Workshop 9-1: Unit Cell Analysis (Infinite Array) 2015.0 Release
ANSYS HFSS for Antenna Design
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Example – Unit Cell Analysis • Infinite Array Analysis of an Open Ended Waveguide with Plug Array • This example is intended to show you how to setup and post-process an a phased array using Unit Cell Analysis using HFSS.
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HFSS: Getting Started • Launching ANSYS Electronics Desktop 2015 • •
Select Programs > ANSYS Electromagnetics > ANSYS Electromagnetics Suite 16.0 Select ANSYS Electronics Desktop 2015.
• Setting Tool Options • Note: In order to follow the steps outlined in this example, verify that the following tool options are set : • Select the menu item Tools > Options > HFSS Options… •
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Click the General tab • Use Wizards for data input when creating new boundaries: Checked • Duplicate boundaries/mesh operations with geometry: Checked • Click the OK button Select the menu item Tools > Options > Modeler Options…. • Click the Operation tab • Select last command on object select: Checked • Click the Display tab • set default transparency to 0.7 • Click the Drawing tab • Edit properties of new primitives: Checked • Click the OK button
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Open Project • Opening the Project • In HFSS Desktop select the menu item File > Open. • Browse to the folder containing the file POEW_WS.aedt and select Open • Get familiar with the model. Look over the geometric details, boundary conditions and excitations.
• If you don’t have the project create the patch using the following dimensions and materials
Ground Plane Radome Thickness = 22.9mil er = 4.1
Waveguide Plug Radius = 284mil Height = 251.3mil er = 1.9
Waveguide Radius = 284mil Height = 641.3mil er = 2.1 4
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Understanding the Lattice • View the array from the Top • • • •
From HFSS’s menu bar select View > Modify Attributes > Orientation list Select the Orientation Named Top Click Apply To View button Click Close button
• Measure the distance between elements • Restrict the cursor to only snap to the center of arcs – From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Arc Center is the only check box checked. Note: Alternatively, you can hold the Alt key and Double Left Click in the top center of the 3D Modeler Window. The 3D Modeler Window is divided into a 3x3 grid where Double Left Clicking in any of the 9 regions will snap the view to a predefined orientation.
• Initiate the Measurement •
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– From HFSS’s Toolbar select Modeler > Measure > Position Select the Measurement Reference – Drag the mouse to the arc of the center element – With the cursor snaps to arc’s center left click the mouse to accept that location as the measurement reference.
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Understanding the Lattice • Restrict the Cursor’s Movement to the XY Plane •
– From HFSS’s Menu Bar select Modeler > Grid Plane... > XY – From HFSS’s Menu Bar select Modeler > Movement Mode… > In Plane Drag the mouse to the arc of one of the adjacent elements
Triangle Side
Note: Having easy access to the Snap Mode, Grid Plane and Movement Mode can greatly simplify work in the 3D Modeler. To include these capabilities on HFSS’s Toolbar select Tools > Customize from HFSS’s Menu Bar. The Toolbars tab provides a list of toolbars that can be added. Make sure there are check marks next to 3D Modeler Draw and 3D Snap Mode.
Note: The waveguide elements are placed on an equilateral triangular lattice; named because an equilateral triangle can be drawn connecting any 3 adjacent element. The distance between adjacent elements (any side of the triangle) is 635mils. The height of the triangle (the distance between rows in the X-Direction) is 549.926mils and each row is shifted in the Y-Direction 317.5mils with respect to the rows above and below it.
Triangle Height
• Observe the results in the Measure Data Window Note: The purpose of this Workshop is to model this array as an infinitely periodic structure using the Unit Cell techniques available in HFSS. These techniques use Master and Slave boundary pairs to enforce a periodicity in the fields that would exist from this infinitely periodic structure while only physically solving a single element. It can significantly reduce the RAM and Solve Time required to evaluate these models while taking into account all the element to element mutual coupling. However, it does not account for array’s edge affect which result from the nature of a finite array. To model these affects the array must be modeled entirely in HFSS by drawing the entire array or using Finite Array Domain Decomposition. 6
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Creating the Unit Cell Design • Copy Array into a New Design • • • •
In the Project Manager right click on the POEW_WS > 00_Array design branch Select Copy Ctrl+C from the pop-up menu In the Project Manager right click on the POEW_WS project design Select Paste Ctrl+V from the pop-up menu
• Change the Name of the Newly Created Design • In the Project Manager right click the POEW_WS > 00_Array1 design branch • Select Rename from the pop-up menu • Change the design’s name to 01_UnitCell
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Create the Unit Cell • Draw the Unit Cell • From HFSS’s Menu Bar select Draw > Regular Polyhedron • Using the coordinate entry fields, enter the Unit Cell’s Center Position • • • • •
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• X: 0.0, Y: 0.0, Z: 0.0, Press the Enter key Using the coordinate entry fields, enter the Polyhedron’s size by specifying the X and Y distance from the Polyhedron’s center to one of it vertices • dX: 183.3087, dY: 317.5, dZ: 0.0, Press the Enter key Using the coordinate entry fields, enter the height of the Unit Cell. – dX: 0.0, dy: 0.0, dZ: 1250.0, Press the Enter key In the Segment number window – Set the Number of segments to 6 – Click OK button. Select the Attribute tab from the Properties window. • Name: UnitCell • Material: Vacuum To fit the view: • Select the menu item View > Fit All > Active View
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Resize Radome • Trim Radome to fit inside UnitCell • Switch to Object Selection Mode
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– From HFSS Menu Bar select Edit > Select > Objects O Create Copy of UnitCell – From the 3D Modeler Tree select Solids > Vacuum > UnitCell branch – From HFSS’s Menu Bar select Edit > Copy Ctrl+C – From HFSS’s Menu Bar select Edit > Paste Ctrl+V Boolean Intersect Radome with copied UnitCell – From the 3D Modeler Tree select: • Solids > Radome > Radome • Solids > Vacuum > UnitCell1 – Note: You may have to hold the CTRL key down to select both objects simultaneously. – From HFSS’s Menu Bar select Modeler > Boolean > Intersect
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Unit Cell Discussion Note: The XY cross-section of the unit cell represents the periodicity of the array during the simulation. A proper unit cell will leave no space between adjacent unit cells when duplicated in accordance with the array’s lattice. To achieve this requirement, only certain shapes can be used for the unit cell. Typical shapes include the Hexagon, Parallelogram and a modified Rectangle. A Regular Hexagon was used since this model represents an equilateral triangular lattice, and the element completely fits inside. The equilateral nature of the lattice also dictates the size of the Regular Hexagon. Four of the 6 vertices are similarly oriented with respect to the hexagon’s center and were used to determine the size of the polyhedron just created. The X and Y components of these vertices can be expressed as follows. 𝑽𝒙 =
𝑨
=
Vy Vx
𝟔𝟑𝟓𝒎𝒊𝒍𝒔
= 𝟏𝟖𝟑. 𝟑𝟎𝟖𝟕𝒎𝒊𝒍𝒔 𝟐 𝟑 𝟐 𝟑 𝑨 𝟔𝟑𝟓𝒎𝒊𝒍𝒔 𝑽𝒚 = = = 𝟑𝟏𝟕. 𝟓𝒎𝒊𝒍𝒔 𝟐 𝟐
In the above equations |A| is the distance between any 2 adjacent elements. These equations generally hold for an equilateral triangular lattice. The only variation might be if one of lattice vectors lined up with the X-axis instead of the Y-axis. In this case the X and Y component would be flipped (newVx = Vy and newVy = Vx).
Note: The height of the unit cell was chosen to minimize the number of modes defined on the Floquet Port. This will be discussed later in the Workshop
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Define Master / Slave Boundaries • View the array from the Trimetric Orientation • • • •
From HFSS’s menu bar select View > Modify Attributes > Orientation list… Alt+O Select the Orientation Named Trimetric Click Apply To View button Click Close button
• Switch to Face Selection Mode • From HFSS’s Menu Bar select Edit > Select > Faces F
• Create Master1 Boundary • Restrict the cursor to only snap to vertices • • •
•
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face that touches the positive Y-axis to select it – Note: you may need to press the b button to select the face behind the initially selected face. From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Master… Master Boundary Window – Name: Master1 – U Vector: New Vector… • Left click on the vertex in the upper, left corner of the face • Left click on the vertex in the upper, right corner of the face – Click Ok button Verify the boundary setup – In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Master1 branch – Make sure the Master Boundary is highlighted in the 3D Modeler and looks like the picture © 2015 ANSYS, Inc.
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Define Master / Slave Boundaries • Note • Master Boundary Window – Name: Master1 – U Vector: New Vector… • When you click on the Vertex, some times an error message “Lines can only be created on selected faces” might pop-up.
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To avoid this, change the movement mode to 3D and draw the U vector Modeler > Movement Mode > 3D
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Define Master / Slave Boundary • Create Slave1 Boundary • Restrict the cursor to only snap to vertices •
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face that touches the negative Y-axis to select it – Note: you may need to press the b button to select the face behind the initially selected face. From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Slave… Master Boundary Window – Name: Slave1 – Master Boundary: Master1 – U Vector: New Vector… • Left click on the vertex in the upper, left corner of the face • Left click on the vertex in the upper, right corner of the face – Click Next button Phase Delay Window – Phi: Phi_Scan • Assign 0 deg to the variable Phi_Scan – Theta: Theta_Scan • Assign 0 deg to the variable Theta_Scan Click Finish button Note: The terms upper, left and upper, right can be ambiguous depending on which side of the face you are looking at. They are used here with respect to the Trimetric Orientation. Refer to the picture on the next page for a visual of how the U © 2015 ANSYS, Inc. May 6, 2015 Vector should look.
Note: The relative UV coordinate system created in the slave boundary should look same as the relative UV coordinate system defined on the slave boundary. The only difference is they are translated linearly along the Y-axis. Note: The Master and Slave boundaries force a periodicity in the fields corresponding to the periodicity of the array. It does this by mapping the fields on the Master boundary to the corresponding Slave boundary. These fields are identical with the exception of a phase shift that allows for plane waves to propagate in different directions. This phase shift is what will be used to enforce the progressive phase delay across the array that steers the beam. These boundaries use these UV coordinate systems to determine the field mapping. That is why they are setup as linear translations of each other. It is also why each master / slave pair are defined on opposite faces of the unit cell. If done correctly, the distance between each boundaries UV coordinate system should correspond to the distance and direction of the next adjacent element. This phase delay can be defined as a specific delay or in terms of the array’s scan angle. If the array’s scan angle is defined HFSS will determine the appropriate phase delay across the various Master / Slave boundaries to properly steer the beam in tat direction.
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Define Master / Slave Boundary • Verify the boundary setup • In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Slave1 branch • Make sure the Master and Slave Boundaries are highlighted in the 3D Modeler and looks like the picture Note: This procedure successfully define a single Master / Slave boundary pair. Two additional pairs need to be defined to complete the definition. The next few pages will step through the creation of these additional boundaries, but with far less explanation.
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Define Master / Slave Boundaries • View the array from the Trimetric Orientation • • • •
From HFSS’s menu bar select View > Modify Attributes > Orientation list… Alt+O Select the Orientation Named Trimetric Click Apply To View button Click Close button
• Switch to Face Selection Mode • From HFSS’s Menu Bar select Edit > Select > Faces F
• Create Master2 Boundary • Restrict the cursor to only snap to vertices •
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face rotated counter-clockwise from the one that touches the positive Y-axis to select it – Note: you may need to press the b button to select the face behind the initially selected face.
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Define Master / Slave Boundaries • From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Master… • Master Boundary Window – Name: Master2 – U Vector: New Vector… • Left click on the vertex in the upper, right corner of the face • Left click on the vertex in the upper, left corner of the face – Click Ok button
• Verify the boundary setup • In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Master2 branch • Make sure the Master Boundary is highlighted in the 3D Modeler and looks like the picture
• Create Slave2 Boundary • Restrict the cursor to only snap to vertices •
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face rotated counter-clockwise from the one that touches the negative Y-axis to select it – Note: you may need to press the b button to select the face behind the initially selected face.
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Define Master / Slave Boundary • From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Slave… • Master Boundary Window
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– Name: Slave2 – Master Boundary: Master2 – U Vector: New Vector… • Left click on the vertex in the upper, right corner of the face • Left click on the vertex in the upper, left corner of the face – Click Next button Phase Delay Window – Phi: Phi_Scan – Theta: Theta_Scan Click Finish button
• Verify the boundary setup – In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Slave2 branch – Make sure the Master Boundary is highlighted in the 3D Modeler and looks like the picture
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Define Master / Slave Boundaries • View the array from the Trimetric Orientation • • • •
From HFSS’s menu bar select View > Modify Attributes > Orientation list… Alt+O Select the Orientation Named Trimetric Click Apply To View button Click Close button
• Switch to Face Selection Mode • From HFSS’s Menu Bar select Edit > Select > Faces F
• Create Master3 Boundary • Restrict the cursor to only snap to vertices •
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face rotated counter-clockwise from the one used to define the Master2 boundary – Note: you may need to press the b button to select the face behind the initially selected face.
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Define Master / Slave Boundaries • From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Master… • Master Boundary Window – Name: Master3 – U Vector: New Vector… • Left click on the vertex in the upper, right corner of the face • Left click on the vertex in the upper, left corner of the face – Click Ok button
• Verify the boundary setup • In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Master3 branch • Make sure the Master Boundary is highlighted in the 3D Modeler and looks like the picture
• Create Slave3 Boundary • Restrict the cursor to only snap to vertices •
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– From HFSS’s Menu Bar select Modeler > Snap Mode… – Make sure Vertex is the only check box checked. Left click the UnitCell face rotated counter-clockwise from the one used to define the Master2 boundary – Note: you may need to press the b button to select the face behind the initially selected face.
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Define Master / Slave Boundary • From HFSS’s Menu Bar select HFSS > Boundaries > Assign > Slave… • Master Boundary Window
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– Name: Slave3 – Master Boundary: Master3 – U Vector: New Vector… • Left click on the vertex in the upper, right corner of the face • Left click on the vertex in the upper, left corner of the face – Click Next button Phase Delay Window – Phi: Phi_Scan – Theta: Theta_Scan Click Finish button
• Verify the boundary setup – In the Project Manager select the POEW_WS > 01_UnitCell > Boundaries > Slave3 branch – Make sure the Master Boundary is highlighted in the 3D Modeler and looks like the picture
Note: The 01_UnitCell design should have 3 pairs of Master / Slave boundaries totaling 6 boundaries all together. Each pair should be defined on opposite sides of the unit cell. Each boundary should have a UV coordinate system defined on it in such a way that the Uaxes point in the same direction and the V-axes point in the same direction. The only difference being a linear translation of their origins across the unit cell. In addition, each slave boundary should have using the Scan Angle method for defining the phase delay between the fields on the Master and Slave boundaries. This scan angle should be controlled by two variables; Phi_Scan and Theta_Scan. 20
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Define Floquet Port • View the array from the Trimetric Orientation • From HFSS’s menu bar select View > Modify Attributes > • • •
Orientation list… Alt+O Select the Orientation Named Top Click Apply To View button Click Close button
• Restrict the cursor to only snap to vertices • From HFSS’s Menu Bar select Modeler > Snap Mode… • Make sure Vertex is the only check box checked.
Note: The Lattice Coordinate System defines the array’s lattice for the Floquet Port. Two vectors need to be defined to completely describe the lattice. They are called the A and B lattice vectors (Directions). Both lattice vector tails much be at the same point. The vectors should describe the distance and direction between two adjacent elements in different direction. As such they should always start from one Master/Slave boundary and end on the paired boundary. For convenience, the vertices below were chosen, but other vertices could have been chosen as well.
• Create Floquet Port Excitation • Left click the face on top of the UnitCell Object to select it. • From HFSS’s Menu Bar select HFSS > Excitations > Assign > •
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Floquet Port… Floquet Port General Tab: – A Direction: New Vector • Left click on the bottom, left corner vertex of the UnitCell • Left click on the bottom, right corner vertex of the Unit Cell – B Direction: New Vector • Left click on the bottom, left corner vertex of the UnitCell • Left click on the top vertex of the Unit Cell – Click Next> button
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B2
A1=B1
A2
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Floquet Modes • Floquet Port: Modes Setup Window – – – –
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Click Modes Calculator… button Number of Modes: 20 Frequency: 10.8 GHz Scan Angles Phi: • Start: 0 deg • Stop: 90 deg • Step Size: 1 deg – Scan Angles Theta: • Start: 0 deg • Stop: 60 deg • Step Size: 1 deg – Click OK button – Observe the attenuation values for the first 20 modes – Change Number of Modes to 2 – Click Next button Floquet Port: Post Processing Window – Click Next button Floquet Port: 3D Refinement Window – Make sure all modes have their Affect Refinement Unchecked – Click Finish button
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Floquet Modes Discussion Note: The radiated waves from the array will be terminated in the Floquet Modes defined by the Floquet Port Setup. Each Floquet Mode is a plane wave supported by the periodic structure. They also correspond to the different beams an array might support. They come in two polarizations; Transverse Electric (TE) and Transverse Magnetic (TM). Assuming the Floquet Port is parallel to the XY plane, TE modes are +/- Phi polarized waves and TM modes are Theta polarized wave. The dominant modes are the TE 00 and TM00 modes which correspond to the phi and theta polarized components of the array’s main beam. All other mode indexes correspond to various grating lobes. The energy associated with any mode not defined in the Floquet Port will be short circuited back into the model so its important to include all propagating mode. However, which modes propagate depends on the angle the array is scanned. The Mode’s Calculator was added to make choosing the appropriate modes easier. It will search a scan volume defined by Theta and Phi angles and report the modes with the smallest attenuation constant over that scan volume. Make sure any mode not included in the port experiences at least 50dB of attenuation as it propagates from the element to the port. That way it has little chance to affect the predicted performance. The attenuation is calculated in dB/length so the total attenuation can be computed by multiplying the calculated attenuation by the unit cell height (0.04dB/length)*1250mils = 50dB of attenuation for mode 7. All modes listed above mode 7 have 0dB/length of attenuation so they must be included. Its important to note that the height of the Unit Cell impacts how many modes need to be included in the Floquet Port Setup. Nonpropagating modes can be removed from the setup by choosing a height large enough to make sure they experience the recommended attenuation for elimination. It’s a good idea to play around with the modes calculator a little to get a feel for how the mode attenuations are affected by frequency and scan volume. You should see that more modes are required at higher frequencies and larger scan volumes. Therefore it is important to specify the highest frequency you expect to simulation and the complete scan volume you expect cover. For this example that corresponds to 10.8GHz and a scan volume extending 60deg from boresite between phi = 0deg and 90deg planes.
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Retain Only Unit Cell Element • Hide all objects associated with the Unit Cell Element • From the 3D Modeler Tree select: – – – –
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Solids > Radome > Radome Solids > Vaccum > UnitCell Solids > WG_Mat > WG Solids > WG_Plug_Mat > WG_Plug • Note: You may have to hold the CTRL key down to select both objects simultaneously. Hide Selected objects – From HFSS’s Menu Bar select View > Visibility > Hide Selection > Active View Ctrl+H
• Delete all other objects • From HFSS’s Menu Bar select Edit > Select All Visible Ctrl+A • From HFSS’s Menu Bar select Edit > Delete
• Show the hidden objects associated with the unit cell • From HFSS’s Menu Bar select View > Visibility > Show All > Active View
• Fit the geometry within the 3D modeler window • From HFSS’s Menu Bar select View > Fit All > Active View Ctrl+D
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Verify Setup • Save Project • Select the menu item File > Save
• Model Validation • Select the menu item HFSS > Validation Check •
Validate Click the Close button Note: To view any errors or warning messages, look at the Message Manager window.
Analyze All
• Check Boundary Conditions • From HFSS’s Menu Bar select HFSS > Boundary Display (Solver View) • Check and Uncheck the visibility of the various boundary conditions to see HFSS’s interpretation.
Note: The Boundary Display (Solver View) creates the initial mesh and then reports the boundary conditions interpreted by HFSS. It is a good way to verify that the boundaries are setup properly. Pay close attention to the outer boundary. This boundary is defined on all external faces that don’t already have a boundary condition defined on them. All faces with the outer boundary will have apply a perfect electric conducting boundary condition applied. This model only has a single face with the outer boundary applied. In this case, it is not an issue because that face corresponds to the array’s ground plane and should be perfectly conducting anyway. 25
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Outer Boundary Release 2015.0
Analyze • Analyze • Select the menu item HFSS > Analyze All • After analysis is complete save the project •
Select the menu item File > Save Analyze All
• Review solution Data • Select the menu item HFSS > Results > Solution Data
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• Select the Profile tab to view solution information • Select the Convergence tab to show convergence, solved element count, and maximum Delta S • Select Matrix Data tab to view S-parameters and Port impedance Click the Close button
Solution Data
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Look at Excitation Modes • Show WavePort1 : Mode 1 Field Distribution • From the Project Manager Left Click on the •
POEW_WS > 01_UnitCell > Port Field Display > WavePort1 > Mode 1 branch Change the View to better see the Port Field Display – From HFSS’s Menu bar select View > Modify Attributes… > Orientation List Alt+O – Left Click on Bottom Orientation – Left Click Apply To View button – Fit All the geometry with Ctrl + D keys • Note: You may need to drag the Update View Orientation Window out of the way to view the geometry
• Show WavePort1 : Mode 2 Field Distribution • From the Project Manager Left Click on the POEW_WS > 01_UnitCell > Port Field Display > WavePort1 > Mode 2 branch
Mode 1 Field
Mode 2 Field
• Change the View Back to Trimetric • From the Update View Orientation Window Left Click Trimetric • Left Click Apply To View button • Click Close button 27
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Note: Mode 1 is a TE11 mode polarized in the Y direction and Mode 2 is a TE11 mode polarized in the X direction. These modes were determined by the port Eigen Mode solution and represent the first 2 propagating modes of the waveguide. The modes and their polarization are important because signals propagating in these modes will eventually radiate out of the array and form the array’s pattern. Mode 1 will mainly contribute to the X-polarized radiation pattern and Mode 2 will mainly contribute to the Ypolarized radiation pattern. Release 2015.0
Evaluating S-Parameter Data
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Setup Excitations • Setup the excitations for Circular Polarization • From HFSS’s menu bar select HFSS > Fields > Edit Sources… • WavePort1:1: • •
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– Magnitude: 1 Watt – Phase: 0 Deg WavePort 1:2: – Magnitude: 1 Watt – Phase: 90 Deg Click OK button
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Note: Since WavePort1’s modes (degenerate TE11 modes) are orthogonally polarized waves propagating down the waveguide, they can be used to excite a circularly polarized radiation pattern. This is accomplished by exciting both modes with equal magnitudes but phased +/90 deg out of phase from each other.
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Evaluating Match • Create Active Return Loss Plot • Select the menu item HFSS > Results > Create Modal Solution Data Report> Rectangular Plot • • • •
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Solution: Setup1: Sweep Domain: Sweep Category: Active S Parameter Quantity: ActiveS(WavePort1:1), ActiveS(WavePort1:2) • Note: Hold Ctrl key to select multiple traces • Function: dB • Click New Report button • Click Close button Change Report Name • In Project Manager window select XY Plot 1 • In Properties window: • Name: Boresight Scan Active S-Parameters
Note: This plot shows the active return loss for both waveguide modes. Since only the unit cell is modeled with Master / Slave boundaries the array is infinite in size. Every element in this infinite array has the same excitation as defined in the Edit Sources Dialog (HFSS > Fields > Edit Sources…). The progressive phase shift between elements is setup for borsight scan (Phi_Scan, Theta_Scan) = (0 deg, 0 deg) as defined in the Slave Boundaries. The Active Return losses are very similar to each other since the isolation between these modes is better than -60dB.
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Evaluating Match Over Scan Volume • Setup Parameteric Sweep Theta_Scan • From HFSS’s Menu Bar select HFSS > Optimetrics Analysis > Add Parametric… • Sweep Definitions Tab: – Click Add… button – Add / Edit Sweep Window: • Variable: Theta_Scan • Start: 0 deg • Stop: 60 deg • Step: 5 deg • Click Add >> button – Click Ok button – Table Tab: • Review Theta Scan angles defined in the Parametric Sweep – General Tab: • Make sure only Setup1 Include Check box is checked. • Starting Point > Design Variables : – Make sure all Override Check boxes are Unchecked – Calculation Tab: • Leave blank – Options Tab: • Check Save Fields And Mesh check box – Click Ok button
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Note: The active impedance of an array changes as the array is scanned in different directions. Since the scan angle is fixed through the Theta_Scan and Phi_Scan variables used in the Slave Boundaries, the unit cell model needs to be simulated explicitly at different scan angles to capture the element’s behavior for each of these conditions. The easiest way to perform the analysis over the scan volume is to use the Optimetrics License to create a Parametric Sweep of the Theta_Scan and Phi_Scan variables. The parametric sweep created here scans the array from boresight out to 60 degrees from boresight along the positive X-axis. This is determined because the Sweep Definitions Tab defined the Theta_Scan sweep from 0deg to 60deg and the General Tab fixes the Phi_Scan variable to 0deg corresponding to the XZ plane. Release 2015.0
Setting Up Scan Volume Parametric Sweep • Define Distribution List • From HFSS’s Menu Bar select Tools > Options > HPC and Analysis Options… • Click Add… button • Analysis Configuration Window
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– Configuration Name: Distributed Analysis – Machine Details: • Local machine • Number of Tasks: 4 • Number of Cores: 4 • Click Add Machine to List button – Click OK button Click Make Active button Click OK button Note: Every Optimetrics License comes with 2 DSO (Distributed Solve Option) licenses allowing a user to run 2 instances of a parametric sweep at the same time. This speeds up the analysis of the scan volume sweep. The number of parametric instances run simultaneously and the number of cores each instance uses is controlled by setting up an Analysis Configuration in the HPC and Analysis Options window. This example assumes that the computer running the analysis has 4 cores and there are 4 DSO licenses available. The number of simultaneous analysis is determined by the Number of Tasks field. The Total Cores field allows for each parametric instance to take advantage of multiple cores. These settings will run for scan angle analyses at the same time with each analysis using a single core.
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If the computer running this sweep does not contain 4 cores or you do not have 4 DSO licenses you will need to reduce then number of tasks and Cores appropriately. If you have more cores and licenses available you can further speed up the analysis by adding more tasks. © 2015 ANSYS, Inc.
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Running Parametric Analysis • Analyze the Parametric Analysis • From HFSS’s Project Manager, Right Click Parametric Setup1 from Optimetrics • Select Analyze from the pop-up menu – Note: Using the Analyze All From HFSS’s tool bar will analyze all setups defined in the Design (including Setup1)
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Active Return Loss Over Scan Volume • Create Active Return Loss Plot over Scan Volume • Select the menu item HFSS > Results > Create Modal Solution Data Report> Rectangular Plot
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– Trace Tab • Solution: Setup1: Sweep • Domain: Sweep • Category: Active S Parameter • Quantity: ActiveS(WavePort1:1) • Function: dB • Families Tab • Theta_Scan Value: All – Note: If the value is not already set to All you may need to change it using the button in the Edit column of the Theta_Scan variable. • Click New Report button • Click Close button Change Report Name • In Project Manager window select XY Plot 1 • In Properties window: • Name: Scan Volume Active S-Parameters
Note: This plot shows the Active Return Loss vs. Frequency for each scan angle solved during the parametric sweep. Multiple curves were created because the Theta_Scan Value was set to All (more than one value) on the Families Tab. The plot shows that each scan angle produces a unique impedance that gets worse as the frequency and scan angle increases.
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Evaluating Pattern Data
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Far Field Radiation Sphere Setup • Create a Radiation Setup • Select the menu item HFSS > Radiation > Insert Far Field Setup > Infinite Sphere – Infinite Sphere Tab • Name: Infinite Sphere 1 (default) • Phi: (Start: 0, Stop: 180, Step Size: 10) • Theta: (Start: -90, Stop: 90, Step Size: 5) Click the OK button
Note: The Infinite Sphere Tab of the Far Field Radiation Sphere Setup determines what directions the far-field pattern is calculated for. This setup will calculate the farfield pattern for a hemisphere extending above the XY plane. Theta is defined from -90 deg to +90 deg so the boresight direction ends up in the middle of the plots we are about to create.
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Far Field Radiation Pattern • Create Far-Field Radiation Pattern • Select the menu item HFSS > Results > Create Far-Field Report> Radiation Pattern
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– Trace Tab • Solution: Setup1: LastAdaptive • Geometry: Infinite Sphere 1 • Domain: Sweep • Primary Sweep: Theta • Category: Realized Gain • Quantity: RealizedGainTotal • Function: dB • Families Tab • Phi: 0 • Freq: 10.8GHz • Theta_Scan Value: All – Note: If the value is not already set to All you may need to change it using the button in the Edit column of the Theta_Scan variable. • Click New Report button • Click Close button Change Report Name • In Project Manager window select Radiation Pattern 1 • In Properties window: • Name: Calculated Far Field
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Note: These curves show HFSS’s calculation of the array’s radiation pattern for different scan angles. They result from the infinite array having a uniform magnitude excitation and a progressive phase shift needed to steer the main beam to the requested scan angle. However, the far-field integration is only performed over the relatively small unit cell area producing the broad beam patterns displayed here. These patterns do not represent the Embedded (Active) Element Pattern used to recreate the finite array’s pattern through Pattern Multiplication.
Release 2015.0
Embedded Element Pattern from Far-Field Pattern • Create Embedded Element Pattern Data Table • Select the menu item HFSS > Results > Create Far-Field Report> Data Table
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– Trace Tab • Solution: Setup1: LastAdaptive • Geometry: Infinite Sphere 1 • Primary Sweep: Theta_Scan Note: Realized Gain is plotted here because its value is • Category: Realized Gain affected by the element’s mismatch. Since the impedance • Quantity: RealizedGainTotal changes as a function of scan, this quantity is typically what is used to represent the element’s pattern instead of Gain. • Function: dB • Families Tab • Theta: 0deg, 5deg, 10deg, 15deg, 20deg, 25deg, 30deg, 35deg, 40deg, 45deg, 50deg, 55deg, 60deg – Note: You may need to change the values using the button in the Edit column of the variable. • Phi: 0 – Note: You may need to change the values using the button in the Edit column of the variable. • Freq: 10.8GHz • Click New Report button • Click Close button Change Report Name • In Project Manager window select Data Table 1 • In Properties window: • Name: Embedded Element Pattern
© 2015 ANSYS, Inc.
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Embedded Element Pattern Discussion
Note: The Embedded (Active) Element Pattern can be extracted from the radiation patterns just plotted by taking the one point on each curve corresponding to the scan angle used to produce that curve. For instance, the Embedded Element Pattern for the angle (theta, phi) = (0deg, 0deg) would correspond to the (theta, phi) = (0deg, 0deg) point on the RealizedGainTotal curve associated with Theta_Scan = 0deg and Phi_Scan = 0deg. All the other points on the curve would be discarded. The points that are part of the Embedded Element Pattern are highlighted with blue boxes in the above data table.
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Scan_CS Infinite Sphere • Create New Radiation Infinite Sphere • From HFSS’s Menu Bar select •
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HFSS > Radiation > Insert Far Field Setup > Infinite Sphere… Infinite Sphere Tab: – Phi Start: 0 deg – Phi Stop: 0 deg – Phi Step: 10deg – Theta Start: 0 deg – Theta Stop: 0 deg – Theta Step: 10 deg Coordinate System Tab: – Select Use local coordinate system – Choose from existing coordinate systems: Scan_CS Click OK button Note: Scan_CS is a relative coordinate system parameterized so the z-axis always points in the scan direction defined by Theta_Scan and Phi_Scan. You can visibly verify this by switching to the Scan_CS coordinate system, changing the value for Theta_Scan to 60deg and observing where the z-axis points. Setting up the infinite sphere using this coordinate system allows us to plot the Embedded Element Pattern while keeping theta and phi at a constant 0deg. This makes is possible to define the trace within HFSS. However, this only works for patterns using the Total, RHCP, LHCP, Phi and Theta polarizations. X, Y and Z polarizations of the Scan_CS coordinate system change with respect to the global coordinate system as the beam is steered producing incorrect results.
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Embedded Element Pattern From Scan_CS • Create Far-Field Radiation Pattern • Select the menu item HFSS > Results > Create Far-Field Report> Radiation Pattern
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– Trace Tab • Solution: Setup1: LastAdaptive • Domain: Infinite Sphere2 • Primary Sweep: Theta_Scan • Category: Realized Gain • Quantity: RealizedGainTotal • Function: dB • Families Tab • Theta: All • Phi: All • Freq: 10.8GHz • Click New Report button • Click Close button Change Report Name • In Project Manager window select Radiation Pattern 1 • In Properties window: • Name: Embedded Element Pattern From Scan_CS Note: This pattern can then be used to predict a finite array’s pattern through the method of pattern multiplication. 𝐸𝐹𝑖𝑛𝑖𝑡𝑒 𝐴𝑟𝑟𝑎𝑦 = 𝐸𝐸𝑚𝑏𝑒𝑑𝑑𝑒𝑑 𝐸𝑙𝑒𝑚𝑒𝑛𝑡 ⋅ 𝐴𝑟𝑟𝑎𝑦𝐹𝑎𝑐𝑡𝑜𝑟 To fill in the rest of the pattern additional simulations would need to be performed at different scan angles.
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Embedded Element Pattern From Floquet • Adding Output Variables for Calculating Gain from Floquet S-Parameters • From HFSS’s Menu Bar select HFSS > Results > Output Variables… • Define the output variables given in the next slide; 1) Add name 2) Insert Expression 3) Click Add
1 2
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Embedded Element Pattern From Floquet/ Output Variables PowerIn = 2 Wavelength_mil = 1.18e13/10.8e9 Transmission_Coefficient = (mag(S(FloquetPort1:1,WavePort1:1)*1*exp(cmplx(0,1)*0*pi/180)+S(FloquetPort 1:1,WavePort1:2)*1*exp(cmplx(0,1)*90*pi/180))^2+ mag(S(FloquetPort1:2,WavePort1:1)*1*exp(cmplx(0,1)*0*pi/180)+S(FloquetPort 1:2,WavePort1:2)*1*exp(cmplx(0,1)*90*pi/180))^2)/PowerIn Gain_Floquet = 4*Pi*349203.08347/wavelength_mil^2*Transmission_Coefficient*cos(Theta_scan)
Note: These equations are based off the well established calculation 𝐺=
4𝜋𝐴𝑟𝑒𝑎 1− Γ 𝜆2
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𝑐𝑜𝑠 𝑇ℎ𝑒𝑡𝑎_𝑆𝑐𝑎𝑛 =
4𝜋𝐴𝑟𝑒𝑎 2 𝑇 𝑐𝑜𝑠 𝑇ℎ𝑒𝑡𝑎_𝑆𝑐𝑎𝑛 𝜆2
where |T|2 is the transmission coefficient (a.k.a. transmitted Power / incident power).
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Embedded Element Pattern From Floquet • Open Trace Properties for Embedded Element Pattern From Scan_CS • From the Project Manager Right Click on POEW_WS > 01_UnitCell > Results > • •
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Embedded Element Pattern From Scan_CS > dB(RealizedGain Total) Select Modify Report… from the Pop-Up Window Trace Tab: – Category: Output Variables – Quantity: Gain_Floquet – Function: dB10 Click Add Trace button Click Close button
Note: The Embedded Element Pattern from both methodologies produces similar results.
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