[[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]]'''Â [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== EM.Tempo in a Nutshell ===
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 Maxwellâs 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>
* [[#Perfect Conductors|Perfect Electric Conductor (PEC) Objects]]* [[#Perfect Conductors|Perfect Magnetic Conductor (PMC) Planes]]* [[#Dielectric Materials|Dielectric Materials]]* [[#Anisotropic Materials|Anisotropic Materials]]* [[#Dispersive Materials|Dispersive Materials]]* Inhomogeneous Materials* Thin Wires=== Sources, Ports & Devices ===
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 & 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 domain computations </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>
* Right click on the name of the desired material in the navigation tree and select '''Insert New Material...''' from the contextual menu. A material dialog opens up.* Specify a '''Label''' and '''Color''' (and optional Texture) for the material group being created.* Either accept the default values of the available material [[parameters]] or enter new values.* Click the '''OK''' button of the dialog to accept the changes and close it.=== 3D FDTD Simulation ===
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'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>
===Moving Objects among Material GroupsData Generation & Visualization ===
[[Image:FDTD21<ul> <li> Near-field intensity (1colorgrid).png|thumb|325px|Moving objects from one FDTD material group to another.]], contour and surface plots (vectorial - amplitude & phase)</li>You can move one or more selected objects at a time among different material groups. The objects can be selected either <li> Near-field probes for monitoring field components in the project workspace, or their names can be selected from the navigation tree. Right click on the highlighted selection both time & frequency domains</li> <li> Far-field radiation patterns: 3D pattern visualization and select '''Move To 2D polar and Cartesian graphs</li> FDTD <li>''' from the contextual menu. This opens up another sub Far-menu with a list 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 all the available material groups already defined FDTD structure or periodic unit cell</li> <li> Bistatic and monostatic radar cross section</li> <li> Huygens surface data generation for use in your other [[EM.Tempo project. Select the desired material nodeCube]] modules</li> <li> Periodic reflection/transmission coefficients and k-β diagrams</li> <li> Port characteristics: S/Y/Z parameters, VSWR and all the selected objects will move 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 that material group[[RF. In the case Spice A/D]]</li> <li> Interanl node voltages and currents of a multiple selection from the navigation tree using the keyboard's '''Shift Key''' or '''Ctrl Key'''Netlist-based one-port and two-port networks</li> <li> Computation of electric, make sure that you continue to hold the keyboard's '''Shift Key''' 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 '''Ctrl Key''' down while selecting the destination material group's name from the contextual menu.Python functions of standard outputs</li></ul>
In a similar way, you can move one or more objects from an FDTD material group to one of [[EM.Cube]]'s other modules. In this case, == Building 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 objects. You can also move one or more objects from [[EM.Cube]]'s other modules to a material group Physical Structure in EM.Tempo. ==
{{Note|You can import external objects only to '''[[CubeCAD]]'''. You need to move the imported objects form [[CubeCAD]] to === Material Variety in EM.Tempo as described above.}}===
Click here to learn more about [[FDTD Material Types]]Your physical structure in EM.Tempo can be made up of several geometric objects with different material compositions. In other words, the geometric objects you draw or import from external files are grouped together based on a common material composition. EM.Tempo's material types are divided into seven categories:
{| class="wikitable"|-! scope="col"| Icon! scope=Geometrical Rules & "col"| Material HierarchyType! 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|-| 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;" | [[File:pmc_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.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 one of the 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|-| style="width:30px;" | [[File:aniso_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%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|}
[[Image:fdtd14_tn.png|thumb|400px|Geometric construction of a dielectric-coated metallic cylinder.]]The following rules apply Click on each category to learn more details about it in the definition of materials and objects in [[Glossary of EM.TempoCube's Materials, Sources, Devices & Other Physical Object Types]]:.
* Under === Organizing the [[#Perfect Conductors|PEC]] category, you can define all types of solid, and surface and [[Curve Objects|curve objects]].* Under the [[#Perfect Conductors|PMC]] category, you can define only define rectangle strip objects parallel to the principal planes. * Under the [[#Dielectric Materials|Dielectric]], [[#Anisotropic Materials|Anisotropic]] and [[#Dispersive Materials|Dispersive]] material categories, you can define only [[Solid Objects|solid objects]].* Under the Inhomogeneous Physical Structure by Material category, you can only import a Cartesian ".CAR" data file.* Under the Thin Wire category, you can only define line objects parallel to the principal axes. Groups ===
[[EM.Tempo]] allows overlapping groups your geometric objects, although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same project workspace based on their material type and group overlap, they are merged using . All the Boolean union operation during the mesh generation process. If two overlapping objects belong belonging to two different the same material categories, then group share the same color and same material properties of the FDTD cells . Under each material node in the overlap region will follow the EM.Tempo's material hierarchy rule. In that casenavigation tree, the overlap area cells will always be regarded as having the you can create new material type groups of the higher prioritysame type but with different properties such as color, texture, or electric and magnetic constitutive parameters. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner:
# [[#Perfect Conductors|Once a new material node has been created on the navigation tree, it becomes the "Active" material group of the project workspace, which is always listed in bold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active material type. There is only one material group that is active at any time. Any material can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create material groups, and then draw new objects under the active material group. However, if you start a new EM.Tempo project from scratch, and start drawing a new object without having previously defined any material groups, a new default PEC]]# [[#Perfect Conductors|PMC]]# [[#Dispersive Materials|Dispersive]]# General [[#Anisotropic Materials|Anisotropic]]# Uniaxial [[#Anisotropic Materials|Anisotropic]]# [[#Dielectric Materials|Dielectric]]group is created and added to the navigation tree to hold your new object.
If planned carefully, taking advantage of EM.Tempo's material hierarchy rule would make the construction of complex {{Note|You can import external objects easieronly to CubeCAD. For example, a dielectric coated metallic cylinder You can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in then move the illustration belowimported objects form CubeCAD to EM. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinderTempo. }}
[[Image:Info_icon.png|30px]] Click here to access the '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.
<table><tr><td> [[Image:Tempo NavTree.png|thumb|left|400px|EM.Tempo's navigation tree.]]</td></tr></table> ==Setting = Material Hierarchy in EM.Tempo === [[EM.Tempo]] allows overlapping objects although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same material type and group overlap, they are merged using the Boolean union operation during the mesh generation process. If two overlapping objects belong to two different material categories, then the material properties of the FDTD cells in the overlap region will follow the [[EM.Tempo]]'s material hierarchy rule. In that case, the overlap area cells will always be regarded as having the material type of the higher priority. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner: # PEC# PMC# Dispersive# Gyrotropic# General Anisotropic# Uniaxial Anisotropic# Dielectric If planned carefully, taking advantage of [[EM.Tempo]]'s material hierarchy rule would make the construction of complex objects easier. For example, a dielectric coated metallic cylinder can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in the illustration below. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinder. <table><tr><td> [[Image:FDTD_MAN2.png|thumb|left|360px|The geometric construction of a dielectric-coated metallic cylinder with a conformal foil.]]</td></tr></table> === Moving Objects Among Different Material Groups or EM.Cube Modules === You can move any geometric object or a selection of objects from one material group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models from CubeCAD to [[EM.Tempo]]. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a material group called "Dielectric_1" in [[EM.Tempo]], then you have to select the menu item '''Move To → [[EM.Tempo]] → Dielectric_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.  <table><tr><td>[[Image:Tempo_L11_Fig2.png|thumb|left|720px|Moving an imported object from CubeCAD to EM.Tempo.]]</td></tr></table> == EM.Tempo's Computational Domain & Boundary Conditions==
===The FDTD Solution Domain===
The FDTD method requires a finite-extent solution domain. This is rather straightforward for shielded structures, where a typical PEC enclosure box defines the computational domain. For open-boundary structures like antennas and scatterers, the computational domain must be truncated using appropriate termination boundary conditions. The objective of termination boundary conditions is to eliminate the reflections from the walls of the domain box back to the computational domain.
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 (0.25λ<sub>0</sub>). 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.
[[Image:FDTD14.png|thumb|300px|[[FDTD Module]]'s Domain Settings dialog.]]
===Changing the Domain Settings===
To set the solution domain of your FDTD project, follow these steps:
* Click the '''Domain''' [[Image:domain_icon.png]] button of the '''Simulate ''' Toolbar or select the menu item '''Menu > Simulate > → Computational Domain > → 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.
* Select one of the two options for '''Domain Type'''<nowiki>: </nowiki>'''Default''' or '''Custom'''.
* If you select the "Default" domain type, the domain box is defined in terms of the offsets along the X, Y and Z directions from the largest extents of your physical structure. Select one of the two options for '''Offset Units: Grid''' and '''Wavelength'''. In the section titled '''"Domain Size"''', enter the amount of domain extension beyond the largest extents of the structure along the ±X, ±Y and ±Z directions. Note that in the case of a default-type domain box, the offset values based on your current project settings (frequency and units).
By default, the domain box is shown as a wireframe box with blue lines. You can change the color of the domain box or hide it.
===Settings the [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Domain_Settings | Domain Boundary Conditions===Settings]]'''.
<table><tr><td> [[Image:FDTD13FDTD14.png|thumb|300pxleft|[[FDTD Module]]480px|EM.Tempo's Boundary Conditions domain settings dialog.]]EM.Tempo supports four types of domain boundary conditions:</td></tr></table>
* PEC* PMC* Convolutional Perfectly Matched Layers (CPML)* Periodic ===Settings the Domain Boundary Conditions (PBC)===
[[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.
To define the boundary conditions of the solution domain, follow these steps:
* Select the menu item '''Menu > Simulate > → Computational Domain > → 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.
* You need to assign the type of boundary condition on each of the six domain boundaries: ±X, ±Y and ±Z. For each face, choose one of the three options available: '''PEC''', '''PMC '''or '''PML'''.
The PEC and PMC boundary conditions are the most straightforward to set up and use. Assigning the PEC boundary to one of the bounding walls of the solution domain simply forces the tangential component of the electric field to vanish at all points along that wall. Similarly, assigning the PMC boundary to one of the bounding walls of the solution domain forces the tangential component of the magnetic field to vanish at all points along that wall. For planar structures with a conductor-backed substrate, you can use the PEC boundary condition to designate the bottom of the substrate (the -Z Domain Wall) as a PEC ground. For shielded waveguide structures, you can designate all the lateral walls as PEC. Similarly to model shielded cavity resonators, you designate all the six walls as PEC.
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 the theory of [[Perfectly Matched Layer Termination]].=== Advanced CPML Setup ===
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===
You can use EM.Tempo to model planar structures of infinite extents. A planar substrate usually consists of one or more dielectric layers, possibly with a PEC ground plane at its bottom. To model a laterally infinite dielectric substrate, you must assign a PML boundary condition to the four lateral sides of the domain box and set the lateral domain offset values along the ±X and ±Y directions all equal to zero. If the planar structure ends in an infinite dielectric half-space from the bottom, you must assign a PML boundary condition to the bottom side of the domain box and set the -Z offset equal to zero. This leaves only the +Z offset with a nonzero value.
When a domain boundary wall is designated as CPML and its has a zero domain offset, meaning it touches a material block, the CPML cells outside the domain wall are reflected back inside the computational domain. In other words, the effective number of CPML layers will be twice the one specified in the CPML Settings dialog. This will effectively extend the material block infinitely beyond the boundary wall and will create an open boundary effect in the specified direction. It goes without saying that only "substrate" objects are supposed to touch the boundary walls in such a scenario. Because of the rolled-back CPML cells inside the domain, it is very important to make sure that other finite-sized parts and objects stay clear from the domain walls as well as from the invisible "interior" CPML cells. Â {{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.}}
<table>
<tr>
<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>
</tr>
</table>
== EM.Tempo's Excitation Sources ==
== 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 projectâs 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.
You have [[Image:Info_icon.png|30px]] More information about all the option to choose one of the three FDTD mesh source types:can be found in the '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.
* Adaptive Mesh* Regular Mesh* Fixed-Cell MeshIn 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.
The default choice A lumped source is the adaptive mesh, which is most commonly used way of exciting a quite sophisticated mesh. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed structure in cells per effective wavelengthEM. Since FDTD Tempo. A lumped source is a time-domain method and the excitation waveform may have voltage source with a wideband spectral content, series internal resistor that must be placed on a PEC or thin wire line object that is parallel to one of the effective wavelength three principal axes. A lumped source is calculated based displayed as a small red arrow on the highest frequency of host line. Lumped sources are typically used to define ports and compute the project: f<sub>max<port characteristics like S/sub> = f<sub>0<Y/sub> + Δf/2Z parameters. Using simple lumped sources, where f<sub>0</sub> is your project's center frequency and Δf (you can simulate a variety of transmission line structures including filters, couplers or BW) is its specified bandwidthantenna 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 other wordssuch cases, it is recommended to use âDistributed Sourcesâ, which utilize accurate modal field distributions at the effective wavelength in ports for calculation of the free space incident and reflected waves. Waveguide source is λused to excite the dominant TE<sub>0,eff</sub> = c / f<sub>max10</sub>mode of a hollow rectangular waveguide. Other special types of distributed sources are microstrip port, c being the speed of light in the free spaceCPW port and coaxial ports that can be used effectively to excite their respective transmission line structures.
The adaptive FDTD mesh, however, produces different grid cell sizes in the free space regions and inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. Therefore, the average ratio When you create an array of the cell size in a dielectric region to the cell size in the free space is 1/√(ε<sub>r</sub>μ<sub>r</sub>). The adaptive FDTD mesh generator also takes note an object type that can host one of the geometrical features of the objects it discretizes. This is more visible in the case of curved solidsabove source types, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using you can also associate a staircase profile. The mesh resolution varies source array 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 structuresthat array object.
According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, [[FDTD ModuleImage:Info_icon.png|30px]]Click here to learn more about '''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.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Finite-Sized_Source_Arrays | Modeling Finite-Sized Source Arrays]]'s FDTD Modules offers a "Uniform" FDTD mesh generator. The uniform mesh consists of three uniform grids along the XY, YZ and ZX principal planes. In other words, the grid cell sizes Δx, Δy and Δz are fixed throughout the entire computational domain. In this case, the uniform mesh generator has to fit your physical structure to the fixed mesh, rather than adapting the mesh to your physical structure''.
{{Note|When choosing A plane wave source is a mesh type popular excitation method that is used for your FDTD simulation, keep in mind 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 adaptive is highly localized as opposed to the uniform plane wave. For both plane wave and regular mesh types are frequencyGaussian 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-dependent field and their density varies with H-field polarization vectors. The time domain plane wave or Gaussian beam excitation is calculated on the highest frequency surface of your specified bandwidththis 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 uniform mesh type Gaussian beam box appears as a green wireframe box. Both boxes have an initial default size with an offset of 0.2λ<sub>0</sub> from the largest bounding box enclosing your entire physical structure. In both source dialogs, the radio button '''Size: Default''' is always fixed 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 independent '''Corner 2''' can now be changed. Corner 1 is the front lower left corner and Corner 2 is the rear upper right corner of your projectthe 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: θ = 105° and φ = 315°.]] </td><td> [[Image:FDTD MAN12.png|thumb|360px|A Gaussian beam box enclosing a PEC cylinder at oblique incidence: θ = 105° and φ = 315°. The concentric circles represent the beam's frequency settingsfocus point and radius.}}]] </td></tr></table>
===Viewing the FDTD MeshSimulating a Multiport Structure in EM.Tempo ===
Because a full 3D FDTD mesh is difficult Ports are used to visualize everywhere in the computational domain, only the discretized objects are displayed in [[EM.Cube]]'s "'''Mesh View'''" modeorder and index sources for circuit parameter calculations like S/Y/Z parameters. In particular, only the outer boundary cells on the surface of [[Solid Objects|solid objects]] are shownEM. HoweverTempo, you can view define ports at the mesh grid planes across location of the domain. You can even step these planes back and forth inside the domain and view different mesh profiles following types of your physical structure.sources:
To generate an FDTD mesh and view it the project workspace*[[Glossary of EM.Cube's Materials, follow these steps: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]]
* First, click the '''Mesh Settings''' [[Image:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > 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 Every time you can set the values of the various mesh [[parameters]] including the '''Mesh Density'''.* After specifying the desired mesh density, you can examine the mesh grid plane. The XY, YZ, and ZX mesh grid planes can be displayed through '''Menu > Simulate > Discretization > Grid Planes > XY Plane''', '''YZ Plane''' or '''ZX Plane''' or by right clicking on create a new source with one of the three '''XY Plane'''above types, '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the Navigation Tree and selecting '''Show''' from the contextual menu. The mesh grid planes give program asks if you want to initiate a good idea of what new port and associate it with the mesh will look like once it is generated and its resolution along different planesnewly created source. To remove a mesh grid plane from If the physical structure of your project workspacehas N sources, select '''Menu > Simulate > Discretization > Grid Planes >''' then N default ports are defined, with one more time and remove the check mark port assigned to each source according to their order 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 menunavigation tree.* To display the FDTD mesh, click the '''Show Mesh''' [[Image:mesh_tool.png]] button You can define any number of the '''Simulate''' '''Toolbar '''ports equal to or select '''Menu > Simulate > Discretization > Show Mesh''' or use less than the keyboard shortcut '''Ctrl+M'''. This takes [[EM.Cube]] into its "Mesh View" mode, and the Yee mesh total number of the whole structure is displayed sources in the your project workspace. 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 > Simulate > Discretization > Show Mesh''' to remove its check mark or simply hit the '''Esc Key''' of the keyboard.
In [[EM.Cube]]'s "Mesh View" modeIf your physical structure has two or more sources, but you can rotate or pan have not defined any ports, all the view of sources will excite the project workspacestructure simultaneously during the simulation. However, but when you cannot edit assign N ports to the objects. '''"Show Mesh"''' generates sources, then you have a new mesh and displays it if there multiport structure that is none in the memorycharacterized by an NÃN scattering matrix, or it simply displays an existing mesh NÃN impedance matrix, and an NÃN admittance matrix. To calculate these matrices, EM.Tempo uses a binary excitation scheme in conjunction with the memoryprinciple of linear superposition. This In this binary scheme, the structure is analyzed a useful feature because generating an FDTD mesh may take a long total of N times. Each time depending on one of the complexity of structure N port-assigned sources is excited, and all the total size of the computational domainother port-assigned sources are turned off. If you change In other words, the structure or alter the mesh settings, FDTD solver runs a new mesh is always generated"port sweep" internally. You can ignore any mesh in When the memory and force [[EM.Cube]] to generate a fresh FDTD mesh from the ground up by selecting ''j'Menu 'th port is excited, all the S<sub> Simulate ij</sub>Discretization > Regenerate Mesh''' or by right clicking parameters are calculated together based on the '''Yee Mesh''' item of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.following definition:
:<math> S_{ij} === Changing the FDTD Mesh Settings ===\sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math>
[[Image:FDTD80where V<sub>i</sub> is the voltage across Port i, I<sub>i</sub> is the current flowing into Port i and Z<sub>i</sub> is the characteristic impedance of Port i.png|thumb|600px|EMThe sweep loop then moves to the next port until all ports have been excited.Tempo's Mesh Settings dialog]]
[[In summary, to analyze an N-port structure, EM.Cube]]'s [[Tempo runs N separate FDTD Module|FDTD module]] discretizes objects using what is often referred time marching loops. The S/Z/Y parameters are frequency-domain quantities. The port voltages and currents are Fourier-transformed to as the âstaircase approximationâ. In this mesh generation schemefrequency domain over the frequency range [fc-bw/2, fc+bw/2], where fc is the structure center frequency and bw is recreated using a large number the bandwidth of cubic cells carefully assembled in a way that approximates your project. You can reduce the shape frequency range of the original structure. By default, a carefully calculated, "<u>Fourier transform by settings new values for '''AdaptiveStart'''</u>" mesh of your physical structure is generated and '''End''' frequencies in order to satisfy the following criteria:"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.
* Optimize the number of mesh cells in each dimension. The product of the number of cells in each 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''' {{Note|In order to a moderately low value to keep the mesh size manageableobtain correct results, but be careful not to set it too low (see the next item below).* Ensure simulation accuracy by requiring an acceptable minimum number of cells per wavelength through each object and in port impedance must equal the empty (free) space between them and the computational domain boundaries. An effective wavelength is defined for each material at the highest frequency characteristic impedance of the project's specified spectrum. We recommend a '''Minimum Mesh Density '''of at least 15-20 cells/ wavelength. But for some resonant structures, 25 or even 30 cells per wavelength may be required to achieve acceptable accuracy. As you reduce the mesh density, the simulation accuracy decreases.* Accurately represent and approximate the boundaries of edges or surfaces that are not grid-aligned by closely adhering to their geometric contours. This is controlled by the '''Minimum Grid Spacing Over Geometric Contours''', transmission line on which can be specified either as a fraction of the free space grid spacing or as an absolute length value in project units.* Maximize the minimum grid spacing in any dimension inside the computational domain and thus maximize the simulation time step. The time step size port is dictated by the CFL stability criterion and is driven by the smallest grid spacing in each dimension. The smaller the time step, the larger the number of time steps required for convergenceestablished. This is controlled using the '''Absolute Minimum Grid Spacing''', which can be specified either as a fraction not automatically taken care of the free space grid spacing or as an absolute value. It is critical to accurately represent and precisely maintain the object edge/surface boundaries in certain structures like resonant antennas and filters, as the phase of the reflected fields/waves is affected by the object boundary positionsEM. When object boundaries are very close to each other, the mesh needs to represent them by two separate, but very closely spaced, grid lines. To control the minimum allowed grid spacing, use the '''Absolute Minimum Grid Spacing '''settings,* Maintain a smooth grid with no abrupt jumps from low-density to high-density regions. This feature is enabled with the '''Create Gradual Grid Transitions '''check box (always checked by default)Tempo.}}
Occasionally, you may prefer a [[Image:Info_icon.png|30px]] Click here to learn more regular FDTD mesh with almost equal grid line spacing everywhere, but still with a frequency-dependent cell size. In that case, you can select about the "<u>'''Regular'''</u>" option of the '''Mesh Type '''dropdown list in the FDTD Mesh Settings dialog. The regular FDTD mesh enforces only two of the above [[parametersGlossary_of_EM.Cube%27s_Simulation_Observables_%26_Graph_Types#Port_Definition_Observable | Port Definition Observable]]: '''Minimum Mesh Density''' and '''Absolute Minimum Grid Spacing'''. Or you may opt for an absolutely "<u>'''Uniform'''</u>" mesh type, for which you need to specify the '''Cell Size '''along the X, Y, Z directions in project units.
[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Advanced Meshing in EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#Modeling_Coupled_Sources_.Tempo26_Ports | Modeling Coupled Sources & Ports]]'''.
==Setting Up an Excitation Source==<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>
Before you can run an FDTD simulation, you have to define a source to excite your projectâs physical structure. EM.Tempo offers a variety of excitation mechanisms for your physical structure depending on your particular type of modeling problem or application:=== Excitation Waveform & Frequency Domain Computations ===
# '''Ideal Source''': A stand-alone localized voltage source with When an internal resistance.# FDTD simulation starts, your project'''Lumped Source''': An ideal s source that must be place on a wire (a PEC line object)starts pumping energy into the computational domain at t > 0.# Maxwell'''Distributed Source''': A source with a prescribed impressed field component that s equations are solved in all cells at every time step until the solution converges, or the maximum number of time steps is defined on a rectangular region of space parallel to a principal planereached.# '''Waveguide Source''': A distributed source that must be placed across a hollow PEC box object.# '''Plane Wave Source''': A distributed source with a plane wave profile defined using a virtual box object enclosing the entire physical structure. # '''Gaussian Beam Source''': A distributed source with has a complex-valued focused Gaussian beam profile defined using zero value at t = 0, but it rises from zero at t > 0 according to a virtual box object enclosing the entire physical structurespecified waveform. EM. # '''Huygens Source'''Tempo currently offers four types of temporal waveform: A distributed source defined based on know tangential electric and magnetic field components on the surface of a virtual box object.
[[Image:FDTD48.png|thumb|300px|The Port Definition dialog]]# Sinusoidal[[Image:FDTD49.png|thumb|300px|Reassigning sources to ports and defining coupled ports.]]# Gaussian Pulse===Defining a New Source===# Modulated Gaussian Pulse# Arbitrary User-Defined Function
To create A sinusoidal waveform is single-tone and periodic. Its spectrum is concentrated around a new sourcesingle frequency, follow these steps:which is equal to your project's center frequency. A Gaussian pulse decays exponentially as t → ∞, but it has a lowpass frequency spectrum which is concentrated around f = 0. A modulated Gaussian pulse decays exponentially as t → ∞, 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.
* Right click on the name The accuracy of the source type in FDTD simulation results depends on the '''Sources''' section right choice of the navigation tree and select '''Insert New Source.temporal waveform.EM.Tempo''' from the contextual menu. This opens up the respective Source Dialog.* You can change the s default name of the source as well as its colorwaveform choice is a modulated Gaussian pulse.* Change At the location end of the sourcean FDTD simulation, if necessary, by the changing the values of the supplied coordinate fields. * Change the polarization of the source, if necessary. * In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and the '''Phase''' in Degrees.* To change time domain field data are transformed into the amplitude and/frequency domain at your specified frequency or phase of a source, click the button labeled '''Excitation Waveform''' bandwidth to open produce the Waveform Dialog.* From the waveform dialog, you can also change the waveform type, if necessarydesired observables.
Once you define {{Note|All of EM.Tempo's excitation sources have a source, default modulated Gaussian pulse waveform unless you can always changes its [[parameters]] later from its property dialog, which can be accessed from its right-click contextual menu. You can also delete sourceschange them. }}
[[Image:Info_icon.png|30px]] Click here to learn more about the various EM.Tempo's '''[[FDTD Source TypesBasic_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 PortsCustom Waveforms in EM.Tempo ===
Ports are used In some time-domain applications, you may want to order and index sources for simulate the propagation of a certain kind of waveform in a circuit parameter calculations like S/Y/Z [[parameters]]or structure. That is why they are defined 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 '''Observables''' property dialog of any source type in EM.Tempo, you will see an {{key|Excitation Waveform...}} button located in the "Source Properties" section of Navigation Treethe dialog. In [[Clicking this button opens up EM.Cube]]Tempo's [[FDTD Module]]Excitation Waveform dialog. From this dialog, you can define ports at the location of '''Lumped Sources''', '''Waveguide Sources''override EM.Tempo' s default waveform and '''Distributed Sources'''. In other words, ideal sources or other types of sources cannot be used to define ports or calculate port characteristicscustomize your own temporal waveform.The Excitation Waveform dialog offers three different options for defining the waveform:
Ports are defined in the '''Observables''' section of the Navigation Tree. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the default port assignments. If you have N sources in your physical structure, then N default ports are defined, with one port assigned to each source according to their order on the Navigation Tree.* Automatically Generate Optimal Waveform* Use Custom Frequency Domain Specifications* Use Custom Time Domain Specifications
You can define any number of ports equal to or less than 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 impedancefirst option, which is 50O by also the 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 portoption, you will have a source in constructs an optimal modulated Gaussian pulse waveform based on 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 's specified center frequency and "available" for either defining new ports or reassignment to the other portsbandwidth. To define a new port, click This optimal waveform guarantees the '''Add '''button of the Port Definition dialog to open the "Add Port" dialogmost accurate frequency domain computations for your simulation. On the left side of this dialog, The second option gives you will see a table containing all choice of the available sources. Select one or more ports three standard waveforms 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 lets you define their waveform parameters in terms of the dialogfrequency domain characteristics like center frequency and bandwidth and spectral contents. You can associate more than one source with the same port. In that case, The third option lets you will have coupled sources, collectively representing define a coupled portcompletely arbitrary temporal waveform for your source.
{{Note|In order to obtain correct results, Select the port impedance must equal the characteristic impedance third option of waveform definition and then choose the transmission line on which '''Custom''' option from the port is established'''Waveform Type''' dropdown list. This is not done automatically 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. [[EMImage:Info_icon.Cubepng|30px]] Click here to learn more about '''[[Using Python to Create Functions, Models & Scripts#Creating Custom Python Functions | Creating Custom Python Functions]]'''.}}
You can change the characteristic impedance of a port by selecting it from the Port List and clicking the <table><tr><td> [[Image:FDTD MAN13.png|thumb|left|720px|EM.Tempo'''Edit '''button of the s excitation waveform dialog. This opens up showing the Edit Port dialog, where you can enter a new value in the box labeled '''Impedance'''default standard modulated Gaussian pulse temporal waveform.]]</td></tr></table>
===Modeling Feeds When you define a custom waveform in Practical Applications===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.
Using simple lumped sources, you can simulate a variety of transmission line structures in [[EMImage:Info_icon.Tempopng|30px]] including filters, couplers or antenna feeds and you can calculate their scattering Click here to learn more about '''[[parametersGlossary of EM.Cube's Python Functions#Standard Python Functions | Python's Standard & Advanced Mathematical Functions]]. This approach may become less accurate at very high frequencies when the details of the feed structures become important and can no longer be modeled with highly localized lumped ports. In such cases, it is recommended to use âDistributed Sourcesâ, which utilize accurate modal field distributions at the ports for calculation of the incident and reflected waves'''.
Click here to learn more about [[Using Lumped Sources to Model Transmission Line Feeds]]{{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.}}
Click here to learn more about <table><tr><td> [[Using Sources & Loads in Antenna ArraysImage: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>
[[File:FDTD56.png|thumb|300px|== EM.Tempo's Lumped Load dialog.]]===Defining Lumped Loads=Active & Passive Devices ==
In [[EM.Tempo]] you can define four lumped load types:=== Defining Lumped Devices ===
# '''Resistor''' with a Resistance value (R) in Ohms.# '''Capacitor''' with a Capacitance value (C) in pF.# '''Inductor''' with an Inductance value (L) in nH. # '''Nonlinear Diode''' with a Saturation Current (I<sub>s</sub>)in fA, ambient temperature (T) in degree Kelvin, and a dimensionless ideality factor (n). The default values of these In [[parametersEM.Tempo]] are 100fA, 300°K and 1, respectively. 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]]''' Â Lumped devices are connected between two adjacent FDTD mesh nodes. Although lumped loads 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. Â A lumped device is characterized by a v-i equation of the form:Â :<math>i(t) = L \{ v(t) \} </math>Â 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 Loads devices are incorporated into the FDTD grid across two adjacent nodes in a similar manner to lumped sources. Likewise, lumped loads are defined on Line objects. In order to create At the location of a lumped loaddevice, you must have 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 least one line object in your projectevery time step. Lumped loads show up as small yellow arrows on their host line object [[Image:Info_icon. Similar to lumped png|30px]] Click here for a source, a lumped load has an offset parameter that determines its location on the host linegeneral 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.}}
==Running <table><tr><td> [[Image:FDTD Simulations==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>
===Strategy For An Accurate & Efficient FDTD SimulationDefining Active Distributed Multiport Networks ===
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 simulationEM. Below are a number Tempo also provides two types of steps that you should typically follow by order when planning your FDTD simulationactive distributed multiport network devices:
* Identify material types and proper domain boundary conditions# '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_One-Port_Device | Active Distributed One-Port Device/Circuit]]''' * Identify the source type and excitation mechanism.* Define the project observables.* Mesh the physical structure and examine the quality of the generated mesh and it geometric fidelity.* Determine the proper temporal waveform.* Select the simulation mode and run the FDTD engine# '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Active_Distributed_Two-Port_Device | Active Distributed Two-Port Device/Circuit]]'''
For certain problemsUnlike the active lumped devices, more than one combination or choice of settings these devices are rather distributed and [[parameters]] may still give acceptable resultstheir behavior is similar to a microstrip port source. In most casesother words, [[EM.Cube]] tries to make these choices convenient 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 you by suggesting default settings or default parameter valuesits definition. For example, [[EM.Cube]] by default generated am "adaptive" type mesh with a default density You can choose one of 20 cells per effective wavelength. The default computational domain features CPML walls placed a quarter free-space wavelength away from the large bounding box edges of the entire physical structurestrip object for establishing the circuit port. A modulated Gaussian waveform with certain optimal [[parameters]] is used to drive In the project's excitation source by default. You can change most case of these settings arbitrarily. For examplea two-port device, you can set up your own computational domain with different types of boundary conditions, customize the FDTD mesh by modifying a large number of mesh settings need two parallel and use other types of excitation waveformsend-to-end aligned strip objects.
{{Note|Keep in mind that you are always responsible The circuit behavior of these devices is defined by a Netlist file. Their property dialog provides a text editor for simply writing the choice Netlist description of excitation source and the project observablesdevice. In other words, [[EM.Cube]] does not automatically provide You can also import an existing external Netlist file with a default excitation source ".CIR" or does not suggest default observables".TXT" file extension using the button labeled {{key|Load Netlist}}..
[[Image:FDTD57.png{{Note|thumb|350px|EM.Tempo's Run dialog.]][[Image:FDTD58RF.png|thumb|500px|EM.Tempo's Simulation Engine Settings dialogSpice A/D]][[Image:FDTD66can generate a Netlist file corresponding to an existing circuit project, which can then be saved to a text file with a ".png|thumb|420px|EMTXT" file extension.Tempo's output 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. <table><tr><td> [[Image:ActiveOnePort.png|thumb|left|480px|EM.Cube]]Tempo's [[FDTD Moduleactive one-port device/circuit dialog.]] currently offers several different simulation modes as follows:</td></tr></table>
# Analysis<table># Frequency Sweep<tr># Parametric Sweep# Angular Sweep# R/T Macromodel# Dispersion Sweep# Huygens Sweep# <td> [[OptimizationImage:ActiveTwoPort.png|thumb|left|720px|EM.Tempo's active two-port device/circuit dialog.]]</td># HDMR</tr></table>
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.=== A Note on Using Active Devices ===
To open When your physical structure contains an active device, EM.Tempo performs an EM-circuit co-simulation that involves both the Simulation Run Dialogfull-wave FDTD EM solver and the SPICE circuit solver. In a global self-consistent co-simulation, click at each time step of the '''Run''' [[Image:run_iconFDTD time marching loop, the electric and magnetic fields at the location of the device ports are used to compute the port voltages and currents.png]] button These quantities are then used in the SPCIE circuit solver to update all the voltages and currents at the internal nodes of the '''Simulate Toolbar''' or select '''Menu > Simulate > Runactive device...''' from The updated port voltages and currents are finally used to update the electric and magnetic fields in the physical mesh cells and the menu bar or use time marching loop proceeds to the keyboard shortcut '''Ctrl+R'''next time step.
To start the FDTD simulation, click the '''Run''' button at the bottom of this dialogEM. Once the simulation startsTempo can handle several active one-ports and two-ports simultaneously. In that case, all the "'''Output Window'''" pops up and reports messages during devices are automatically compiled into a single Netlist that serves as the different stages input of the FDTD simulationSPICE solver. During the FDTD time marching loop, after every 10th time step, the output window updates the values The individual internal nodes of each device need to be renamed for the time step, elapsed time, global Netlist. Besides the engine performance in Mega-cells per secondsmain circuit, and the value Netlist of the convergence ratio U<sub>n</sub>/U<sub>max</sub> in dBeach device may contain several "subcircuits". An [[EM.Cube]] FDTD simulation is terminated when Note that the ratio U<sub>n</sub>/U<sub>max</sub> falls below subcircuit nodes are not re-indexed for the specified power threshold or when the maximum number of time steps global Netlist as is reached. You can, however, terminate the FDTD engine earlier by clicking the '''Abort Simulation''' buttonexpected.
=== The FDTD Simulation Engine Settings ==={{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.}}
An FDTD simulation involves The figure below shows the geometry of a number of numerical [[parameters]] that can be accessed two-port amplifier device with microstrip input and modified from the FDTD Engine Settings Dialogoutput transmission lines. To open this dialog, select '''Menu > Simulate > Simulation Engine Settings... '''or open The Netlist of the '''Run Dialog''', and click the '''Settings''' button next to the engine dropdown list.two-port device is given below:
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 Module]] provides two mechanism to terminated the time loop. In the first approach, an energy-like quantity defined as U<sub>n</sub> = Σ [ ε<sub>0</sub>|'''E<sub>i,n</sub>'''|<sup>2</sup> + μ<sub>0</sub>|'''H<sub>i,n</sub>'''|<sup>2</sup> ].ΔV<sub>i</sub> 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<sub>n</sub> 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<sub>n</sub> reach a maximum value U<sub>max</sub> at some time step and starts to decline thereafter. The ratio 10.log( U<sub>n</sub>/ U<sub>max</sub>) 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<sub>n</sub> 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.Cube]]'s default setting (labeled "'''Both'''"), terminates the simulation as soon as either of the first two criteria is met first. --
{{Note|Keep in mind that for highly resonant structures, you may have to increase the maximum number of time steps to very large values above 20,000.}}C1 1 0 1p
The "'''Acceleration'''" section of the FDTD Simulation Engine Settings dialog give three options for the FDTD kernel:R1 1 0 50
# Serial CPU Solver# Multi-Core CPU Solver# GPU SolverE1 2 0 1 0 20
The serial CPU solver is [[EM.Cube]]'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.RS 2 3 10
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. R2 3 0 50
=== Excitation Waveform & Frequency Domain Computations ===C2 3 0 1p
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 UserIn this case, a linear voltage-Defined Functioncontrolled voltage source (E1) with a voltage gain of 20 has been used. The input and output nodes are 1 and 3, respectively.
A sinusoidal waveform is single-tone and periodic<table><tr><td> [[Image:Amp circ. Its spectrum is concentrated around a single frequency, which is equal to your project's center frequencypng|thumb|left|420px|The schematic of the amplifier circuit in RF. Spice A Gaussian pulse decays exponentially as t → ∞, but it has a lowpass frequency spectrum which is concentrated around f = 0/D. A modulated Gaussian pulse decays exponentially as t → ∞, 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. </td></tr></table>
If you use The same Netlist can be written using a Gaussian pulse or a modulated Gaussian pulse waveform to drive your FDTD B-type nonlinear dependent 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 reached.as follows:
The accuracy of the FDTD simulation results depends on the right choice of temporal waveform. [[EM.Cube]]'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. ----
In addition to the default waveforms, [[EM.Cube]] allows the ability to define custom waveforms by either time or frequency specifications on a per source basis.C1 1 0 1p
Click here to learn more about EM.Tempo's [[Waveforms and Discrete Fourier Transforms]].X1 1 0 2 0 amp_dev
== Working with FDTD Simulation Data ==.subckt amp_dev 1 2 3 4
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<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub>, H<sub>x</sub>, H<sub>y</sub> and H<sub>z</sub>) at every mesh grid node at all time steps from t = 0 until the end of the time loop. However, 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.R1 1 2 50
[[EM.Cube]]'s FDTD Modules currently offers the following types of observable:B1 3 4 v = 20*v(1,2)
* '''Field Probe''' for monitoring E- and H-field components at a fixed location in both time and frequency domains. * '''Field Sensor''' for monitoring E- and H-field components on a cross section of the computational domain in both time and frequency domains.* '''Far Field Radiation Pattern''' for monitoring the radiation behavior of your structure.* '''Far Field RCS''' for monitoring the scattering behavior of your structure.* '''Huygens Surface''' for collecting tangential field data on a box. * '''Port Definition''' for calculating the S/Y/Z [[parameters]] and voltage standing wave ratio (VSWR). * '''Domain Energy''' for calculating the total electric and magnetic energy in the computational domain.* '''Periodic Characteristics''' for calculating the reflection and transmission coefficients when your periodic structure is excited by a plane wave source. ends
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. On the other hand, port characteristics like S/Y/Z [[parameters]], VSWR and periodic characteristics like reflection and transmission coefficients, are calculated over the entire specified bandwidth of your project.RS 2 3 10
===Defining a New Observable===R2 3 0 50
To create a new observable, follow these steps:C2 3 0 1p
* Right click on the name of the observable type in the '''Observables''' section of the navigation tree and select '''Insert New Observable...''' from the contextual menu. This opens up the respective Observable Dialog.* You can change the default name of the observable as well as its color.* Change the location of the observable, if necessary, by the changing the values of the supplied coordinate fields. * Change the orientation of the observable, if necessary. * In the case of frequency domain observables, change the observed frequency or frequency range, if necessary. ----
Once you define an observable, you {{Note|You can always changes its [[parameters]] later from its property dialog, which can be accessed from its rightuse active one-click contextual menu. You can also delete observablesports 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. }}
===Understanding Different FDTD Observable Types===<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>
====Probing Fields in Time and Frequency Domains==EM.Tempo's Observables & Simulation Data Types==
[[Image:FDTD75.png|thumb|300px|FDTD Field Probe Dialog]]Field probes monitor === Understanding the field components at a certain point in the computational domain. They record the time-domain field data during the entire time loop and compute their frequency spectrum using a discrete Fourier transform. By computing the time domain fields at a certain location, you can examine the transient response of a system at that location. This is also very useful for monitoring the convergence of FDTD time marching loop. [[EM.Cube]]'s field probes allow you to save the temporal values of a field component at a specified point in the computational domain during the entire time marching loop. You can plot the time domain field components as a function of the time step index. You can also plot the spectral contents of those field components, i.e. their Fourier transform, over the project's specified frequency bandwidth. To define a new field probe, follow these steps:Observable Types ===
* Right click on the EM.Tempo'''Field Probe''' item in s FDTD simulation engine calculates all the '''Observables''' section of the Navigation Tree six electric and select '''Insert New Observable...'''* You can change the default name of the probe as well as its color. The magnetic field probe is displayed as a small green arrow in the Project Workspace.* By default [[EM.Cube]] creates a field probe located at the origin of coordinates components (0E<sub>x</sub>,0E<sub>y</sub>,0). You can move the probe to any location by changing its XE<sub>z</sub>, Y H<sub>x</sub>, H<sub>y</sub> and Z coordinates.* In H<sub>z</sub>) at every mesh grid node at all time steps from t = 0 until the Probe Location section end of the dialogtime marching loop. However, in order to save memory usage, you can also set the '''Direction''' of engine discards the probe temporal field data from a dropdown list that contains ±Xeach time step to the next. Storage, ±Y manipulation and visualization of 3D data can become overwhelming for complex structures and ±Z optionslarger computational domains. The default direction 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 +Zwhy EM.Tempo asks you to define project observables to instruct what types of output data you want in each simulation process.
[[ImageEM.Tempo offers the following types of output simulation data:FDTD76.png|thumb|300px|An X-directed probe placed above a PEC plate illuminated by a normally incident plane wave.]]
At the end {| 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 an FDTD simulation, the EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]| style="width:300px;" | Computing electric and magnetic field components along the specified probe direction are saved at a fixed location in the probetime 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. Both in the time frequency domain fields from t | style= 0 to "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 last time step amplitude and their phase of electric and magnetic field components on a planar cross section of the computational domain in the frequency domain spectrum | 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 recordedgenerated at certain specified time intervals|-| style="width:30px;" | [[File:farfield_icon. You can plot these data 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.GridCube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing additional radiation characteristics such as directivity, which can be accessed from 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 Manager| style="width:150px;" | [[Glossary of EM. To open data manager, click the '''Data Manager''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;" | [[ImageFile:data_manager_iconport_icon.png]] button | style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of the '''Simulate Toolbar''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 select 'waveguide port|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Voltages, Currents & Powers| style="width:150px;" | [[Glossary of EM.Cube''Simulate > Data Manager''' from s Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]] | style="width:300px;" | Computing the menu barport 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 right click on the '''Data Manager''' item 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 Navigation Tree reflection and select Open Data Managertransmission 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.. from Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the contextual menuelectric, or use magnetic and total energy inside the keyboard shortcut '''Ctrl+D'''. In entire computational domain in the Data manager Dialog, you see a list time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power| style="width:150px;" | [[Glossary of all the data files available for plottingEM. These include 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 and frequency| style="width:250px;" | None|-domain probe data files with '''| style="width:30px;" | [[File:energy_icon.DAT''' png]]| style="width:150px;" | Electric and '''Magnetic Energy Density| style="width:150px;" | [[Glossary of EM.CPXCube''' file extensionss Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the electric, respectively. Select any data file by clicking magnetic and highlighting its row total energy density on a field sensor plane in the table 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 then click the '''Plot''' button to plot the graphSpecific Absorption Rate (SAR) Density| style="width:150px;" | [[Glossary of EM. The timeCube'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 probe is plotted 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 Cartesian graph showing field sensor plane in the selected frequency domain| style="width:250px;" | Requires at least one field component 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 function of time stepHuygens source in other [[EM. The frequencyCube]] modules| style="width:250px;" | None|-domain probe contains two | style="width:30px;" | [[File:CartData_icon.png]]| style="width:150px;" | Generic 3D Cartesian graphsSpatial Data| style="width: amplitude and phase 150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#3D_Cartesian_Data_Observable | 3D Cartesian Data]]| style="width:300px;" | Visualizing the selected field component over contents of generic 3D Cartesian spatial data files overlaid on the project's frequency rangeworkspace | style="width:250px;" | Requires import of an existing ".CAR" data file|}
{{twoimg|FDTD77Click on each category to learn more details about it in the [[Glossary of EM.png|Time domain component plotted vsCube's Simulation Observables & Graph Types]]. time|FDTD78.png|Probed field plotted vs. frequency.}}
====FrequencyOf 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 Near Field Visualization====domain solvers is its ability of generate wideband S/Z/Y parameter data in a single simulation run.
[[Image:FDTD71(1).png|thumb|300px|[[FDTD Module]]'s Field Sensor dialog]]=== Examining the Near Fields in Time and Frequency Domains ===
In [[EM.Cube]] you can visualize Tempo's FDTD time marching loop computes all the near fields six electric and magnetic field components at every Yee cell of your structure's mesh at every time step. This amounts to a specific frequency in a specific plane formidable amount of the computational domaindata that is computationally very inefficient to store. At the end Instead, you can instruct EM.Tempo to save a small potion of an FDTD simulationthese data for visualization and plotting purposes. Using a '''Field Probe''' at a specified point, all you can record the a time -domain electric and magnetic field values are available at all mesh nodescomponent over the entire FDTD loop. These temporal quantities The time-domain results are also transformed into to the frequency domain within the specified bandwidth using a discrete Fourier transforms to calculate transform (DFT). <table><tr><td> [[Image:FDTD77.png|thumb|left|480px|Time-domain evolution of the electric and magnetic fields on field at a specified sensor planegiven point. To define a new Field Sensor, follow these steps:]]</td></tr></table>
* Right click on In EM.Tempo, you can visualize the '''Field Sensors''' item near fields at a specific frequency in the '''Observables''' section a specific plane of the Navigation Tree and select '''Insert New Observablecomputational domain...'''* The '''Label''' box allows To do so, you need to change the sensorâs name.* Set the define a '''DirectionField Sensor''' of the field sensorobservable. This is specified by the normal vector of the sensor planeEM. The available options are Tempo'''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[EM.Cube]] creates a s field sensor defines a plane passing through the origin of coordinates (0,0,0) and coinciding with the XY plane. Note that the sensor plane extends across the entire computational domainparallel to one of the three principal planes. You can change The magnitude and phase of all the location six components of the sensor plane to any point by typing in new values for the X, Y electric and Z coordinates. Keep in mind that you can move a sensor plane only along magnetic fields on the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe mesh grid points on the sensor plane moving along that direction in the project workspace.* The frequency at which the field is evaluated has to be specified in the box labeled '''Near Field Frequency''' in the project's frequency unit. By default, this is equal to the project's center frequencyare computed and displayed.
After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the <table><tr><td> [[Image:FDTD_FS2.png|thumb|left|420px|EM.Tempo'''Observables''' section in the Navigation Tree and can be right clicked for additional editing. Once an FDTD simulation is finished, a total of 14 plots are added to every s Field Sensor node in the Navigation Treedialog. These include the magnitude and phase of all three components of E and H fields and the total electric and magnetic field values at the specified frequency]] </td></tr><tr><td> [[Image:FDTD_FS1_new. Click on any of these items and a color-coded intensity plot of it is visualized in the project workspace. A legend box appears in the upper right corner of the png|thumb|left|480px|Three field plot, which can be dragged sensor planes defined around using the left mouse buttona PEC ellipsoid illuminated by a plane wave source. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V]] </m for E-field and Atd></m for H-fieldtr></table><table><tr><td> [[Image:FDTD_FS3_new. The values of phase plots are always shown in Radians between -p and p. To display the fields properly, the structure is cut through the png|thumb|left|360px|Electric field sensor plane, and only part of it is shown. If distribution above the structure still blocks your view, you can simply hide or freeze itPEC plate. You can change the view of the ]] </td><td> [[Image:FDTD_FS4_new.png|thumb|left|360px|Magnetic field plot with distribution above the available view operations such as rotating, panning, zooming, etcPEC plate.]] </td></tr></table>
{{twoimg|FDTD72.png|Field Sensor (E=== Computing Far-field) |FDTD74.png|Field Sensor (H-field)}}Characteristics in FDTD ===
[[Image:FDTD73.png|thumb|300px|Cartesian graph of total magnetic field vs. Y-index along Far fields are the crosshair in asymptotic form the field senor planefields when r → ∞ or k<sub>0</sub>r >> 1.]]Under these assumptions, the fields propagate outward as transverse electromagnetic (TEM) waves:
You can plot frequency domain fields in EM.Grid on 2D Cartesian graphs. Using field probes, you can plot any frequency domain field component as a function of frequency over the specified bandwidth at any point within the computational domain. Using field sensors, you can plot the total frequency domain fields as a function of position <math> \mathbf{H^{ff}(spatial coordinatesr) across the computational domain. Every field sensor has a crosshair made up of two perpendicular lines parallel to the boundaries of the sensor plane. When you define a field sensor for the first time, the crosshair passes through the origin of coordinates. You can change the location of the crosshair on the sensor plane using the other two coordinate boxes besides the one that moves the location of the sensor plane. At the end of an FDTD simulation, in addition to the 3D near field maps, [[EM.Cube]] also generates 2D Cartesian graphs of the total electric and magnetic fields along the two perpendicular crosshair lines. A total of four Cartesian data files are generated, two for total } = \frac{1}{\eta_0} \mathbf{ \hat{k} \times E-field and two for total H-field along the two lines. You can plot these data in EM.Grid, which can be accessed from [[EM.Cube]]'s Data Manager. To open data manager, click the '''Data Manager''' [[Image:data_manager_icon.png]] button of the '''Simulate Toolbar''', or select '''Simulate ^{ff}(r)} </math> Data Manager''' from the menu bar, or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu, or use the keyboard shortcut '''Ctrl+D'''. In the Data Manager dialog, you see a list of all the data files available for plotting including the frequency-domain sensor data files with a '''.DAT''' file extension. Select any data file by clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph. Frequency domain field sensor graphs show the total field as a function of cell index along one of the principal axes. If the FDTD mesh is uniform in that direction, the position is found by multiplying the cell index by the cell dimension and offsetting with respect to lower-front-left corner of the computational domain.
====Visualizing Far fields are typically computed in the spherical coordinate system as functions of the elevation and azimuth observation angles θ and φ. 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 Evolution 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 Time Domain====a partial radiation pattern.
In the course of the FDTD time marching process, a tremendous amount of data are generated that include all the six E/H field components at every Yee cell and at every time step. The temporal field values at a sensor plane are of particular interest. Such plots show the evolution of the fields as a function of time starting from time t = 0, when all the fields are zero everywhere in the computational domain. <table><tr><td> [[Image:FDTD_FF1.png|thumb|left|720px|EM.CubeTempo's Radiation Pattern dialog.]] can record snapshots of the field sensor data as the time loop marches forward</td></tr><tr><td> [[Image:FDTD_FF3. When you define a field sensor for the first time, by default it displays the frequency domain near field datapng|thumb|left|600px|EM. In order to record and save the time domain data, you have to open the field sensorTempo's property Radar Cross Section dialog by right clicking on the field sensor's name in the Navigation Tree and selecting '''Properties...'''from the contextual menu. In the section titled '''Sensor Domain''', select the radio button labeled '''Time Domain'''. Also, in the section titled "Field Display - Multiple Plots", select one of the two radio buttons labeled '''E-Field''' or '''H-Field'''. By default, the time domain field data are saved every 100 time steps. To change this setting, right click on the '''Field Sensors''' item in the Navigation Tree and select '''Time Domain Settings...''' from the contextual menu. In the Time Domain Settings Dialog, change the value of the box labeled '''Sampling Interval (in time steps)'''.]] </td></tr></table>
The default radiation box is placed at an offset of 0.1λ<sub>0</sub> 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.
Time domain <table><tr><td> [[animation]] is available only for FDTD simulations of "Analysis" typeImage:FDTD_FF2. It cannot be used in conjunction with sweep simulationspng|thumb|left|480px|EM. Once the FDTD Analysis is finished, you can click any of the field plots and visualize it in the main window or you can animate them by right clicking on the field sensorTempo's name in the Navigation Tree and selecting '''[[Animation]]''' from the contextual menufar field acceleration dialog. You can change the [[animation]] settings from the '''[[Animation]] Controls Dialog'''. Note that the [[animation]] loop repeats itself indefinitely until you close the [[Animation]] Controls dialog or hit the keyboardâs '''Esc Key'''.</td></tr></table>
{{twoimg|FDTD121.png|Field sensor setup for time=== Radiation Pattern Above a Half-domain output|FDTD126.png|Time interval settings}}Space Medium ===
====Scattering Parameters and Port Characteristics====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:
If your physical structure is excited by a Lumped Source or a Waveguide Source or a Distributed Source, and one or more ports have been defined, # Free space background# Free space background terminated in an infinite PEC ground plane at the FDTD engine calculates the scattering (S) [[parameters]], impedance (Z) [[parameters]] and admittance (Y) [[parameters]] of the selected ports. The S [[parameters]] are calculated based on the port impedances specified bottom# Free space background terminated in an infinite PMC ground plane at the project's "Port Definition". If more than one port has been defined bottom# Free space background terminated in the project, the FDTD engine runs an internal port sweep. Each port is excited separately with all the other ports turned off. When the ''j''th port is excited, all the S<sub>ij</sub> [[parameters]] are calculated together based on the following definition:infinite dielectric half-space medium
:<mathtable> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </mathtr><!--td> [[Image:FDTD82(1)FDTD133.png|thumb|left|480px|EM.Tempo's far field background medium dialog.]]--</td></tr></table>
where V<sub>i</sub> is the voltage across Port iIn other words, I<sub>i</sub> is EM.Tempo lets you calculate the current flowing into Port i and Z<sub>i</sub> is far field radiation pattern of a structure in the characteristic impedance presence of any of Port i. The sweep loop then moves to the next port until all ports have been excitedabove four background structure types. After the FDTD simulation is finished, the S [[parameters]] are written into output ASCII data files. Since You can set these data are complex, they are stored as '''choices in EM.CPXTempo''' files. Every file begins with a header starting with s "#Far Field Background Medium"dialog. Besides the scattering [[parameters]]To access this dialog, open the admittance (Y) Radiation Pattern dialog and impedance (click the button labeled {{key|Background...}}. From this dialog, you can also set the Z) [[parameters]] -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 also calculated automatically selected, respectively, and saved in complex data files with '''.CPX''' file extensionsthe Z-coordinates of the ground plane and the bottom face of the computational domain will be identical.
Click here for more details on The fourth case applies when your computational domain ends from the computation 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 ε<sub>r</sub> and electric conductivity σ 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 [[Data_Visualization_and_Processing#Port_Characteristics | Port Characteristics]]EM.Tempo, your structure can have either an infinite PEC/PMC ground or a dielectric half-space termination.
<table><tr><td> [[Image:FDTD116fdtd_out36_tn.png|thumb|300pxleft|360px|Radiation pattern of a vertical dipole above PEC ground.]] </td><td> [[FDTD ModuleImage:fdtd_out37_tn.png|thumb|left|360px|Radiation pattern of a vertical dipole above PMC ground.]]'s </td></tr><tr><td> [[Image:fdtd_out38_tn.png|thumb|left|360px|Radiation Pattern dialogpattern of a horizontal dipole above PEC ground.]]</td><td> [[Image:fdtd_out26_tnfdtd_out39_tn.png|thumb|300pxleft|The 3D total radiation 360px|Radiation pattern of a horizontal dipole antenna: polar typeabove PMC ground.]]</td></tr>====Far Field Calculations in FDTD====</table>
For radiating structures or scatterers, the far field quantities are of primary interest. [[EM.Tempo]] computes the far field radiation patterns of an antenna or the radar cross section (RCS) of a target. In general, by far fields we mean the electric fields evaluated in the far zone of a physical structure. In the FDTD method, the far fields are calculated using a near=== Generating and Working with Multi-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. Normally, the radiation box should enclose the entire FDTD structure. In this case, the calculated radiation pattern corresponds to the entire radiating structure. The radiation box may also contain only parts of a structure, which results in partial radiation patterns.Frequency Simulation Data ===
Click here One of the primary advantages of the FDTD method is its ability to learn more about [[Data_Visualization_and_Processing#Computing_Far_Field_Radiation_Patterns | Computing Far Field Radiation Patterns]]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:
Click here to learn about [[Advanced Features of FDTD * Near-Field Sensor* Far-field Radiation Patterns]]. Pattern* RCS* Huygens Surface
====Defining The Far 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 Box====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.
For any far field calculations in <table><tr><td> [[Image:RadPattern multi.png|thumb|left|360px|EM.CubeTempo's Multi-frequency Radiation Pattern dialog.]], first you have to define a far field observable in the Navigation Tree. In </td><td> [[FDTD Module]], defining a far field observable also initiates a far field box in the computational domainImage:RCS multi. This box is used to perform the near-topng|thumb|left|360px|EM.Tempo's Multi-far-field transformation at the end of an FDTD simulationfrequency Radar Cross Section dialog. To insert a new far field box, follow these steps:]] </td></tr></table>
* Right click on Using the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Radiation Pattern...''' to open the Radiation Pattern Dialog.* Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button.* The multi-frequency of radiation pattern calculation dialogs, you can be specified in set the box labeled '''Far Field value of Start Frequency'''. By default, this is equal to the center frequency of the projectStop Frequency and Step Frequency in Hz. However, you You can calculate also set the far field data at any other frequency within the project's frequency range.* The resolution values of far field calculations is specified by '''Theta Angle Increment and Phi Angle Increment''' expressed in degrees. By The default, the values of both quantities are 5&thetadeg; and φ angles are incremented by 5 degrees.* Define the desired box for far field calculations in the '''Radiation Box''' section of the dialog. As in In the case of plane waves and Gaussian beamsRCS, there are two options available, a default radiation box (radio button '''Size: Default''') or a user defined radiation box (radio buttons '''Size: Custom'''). If you check '''Size: Default''', no radiation box corner coordinates need to be specified. The radiation box will always be 0.1 free space wavelength away from the bounding box have choose one of the entire structure. Select '''Sizetwo options: Custom''' to set the far field box manually. The values for the coordinates of Bistatic RCS'''Corner 1''' and '''Corner 2''' can now be changed. '''Corner 1''' is the lower-front-left corner and '''Corner 2''' is the upper-rear-right corner of the radiation box. The dimensions are specified in the world coordinate system (WCS).* At the end of an FDTD simulation, besides calculating the radiation data over the entire (spherical) 3D space, a number of 2D pattern graphs are also generated. These are indeed pattern cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant f-cut. This latter cut is at φ = 45° by default. You can assign another phi angle in degrees in the box labeled '''Non-Principal Phi Plane'''. Also, the 2D radiation pattern graphs are normalized by default. You can instruct [[EM.Cube]] to plot the 2D pattern graphs un-normalized (as calculated) by removing the check mark from the box labeled or '''Normalize 2D PatternsMonostatic RCS'''.
After closing To facilitate the Far Field Dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item process of all the '''Observables''' section defining multi-frequency observables in the Navigation TreeEM. A far field box shows up as a light blue wireframe box in the project workspace. You Tempo, you can right click on also use the far field item's name in following Python functions at the navigation tree and select '''Properties...''' to open up the radiation pattern dialog for further editing. Bear in mind that a full 3D radiation pattern calculation with a high angular resolution might be very time-consuming.command line:
Once an FDTD simulation is finished, three far field items are added to the Far Field section of the Navigation Tree. These are the far-zone E-field component along φ direction, the far-zone E-field component along φ direction and the total far-zone E-field.The 3D plots can be viewed in the project workspace by clicking on each item.
The view of the 3D far field plot can be changed with the available view operations such as rotateemag_field_sensor_multi_freq(f1, pan and zoom. A legend box appears in the upper right corner of the 3D radiation pattern plotf2, which can be dragged around with the left mouse button. If the structure blocks the view of the radiation patterndf, you can simply hide or freeze the entire physical structure or parts of it. Note that 3D radiation patterns are always positioned at the origin (0dir_coordinate,0x0,0) of the spherical world coordinate system even though the radiation center of the structure may not be located at that point. The (maximumy0,z0) '''Directivity''' of the radiating structure is displayed at the bottom of the legend box and is calculated using the definition:
At the end of an FDTD simulationemag_farfield_multi_freq(f1, the radiation pattern data E<sub>θ</sub>f2, E<sub>φ</sub> and E<sub>tot</sub> in the three principal XYdf, YZ and ZX planes plus one additional user defined phi plane cut are available for plotting on 2D graphs in '''EM.Grid'''. There are a total of eight 2D pattern graphs in the data manager: 4 polar graphs and 4 Cartesian graphs of the same pattern data. theta_incr,phi_incr)
At the end of an FDTD sweep simulation, other radiation characteristics are also computed as a function of the sweep variable emag_rcs_bistatic_multi_freq(frequencyf1, anglef2, or any other user defined variable). These include the '''Directivity (D0)'''df, '''Total Radiated Power (PRAD)''' and '''Directive Gain (DG)''' as a function of the θ and φ angles. Another radiation characteristic of interest especially in circularly polarized scenarios is the Axial Ratio. In [[EM.Cube]]theta_incr, the axial ratio is always defined in the LCP<sub>z</sub> or RCP<sub>z</sub> sense based on the X- and Y-components of the electric field. In order to calculate the directive gain or axial ratio, you have to check the boxes labeled '''Axial Ratio (ARphi_incr)''' or '''Directive Gain (DG)''' in the "Additional Radiation Characteristics" section of the '''Radiation Pattern Dialog'''. Four 2D Cartesian graphs of the axial ratio as functions of the theta angle are generated in the three principal XY, YZ and ZX planes as well as the additional user defined phi plane cut. At the end of an FDTD sweep simulation, the directive gain and axial ratio can also be plotted as functions of the sweep variable. In that case, either quantity needs to be computed at a fixed pair of θ and φ angles. These angles are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the '''Radiation Pattern Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the zenith.
[[Image:FDTD131.png|thumb|300px|EM.Tempo's RCS dialog]]====Radar Cross Section====emag_rcs_monostatic_multi_freq(f1,f2,df,theta_incr,phi_incr)
When the physical structure is illuminated by a plane wave sourceemag_huygens_surface_multi_freq(f1, the calculated far field data indeed represent the scattered fields. In that casef2, the incident and scattered fields can be separated. To compute the RCS of your physical structuredf, you must define an RCS observable instead of a radiation pattern. Follow these steps:x1,y1,z1,x2,y2,z2)
* Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New RCS...''' to open the Radar Cross Section Dialog.* Use the '''Label''' box to change the name of the far field or change the color of the far field box using the '''Color''' button.* The frequency of RCS calculation can be specified in the box labeled '''Far Field Frequency'''. By default, this is equal to the center frequency of the project. However, you can calculate the far field data at any other frequency within the project's frequency range.* The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By default, the θ and φ angles are incremented by 5 degrees.* Define the desired box for far field calculations in the '''Scattering Box''' section of the dialog. As in the case of radiation pattern, there are two options available, a default radiation box (radio button '''Size: Default''') or a user defined radiation box (radio buttons '''Size: Custom'''). If you check '''Size: Default''', no radiation box corner coordinates need to be specified. The radiation box will always be 0.1 free space wavelength away from the bounding box of the entire physical structure. Select '''Size: Custom''' to set the far field box manually. The values for the coordinates of '''Corner 1''' and '''Corner 2''' can now be changed. '''Corner 1''' is the lower-front-left corner and '''Corner 2''' is the upper-rear-right corner of the radiation box. The dimensions are entered in world coordinate system (WCS).* At the end of an FDTD simulation, besides calculating the RCS data over the entire (spherical) 3D space, a number of 2D RCS graphs are also generated. These are indeed RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant φ-cut. This latter cut is at φ = 45° by default. You can assign another φ angle in degrees in the box labeled '''Non-Principal Phi Plane'''.
At In the end of an FDTD simulationabove Python functions, in f1 and f2 are the far field section of the Navigation Treestart and stop frequencies, respectively, you will have the θ and φ components of RCS as well as df is the total radar cross section: σ<sub>θ</sub>frequency increment, σ<sub>φ</sub>, and σ<sub>tot</sub>. The RCS values (σ) are all expressed in m<sup>2</sup>Hz. The 3D plots are normalized to Note that the maximum RCS value, which is displayed in above commands simply create and insert the legend box. The 2D RCS graphs can be plotted in '''EM.Grid '''exactly specified observables in the same way that you plot 2D radiation pattern graphsnavigation tree. A total of eight 2D RCS graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts. at the end of They do not run perform a sweep simulation, [[EM.Cube]] calculates some other quantities including The created observables have the backscatter RCS (BRCS)same "base name" with ordered numeric indices. For example, forwardfar-scatter RCS (FRCS) and the maximum RCS (MRCS) field radiation patterns are names as functions of the sweep variable. In this caseMulti_FF_1, Multi_FF_2, the RCS needs to be computed at a fixed pair of φ and θ angles. These angles are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the '''Radar Cross Section Dialog'''. The default values of the user defined azimuth and elevation are both zero corresponding to the bore sight.
==Modeling 3D Periodic Structures in EM.Tempo==also provides some additional Python functions for the far-field radiation patterns and RCS observables.
EM.Tempo allows you to simulate doubly periodic structures with periodicities along the X and Y directions. Many interesting structures such as frequency selective surfaces (FSS), electromagnetic band-gap (EBG) structures and metamaterial structures can be modeled using periodic geometries. In the case of an infinitely extended periodic structure, it is sufficient to analyze only a unit cell. In the FDTD method, this is accomplished by applying periodic boundary conditions (PBC) at the side walls of the computational domain. ---
Click here to learn more about [[Time Domain Simulation of Periodic Structures]].emag_farfield_consolidate(x1,x2,dx,base_name)
[[Image:FDTD134.png|thumb|320px|EM.Tempo's Periodicity Settings dialog]]===Setting Up A Periodic Unit Cell===emag_rcs_consolidate(x1,x2,dx,base_name)
A periodic structure is one that repeats itself infinitely along one, two or three directions. In this release of [[EM.Tempo]], the periodicity is limited to the X-Y plane. In other words, the periodic structure repeats itself along the X- and Y-axes, but not along the Z-axis. By default, your physical structure is not periodic, and you have to instruct [[EM.Cube]] to turn it into a periodic structure through [[FDTD Module]]'s Periodicity Dialog. By designating a structure as periodic, you enforce periodic boundary conditions emag_farfield_explode(PBCbase_name) on the side walls of its computational domain. Your structure in the project workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines.
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: * Adaptive Mesh* Regular Mesh* Fixed-Cell Mesh EM.Tempo's default mesh generator produces an adaptive brick mesh of your physical structure, whose mesh resolution varies with the frequency. As the operating frequency of your project increases, the default '''Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. The adaptive mesh is optimized in such a way as to capture all the geometric details, curvatures and thin slanted plates or sheets, which often pose a challenge to staircase meshing. It usually provides a reasonably accurate discretization of most complex structures. Occasionally, you may opt for a more regularized FDTD mesh with almost equal grid line spacings everywhere, but still with a frequency-dependent cell size. In that case, you can use EM.Tempo's '''Regular''' FDTD mesh generator, which is indeed a simplified version of its adaptive mesh generator. The regular FDTD mesh enforces only two criteria: minimum mesh density and absolute minimum grid spacing. The grid cell sizes in this mesh are almost uniform in objects of the same material composition or in free-space regions. EM.Tempo also offers a uniform, frequency-independent, '''Fixed-Cell''' FDTD mesh generator. The fixed-cell mesh consists of three uniform grids in the XY, YZ and ZX principal planes. However, the uniform mesh cell dimensions along the three direction, i.e. Δx, Δy and Δz do not have to be equal. The fixed-cell mesh generator tries to fit your physical structure to the mesh grid rather than adapting the mesh to your physical structure.  {{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed and independent of your project's frequency settings.}} [[Image:FDTD140Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Adaptive_Yee_Mesh | EM.Tempo's Adaptive Brick Mesh Generator]]'''. [[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]]'''. <table><tr><td> [[Image:Tempo L11 Fig5.png|thumb|left|550px|A human head model and a cellular phone handset on its side.]] </td></tr><tr><td> [[Image:Tempo L11 Fig7.png|thumb|left|550px|The FDTD mesh of the human head model and the cellular phone handset.]] </td></tr><tr><td> [[Image:Tempo L11 Fig8.png|thumb|left|550px|Another view of the FDTD mesh of the human head model and the cellular phone handset.]] </td></tr></table> === Discretizing the Physical Structure Using the Adaptive Yee Mesh === EM.Tempo's default mesh generator creates an adaptive brick volume mesh that uses a variable staircase profile, where the grid line spacings vary with the curvature (derivative) of the object edges or faces. As a result, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed in cells per effective wavelength. Since FDTD is a time-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency of the project: f<sub>max</sub> = f<sub>0</sub> + Δf/2, where f<sub>0</sub> (or fc) is your project's center frequency and Δf (or bw) is its specified bandwidth. In other words, the effective wavelength in the free space is λ<sub>0,eff</sub> = c / f<sub>max</sub>, c being the speed of light in the free space. The effective wavelength in a dielectric material with relative permittivity ε<sub>r</sub> and permeability μ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>.  The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. Therefore, the average ratio of the cell size in a dielectric region to the cell size in the free space is 1/√(ε<sub>r</sub>μ<sub>r</sub>). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is more visible in the case of curved solids, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using a staircase profile. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best way. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regions. For example, this often happens around the interface between the free space and high permittivity dielectric objects. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structures. A carefully calculated, "<u>'''Adaptive'''</u>" mesh of your physical structure is generated in order to satisfy the following criteria: * Optimize the number of mesh cells in each dimension. The product of the number of cells in all the three dimension determines the total mesh size. The larger the mesh size, the longer the simulation time, especially with the CPU version of the FDTD engine. Also, a very large mesh size requires more RAM, which may exceed your GPU memory capacity. Set the '''Minimum Mesh Density''' to a moderately low value to keep the mesh size manageable, but be careful not to set it too low (see the next item below).* Ensure simulation accuracy by requiring an acceptable minimum number of cells per wavelength through each object and in the empty (free) space between them and the computational domain boundaries. An effective wavelength is defined for each material at the highest frequency of the project's specified spectrum. We recommend a '''Minimum Mesh Density '''of at least 15-20 cells/ wavelength. But for some resonant structures, 25 or even 30 cells per wavelength may be required to achieve acceptable accuracy. As you reduce the mesh density, the simulation accuracy decreases.* Accurately represent and approximate the boundaries of edges or surfaces that are not grid-aligned by closely adhering to their geometric contours. This is controlled by the '''Minimum Grid Spacing Over Geometric Contours''', which can be specified either as a fraction of the free space grid spacing or as an absolute length value in project units.* Maximize the minimum grid spacing in any dimension inside the computational domain and thus maximize the simulation time step. The time step size is dictated by the CFL stability criterion and is driven by the smallest grid spacing in each dimension. The smaller the time step, the larger the number of time steps required for convergence. This is controlled using the '''Absolute Minimum Grid Spacing''', which can be specified either as a fraction of the free space grid spacing or as an absolute value. It is critical to accurately represent and precisely maintain the object edge/surface boundaries in certain structures like resonant antennas and filters, as the phase of the reflected fields/waves is affected by the object boundary positions. When object boundaries are very close to each other, the mesh needs to represent them by two separate, but very closely spaced, grid lines. To control the minimum allowed grid spacing, use the '''Absolute Minimum Grid Spacing '''settings,* Maintain a smooth grid with no abrupt jumps from low-density to high-density regions. This feature is enabled with the '''Create Gradual Grid Transitions '''check box (always checked by default). When [[EM.Cube]] generates an FDTD mesh, a large number of geometrical considerations are taken into account. These include the bounding box of each object and its corners, the ends of a line, the apex of a cone or pyramid, or the locations of lumped sources, field probes and sensors, vertices of plane wave or far field boxes, to name a few examples. These points are âlockedâ as fixed grid nodes in the FDTD mesh. [[EM.Cube]] determines these points internally to generate a mesh that best approximates the original structure. As you saw earlier, you can use the FDTD mesh settings to control the shape and resolution of the mesh, for example, around the curved portions of your structure, or on slanted lines or faces, etc. These settings are global and apply to all the objects making up your physical structure. You can control the global mesh more selectively using the Advanced FDTD Mesh Settings Dialog. To open this dialog, click the '''Advanced '''button at the bottom of the FDTD Mesh Settings dialog. For example, you can control the quality of the gradual grid transitions by setting the value of '''Max Adjacent Cell Size Ratio'''. The default value of this parameter is 1.3, which maintains a smooth grid line spacing scheme with no more than 1:1.3 ratio for adjacent cells. By default, grid lines are enforced at all source and observable locations. You have the option to disable this feature and round up source locations to their closest grid lines. You may also uncheck the box labeled "Adapt mesh resolution to material properties". In that case, the same effective wavelength will be used to determine the mesh resolution inside all materials as well as the free-space regions. <table><tr><td> [[Image:FDTD80.png|thumb|320pxleft|Setting 720px|EM.Tempo's mesh settings dialog.]]</td></tr></table> The figures below compare the three types of the FDTD mesh for a dielectric ellipsoid with ε<sub>r</sub> = 4. Note that the cell size inside the dielectric region is half the cell size in the air region.  <table><tr><td> [[Image:FDTD MAN21.png|thumb|left|360px|The geometry of a dielectric ellipsoid with ε<sub>r</sub> = 4.]]</td><td> [[Image:FDTD MAN22.png|thumb|left|360px|The adaptive mesh of the dielectric ellipsoid.]]</td></tr></table> <table><tr><td> [[Image:FDTD MAN18.png|thumb|left|360px|The top view of the adaptive FDTD mesh of the dielectric ellipsoid.]]</td><td> [[Image:FDTD MAN19.png|thumb|left|360px|The top view of the regular FDTD mesh of the dielectric ellipsoid with the same mesh density.]]</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> The figures below compare the low resolution and high resolution adaptive FDTD meshes of a PEC parabolic reflector. This structure involves both a curved surface and a very thin surface.  <table><tr><td> [[Image:FDTD MAN23.png|thumb|left|450px|The geometry of a PEC parabolic reflector.]]</td></tr></table> <table><tr><td> [[Image:FDTD MAN24.png|thumb|left|360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN27.png|thumb|left|360px|The high-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr><tr><td> [[Image:FDTD MAN26.png|thumb|left|360px|The top (XY) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN25.png|thumb|left|360px|The right (YZ) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr></table> === Adding Fixed Grid Points to the Adaptive Yee Mesh === Adding fixed grid points to an FDTD mesh increases its resolution locally. Each fixed grid point adds three grid lines along the three principal axes passing through that point. You can add as many fixed grid points as you desire and create dense meshes at certain regions. Fixed grid points appear as grey points in the project workspace. To insert a new fixed grid point, follow these steps: * Open the Fixed Grid Points Dialog by selecting '''Menu > Simulate > Discretization > Fixed Grid Points...''' or by right-clicking on the '''FDTD''' '''Mesh''' item of the navigation tree and selecting '''Fixed Grid Points Settings...'''* Click the {{key|Add/Edit}} button to open the "Add Fixed Grid Point" dialog.* Enter the (X, Y, Z) coordinates of the new fixed point in the coordinate boxes and click the {{key|OK}} button.* To modify the coordinates of an existing fixed grid point, select it from the table and click the {{key|Add/Edit}} button.* You can also remove a fix grid point from the FDTD mesh using the {{key|Delete}} button. <table><tr><td> [[Image:FDTD36.png|thumb|left|480px|A user-defined fixed grid point in an FDTD mesh.]] </td></tr><tr><td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.Tempo's fixed grid points settings dialog.]] </td></tr><tr><td> [[Image:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]] </td></tr></table> According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, EM.Tempo's adaptive mesh generator may create extremely tiny grid cells that would result in extremely small time steps. This would then translate into a very long computation time. [[EM.Cube]] offers the "Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. In a regular FDTD mesh, the grid cell sizes stay rather the same in objects of the same material composition. The mesh resolution increases in materials of higher permittivity and/or permeability based on the effective wavelength in exactly the same way as the adaptive mesh. === Profiling the Brick Mesh === A volumetric brick mesh is overwhelming for visualization in the 3D space. For this reason, [[EM.Cube]]'s mesh view shows only the outline of the cells on exterior surface of the (staircased) meshed objects. The mesh grid planes provide a 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. While a mesh grid plane is visible, you can move it back and forth between the two boundary planes at the two opposite sides of the computational domain. You can do this in one of the following four ways: * Using the keyboard's Page Up {{key|PgUp}} key and Page Down {{key|PgDn}} key.* By selecting '''Menu > Simulate > Discretization > Grid Planes > Increment Grid''' or ''' Decrement Grid'''.* By right clicking on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and selecting '''Increment Grid''' or ''' Decrement Grid''' from the contextual menu.* Using the keyboard shortcut {{key|>}} or {{key|<}}. As you âstep throughâ or profile the mesh grid, you can see how the structure is discretized along internal planes of the computational domain. <table><tr><td> [[Image:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]] </td><td> [[Image:Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td></tr></table> === The FDTD Grid Coordinate System (GCS) === When your physical structure is discretized using the brick mesh generator, a second coordinate system becomes available to you. The mesh grid coordinate system allows you to specify any location in the computational domain in terms of node indices on the mesh grid. [[EM.Cube]] displays the total number of mesh grid lines of the simulation domain (N<sub>x</sub> à N<sub>y</sub> à N<sub>z</sub>) 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<sub>x</sub>-1)à (N<sub>y</sub>-1) à (N<sub>z</sub>-1). The lower left front corner of the domain box (Xmin, Ymin, Zmin) becomes the origin of the mesh grid coordinate system (I = 0, J = 0, K = 0). The upper right back corner of the domain box (Xmax, Ymax, Zmax) therefore becomes (I = N<sub>x</sub>-1, J = N<sub>y</sub>-1, K = N<sub>z</sub>-1). [[EM.Cube]] allows you to 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. <table><tr><td> [[Image:FDTD35(1).png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.]]</td></tr></table> == Running FDTD Simulations in EM.Tempo == === EM.Tempo's Simulation Modes === Once you build your physical structure in the project workspace and define an excitation source, you are ready to run an FDTD simulation. The simulation engine will run even if you have not defined any observables. Obviously, no simulation data will be generated in that case. [[EM.Tempo]] currently offers several different simulation modes as follows: {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Wideband FDTD Analysis | 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 custom 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: * Identify material types and proper domain boundary conditions.* Identify the source type and excitation mechanism.* Define the project observables.* Mesh the physical structure and examine the quality of the generated mesh and it geometric fidelity.* Determine the proper temporal waveform.* Select the simulation mode and run the FDTD engine. Wideband analysis is [[EM.Tempo]]'s simplest and most straightforward simulation mode. It runs the FDTD time marching loop once. At the end of the simulation, the time-domain field data are transformed into the frequency domain using a discrete Fourier transform (DFT). As a result, you can generate wideband frequency data from a single time-domain simulation run. The other simulation modes will be explained later in this manual. To open the Simulation Run Dialog, click the '''Run''' [[Image:run_icon.png]] button of the '''Simulate Toolbar''' or select the menu item '''Simulate → Run...''' from the menu bar or use the keyboard shortcut {{key|Ctrl+R}}. To start the FDTD simulation, click the {{key|Run}} button at the bottom of this dialog. Once the simulation starts, the "Output Message Window" pops up and reports messages during the different stages of the FDTD simulation. During the FDTD time marching loop, after every 10th time step, the output window updates the values of the time step, elapsed time, the engine performance in Mega-cells per seconds, and the value of the convergence ratio U<sub>n</sub>/U<sub>max</sub> in dB. An [[EM.Tempo]] simulation is terminated when the ratio U<sub>n</sub>/U<sub>max</sub> falls below the specified power threshold or when the maximum number of time steps is reached. You can, however, terminate the FDTD engine earlier by clicking the '''Abort Simulation''' button. <table><tr><td> [[Image:Tempo L1 Fig13.png|thumb|left|480px|EM.Tempo's simulation run dialog.]]</td></tr><tr><td> [[Image:Tempo L1 Fig15.png|thumb|left|550px|EM.Tempo's output message window.]]</td></tr></table> === The FDTD Simulation Engine Settings === 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.Tempo]] provides two mechanism to terminated the time loop. In the first approach, an energy-like quantity defined as U<sub>n</sub> = Σ [ ε<sub>0</sub>|'''E<sub>i,n</sub>'''|<sup>2</sup> + μ<sub>0</sub>|'''H<sub>i,n</sub>'''|<sup>2</sup> ].ΔV<sub>i</sub> 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<sub>n</sub> 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<sub>n</sub> reach a maximum value U<sub>max</sub> at some time step and starts to decline thereafter. The ratio 10.log( U<sub>n</sub>/ U<sub>max</sub>) 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<sub>n</sub> drops to 1/1000 of its maximum value ever. The second termination criterion is simply reaching a '''Maximum Number of Time Steps''' , whose default value set to 10,000. A third option, which is [[EM.Tempo]]'s default setting (labeled "'''Both'''"), terminates the simulation as soon as either of the first two criteria is met first.  {{Note|Keep in mind that for highly resonant structures, you may have to increase the maximum number of time steps to very large values above 20,000.}} The "'''Acceleration'''" section of the FDTD Simulation Engine Settings dialog give three options for the FDTD kernel: # Serial CPU Solver# Multi-Core CPU Solver# GPU Solver The serial CPU solver is [[EM.Tempo]]'s basic FDTD kernel that run the time marching loop on a single central processing unit (CPU) of your computer. The default option is the multi-core CPU solver. This is a highly parallelized version of the FDTD kernel based on the Open-MP framework. It takes full advantage of a multi-core, multi-CPU architecture, if your computer does have one. The GPU solver is a hardware-accelerated FDTD kernel optimized for CUDA-enabled graphical processing unit (GPU) cards. If your computer has a fast NVIDIA GPU card with enough onboard RAM, the GPU kernel can speed up your FDTD simulations up to 50 times or more over the single CPU solver. For structures excited with a planewave 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. <table><tr><td> [[Image:FDTD58.png|thumb|left|720px|EM.Tempo's simulation engine settings dialog.]]</td></tr></table> ==Modeling 3D Periodic Structures in EM.Tempo== [[EM.Tempo]] allows you to simulate doubly periodic structures with periodicities along the X and Y directions. In the FDTD method, this is accomplished by applying periodic boundary conditions (PBC) at the side walls of the computational domain.  {{Note| [[EM.Tempo]] can only handle regular, non-skewed periodic lattices with no secondary offsets.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]]'''. ===Defining a Periodic Structure in EM.Tempo=== By default, your physical structure in the project workspace is not periodic, and you have to instruct [[EM.Tempo]] to turn it into a periodic structure using its Periodicity Dialog. By designating a structure as periodic, you enforce periodic boundary conditions (PBC) on the side walls of its computational domain. Your structure in the project workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines.
To define a periodic structure, follow these steps:
* 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.
<table><tr><td> [[Image:FDTD139FDTD134.png|thumb|320px360px|Placing a field probe above a periodic structure excited by an obliquely incident plane wave sourceEM.Tempo's periodicity settings dialog.]]===Exciting Periodic Structures===</td></tr></table>
In [[===Exciting Periodic Structures as Radiators in EM.Tempo]], 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>11</sub> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data.===
Click here In [[EM.Tempo]], a periodic structure can be excited using various source types. Exciting the 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 S<sub>11</sub> parameter or input impedance of 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 learn 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 '''Lumped Source Dialog''' or '''Waveguide Source Dialog''', there is a section titled '''Periodic Beam Scan Angles'''. This section is grayed out when the project structure is not periodic. You can enter desired beam scan angle values for both '''Theta''' and '''Phi''' in degrees. To visualize the radiation pattern of the beam-steered array, you have to define a finite-sized array factor. You do this in the "Impose Array Factor" section of the '''Radiation Pattern Dialog'''.  {{Note|For large θ scan angles, the periodic FDTD time marching loop may take far more about time steps to converge.}} <table><tr><td> [[Modeling Infinite Phased ArraysImage:Period1.png|thumb|350px|Setting periodic scan angles in EM.Tempo's Lumped Source dialog.]]</td></tr></tr></table> <table><tr><tr><td> [[Image:Period2.png|thumb|720px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td></tr></table> <table><tr><td> [[Image:Period3.png|thumb|360px|Radiation pattern of an 8Ã8 finite-sized periodic wire dipole array with 0° phi and theta scan angles.]] </td><td> [[Image:Period4.png|thumb|360px|Radiation pattern of a beam-steered 8Ã8 finite-sized periodic wire dipole array with 45° phi and theta scan angles.]] </td></tr></table> ===Exciting Periodic Structures Using Plane Waves in EM.Tempo=== 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. <table><tr><td> [[Image: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>
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° < θ < 180°), 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° < θ < 90°), 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<sub>z</sub>''' and '''TE<sub>z</sub>''' polarization options are available.
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 θ > 0°. [[EM.Cube]]'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.
===Reflection {{Note|It is very important to keep in mind that only in the case of normal incidence does [[EM.Cube]] compute the reflection and transmission coefficients over the entire specified bandwidth of the project. At oblique incidences when & Transmission Characteristics===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 θ<sub>0</sub> 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 θ 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".}}
At the end of the FDTD simulation of === Running a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files with '''.CPX''' file extensions. These coefficients behave like the S<sub>11</sub> and S<sub>21</sub> [[parameters]] of a two-port network. You can think of the upper half-space as Port 1 and the lower half-space as Port 2 of this network. The reflection and transmission (R/T) coefficients can be plotted on 2D graphs Dispersion Sweep in '''EM.Grid '''similar to the scattering [[parameters]]. You can plot them from the Navigation Tree. To do so, right click on the '''Periodic Characteristics''' item in the '''Observables''' section of the Navigation Tree and select '''Plot Reflection Coefficients''' or '''Plot Transmission Coefficients'''. The complex data files are also listed in [[EM.Cube]]'s data manager. To open data manager, click the '''Data Manager''' [[Image:data_manager_icon.png]] button of the '''Simulate Toolbar''' or select '''Simulate > Data Manager''' from the menu bar or right click on the '''Data Manager''' item of the Navigation Tree and select Open Data Manager... from the contextual menu or use the keyboard shortcut '''Ctrl+D'''. Select any data file by selecting its row in the table and then click the '''Plot''' button to plot the graph in EM.Grid.Tempo ===
{{Note|It is very important to keep in mind that only in The '''Dispersion Sweep '''option of the case Simulation Mode drop-down list performs a sweep of normal incidence does constant k<sub>l</sub> wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.CubeTempo]] compute uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k<sub>li</sub>, you can find the reflection and transmission coefficients over the entire specified bandwidth for all combinations of the projectfrequency f<sub>j</sub> and incident angle θ<sub>j</sub> such that (2π/c) . f<sub>j</sub>. At oblique incidences when sin θ <sub> 0, the computed Rj</T coefficients after the discrete Fourier transformation are valid only at sub> = k<sub>li</sub>. This provides a complete picture of the center frequency dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the project for the given value eigenvalues of the incident θperiodic structure. The horizontal axis represents the constant transverse wavenumber k<sub>0l</sub> angle(or beta). The vertical axis represents frequency. In other wordsSometimes, the computed Rfree space wave number k<sub>0</T coefficients at all the other frequencies away from the center frequency correspond to different values of the incident sub> = (2&thetapi; angle/c). As a resultf is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] only saves plots frequency vs. wavenumber. Both the reflection horizontal and transmission coefficients at vertical axes start from 0 and extend to f<sub>max</sub> and k<sub>l,max</sub>, respectively, where f<sub>max</sub> = f<sub>0</sub> + Δf/2, and Δf is the center frequency into specified bandwidth of the output data files "reflection_coefficientproject.CPX" and "transmission_coefficientFor this sweep option you have to specify the number of wavenumber samples.CPX"Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle φ as specified in [[EM.Tempo]]'s Plane Wave Dialog.}}
===Periodic FDTD Simulation Types===<table><tr><td>[[Image:KBT Settings.png|thumb|360px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]</td></tr></table>
<table><tr><td>[[Image:FDTD143KBT R.png|thumb|250px360px| [[EMA typical reflection coefficient dispersion diagram of a periodic structure.Tempo]]'s R</T Macromodel Settings Dialog.]]td><td>[[Image:FDTD144KBT T.png|thumb|250px360px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]Besides analyzing A typical transmission coefficient dispersion diagram of a periodic structure in a single-run simulation and other standard type sweeps, [[EM.Tempo]] offers a number of specialized sweep simulations for periodic structures. These include '''R</T Macromodel Sweep ''', '''Dispersion Sweep''' and '''Huygens Sweep'''. These options are available from the '''Simulation Mode''' dropdown list of the [[EM.Tempo]]'s '''Run Dialog'''. td></tr></table>
The '''R<br /T Macromodel Sweep''' option of the Simulation Mode dropdown list is only available for periodic structures. It is used to generate a lookup table model for the reflection and transmission coefficients of a periodic surface for both TM and TE polarizations. The results are written into a file named "PW_UserDefinedMacroData.mat". Through the Macromodel Settings dialog you can set the start and end value and number of samples for both the Theta (θ) and Phi (φ) angles of the incident plane wave. The R/T macormodels can be used by [[EM.Cube]]'s [[Propagation Module]] to calculate the reflection and transmission coefficients of incident rays at the facets of obstructing blocks with "non-standard" periodic surfaces.>
The '''Dispersion Sweep '''option of the Simulation Mode dropdown list performs a sweep of constant k<subhr>l</sub> wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.Cube]]'s [[FDTD Module]] uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k<sub>li</sub>, you can find the reflection and transmission coefficients for all combinations of frequency f<sub>j</sub> and incident angle θ<sub>j</sub> such that (2π/c) . f<sub>j</sub>. sin θ<sub>j</sub> = k<sub>li</sub>. This provides a complete picture of the dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the eigenvalues of the periodic structure. The horizontal axis represents the constant transverse wavenumber k<sub>l</sub> (or beta). The vertical axis represents frequency. Sometimes, the free space wave number k<sub>0</sub> = (2π/c).f is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] plots frequency vs. wavenumber. Both the horizontal and vertical axes start from 0 and extend to f<sub>max</sub> and k<sub>l,max</sub>, respectively, where f<sub>max</sub> = f<sub>0</sub> + Δf/2, and Δf is the specified bandwidth of the project. For this sweep option you have to specify the number of wavenumber samples. Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle φ as specified in [[FDTD Module]]'s Plane Wave Dialog.
{{isoimg|FDTD148[[Image:Top_icon.png|A typical dispersion diagram 30px]] '''[[EM.Tempo#Product_Overview | Back to the Top of a periodic structure}}the Page]]'''
<p> </p>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube #EM.Tempo_Documentation | Back to EM.Cube Main PageTempo Tutorial Gateway]]'''
{{FDTD Details}}[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''