60 GHz Phased Array Antenna – XFdtd

A 60 GHz phased array antenna is created and simulated to determine its performance in the channel 2 WiGig band centered at 60.48 GHz.

This tutorial begins by importing and creating materials and defining a parameter in order to evaluate the antenna's performance at 60.48 GHz. The materials are assigned to imported CAD geometry that includes two arrays, each with four patch antennas excited by four modal waveguide interfaces with an automatic waveform that covers the project's frequency range of interest from 55 to 65 GHz.

The grid is then defined by increasing the cells per wavelength and setting the minimum feature sizes to improve the grid's resolution and accuracy. Far Zone and planar sensors collect data during simulation in order to evaluate 2-D and 3-D radiation patterns.

Steady-state results and computed S-parameters from a single FDTD simulation are post-processed to define one superposition simulation for each array. The two arrays are then optimized 90 degrees offset from each other in order to produce max hold data.

This tutorial utilizes the following skills:

Importing copper from XF's materials library and using it to define the antenna's electromagnetic properties.
Adding three nondispersive Rogers materials and assigning them to the dielectric layers.
Adding a material frequency parameter to define the Rogers materials.
Importing a downloaded .stp file and with CAD geometry that includes two arrays connected by an L-frame, each with four patch antennas.
Exchanging the CAD model's default materials for user-defined materials.
Adding four waveguide excitations to each array for a total of eight modal waveguide interfaces.
Discretizing CAD geometry for improved resolution and increased accuracy.
Applying grid alignment to all parts.
Using far zone and planar sensors to save the antenna's far zone pattern at 60.48 GHz, and record the steady electric field versus frequency data, respectively, in order to evaluate 2-D and 3-D radiation patterns.
Create an FDTD simulation that computes S-parameters and collects steady-state results.
Post-process FDTD results to define a superposition simulation for each array.
Optimize the two arrays 90 degrees offset from each other in order to produce max hold data.

Step 1: Set the Project Properties

Setting the frequency range of interest is the first step in the workflow because XFdtd uses this information when constructing the grid, creating a waveform, and setting the bounds of output plots. This simulation focuses on the antenna's performance from 55 GHz to 65 GHz because these values cover the antenna's performance in the channel 2 WiGig band centered at 60.48 GHz.

In the upper-left corner of XF, click Edit, then select Project Properties to open the editor.
Under the Frequency Range of Interest tab, enter 55 GHz as the Minimum.
Enter 65 GHz as the Maximum.
Click Done to close the editor.

Step 2: Add the Materials

A material must be associated with each part in order to define its electromagnetic properties, so the necessary materials are first defined and then assigned to each part. The copper material is added to the project from the library, and three user-defined Rogers materials are created in XF. The project tree's materials node allows users to define a set of electromagnetic properties once and use it in multiple places.

First, add the copper material.

Click the Libraries button on the right side of the XF window.
In the Libraries section of the editor, select Materials- Pure Metals.
In the Filters section, select Materials.
In the lower portion of the editor, click on Copper (Pure) [ND] and drag it to the Materials node of the Project Tree.
Close the Libraries window.
Double-click on Copper (Pure) [ND] in the Project Tree to open the Material Editor.

Next, add a parameter to validate the copper material.

Click the Parameters button on the right side of the XF window.
Click the button in the upper-left corner of the Parameters window.
Enter the Name by typing materialFrequency into the highlighted field.
Press Tab and type 60.48 GHz into the Formula field.
Click Apply to populate the Value field and apply the Parameter to the project.
Close the Parameters window.
Click Done to close the Material Editor.

Then, create the Rogers 5880 material.

Right-click on the Materials node in the Project Tree and select New Material Definition.
Name the material by typing Rogers 5880 into the highlighted field.
Press Enter to save the name to the project.
Double-click on Rogers 5880 in the Project Tree to open the Material Editor.
Under the Electric tab, change the Entry Method by selecting Loss Tangent from the drop-down menu.
Enter 2.2 as the Relative Permittivity.
Enter 0.0009 as the Loss Tangent.
Enter materialFrequency as the Evaluation Frequency.
If desired, navigate to the Appearance tab and change the Rogers 5880 material’s display color.
Click Done to close the Material Editor.

Repeat steps 14-23 for each remaining material. Create the Rogers 2929 material with a Relative Permittivity of 2.9, Loss Tangent of 0.003, and materialFrequency as the Evaluation Frequency. Finally, create the Rogers 4003 material with a Relative Permittivity of 3.55, Loss Tangent of 0.0027, and materialFrequency as the Evaluation Frequency.

Step 3: Import the CAD Model

Users can import geometry into XF as a CAD model. For this project, a downloaded *.stp file is imported to add geometry and its associated materials. The CAD model's default materials are exchanged for the user-defined materials added in the previous step.

First, download the CAD file.

Download the 60-ghz-antenna-array.stp file and save it to the desired location.

Next, import the CAD model.

In the upper-left corner of XF, click File ❯ Import ❯ CAD file(s) to open the Import CAD file(s) window.
Select the desired file and click Open to open the CAD Import Options window.

The default settings are desired for this project. Verify that Interpret modeling units as is set to millimeters, and all options are unchecked except for Assign materials to imported parts.

Click OK to import the CAD file.
Click OK to close the CAD Import Log.

Then, replace the imported default materials.

In the upper-left corner of XF, click View ❯ Parts List (All Parts) to open the Parts List window.
Click on the Material column header.
Click on the first listed Default Material Name.
Press Shift and click on the last Default Material Name to select them all.
Right-click on the selected materials and choose Material ❯ Assign Material to open the Assign Material window.
In the window, select Copper (Pure) [ND].
Click OK to apply the copper material’s properties to the Default Material Name material.

In the Parts List, repeat steps 8-12 to apply the Rogers 5880 material to Default Material Name 1, the Rogers 2929 material to Default Material Name 2, and the Rogers 4003 material to Default Material Name 3.

Close the Parts List window.
Right-click on the Materials node of the Project Tree and select Remove Unused Material Definitions.

Step 4: Add the Waveguide Excitations

Waveguide interfaces launch a modal excitation into the simulation space. Each excitation has a field distribution associated with it and the interface's geometry defines the two-dimensional area that launches the excitation. For this project, four waveguide interfaces are added to each array, for a total of eight waveguide interfaces exciting the antennas.

First, adjust the geometry view.

In the Project Tree, click on Feed 1 in Array 1.
In the Geometry window, click-and-drag to view Feed 1 from +X, then rotate along the YZ plane to place Array 1 in a horizontal position with Feed 1 on the left.

Add a waveguide interface to array 1.

Right-click on the Waveguide Interfaces branch of the Project Tree and select New Modal Waveguide Interface to open the editor.
Under the Properties tab, type A1.1 into the Name field.
Use the Impedance Type drop-down arrow to select Zpi.

The remaining Properties tab default values are desired for this project. Verify that the Enable, Use PrOGrid Grid Regions, and Active options are checked, Use Fixed Point is unchecked, Power is 1 W, Phase Shift is 0 degrees, Time Delay is 0 ns, and the Reference Plane Offset is 0 mm. The only available Waveform selection is None.

Under the Geometry tab, click the button in the Tools section.
In the Geometry window, mouse over Layer 2 and press h.
Press v and mouse over the center of the lower, y-directed edge of Feed 1 so that Center of Edge is indicated by the on-screen display.
Press the spacebar twice to point the arrow into the stripline.
Click to select the Center of Edge, as indicated by the on-screen display.

In the editor, verify that the Location is set to Center of Edge and the Propagation Direction is set to negative X.

In the Extensions section, enter 0.75 mm as the Lower U value.
Enter 0.75 mm as the Upper U value.
Enter 0.4064 mm as the Lower V value.
Enter 0.127 mm as the Upper V value.
Under the Boundaries tab, use the drop-down arrow to select PMC as the Lower U Boundary Type.
Select PMC as the Upper U Boundary Type.

The default settings for the V boundary are desired for this project. Verify that PEC is selected as both the Upper and Lower V Boundary Type.

Under the Port Specification tab, click the button to add a WaveguidePort.
Enter materialFrequency as the Evaluation Frequency.
In the Port Info section, change the Mode value to 1.
Click Compute Modes to open the Compute Modes dialog window.
Click Yes.
Click on WaveguidePort.
Rename the port by typing Stripline into the highlighted field.
Press Enter to apply the name change.
Click Apply.

Next, add a waveform definition.

Right-click on the Waveforms node of the Project Tree and select New Waveform Definition.
Press Enter to apply the default Automatic waveform name to the project.

Next, apply the waveform definition to the waveguide interface.

In the waveguide interface editor's Properties tab, use the Waveform drop-down arrow to select Automatic.
Click Done.

Then, add a second waveguide interface.

In the Project Tree, right-click on A1.1 [Port 1] and select Edit ❯ Copy.
Right-click on Waveguide Interfaces and select Edit ❯ Paste.
Double-click on A1.1 1 [Port 2] to open the Editing Modal Waveguide editor.
Under the Properties tab, type A1.2 into the Name field.
Under the Geometry tab, click the button to the right of the Y field.
In the Geometry window, hover over Layer 2 and press h.
Press v and mouse over the center of the lower, y-directed edge of Feed 2 so that Center of Edge is indicated by the on-screen display.
Click to select the Center of Edge, as indicated by the on-screen display.
Click Done.

Repeat steps 30-38 to add two more waveguides to the first array. Rename one of these waveguides A1.3 and position it on the lower, y-directed edge of Feed 3. Rename the other waveguide A1.4 and position it on the lower, y-directed edge of Feed 4.

Adjust the geometry view.

In the Geometry window, click-and-drag to view Array 2 from -Z, then rotate along the XY plane to place it in a horizontal position with Feed 1 on the left.

Add a waveguide interface to array 2.

Right-click on the Waveguide Interfaces branch of the Project Tree and select Edit ❯ Paste.
Double-click on A1.1 1 [Port 5] to open the Editing Modal Waveguide editor.
Under the Properties tab, type A2.1 into the Name field.
Under the Geometry tab, click the button in the Tools section.
In the Geometry window, mouse over Layer 2 and press h.
Press v and mouse over the center of the lower, y-directed edge of Feed 1 so that Center of Edge is indicated by the on-screen display.
Press the spacebar twice to point the arrow into the stripline.
Click to select the Center of Edge, as indicated by the on-screen display.

In the editor, verify that the Location is set to Center of Edge and the Propagation Direction is set to positive Z.

In the Extensions section, enter 0.127 mm as the Lower U value.
Enter 0.4064 mm as the Upper U value.
Enter 0.75 mm as the Lower V value.
Enter 0.75 mm as the Upper V value.
Under the Boundaries tab, use the drop-down arrow to select PEC as the Lower U Boundary Type.
Select PEC as the Upper U Boundary Type.
Select PMC as the Lower V Boundary Type.
Select PMC as the Upper V Boundary Type.
Click Done.

Repeat steps 30-38 to copy A2.1 and paste three more waveguides into the second array. Rename one of these waveguides A2.2 and position it on the lower, y-directed edge of Feed 2. Rename another waveguide A2.3 and position it on the lower, y-directed edge of Feed 3. Rename another waveguide A2.4 and position it on the lower, y-directed edge of Feed 4.

Step 5: Define the Grid

XF's gridding and meshing controls are used to discretize the CAD geometry into cell edges. This discretized representation is passed to the calculation engine, so it is important to update and define the grid before creating a simulation.

First, set the grid dimensions.

In the sidebar, use the button's drop-down arrow to select View from -X (Left) for a horizontal view of the L-Frame.
In the Project Tree, double-click on Grid to open the Editing Grid window.
Double-click on Mesh to open the meshing controls.
In the Mesh Cutplanes options, select the YZ Plane setting.
In the Editing Grid window, enter 20 as the Min Cells per Wavelength.
In the Min Feature Size section, uncheck the Ratio option to the right of the Good Conductors field.
Enter 0.035 mm as the Good Conductors value.
In the Cells Across section, enter 1 into the field associated with Good Conductors.
Uncheck the Ratio option to the right of the Poor Conductors field.
Enter 0.127 mm as the Poor Conductors value.

The default Cells Across value associated with Poor Conductors is desired for this project. Verify that 5 is the Cells Across value.

Under the Advanced tab, enter 21 as the Good Conductor Boundary Refinement Ratio.
Click Apply.

Then, align the PE 4 cells.

In the Project Tree, select PE 4 in Array 2, Patch 1.
Right-click in the Geometry window and select Gridding / Meshing, then Gridding Properties to open the Gridding Properties Editor.
In the Fixed Points section, select the Use Automatic Fixed Points option.
Click Apply.
Click Copy to clipboard.
Click Done to close the editor.

Paste the automatic fixed points to align the PE 1 cells.

In the Project Tree, right-click on PE 1 in Array 2, Patch 1 and select Edit ❯ Paste.

Correct the remaining spaces in both arrays.

In the upper-left corner of XF, click View, then Parts list (All Parts) to open the Parts List.
Click on the Name column header.

Paste the fixed points to align all parasitic element cells in every patch in both arrays.

Click to select the first listed PE 1.
Press Shift and click on the last listed PE 4.
Press Ctrl and click on the first listed Patch.
Press Shift and click on the last listed Patch.
Right-click on the selected parts and select Edit ❯ Paste.

Align the metal cells.

Click on the first listed Metal 2.
Press Shift and click on the last listed Metal 4.
Right-click on the selected parts and select Edit ❯ Paste.

Align the feed cells.

Click on the first listed Feed 1.
Press Shift and click on the last listed Feed 4.
Right-click on the selected parts and select Edit ❯ Paste.

Close the parts list, save grid settings, and close the mesh controls.

Close the Parts List.
Click Done to close the Editing Grid window.

Step 6: Check the Mesh

After the applied grid settings discretize the geometry, the cell edges and faces determine where the electric field and magnetic field values are computed during simulation. The mesh is checked in order to verify that the correct electromagnetic properties are assigned to each part.

In the lower-right portion of the Mesh controls, check the Spatial option in the View Mesh Information section.
Check the Material option.

The default Synchronize Sliders setting is desired for this project. Verify that the Synchronize Sliders option is checked.

In the lower-left portion of the controls, verify that the Mesh Cutplanes viewing mode is selected.
Verify that the YZ Plane setting is checked.
In the sidebar, click the Toggle Parts Visibility button to hide the geometry.
Click the Toggle Waveguide Interface Visibility button to hide the waveguides.
Adjust the X Slice slider until its corresponding value is 144.
Compare the grid to the geometry to ensure the Patch, Layer 1, Metal 2, Layer 2, Feed, Layer 3, and Metal 4 are accurately meshed.
In the upper-left corner of XF, click View, then Parts List (All Parts) to open the Parts List window.
Click on the Material column header.
Click on the first listed Rogers 2929 material.
Press Shift and click on the last Rogers 5880 material to select all Rogers materials.
Right-click on the selected materials and select Gridding / Meshing ❯ Enable dielectric volume averaging.
Close the Parts List.
In the sidebar, click the Toggle Parts Visibility button to display the geometry.
Click the Toggle Waveguide Interface Visibility button to display the waveguides.
In the Project Tree, double-click on Mesh to close the controls.

Step 7: Request Results

The last step before running a simulation is requesting results, which is done through sensors. This project utilizes two sensors: far zone and planar. The far zone sensor saves the antenna's far-zone radiation pattern at certain frequencies once the simulation is performed. The planar sensor records the steady electric field versus frequency data. The desired frequencies are input when the simulation is launched.

First, enable the first far zone sensor.

In the sidebar, use the button’s drop-down arrow to select View from +X (Right) to place Array 1 in the top, horizontal position.
In the Project Tree, right-click on Far Zone Sensors and select New Far Zone Sensor to open the editor.

In the upper-left portion of the editor, verify that Theta, Phi is selected as the Coordinate System Type.

In the Geometry tab’s Phi section, check the Use Single Phi Value option.
Enter 90 degrees as the Start Angle.

Some default settings in the Theta section are desired for this sensor. Verify that the Use Single Theta Value option is unchecked and the Stop Angle is 180 degrees.

Enter -180 degrees as the Start Angle.
Enter 2 degrees as the Increment.
Under the Properties tab, type Far Zone A1 into the Name field.

The default settings for the remaining enabled options are desired for this project. Verify that the Enable Far Zone Sensor and Collect Steady State Data options are checked, and the Collect Broadband Data option is unchecked.

Click Done.

Enable the second far zone sensor.

In the sidebar, use the button’s drop-down arrow to select View from -Z (Bottom).
Press Shift and click the button three times to place Array 2 in the top, horizontal position.
In the Project Tree, right-click on Far Zone Sensors and select New Far Zone Sensor to open the editor.

In the upper-left portion of the editor, verify that Theta, Phi is selected as the Coordinate System Type.

In the Geometry tab’s Theta section, check the Use Single Theta Value option.
Enter 90 degrees as the Start Angle.

Some default settings in the Phi section are desired for this sensor. Verify that the Use Single Phi Value option is unchecked, the Start Angle is 0 degrees, and the Stop Angle is 360 degrees.

Enter 2 degrees as the Increment.
Under the Properties tab, type Far Zone A2 into the Name field.

The default settings for the remaining enabled options are desired for this sensor. Verify that the Enable Far Zone Sensor and Collect Steady State Data options are checked, and the Collect Broadband Data option is unchecked.

Click Done.

Enable the third far zone sensor.

In the Project Tree, right-click on Far Zone Sensors and select New Far Zone Sensor to open the editor.

In the upper-left portion of the editor, verify that Theta, Phi is selected as the Coordinate System Type. Some default settings in the Geometry tab’s Theta section are desired for this sensor. Verify that the Use Single Theta Value option is unchecked, the Start Angle is 0 degrees, and the Stop Angle is 180 degrees.

Enter 2 degrees as the Increment.

Some default settings in the Phi section are desired for this sensor. Verify that the Start Angle is 0 degrees and the Stop Angle is 360 degrees.

Enter 2 degrees as the Increment.
Under the Properties tab, type Far Zone 3D into the Name field.

Click Done.

Enable the near-field sensor.

In the sidebar, use the button’s drop-down arrow to select View from +X (Right) to place Array 1 in the top, horizontal position.
In the Geometry window, click and drag downward along the XZ plane for a clearer view of Layer 1 in Array 1.
In the Project Tree, right-click on Near Field Sensors and select New Planar Sensor to open the editor.
Under the Specify Orientation tab, click the Pick Simple Plane button.
In the Geometry window, click on Layer 1 to place the sensor.
Under the Properties tab, type E-Fields A1 into the Name field.

The remaining Properties tab default settings are desired for this project. Verify that the Sensor Definition and Sampling Method options are set to Surface Sensor Definition and Snapped to E-Grid, respectively, and the Enable Surface Sensor option is checked.

Click Done.
In the Definitions branch of the Project Tree, double-click on Surface Sensor Definitions to open the editor.
In the Field vs Time section, uncheck the E option.
In the Fields vs Frequency section, check the Steady E option.
Click Done.

Step 8: Create an FDTD Simulation

Once the project is complete, it must be saved in order to create a new simulation and write output files. When creating a simulation, XF provides options for collecting S-parameters and specifying the frequency at which the far zone and planar patterns are saved.

First, save the project.

Save the project by selecting File ❯ Save Project As.
Enter the Project Name by typing 60-ghz-phased-array-antenna into the field.
Click Save.

Then, create and run an FDTD simulation.

Click the Simulations button in the upper-right corner of XF to open the Simulations window.
Use the Create Simulation drop-down menu to select FDTD to open the editor.
In the Create FDTD Simulation window, enter the simulation Name by typing FDTD Simulation into the field.
Under the Setup S-Parameters tab, click the Select All button.
Under the Frequencies of Interest tab, check the Collect Steady-State Data option.
Click the button on the right side of the tab.
Enter 60.48 GHz into the highlighted field.
Click Create & Queue Simulation.
Close the Simulations window once the Status changes to Completed.

Step 9: View FDTD Results

Once the simulation is complete, the results are available to view through the results browser. The planar sensor saved steady-E data from array 1, so electric fields progressing over time at the specified frequency are viewed in the geometry window. Steady-state data collected by far zone sensors is displayed as a gain pattern for array 1, and S-parameter computation provides additional data for comparison.

First, adjust the application preferences.

In the upper-left corner of XF, click Edit, then Application Preferences to open the editor.
Under the Graphs tab, change the Plot Name Information by deselecting the default Project : Simulation : Run setting.

The default Misc Info setting is desired for this project. Verify that Misc Info is selected.

Select Simulation Name, Result Type, and Sensor.
Click OK.

Next, view the E-field distribution for array 1.

Click the Results button on the right side of the XF window to open the Results browser.
Select E-Fields A1 as the Sensor.
In the lower portion of the browser, select the first result line with Active port: 1 in the Misc Info column.
Press Shift and click on the result line with Active port: 4 in the Misc Info column to select the first four runs.
Right-click on the selected results and choose View (default).
In the Geometry window, click and drag to rotate the view as needed for a clearer view of the loaded results.
In the upper-left portion of the editor, use the drop-down arrow to select | Total E |, FDTD Simulation, E-Field (E), E-Fields A1, Active port: 1.
Click the Hide Others button.
Use the drop-down arrow to select | Total E |, FDTD Simulation, E-Field (E), E-Fields A1, Active port: 2.
Use the drop-down arrow to select | Total E |, FDTD Simulation, E-Field (E), E-Fields A1, Active port: 3.
Use the drop-down arrow to select | Total E |, FDTD Simulation, E-Field (E), E-Fields A1, Active port: 4.
Click the Unload button four times.

Then, view the gain pattern for array 1.

In the Results browser, select Far Zone A1 as the Sensor.
Select Gain as the Result Type.
In the lower portion of the browser, select the first result line with Active port: 1 in the Misc Info column.
Press Shift and click on the result line with Active port: 4 in the Misc Info column to select the first four runs.
Right-click and select View (default) to view the Gain vs. Theta graph.
Click the Legend Visible button in the toolbar to hide the legend.
Click the Graph Properties button in the toolbar to open the editor.
In the Axes Properties tab's Polar Axis section, click the Units drop-down arrow to enter 90 degrees as the Start Angle.
Press Enter to apply the change to the graph.
Close the graph.

Then, view the S-parameter results for array 1.

In the Results browser, select A1.1:Stripline as the Sensor.
Press Ctrl and click on A1.2:Stripline, A1.3:Stripline, and A1.4:Stripline.
Select Frequency as the Domain.
Select S-Parameters as the Result Type.
In the lower portion of the browser, select the first result line with S[3,1] in the Misc Info column.
Press Shift and click on the result line with S[2,1] in the Misc Info column to select the first four results.
Right-click and select View (default) to view the | S31 | v. Frequency graph.
Close the graph.
Close the Results browser.

Step 10: Create a Superposition Simulation

The superposition simulation post-processing option combines steady-state results from a single FDTD simulation that computed S-parameters for multiple ports. XF provides options for defining which ports to combine and for specifying the magnitude and phase. Two superpositions are defined, one for each array at 0 degrees.

First, adjust the project properties.

In the upper-left corner of XF, click Edit and select Project Properties to open the editor.
Under the Display Units tab, use the Power drop-down arrow to select milliwatt decibels (dBmW, dBm).
Click Done to close the editor.

Then, create a superposition simulation.

Click the Simulations button in the upper-right corner of XF to open the Simulations window.
Use the Create Simulation drop-down menu to select Post Processing ❯ Superposition Simulation to open the editor.
In the Create Superposition Simulation window, enter the simulation Name by typing Superposition Simulation into the field.

In the Superpositions tab, verify that This Project and 000001: FDTD Simulation are selected as the Input Project and Input Simulation, respectively, in order to create a superposition using the current project and the FDTD Simulation created and run in this tutorial's previous steps.

Click the button on the right side of the window.
Enter the superposition Name by typing A1 0 deg into the field.
Select A1.1:Stripline, A1.2:Stripline, A1.3:Stripline, and A1.4:Stripline as the Active Ports.
Click Edit Superposition Definition to open the editor.
Double-click in the Available Power field associated with A1.1:Stripline.
Enter 23 dBmW into the highlighted field.

Repeat steps 11-12 for the three remaining ports.

Click OK to close the Superposition Definition Editor.
Click OK to close the Edit Superposition editor.
Click the button.
Enter the superposition Name by typing A2 0 deg into the field.
Select A2.1:Stripline, A2.2:Stripline, A2.3:Stripline, and A2.4:Stripline as the Active Ports.
Click Edit Superposition Definition to open the editor.
Double-click in the Available Power field associated with A2.1:Stripline.
Enter 23 dBmW into the highlighted field.

Repeat steps 19-20 for the three remaining ports.

Click OK to close the Superposition Definition Editor.
Click OK to close the Edit Superposition editor.
Click the Create Simulation button.
Close the Simulations window once the Status changes to Completed.

Step 11: View Superposition Results

The superposition simulation results are available immediately because existing results are accessed without the need for a separate executable. Array 1 E-field results from the FDTD and superposition simulations are compared, and the superposition pattern is added to the FDTD gain results.

First, compare array 1 E-field results.

Click the Results button on the right side of the XF window to open the Results browser.
Select E-Fields A1 as the Sensor.
Press Ctrl and select E-Fields A1 (A1 0 deg).
In the lower portion of the browser, select the first FDTD result line with Active port: 1 in the Misc Info column.
Press Shift and click on the FDTD result line with Active port: 4 in the Misc Info column to select the first four runs.
Press Ctrl and select the superposition result line with no active port listed in the Misc Info column.
Right-click on the selected results and choose View (default).
In the upper-left portion of the editor, use the drop-down arrow to select | Total E |, FDTD Simulation, E-Fields A1, Active port: 1.
Press the keyboard's down arrow four times to display the superposition results.

Leave the E-Field results loaded for use in subsequent steps.

Next, add the superposition pattern to the FDTD gain results

In the Results browser, select Far Zone A1 (A1 0 deg) as the Sensor.
Select Gain as the Result Type.
In the lower portion of the browser, right-click on the result line and select Create Line Graph to open the editor.
Select Polar as the Graph Type.

Some default line graph settings are desired for this project. Verify that Line is selected as the Plot Type, Total is selected as the Component, and Theta is selected as the Independent Axis.

Select Gain vs. Theta as the Target Graph.
Click View.
Click the Legend Visible button in the toolbar to hide the legend.

Leave the graph open for use in subsequent steps.

Then, edit the superposition definition and view updated data.

In the Results browser, right-click on the Gain result line with Far Zone A1 (A1 0 deg) in the Sensor column and select View Superposition Definition to open the editor.
Close the Results browser.

Click-and-drag the open windows as needed, positioning each one for a clear view of updated results in subsequent steps.

Double-click in the Phase column of the A1.2:Stripline row.
Enter 90 degrees into the highlighted field.
Press Tab twice and enter 180 degrees as the Phase for the A1.3:Stripline port.
Press Tab twice and enter 270 degrees as the Phase for the A1.4:Stripline port.
Click Apply to update the gain and E-Field results.
Click Done to close the editor.
Close the Gain vs. Theta graph.
In the editor, click the Unload button five times.
In the sidebar, click the Zoom to Selection button to recenter the geometry.

Step 12: Create Array Optimization

The array optimization post-processing option relies on the superposition principle in order to combine steady-state results from a single FDTD simulation that computed S-parameters for multiple ports and included a far zone sensor. Unlike a superposition simulation, the magnitude and phase for each port is unknown when performing array optimization. It determines the port values that produce a beam in a certain direction. The two arrays are optimized 90 degrees offset from each other.

Click the Simulations button in the upper-right corner of XF to open the Simulations window.
Use the Create Simulation drop-down menu to select Post Processing ❯ Array Optimization to open the editor.
In the Create Array Optimization window, enter the simulation Name by typing Array Optimization into the field.

In the Input Simulation tab, verify that This Project and 000001: FDTD Simulation are selected as the Input Project and Input Simulation, respectively, in order to define an array using the current project and the FDTD Simulation created and run in this tutorial's previous steps.

In the Array Definitions tab, click the button to open the New Array Definition editor.
Enter the array Name by typing A1 into the field.
Select A1.1:Stripline (Port 1), A1.2:Stripline (Port 2), A1.3:Stripline (Port 3), and A1.4:Stripline (Port 4) as the ports to use.
Enter 23 dBmW as the Total Available Power.
Click OK to close the editor.
Click the button.
Enter the array Name by typing A2 into the field.
Click the Deselect All button.
Select A2.1:Stripline (Port 5), A2.2:Stripline (Port 6), A2.3:Stripline (Port 7), and A2.4:Stripline (Port 8) as the ports to use.
Click OK to close the editor.
In the Analysis Definitions tab, click the button to open the Analysis Definition Editor.
Enter the analysis Name by typing A1 Boresight into the field.

Verify that A1 is selected as the Array Definition.

Use the drop-down arrow to select Far Zone 3D as the Far Zone Sensor.
Click the button.
Enter -30 degrees as the Theta value.
Press Tab and enter 90 degrees as the Phi value.

Repeat steps 17-19 to define four additional analyses at the following Theta, Phi angles, respectively: -15, 90 degrees; 0, 90 degrees; 15, 90 degrees; 30, 90 degrees.

Click OK.
Click the button.
Enter the analysis Name by typing A2 Boresight into the field.
Use the drop-down arrow to select A2 as the Array Definition.

Verify that Far Zone 3D is selected as the Far Zone Sensor.

Click the Delete All button.
Click the button.
Enter 90 degrees as the Theta value.
Press Tab and enter 150 degrees as the Phi value.

Repeat steps 25-27 to define four additional analyses at the following Theta, Phi angles, respectively: 90, 165 degrees; 90, 180 degrees; 90, 195 degrees; 90, 210 degrees.

Click OK.
Click the Create & Queue Optimization button.
Close the Simulations window once the Status changes to Completed.

Step 13: View Array Results

The array optimization results are available immediately because existing FDTD and superposition results are accessed. EIRP results from array 1 are compared and used to create a CDF of EIRP plot. A CDF plot of the max hold is created for each array, and then added to a composite graph.

First, compare array 1 EIRP results.

Click the Results button on the right side of the XF window to open the Results browser.
Select Far Zone 3D (A1 Boresight:A1 at [-15, 90]) as the Sensor.
Press Shift and click on Far Zone 3D (A1 Boresight:A1 at [30, 90]) to select the five array 1 analyses.
Select Effective Isotropic Radiated Power as the Result Type.
In the lower portion of the browser, select the first result line with Far Zone 3D (A1 Boresight:A1 at [-30, 90]) in the Sensor column.
Press Shift and click on the last result line to select the five results.
Right-click on the selected results and choose View (default).
In the upper-left portion of the editor, use the drop-down arrow to select the first listed result.
Press the keyboard's down arrow to display individual patterns.
Click the Unload button for each listed result except EIRP total, Array Optimization, Effective Isotropic Radiated Power, Far Zone 3D (A1 Boresight:A1 at [0, 90]).

Do not click Unload for the last result. Leave the EIRP total, Array Optimization, Effective Isotropic Radiated Power, Far Zone 3D (A1 Boresight:A1 at [0, 90]) result loaded for use in subsequent steps.

Next, create a CDF plot of array 1 EIRP results.

In the Results browser, right-click on the result line with Far Zone 3D (A1 Boresight:A1 at [0, 90]) in the Sensor column and select Create CDF Plot.

Clicking the Maximize button in the upper-right corner of the graph increases the size of the displayed results.

Click the Vertical Marker Tool button in the toolbar.
Left-click in the graph to create a marker.
Click the Select tool in the toolbar.
Right-click on the marker in the graph and select Properties to open the Marker Properties editor.
Enter 23 dBmW as the Requested Location X.
Click Close.
Click the Graph Properties button in the toolbar.
In the Plot Properties tab, double-click on CDF of Isotropic Radiated Power from Far Zone 3D (A1 Boresight:A1 at [0, 90] at 60.48 GHz and rename it by typing CDF of A1 Boresight into the highlighted field.
Press Enter to apply the name change.
Click the Graph Properties button to close the editor.
Click the Legend Visible button in the toolbar to display the legend.

View the array 1 max hold result.

In the Results browser, select Max Hold A1 Boresight:A1 as the Sensor.
In the lower portion of the browser, double-click on the result line to view the max hold.

Create CDF of max hold for array 1.

In the lower portion of the Results browser, right-click on the Max Hold A1 Boresight:A1 result and select Create CDF Plot.

Clicking the Maximize button in the upper-right corner of the graph increases the size of the displayed results.

Right-click on the plot line and select Copy.
On the right side of the XF window, use the Data button's drop-down arrow to select CDF of Effective Isotropic Radiated Power from Far Zone 3D (A1 Boresight:A1 at [0, 90]).
Right-click in the graph and select Paste.
In the Graphs branch of the Project Tree, right-click on CDF of Effective Isotropic Radiated Power from Max Hold A1 Boresight:A1 and select Delete.
In the CDF of Effective Isotropic Radiated Power from Far Zone 3D (A1 Boresight:A1 at [0, 90]) graph, click the Graph Properties button in the toolbar to open the editor.
In the Plot Properties tab, double-click on CDF of Effective Isotropic Radiated Power from Max Hold A1 Boresight:A1 at 60.48 GHz and rename it by typing CDF of A1 into the field.
Press Enter to apply the name change.
On the right side of the editor, click on the Color box to open the color controls.
Select Red from the Preset drop-down menu.
Click the Graph Properties button to close the editor.

Create CDF of max hold for array 2.

In the Results browser, select Max Hold A1 Boresight:A1 as the Sensor.
Press Ctrl and click on Max Hold A2 Boresight:A2 to select both sensors.
In the lower portion of the Results browser, double-click on the result line with Max Hold A2 Boresight:A2 in the Sensor column.
Press the keyboard's up arrow once to view the Max Hold A1 Boresight:A1 pattern for comparison.

Create composite CDF plot.

In the lower portion of the Results browser, press Ctrl and click on the result with Max Hold A1 Boresight:A1 in the Sensor column to select both results.
Right-click on the selected results and select Create Composite CDF Plot.
Right-click on the plot line and select Copy.
On the right side of the XF window, use the Data button's drop-down arrow to select CDF of Effective Isotropic Radiated Power from Far Zone 3D (A1 Boresight:A1 at [0, 90]).
Right-click in the graph and select Paste.
In the Graphs branch of the Project Tree, right-click on Composite CDF of Effective Isotropic Radiated Power at 60.48 GHz and select Delete.
In the CDF of Effective Isotropic Radiated Power from Far Zone 3D (A1 Boresight:A1 at [0, 90]) graph, click the Graph Properties button in the toolbar to open the editor.
Double-click on Composite CDF of Effective Isotropic Radiated Power at 60.48 GHz and rename it by typing CDF of A1 + A2 into the field.
Press Enter to apply the name change.
On the right side of the editor, click on the Color box to open the color controls.
Select Black from the Preset drop-down menu.
Click the Graph Properties button to close the editor.