Changes

EM.Tempo

23,905 bytes removed, 22:55, 1 June 2015
/* Working with FDTD Simulation Data */
Click here to learn more about the various [[FDTD Observable Types]].
 
====Probing Fields in Time and Frequency Domains====
 
[[Image:FDTD75.png|thumb|300px|FDTD Field Probe Dialog]]
Field probes monitor 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:
 
* Right click on the '''Field Probe''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''
* You can change the default name of the probe as well as its color. The 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 (0,0,0). You can move the probe to any location by changing its X, Y and Z coordinates.
* In the Probe Location section of the dialog, you can also set the '''Direction''' of the probe from a dropdown list that contains ±X, ±Y and ±Z options. The default direction is +Z.
 
[[Image:FDTD76.png|thumb|300px|An X-directed probe placed above a PEC plate illuminated by a normally incident plane wave.]]
 
At the end of an FDTD simulation, the electric and magnetic field components along the specified probe direction are saved at the probe's location. Both the time domain fields from t = 0 to the last time step and their frequency domain spectrum are recorded. 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 > 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. These include the time-domain and frequency-domain probe data files with '''.DAT''' and '''.CPX''' file extensions, respectively. Select any data file by clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph. The time-domain field probe is plotted on a Cartesian graph showing the selected field component as a function of time step. The frequency-domain probe contains two Cartesian graphs: amplitude and phase of the selected field component over the project's frequency range.
 
{{twoimg|FDTD77.png|Time domain component plotted vs. time|FDTD78.png|Probed field plotted vs. frequency.}}
 
====Frequency-Domain Near Field Visualization====
 
[[Image:FDTD71(1).png|thumb|300px|[[FDTD Module]]'s Field Sensor dialog]]
 
In [[EM.Cube]] you can visualize the near fields at a specific frequency in a specific plane of the computational domain. At the end of an FDTD simulation, all the time domain electric and magnetic field values are available at all mesh nodes. These temporal quantities are transformed into the frequency domain using discrete Fourier transforms to calculate the electric and magnetic fields on a specified sensor plane. To define a new Field Sensor, follow these steps:
 
* Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''
* The '''Label''' box allows you to change the sensor’s name.
* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.
* By default [[EM.Cube]] creates a field sensor 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 domain. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z coordinates. Keep in mind that you can move a sensor plane only along the specified direction of the sensor. Therefore, only one coordinate can effectively be changed. As you increment or decrement this coordinate, you can observe 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 frequency.
 
After closing the Field Sensor Dialog, the a new field sensor item immediately appears under the '''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 Field Sensor node in the Navigation Tree. 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. 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 field plot, which can be dragged around using the left mouse button. 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 A/m for H-field. 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 field sensor plane, and only part of it is shown. If the structure still blocks your view, you can simply hide or freeze it. You can change the view of the field plot with the available view operations such as rotating, panning, zooming, etc.
 
{{twoimg|FDTD72.png|Field Sensor (E-field) |FDTD74.png|Field Sensor (H-field)}}
 
[[Image:FDTD73.png|thumb|300px|Cartesian graph of total magnetic field vs. Y-index along the crosshair in the field senor plane.]]
 
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 (spatial coordinates) 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 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 > 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 Field Evolution in Time Domain====
 
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. [[EM.Cube]] can record snapshots of the field sensor data as the time loop marches forward. When you define a field sensor for the first time, by default it displays the frequency domain near field data. In order to record and save the time domain data, you have to open the field sensor's property 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)'''.
 
 
Time domain [[animation]] is available only for FDTD simulations of "Analysis" type. It cannot be used in conjunction with sweep simulations. 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 sensor's name in the Navigation Tree and selecting '''[[Animation]]''' from the contextual menu. 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 keyboard’s '''Esc Key'''.
 
{{twoimg|FDTD121.png|Field sensor setup for time-domain output|FDTD126.png|Time interval settings}}
 
====Scattering Parameters and Port Characteristics====
 
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, 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 in the project's "Port Definition". If more than one port has been defined 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:
 
:<math> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math>
<!--[[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.
 
Click here for more details on the computation of [[Data_Visualization_and_Processing#Port_Characteristics | Port Characteristics]].
 
[[Image:FDTD116.png|thumb|300px|[[FDTD Module]]'s Radiation Pattern dialog]]
[[Image:fdtd_out26_tn.png|thumb|300px|The 3D total radiation pattern of a dipole antenna: polar type.]]
====Far Field Calculations in FDTD====
 
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-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.
 
Click here to learn more about [[Data_Visualization_and_Processing#Computing_Far_Field_Radiation_Patterns | Computing Far Field Radiation Patterns]].
 
Click here to learn about [[Advanced Features of FDTD Radiation Patterns]].
 
====Defining The Far Field Box====
 
For any far field calculations in [[EM.Cube]], first you have to define a far field observable in the Navigation Tree. In [[FDTD Module]], defining a far field observable also initiates a far field box in the computational domain. This box is used to perform the near-to-far-field transformation at the end of an FDTD simulation. To insert a new far field box, follow these steps:
 
* Right click on 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 frequency of radiation pattern 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 far field calculations is specified by '''Angle Increment''' expressed in degrees. By default, the &theta; and &phi; angles are incremented by 5 degrees.
* Define the desired box for far field calculations in the '''Radiation Box''' section of the dialog. As in the case of plane waves and Gaussian beams, 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 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 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 &phi; = 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 '''Normalize 2D Patterns'''.
 
After closing the Far Field Dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the '''Observables''' section in the Navigation Tree. A far field box shows up as a light blue wireframe box in the project workspace. You can right click on the far field item's name in 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.
 
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 &phi; direction, the far-zone E-field component along &phi; 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 rotate, pan and zoom. A legend box appears in the upper right corner of the 3D radiation pattern plot, which can be dragged around with the left mouse button. If the structure blocks the view of the radiation pattern, 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 (0,0,0) of the spherical world coordinate system even though the radiation center of the structure may not be located at that point. The (maximum) '''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 simulation, the radiation pattern data E<sub>&theta;</sub>, E<sub>&phi;</sub> and E<sub>tot</sub> in the three principal XY, 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.
 
At the end of an FDTD sweep simulation, other radiation characteristics are also computed as a function of the sweep variable (frequency, angle, or any other user defined variable). These include the '''Directivity (D0)''', '''Total Radiated Power (PRAD)''' and '''Directive Gain (DG)''' as a function of the &theta; and &phi; angles. Another radiation characteristic of interest especially in circularly polarized scenarios is the Axial Ratio. In [[EM.Cube]], 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 (AR)''' 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 &theta; and &phi; 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====
 
When the physical structure is illuminated by a plane wave source, the calculated far field data indeed represent the scattered fields. In that case, the incident and scattered fields can be separated. To compute the RCS of your physical structure, you must define an RCS observable instead of a radiation pattern. Follow these steps:
 
* 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 &theta; and &phi; 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 &phi;-cut. This latter cut is at &phi; = 45° by default. You can assign another &phi; angle in degrees in the box labeled '''Non-Principal Phi Plane'''.
 
At the end of an FDTD simulation, in the far field section of the Navigation Tree, you will have the &theta; and &phi; components of RCS as well as the total radar cross section: &sigma;<sub>&theta;</sub>, &sigma;<sub>&phi;</sub>, and &sigma;<sub>tot</sub>. The RCS values (&sigma;) 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. In this case, the RCS needs to be computed at a fixed pair of &phi; and &theta; 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==
Kazem Sabet
28,333
edits