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Polarized Circular Ports
Introduction
This example of a circular waveguide demonstrates how to excite and terminate ports with degenerate port modes. In particular it shows how to model and excite the TE11 mode of circular waveguides in 3D.
Model Definition
A straight piece of circular waveguide with perfect metallic walls is excited by a linearly polarized TE11 mode at one end and ideally terminated at the other end.
The TE11 mode of a circular waveguide is degenerate, meaning that there is an infinite number of possible variants of the TE11 mode that only differ in polarization. Any type of polarization (for example circular polarization) of the TE11 mode can be constructed by or decomposed into two linearly polarized modes. The direction of polarization of the first one can be chosen freely and the second one is obtained from the first one by a rotation of 90 degrees around the waveguide axis.
As a general structure may change the polarization of the incident field as it is transmitted or reflected, ideal termination means that any circular waveguide port that operates in the TE11 mode need to have two port features which are tuned to mutually orthogonal, linear polarizations of the TE11 mode respectively. The reference directions for the two port features are subject to a manual choice but must differ by a rotation of 90 degrees around the waveguide axis.
The Port subfeature, Circular Port Reference Axis is used to determine the reference direction for the polarization of each mode/port by means of selecting two vertices (points) on the port circumference. In this example, extra vertices that are equally distributed along the port edge are added to the geometry to allow for the definition of the desired reference directions.
With the stipulated excitation using the two mutually orthogonal TE11 ports as boundary conditions, the following equation is solved for the electric field vector E inside the waveguide:
Results and Discussion
The first TE11 mode of the inport is shown in Figure 1.
Figure 1: The first TE11 mode of the inport
Note: Depending on the details of the mesh, which in turn may depend on the origin of the CAD geometry, a mode that is rotated 180 degrees may be found.
The first TE11 mode of the outport is shown in Figure 2.
Figure 2: The first TE11 mode of the outport.
Note: Depending on the details of the mesh, which in turn may depend on the origin of the CAD geometry, a mode that is rotated 180 degrees may be found.
The transmission coefficients between the inport and outport modes are shown in Figure 3.
Figure 3: The transmission coefficients between inport modes and outport modes are plotted as a function of frequency. As the port modes are misaligned by 45 degrees the transmission coefficients approach the -3dB level.
Application Library path: RF_Module/Tutorials/polarized_circular_ports
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Frequency Domain.
6
Click  Done.
Global Definitions
Add a parameter for the operating frequency.
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
frq
c_const/0.03[m]
9.9931E9 1/s
Operating frequency
Study 1
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type range(0.9*frq,(1.5*frq-(0.9*frq))/10,1.5*frq).
Geometry 1
The geometry is essentially a cylinder.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 0.01.
4
In the Height text field, type 0.1.
5
Click  Build Selected.
6
Click the  Wireframe Rendering button in the Graphics toolbar.
You need to add a reference direction for the port polarization. Add a couple of lines on the cylinder end to generate extra vertices. This is done in a work plane.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
In the z-coordinate text field, type 0.1.
Work Plane 1 (wp1)>Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1)>Line Segment 1 (ls1)
1
In the Work Plane toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
Locate the Endpoint section. From the Specify list, choose Coordinates.
5
Locate the Starting Point section. In the yw text field, type 0.01.
6
Locate the Endpoint section. In the yw text field, type -0.01.
Work Plane 1 (wp1)>Rotate 1 (rot1)
1
In the Work Plane toolbar, click  Transforms and choose Rotate.
2
Select the object ls1 only.
3
In the Settings window for Rotate, locate the Rotation section.
4
In the Angle text field, type 45 135.
5
Click  Build Selected.
Ignore Edges 1 (ige1)
1
In the Model Builder window, right-click Geometry 1 and choose Virtual Operations>Ignore Edges.
2
On the object fin, select Edges 7, 8, 13, and 14 only.
3
In the Settings window for Ignore Edges, locate the Input section.
4
Clear the Ignore adjacent vertices check box.
5
In the Geometry toolbar, click  Build All.
Materials
Next, add a material for the interior (air) of the waveguide.
Material 1 (mat1)
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Electromagnetic Waves, Frequency Domain (emw)
Set up one inport and three outports.
Port 1
1
In the Model Builder window, under Component 1 (comp1) right-click Electromagnetic Waves, Frequency Domain (emw) and choose Port.
2
Select Boundary 3 only.
It might be easier to select the correct boundary by using the Selection List window. To open this window, in the Home toolbar click Windows and choose Selection List. (If you are running the cross-platform desktop, you find Windows in the main menu.)
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Circular.
Circular Port Reference Axis 1
1
In the Physics toolbar, click  Attributes and choose Circular Port Reference Axis.
2
In the Settings window for Circular Port Reference Axis, locate the Point Selection section.
3
Click  Clear Selection.
4
Select Points 5 and 8 only.
Port 2
1
In the Physics toolbar, click  Boundaries and choose Port.
2
Select Boundary 3 only.
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Circular.
Circular Port Reference Axis 1
1
In the Physics toolbar, click  Attributes and choose Circular Port Reference Axis.
2
In the Settings window for Circular Port Reference Axis, locate the Point Selection section.
3
Click  Clear Selection.
4
Select Points 1 and 12 only.
Port 3
1
In the Physics toolbar, click  Boundaries and choose Port.
2
Select Boundary 4 only.
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Circular.
Circular Port Reference Axis 1
1
In the Physics toolbar, click  Attributes and choose Circular Port Reference Axis.
2
In the Settings window for Circular Port Reference Axis, locate the Point Selection section.
3
Click  Clear Selection.
4
Select Points 4 and 10 only.
Port 4
1
In the Physics toolbar, click  Boundaries and choose Port.
2
Select Boundary 4 only.
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Circular.
Circular Port Reference Axis 1
1
In the Physics toolbar, click  Attributes and choose Circular Port Reference Axis.
2
In the Settings window for Circular Port Reference Axis, locate the Point Selection section.
3
Click  Clear Selection.
4
Select Points 3 and 11 only.
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Study 1
Step 1: Frequency Domain
In the Home toolbar, click  Compute.
Results
Electric Field (emw)
Inspect the electric field norm.
Next, inspect the S-parameters representing transmission.
S-parameter (emw)
As expected, the transmitted energy is evenly divided between the outport modes (Figure 3).
Smith Plot (emw)
Port 1
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Port 1 in the Label text field.
Surface 1
1
Right-click Port 1 and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>Ports>emw.normtEmode_1 - Port tangential electric mode field norm - V/m.
Arrow Surface 1
1
In the Model Builder window, right-click Port 1 and choose Arrow Surface.
2
In the Settings window for Arrow Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>Ports>emw.tEmodex_1,...,emw.tEmodez_1 - Port tangential electric mode field.
3
Locate the Arrow Positioning section. In the Number of arrows text field, type 1000.
4
Locate the Coloring and Style section. From the Color list, choose Black.
5
In the Port 1 toolbar, click  Plot.
6
Click  Plot.
Port 2
1
Right-click Port 1 and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Port 2 in the Label text field.
Surface 1
1
In the Model Builder window, expand the Port 2 node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type emw.normtEmode_2.
Arrow Surface 1
1
In the Model Builder window, click Arrow Surface 1.
2
In the Settings window for Arrow Surface, locate the Expression section.
3
In the X component text field, type emw.tEmodex_2.
4
In the Y component text field, type emw.tEmodey_2.
5
In the Z component text field, type emw.tEmodez_2.
6
In the Port 2 toolbar, click  Plot.
Port 3
1
In the Model Builder window, right-click Port 2 and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Port 3 in the Label text field.
Surface 1
1
In the Model Builder window, expand the Port 3 node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type emw.normtEmode_3.
Arrow Surface 1
1
In the Model Builder window, click Arrow Surface 1.
2
In the Settings window for Arrow Surface, locate the Expression section.
3
In the X component text field, type emw.tEmodex_3.
4
In the Y component text field, type emw.tEmodey_3.
5
In the Z component text field, type emw.tEmodez_3.
6
In the Port 3 toolbar, click  Plot.
Port 4
1
In the Model Builder window, right-click Port 3 and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Port 4 in the Label text field.
Surface 1
1
In the Model Builder window, expand the Port 4 node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type emw.normtEmode_4.
Arrow Surface 1
1
In the Model Builder window, click Arrow Surface 1.
2
In the Settings window for Arrow Surface, locate the Expression section.
3
In the X component text field, type emw.tEmodex_4.
4
In the Y component text field, type emw.tEmodey_4.
5
In the Z component text field, type emw.tEmodez_4.
6
In the Port 4 toolbar, click  Plot.
Next, display numerical values for the transmission at the highest frequency.
Global Evaluation 1
1
In the Results toolbar, click  Global Evaluation.
2
In the Settings window for Global Evaluation, locate the Data section.
3
From the Parameter selection (freq) list, choose Last.
4
Click Replace Expression in the upper-right corner of the Expressions section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>emw.S31dB - S31.
5
Click  Evaluate.
Global Evaluation 2
1
In the Results toolbar, click  Global Evaluation.
2
In the Settings window for Global Evaluation, locate the Data section.
3
From the Parameter selection (freq) list, choose Last.
4
Click Replace Expression in the upper-right corner of the Expressions section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>Ports>S-parameter, dB>emw.S41dB - S41.
5
Click  Evaluate.
As expected, the result is about -3 dB for both modes.