give acceptable results. In most cases, Wideband analysis is [[EM.CubeTempo]] tries to make these choices convenient for you by suggesting default settings or default parameter values's simplest and most straightforward simulation mode. For example, [[EMIt runs the FDTD time marching loop once.Cube]] by default generated am "adaptive" type mesh with a default density of 20 cells per effective wavelength. The default computational domain features CPML walls placed a quarter free-space wavelength away from At the large bounding box end of the entire physical structure. A modulated Gaussian waveform with certain optimal [[parameters]] is used to drive simulation, the project's excitation source by defaulttime-domain field data are transformed into the frequency domain using a discrete Fourier transform (DFT). You can change most of these settings arbitrarily. For exampleAs a result, you can set up your own computational generate wideband frequency data from a single time-domain with different types of boundary conditions, customize the FDTD mesh by modifying a large number of mesh settings and use simulation run. The other types of excitation waveformssimulation 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 {{Notekey|Keep in mind that you are always responsible for Ctrl+R}}. To start the choice FDTD simulation, click the {{key|Run}} button at the bottom of excitation source this dialog. Once the simulation starts, the "Output Message Window" pops up and reports messages during the project observablesdifferent stages of the FDTD simulation. In other wordsDuring 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.CubeTempo]] does not automatically provide a default excitation source simulation is terminated when the ratio U_n/U_max falls below the specified power threshold or does not suggest default observableswhen 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:FDTD57Tempo L1 Fig13.png|thumb|350pxleft|480px|EM.Tempo's Run simulation run dialog.]]</td></tr><tr><td> [[Image:FDTD58Tempo L1 Fig15.png|thumb|500px|EM.Tempo's Simulation Engine Settings dialog]][[Image:FDTD66.png|thumbleft|420px550px|EM.Tempo's output message window.]]===Running A Wideband FDTD Simulation=== 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.Cube]]'s [[FDTD Module]] currently offers several different simulation modes as follows: # Analysis# Frequency Sweep# Parametric Sweep# Angular Sweep# R</T Macromodel# Dispersion Sweep# Huygens Sweep# [[Optimization]]# HDMR Analysis is the simplest and most straightforward simulation mode of the [[FDTD Module]]. 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 '''Menu td> Simulate > Run...''' from the menu bar or use the keyboard shortcut '''Ctrl+R'''. To start the FDTD simulation, click the '''Run''' button at the bottom of this dialog. Once the simulation starts, the "'''Output 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<sub>n</subtr>/U<sub>max</subtable> in dB. An [[EM.Cube]] FDTD 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.

An FDTD simulation involves a number of numerical [[parameters]] that can be accessed and modified from the FDTD Engine Settings Dialog. To open this dialog, select '''Menu > Simulate > Simulation Engine Settings... '''or open the '''Run Dialog''', and click the '''{{key|Settings''' }} button next to the engine dropdown list.

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.Cube]]'s [[FDTD ModuleTempo]] 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.CubeTempo]]'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.CubeTempo]]'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.

For structures excited with a plane wave source, there are two standard FDTD formulations: '''Scattered Field '''(SF) formulation and '''Total Field - Scattered Field''' (TF-SF) formulation. [[EM.Tempo]] offers both formulations. The TF-SF solver is the default choice and is typically much faster than the SF solver for most problems. In two cases, when the structure has periodic boundary conditions or infinite CPML boundary conditions (zero domain offsets), only the SF solver is available.

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. [[=Modeling 3D Periodic Structures in EM.Tempo]] currently offers four types of temporal waveform:==

A sinusoidal waveform is single{{Note| [[EM.Tempo]] can only handle regular, non-tone and skewed periodiclattices with no secondary offsets. Its spectrum is concentrated around a single frequency, which is equal }} [[Image:Info_icon.png|30px]] Click here to your projectlearn more about the theory of '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 [[parametersBasic_Principles_of_The_Finite_Difference_Time_Domain_Method#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]] provides an adequate performance'''.

If you use ===Defining a Gaussian pulse or a modulated Gaussian pulse waveform to drive your FDTD source, after a certain number of time steps, the total energy of the computational domain drops to very negligible levels. At the point, you can consider your solution to have converged. If you drive your FDTD source by a sinusoidal waveform, the total energy of the computational domain will oscillate indefinitely, and you have to force the time loop to terminate after a certain number of time steps assuming a steady state have been reachedPeriodic Structure in EM.Tempo===

The accuracy of By default, your physical structure in the FDTD simulation results depends on the right choice of temporal waveform. project workspace is not periodic, and you have to instruct [[EM.CubeTempo]]'s default waveform choice is to turn it into a modulated Gaussian pulseperiodic structure using its Periodicity Dialog. At the end of an FDTD simulationBy designating a structure as periodic, you enforce periodic boundary conditions (PBC) on the time side walls of its computational domain field data are transformed into . Your structure in the frequency domain at your specified frequency or bandwidth to produce the desired observablesproject workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines.

In addition to the default waveforms, [[EM.Cube]] allows the ability to To define custom waveforms by either time or frequency specifications on a per source basis.periodic structure, follow these steps:

Click here * Select '''Menu > Simulate > Computational Domain > Periodicity Settings...''' or right click on the '''Periodicity''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Periodicity Settings...''' from the contextual menu. This open up the Periodicity Settings Dialog.* Check the box labeled '''Periodic Structure''' and click the '''Apply''' button of this dialog. The default domain box initially shrinks to learn more about EMthe edges of the physical structure in the project workspace.TempoThe default periods along the X and Y axes appear in the dialog, which are equal to the dimensions of the structure's [[Waveforms bounding box.* Enter new values for '''X Spacing''' and Discrete Fourier Transforms]]'''Y Spacing '''in project units and close the dialog.* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC.

In [[EM.Cube]], project observables are the simulation data that are generated by the simulation engine at the end of each simulation run. [[EM.Cube]]'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 loop. However, ==Exciting Periodic Structures as Radiators in order to save memory space, the engine has to destroy the temporal field data from each time step to the next and reuse the memory. 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.Cube]] asks you to define project observables to instruct why types of simulation data you seek in each simulation effort.Tempo===

In [[EM.CubeTempo]]'s FDTD Modules currently offers , a periodic structure can be excited using various source types. Exciting the following unit cell structure using a lumped source, a waveguide source, or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types , you excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S₁₁ parameter or input impedance of observable:the periodic antenna array. You can also compute the near-field and far-field data.

* [[EM.Tempo]]'s periodic FDTD simulator uses periodic boundary conditions (PBC) to model an infinite periodic array. All the periodic replicas of the unit cell structure are excited. In this case, you can impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the lumped source or waveguide source. At the bottom of the ''Field Probe'Lumped Source Dialog'' for monitoring E- and H-field components at a fixed location in both time and frequency domains. * 'or ''Field Sensor'Waveguide Source Dialog'' for monitoring E- and H-field components on ', there is a cross section of the computational domain in both time and frequency domains.* titled '''Far Field Radiation PatternPeriodic Beam Scan Angles''' for monitoring the radiation behavior of your structure.* '''Far Field RCS''' for monitoring This section is grayed out when the scattering behavior of your project structureis not periodic.* '''Huygens Surface''' You can enter desired beam scan angle values for collecting tangential field data on a box. * both '''Port DefinitionTheta''' for calculating the S/Y/Z [[parameters]] and voltage standing wave ratio (VSWR). * '''Domain EnergyPhi''' for calculating in degrees. To visualize the total electric and magnetic energy radiation pattern of the beam-steered array, you have to define a finite-sized array factor. You do this in the computational domain.* "Impose Array Factor" section of the '''Periodic CharacteristicsRadiation Pattern Dialog''' for calculating the reflection and transmission coefficients when your periodic structure is excited by a plane wave source.

Of [[EM.Tempo]]'s frequency domain observables{{Note|For large &theta; scan angles, the near fields, periodic FDTD time marching loop may take 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. 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 projectmore time steps to converge.}}

To create a new observable, follow these steps<table><tr><tr><td> [[Image:Period2.png|thumb|720px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td></tr></table>

* Right click on the name <table><tr><td> [[Image:Period3.png|thumb|360px|Radiation pattern of the observable type in the '''Observables''' section of the navigation tree an 8×8 finite-sized periodic wire dipole array with 0&deg; phi and select '''Insert New Observable...''' from the contextual menu. This opens up the respective Observable Dialogtheta scan angles.]] </td>* You can change the default name of the observable as well as its color<td> [[Image:Period4.* Change the location png|thumb|360px|Radiation pattern of the observable, if necessary, by the changing the values of the supplied coordinate fieldsa beam-steered 8×8 finite-sized periodic wire dipole array with 45&deg; phi and theta scan angles. ]] </td>* Change the orientation of the observable, if necessary. </tr>* In the case of frequency domain observables, change the observed frequency or frequency range, if necessary. </table>

Once you define an observable, you can always changes its [[parameters]] later from its property dialog, which can be accessed from its right-click contextual menu===Exciting Periodic Structures Using Plane Waves in EM. You can also delete observables. Tempo===

===Understanding Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD Observable Types===or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. At the end of the FDTD simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into ASCII data files.

Click here to learn more about the various <table><tr><td> [[FDTD Observable TypesImage:Period11.png|thumb|380px|Geometry of a periodic printed strip FSS in EM.Tempo.]]</td><td> [[Image:Period12.png|thumb|340px|Define a custom periodic plane wave box in EM.Tempo.]] </td></tr></table>

==Modeling 3D Periodic Structures Using a plane wave source to excite a periodic structure in [[EM.Tempo==]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. If the plane wave source illuminates the periodic unit cell from the top (90&deg; < &theta; < 180&deg;), the excitation surface is placed above the structure's bounding box. If the plane wave source illuminates the periodic unit cell from the bottom up (0&deg; < &theta; < 90&deg;), the excitation surface is placed below the structure's bounding box. In either case, the plane wave must intercept the excitation surface before hitting the unit cell's physical structure. It is highly recommended that you accept [[EM.Tempo]]'s default settings for the plane wave box of periodic structures. Nevertheless, you can change the location of the excitation surface if you wish. To do so, you have to open the '''Plane Wave Dialog'''. In the Excitation Box section of the dialog, select the '''Size: Custom''' option. Only the '''Z Coordinate''' of '''Corner 1''' is available for editing. The rest of the coordinates are enforced by the periodic domain. You can enter the incidence angles '''Theta''' and '''Phi''' in degrees. For periodic structures, only the '''TM_z''' and '''TE_z''' polarization options are available.

EM.Tempo allows you One of the pitfalls of the direct spectral FDTD method is the possibility of horizontal resonances, which may lead to simulate doubly periodic structures with periodicities along indefinite oscillation or even divergence of field values during the X and Y directionstime marching loop. Many interesting structures This happens in the case of oblique plane wave incidence when &theta; > 0&deg;. [[EM.Cube]]'s FDTD engine automatically detects such as frequency selective surfaces (FSS), electromagnetic band-gap (EBG) structures cases and metamaterial structures can be modeled using periodic geometriesavoids those resonances by shifting the modulation frequency of the modulated Gaussian pulse waveform away from the resonant frequency. In However, in some cases, the case size of an infinitely extended periodic structureoscillations may still remain large after a large number of time steps. Occasionally, it is sufficient to analyze only a unit celllate-time diverging behavior may appear. In the FDTD methodTo avoid situations like these, this it is accomplished by applying periodic boundary conditions (PBC) at highly recommended that you place a time-domain field probe above your structure and monitor the side walls of temporal field behavior during the computational domaintime marching loop as shown in the figure below.

Click here {{Note|It is very important to learn more about keep in mind that only in the theory case of normal incidence does [[Time Domain Simulation EM.Cube]] compute the reflection and transmission coefficients over the entire specified bandwidth of Periodic Structuresthe project. At oblique incidences when &theta; > 0, the computed R/T coefficients after the discrete Fourier transformation are valid only at the center frequency of the project for the given value of the incident &theta;₀ angle. In other words, the computed R/T coefficients at all the other frequencies away from the center frequency correspond to different values of the incident &theta; angle. As a result, [[EM.Cube]]only saves the reflection and transmission coefficients at the center frequency into the output data files "reflection_coefficient.CPX" and "transmission_coefficient.CPX".}}

[[Image:FDTD134.png|thumb|320px|=== Running a Dispersion Sweep in EM.Tempo's Periodicity Settings dialog]]===Setting Up A Periodic Unit Cell===

A periodic structure The '''Dispersion Sweep '''option of the Simulation Mode drop-down list performs a sweep of constant k_l wavenumber values. This is one a specialized sweep for the constant transverse wavenumber method that repeats itself infinitely along one, two or three directions. In this release of [[EM.Tempo]], the periodicity is limited uses to the X-Y model periodic structures illuminated by a planewave source. In other wordsThe 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 repeats itself along the X. The sweep data can be graphed as a wavenumber- and Yfrequency intensity plot (also known as beta-axes, but not along k diagram) that projects the Z-eigenvalues of the periodic structure. The horizontal axisrepresents the constant transverse wavenumber k_l (or beta). By defaultThe vertical axis represents frequency. Sometimes, your physical structure the free space wave number k₀ = (2&pi;/c).f is not periodicused as the vertical axis, hence, the term beta-k diagram. However, and you have to instruct [[EM.Cube]] to turn it into a periodic structure through [[FDTD Module]]'s Periodicity Dialogplots frequency vs. By designating a structure as periodicwavenumber. 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 enforce periodic boundary conditions (PBC) on have to specify the side walls number of its computational domainwavenumber samples. Your structure in Note that the project workspace then turns into dispersion sweep is run for a periodic unit cellfixed given value of the plane wave incident angle &phi; as specified in [[EM. The periodic side walls are displayed with dashed blues linesTempo]]'s Plane Wave Dialog.

To define a periodic structure, follow these steps<table><tr><td>[[Image:KBT Settings.png|thumb|360px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]</td></tr></table>

* Select '''Menu <table> Simulate <tr> Computational Domain <td> Periodicity Settings...''' or right click on the '''Periodicity''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Periodicity Settings...''' from the contextual menu. This open up the Periodicity Settings Dialog.* Check the box labeled '''Periodic Structure''' and click the '''Apply''' button of this dialog[[Image:KBT R. The default domain box initially shrinks to the edges png|thumb|360px|A typical reflection coefficient dispersion diagram of the physical a periodic structure in the project workspace. The default periods along the X and Y axes appear in the dialog, which are equal to the dimensions of the structure's bounding box.]]* Enter new values for '''X Spacing''' and '''Y Spacing '''in project units and close the dialog.</td>* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC.<td> ===Exciting Periodic Structures as Radiators=== In [[EMImage:KBT T.Tempo]], png|thumb|360px|A typical transmission coefficient dispersion diagram of a periodic structure can be excited using various source types. Exciting the unit cell structure using a lumped source, a waveguide source, an ideal source or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types, you will excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S]]<sub/td>11</subtr></table> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data.

Click here to learn more about [[Modeling Infinite Phased Arrays]]. [[Image:FDTD139.png|thumb|320px|Placing a field probe above a periodic structure excited by an obliquely incident plane wave source.]]===Exciting Periodic Structures Using Plane Waves=== Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. At the end of the FDTD simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into ASCII data files.<br />

One of the pitfalls of the direct spectral FDTD method is the possibility of horizontal resonances, which may lead to indefinite oscillation or even divergence of field values during the time marching loop. This happens in the case of oblique plane wave incidence when &theta; <hr> 0&deg;. [[EM.Tempo]]'s FDTD engine automatically detects such cases and avoids those resonances by shifting the modulation frequency of the modulated Gaussian pulse waveform away from the resonant frequency. However, in some cases, the size of oscillations may still remain large after a large number of time steps. Occasionally, a late-time diverging behavior may appear. To avoid situations like these, it is highly recommended that you place a time-domain field probe above your structure and monitor the temporal field behavior during the time marching loop as shown in the figure below.

Click here to learn more about [[Reflection & Transmission Characteristics of Periodic StructuresImage:Top_icon.png|30px]]'''[[EM.Tempo#Product_Overview | Back to the Top of the Page]]'''

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