<!--[[Image:FDTD82(1).png]]-->
where 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. The sweep loop then moves to the next port until all ports have been excited. After the FDTD simulation is finished, the S [[parameters]] are written into output ASCII data files. Since these data are complex, they are stored as '''.CPX''' files. Every file begins with a header starting with "#". Besides the scattering [[parameters]], the admittance (Y) and impedance (Z) [[parameters]] are also calculated and saved in complex data files with '''.CPX''' file extensions. The following relationships are used:
:<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot ([U]+[S]) \cdot ([U]-[S])^{-1} \cdot [\sqrt{Z_0}] }</math> :<math> \mathbf{ [Y] = [Z]^{-1} } </math><!--[[Image:FDTD83.png]]--> where <math>\mathbf{[U]}</math> is the identity matrix of order N, and <math>\mathbf{\sqrt{Z_0}}</math> is a diagonal matrix whose diagonal elements are the square roots of port characteristic impedances. The voltage standing wave ratio (VSWR) of the structure at the first port is also computed and saved to a real data '''.DAT''' file. The following definition is used: :<math> \text{VSWR} = \frac{|V_{max}|}{|V_{min}|} = \frac{1+|S_{11}|}{1-|S_{11}|} </math><!--[[Image:FDTD84.png]]--> You can plot the port characteristics from the Navigation Tree. Right click Click here for more details on the '''Port Definition''' item in the '''Observables''' section computation of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]]. Keep in mind that in multi-port structures, each individual port parameter has its own graph. You can also see a list of all the port characteristics data files 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 clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph in '''EM.Grid'''. By default, the S [[parameters]] are plotted as dual magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as dual real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You change the format of complex data plots. In general complex data can be plotted in three forms: Data_Visualization_and_Processing# Magnitude and Phase# Real and Imaginary Parts# Smith Chart In particular, it may be useful to plot the S<sub>ii</sub> [[parameters]] on a Smith chart. To change the format of a data plot, select it and click the '''Edit '''button of Data Manager and select one of the available graph type options.<br /> {{twoimgPort_Characteristics |FDTD114.png|[[EM.CubePort Characteristics]]'s data manager showing a list of complex data files available for plotting in EM.Grid.|FDTD115.png|Plot of S<sub>21</sub> of a filter in EM.Grid.}}
===Far Field Calculations in FDTD===
At the end of an FDTD simulation, in the far field section of the Navigation Tree, you will have the θ and φ components of RCS as well as the total radar cross section: σ<sub>θ</sub>, σ<sub>φ</sub>, and σ<sub>tot</sub>. You can view a 3D visualization of these quantities by clicking on their entries in the Navigation Tree. The RCS values (σ) are expressed in m<sup>2</sup>. The 3D plots are normalized to the maximum RCS value, which is displayed in the legend box. The 2D RCS graphs can be plotted in '''EM.Grid '''exactly in the same way that you plot 2D radiation pattern graphs. 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 a sweep simulation, [[EM.Cube]] calculates some other quantities including the backscatter RCS (BRCS), forward-scatter RCS (FRCS) and the maximum RCS (MRCS) as functions of the sweep variable (frequency, angle, or any user defined variable). In this case, 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 zenith.
Â
{{Note|Unlike [[EM.Cube]]'s Planar, MoM3D and Physical Optics Modules, the [[FDTD Module]] currently does not support 3D mono-static RCS calculation due to the enormous amount of computational work needed. Only the bi-static RCS is calculated for a given plane wave source.}}
Â
===Angular Sweeps===
If your FDTD project has a plane wave excitation, then you can also run an angular sweep. In this sweep, the values of the incidence angles θ and φ are varied at each sweep run. To run an angular sweep, open the FDTD '''Run Dialog''' and from the '''Simulation Mode '''dropdown list select the '''Angular Sweep''' option. Click the '''Settings''' button next to this dropdown list to open up the Angle Settings Dialog. In an angular sweep, only one of the two angles, θ and φ, can be varied at a time. Choose the radio button corresponding to the angle that you want to sweep. Then, set the values of the '''Start Angle''' and '''End Angle''' as well as the '''Number of Samples'''. Under normal circumstances, you would sweep θ from 180°to 90° backward and sweep φ from zero to 360° forward.<br />
Â
{{isoimg|FDTD128.png|[[FDTD Module]]'s Angle Settings dialog.}}
Â
===Defining Custom Output Parameters===
Â
{{mainpage|Custom Output}}
Â
At the end of an FDTD simulation, a number of computed quantities are designated as "Standard Output" [[parameters]] and can be used for various post-processing data operations. For example, you can define design objectives based on them, which you need for [[optimization]]. The table below gives a list of all the currently available standard output [[parameters]] in [[EM.Cube]]'s [[FDTD Module]]:
Â
{| class="wikitable"
!scope="col"| Standard Output Name / Syntax
!scope="col"| Description
|-
| SijM
| Magnitude of (i,j)-th Scattering Parameter
|-
| SijP
| Phase of (i,j)-th Scattering Parameter (in radians)
|-
| SijR
| Real Part of (i,j)-th Scattering Parameter
|-
| SijI
| Imaginary Part of (i,j)-th Scattering Parameter
|-
| ZijM
| Magnitude of (i,j)-th Impedance Parameter
|-
| ZijP
| Phase of (i,j)-th Impedance Parameter (in radians)
|-
| ZijR
| Real Part of (i,j)-th Impedance Parameter
|-
| ZijI
| Imaginary Part of (i,j)-th Impedance Parameter
|-
| YijM
| Magnitude of (i,j)-th Admittance Parameter
|-
| YijP
| Phase of (i,j)-th Admittance Parameter (in radians)
|-
| YijR
| Real Part of (i,j)-th Admittance Parameter
|-
| YijI
| Imaginary Part of (i,j)-th Admittance Parameter
|-
| VSWR
| Voltage Standing Wave Ratio
|-
| D0
| Directivity
|-
| PRAD
| Total Radiated Power
|-
| THM
| Main Beam Theta
|-
| PHM
| Main Beam Phi
|-
| DGU
| Directive Gain along User Defined Direction
|-
| ARU
| Axial Ratio along User Defined Direction
|-
| FBR
| Front-to-Back Ratio
|-
| HPBWXY
| Half Power Beam Width in XY Plane
|-
| HPBWYZ
| Half Power Beam Width in YZ Plane
|-
| HPBWZX
| Half Power Beam Width in ZX Plane
|-
| HPBWU
| Half Power Beam Width in User Defined Plane
|-
| SLLXY
| Maximum Side Lobe Level in XY Plane
|-
| SLLYZ
| Maximum Side Lobe Level in YZ Plane
|-
| SLLZX
| Maximum Side Lobe Level in ZX Plane
|-
| SLLU
| Maximum Side Lobe Level in User Defined Plane
|-
| FNBXY
| First Null Beam Width in XY Plane
|-
| FNBYZ
| First Null Beam Width in YZ Plane
|-
| FNBZX
| First Null Beam Width in ZX Plane
|-
| FNBU
| First Null Beam Width in User Defined Plane
|-
| FNLXY
| First Null Level in XY Plane
|-
| FNLYZ
| First Null Level in YZ Plane
|-
| FNLZX
| First Null Level in ZX Plane
|-
| FNLU
| First Null Level in User Defined Plane
|-
| BRCS
| Back-Scatter RCS
|-
| FRCS
| Forward-Scatter RCS along User Defined Incident Direction
|-
| MRCS
| Maximum Bi-static RCS
|-
| RCM
| Magnitude of Reflection Coefficient
|-
| RCI
| Phase of Reflection Coefficient (in radians)
|-
| RCR
| Real Part of Reflection Coefficient
|-
| RCI
| Imaginary Part of Reflection Coefficient
|-
| TCM
| Magnitude of Transmission Coefficient
|-
| TCP
| Phase of Transmission Coefficient (in radians)
|-
| TCR
| Real Part of Transmission Coefficient
|-
| TCI
| Imaginary Part of Transmission Coefficient
|}
Â
All the radiation- and scattering-related standard outputs are available only if you have defined a radiation pattern far field observable or an RCS far field observable, respectively. The standard output [[parameters]] DGU and ARU are the directive gain and axial ratio calculated at the certain user defined direction with spherical observation angles (θ, φ). These angles are specified in degrees as '''User Defined Azimuth & Elevation''' in the "Output Settings" section of the '''Radiation Pattern Dialog'''. The standard output [[parameters]] HPBWU, SLLU, FNBU and FNLU are determined at a user defined f-plane cut. This azimuth angle is specified in degrees as '''Non-Principal Phi Plane''' in the "Output Settings" section of the '''Radiation Pattern Dialog''', and its default value is 45°. The standard output [[parameters]] BRCS and MRCS are the total back-scatter RCS and the maximum total RCS of your planar structure when it is excited by an incident plane wave source at the specified θ<sub>s</sub> and φ<sub>s</sub> source angles. FRCS, on the other hand, is the total forward-scatter RCS measured at the predetermined θ<sub>o</sub> and φ<sub>o</sub> observation 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 zenith.