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Double-Ridged Horn Antenna
Introduction
A double-ridged horn antenna is popularly used in an anechoic chamber to characterize an antenna under test (AUT) from S-band to Ku-band due to its reliable performance in a wideband frequency range. The model computes the voltage standing wave ratio (VSWR), far-field radiation pattern, and antenna directivity.
Figure 1: Double-ridged horn antenna excited by a coaxial port. The surrounding air domain and a perfectly matched layer, which is required for the simulation, are not included in this figure.
Note: This example requires the RF Module and the Design Module.
Model Definition
The simulation frequency range is from 2 GHz to 6 GHz. The conductivity of the metallic material in the model is assumed to be high enough to neglect the loss in the given frequency range. Thus, all metal parts are modeled using a perfect electric conductor (PEC) feature. An exponential function, e0.028x is used in a parametric curve to create the tapered metallic ridges that are excited by an SMA type dielectric-filled coaxial connector. A lumped port is assigned on the boundary between the inner and outer conducting surface at the end of the coaxial connector. The antenna is enclosed by a spherical air domain. The outermost layer of the air domain is configured as a perfectly matched layer (PML) where the thickness of the layer is slightly greater than 0.1 wavelengths at the lowest simulation frequency. The PML absorbs all outgoing radiation from the antenna and work as an anechoic chamber during the simulation. The mesh is controlled by the Electromagnetic Waves, Frequency Domain physics interface and it has to be defined dynamically based on each simulation frequency, so frequency parametric sweep is over Frequency Domain study step.
Results and Discussion
In Figure 2, the slice and contour plot of Ez is visualized in the zx-plane. The electric field is guided by two symmetric metallic ridges and propagating toward the aperture of the horn.
Figure 2: z-component of the electric field and its contour plot at 6 GHz.
Figure 3 shows the 3D far-field radiation pattern. When it is plotted, the directivity is also calculated which is around 12.9 dB. Other antenna far-field postprocessing variables such as antenna gain and axial ratio can be visualized using the same plot by replacing the default input fields both for expression and color. These steps are not included in this tutorial but you are encouraged to try.
Figure 3: 3D far-field radiation pattern that is directive toward the open aperture.
Voltage standing wave ratio (VSWR) is a measure commonly used to characterize the input impedance matching properties for off-the-shelf antenna products. Figure 4 presents the VSWR of the double-ridged horn antenna that is lower than 1.7 in the simulated frequency range.
Figure 4: Voltage standing wave ratio (VSWR) plot. It is better than 2:1 in the simulated frequency range.
Notes About the COMSOL Implementation
The antenna model is memory intensive and requires more than 12 GB RAM for the simulation up to 6 GHz. It may require much more for higher frequency simulations.
Application Library path: RF_Module/Antennas/double_ridged_horn_antenna
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
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
w_slot
1.8[mm]
0.0018 m
Slot width
f0
2[GHz]
2E9 Hz
Frequency
Study 1
Step 1: Frequency Domain
Define the study frequency ahead of performing any frequency-dependent operation such as building mesh. The physics-controlled mesh uses the specified frequency value.
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 f0.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
4
Locate the Advanced section. From the Geometry representation list, choose CAD kernel.
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
From the Plane list, choose xz-plane.
4
In the y-coordinate text field, type 3.5.
Work Plane 1 (wp1) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1) > Parametric Curve 1 (pc1)
1
In the Work Plane toolbar, click  More Primitives and choose Parametric Curve.
2
In the Settings window for Parametric Curve, locate the Parameter section.
3
In the Maximum text field, type 150.
4
Locate the Expressions section. In the xw text field, type s-100.
5
In the yw text field, type exp(0.028*s)-1+w_slot/2.
Work Plane 1 (wp1) > Mirror 1 (mir1)
1
In the Work Plane toolbar, click  Transforms and choose Mirror.
2
Select the object pc1 only.
3
In the Settings window for Mirror, locate the Input section.
4
Select the Keep input objects checkbox.
5
Locate the Normal Vector to Line of Reflection section. In the xw text field, type 0.
6
In the yw text field, type 1.
Work Plane 1 (wp1) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 20.15.
4
In the Height text field, type w_slot.
5
Locate the Position section. In the xw text field, type -120.15.
6
In the yw text field, type -w_slot/2.
7
Click  Build Selected.
8
Click the  Zoom Extents button in the Graphics toolbar.
Work Plane 1 (wp1) > Rectangle 2 (r2)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 20.15.
4
In the Height text field, type 30.
5
Locate the Position section. In the xw text field, type -120.15.
6
In the yw text field, type -15.
Work Plane 1 (wp1) > Polygon 1 (pol1)
1
In the Work Plane toolbar, click  Polygon.
2
In the Settings window for Polygon, locate the Coordinates section.
3
From the Data source list, choose Vectors.
4
In the xw text field, type 50 -100 -100 -100 -100 50.
5
In the yw text field, type exp(0.028*150)-1+w_slot/2 15 15 -15 -15 -(exp(0.028*150)-1+w_slot/2).
Extrude 1 (ext1)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the Distances section.
3
In the table, enter the following settings:
Distances (mm)
7
Delete Entities 1 (del1)
1
Right-click Geometry 1 and choose Delete Entities.
2
In the Settings window for Delete Entities, locate the Entities or Objects to Delete section.
3
From the Geometric entity level list, choose Domain.
4
On the object ext1, select Domains 2 and 5 only.
5
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
Work Plane 2 (wp2)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane list, choose yz-plane.
4
In the x-coordinate text field, type 50.
Work Plane 2 (wp2) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 2 (wp2) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 190.
4
In the Height text field, type (exp(0.028*150)-1+w_slot/2)*2.
5
Locate the Position section. In the xw text field, type -95.
6
In the yw text field, type -(exp(0.028*150)-1+w_slot/2).
Work Plane 3 (wp3)
1
In the Model Builder window, right-click Geometry 1 and choose Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane list, choose yz-plane.
4
In the x-coordinate text field, type -100.
Work Plane 3 (wp3) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 3 (wp3) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 50.
4
In the Height text field, type 30.
5
Locate the Position section. In the xw text field, type -25.
6
In the yw text field, type -15.
Extrude 2 (ext2)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the General section.
3
From the Input object handling list, choose Keep.
4
Locate the Distances section. In the table, enter the following settings:
Distances (mm)
28
5
Select the Reverse direction checkbox.
Loft 1 (loft1)
1
In the Geometry toolbar, click  Loft.
2
Click the  Wireframe Rendering button in the Graphics toolbar.
3
Click the  Zoom Extents button in the Graphics toolbar.
4
Select the objects wp2 and wp3 only.
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 2.05.
4
In the Height text field, type 15-w_slot/2.
5
Locate the Position section. In the x text field, type -117.5.
6
In the z text field, type w_slot/2.
Cylinder 2 (cyl2)
1
Right-click Cylinder 1 (cyl1) and choose Duplicate.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 0.635.
4
In the Height text field, type 15+w_slot/2.
5
Locate the Position section. In the z text field, type -w_slot/2.
Part Libraries
1
In the Geometry toolbar, click  Part Libraries.
2
In the Model Builder window, click Geometry 1.
3
In the Part Libraries window, select RF Module > Connectors > SMA Connectors > connector_sma_flange2 in the tree.
4
Click  Add to Geometry.
Geometry 1
SMA Connector, Flange with Two Holes 1 (pi1)
1
In the Model Builder window, under Component 1 (comp1) > Geometry 1 click SMA Connector, Flange with Two Holes 1 (pi1).
2
In the Settings window for Part Instance, locate the Input Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
solder_o
0
0
Soldering block option
4
Locate the Position and Orientation of Output section. Find the Displacement subsection. In the xwi text field, type -117.5.
5
In the zwi text field, type 15.
6
Find the Rotation subsection. From the Axis type list, choose ywi-axis.
7
In the Rotation angle text field, type 90.
8
Click to expand the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
None
Conductive surface
√
√
None
9
Click to expand the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
None
Dielectric
√
√
None
Conductor
 
√
None
10
Click  Build Selected.
Sphere 1 (sph1)
1
In the Geometry toolbar, click  Sphere.
2
In the Settings window for Sphere, locate the Size section.
3
In the Radius text field, type 170.
4
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
20
5
In the Geometry toolbar, click  Build All.
6
In the Model Builder window, click Geometry 1.
Disable the analysis of the geometry as the remaining small geometric details can be kept.
7
In the Model Builder window, click Geometry 1.
8
In the Settings window for Geometry, locate the Cleanup section.
9
Clear the Automatic detection of small details checkbox.
Definitions
Perfectly Matched Layer 1 (pml1)
1
In the Definitions toolbar, click  Perfectly Matched Layer.
2
Select Domains 1–4 and 21–24 only.
3
In the Settings window for Perfectly Matched Layer, locate the Geometry section.
4
From the Type list, choose Spherical.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Air.
4
Right-click and choose Add to Component 1 (comp1).
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Material 2 (mat2)
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
Select Domain 12 only.
3
In the Settings window for Material, locate the Material Contents section.
4
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
2.1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Material 3 (mat3)
1
Right-click Material 2 (mat2) and choose Duplicate.
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Dielectric (SMA Connector, Flange with Two Holes 1).
Electromagnetic Waves, Frequency Domain (emw)
Perfect Electric Conductor 2
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
In the Settings window for Perfect Electric Conductor, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 13-17, 121-123, 133, 135, 136 in the Selection text field.
5
Click OK.
Perfect Electric Conductor 3
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
In the Settings window for Perfect Electric Conductor, locate the Boundary Selection section.
3
From the Selection list, choose Conductive surface (SMA Connector, Flange with Two Holes 1).
Perfect Electric Conductor 4
1
In the Physics toolbar, click  Domains and choose Perfect Electric Conductor.
2
Select Domains 9, 10, 14, 15, 19, and 20 only.
Lumped Port 1
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
Select Boundary 58 only.
3
In the Settings window for Lumped Port, locate the Lumped Port Properties section.
4
From the Type of lumped port list, choose Coaxial.
For the first port, wave excitation is on by default.
Far-Field Domain 1
In the Physics toolbar, click  Domains and choose Far-Field Domain.
Definitions
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 3, 6, 8, 10, and 12 only.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Coarser.
Use Coarser mesh to avoid unnecessarily fine mesh on small parts.
4
Click  Build All.
Study 1
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
f0 (Frequency)
range(2[GHz],0.5[GHz],6[GHz])
Hz
Step 1: Frequency Domain
In the Study toolbar, click  Compute.
Results
Multislice 1
1
In the Model Builder window, expand the Electric Field (emw) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type emw.Ez.
4
Locate the Multiplane Data section. Find the X-planes subsection. In the Planes text field, type 0.
5
Find the Z-planes subsection. In the Planes text field, type 0.
6
Click to expand the Range section. Select the Manual color range checkbox.
7
In the Minimum text field, type -20.
8
In the Maximum text field, type 20.
Selection 1
1
Right-click Multislice 1 and choose Selection.
2
Select Domains 5 and 18 only.
3
In the Electric Field (emw) toolbar, click  Plot.
Cut Plane 1
1
In the Results toolbar, click  Cut Plane.
2
In the Settings window for Cut Plane, locate the Data section.
3
From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
4
Locate the Plane Data section. From the Plane list, choose XZ-planes.
Contour 1
1
In the Model Builder window, right-click Electric Field (emw) and choose Contour.
2
In the Settings window for Contour, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
Locate the Expression section. In the Expression text field, type emw.Ez.
5
Locate the Levels section. In the Total levels text field, type 30.
6
Locate the Coloring and Style section. From the Color table list, choose Cividis.
Surface 1
1
Right-click Electric Field (emw) and choose Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
Clear the Color legend checkbox.
4
From the Color table list, choose AuroraAustralis.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Conductive surface (SMA Connector, Flange with Two Holes 1).
Material Appearance 1
1
In the Model Builder window, right-click Surface 1 and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Gold.
Surface 2
1
In the Model Builder window, right-click Electric Field (emw) and choose Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose AuroraAustralis.
4
Clear the Color legend checkbox.
Selection 1
1
Right-click Surface 2 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Delete Entities 1.
5
In the Electric Field (emw) toolbar, click  Plot.
Material Appearance 1
1
In the Model Builder window, right-click Surface 2 and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Aluminum (anodized).
5
In the Electric Field (emw) toolbar, click  Plot.
Electric Field (emw)
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, locate the Color Legend section.
3
Select the Show legends checkbox.
4
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
5
In the Electric Field (emw) toolbar, click  Plot.
Compare the reproduced plot with that shown in Figure 2.
Multislice 1
1
In the Model Builder window, expand the Results > Electric Field, Logarithmic (emw) node, then click Multislice 1.
2
In the Electric Field, Logarithmic (emw) toolbar, click  Plot.
3
In the Settings window for Multislice, locate the Expression section.
4
In the Expression text field, type emw.normE+1e-1.
5
In the Electric Field, Logarithmic (emw) toolbar, click  Plot.
Radiation Pattern 1
1
In the Model Builder window, expand the 2D Far Field (emw) node, then click Radiation Pattern 1.
2
In the Settings window for Radiation Pattern, click to expand the Legends section.
3
From the Legends list, choose Evaluated.
4
In the Legend text field, type eval(f0/1e9) GHz.
5
In the 2D Far Field (emw) toolbar, click  Plot.
Radiation Pattern 1
1
In the Model Builder window, expand the Results > 3D Far Field, Gain (emw) node, then click Radiation Pattern 1.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Angles subsection. In the Number of elevation angles text field, type 90.
4
In the Number of azimuth angles text field, type 90.
5
In the 3D Far Field, Gain (emw) toolbar, click  Plot.
Directivity
1
Go to the Directivity window.
3D far-field radiation pattern is directive toward the aperture of the horn antenna (Figure 3).
Results
VSWR
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type VSWR in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
Global 1
1
Right-click VSWR and choose Global.
2
In the Settings window for Global, click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Electromagnetic Waves, Frequency Domain > Ports > emw.VSWR_1 - Voltage standing wave ratio - 1.
3
Locate the x-Axis Data section. From the Axis source data list, choose Outer solutions.
4
In the VSWR toolbar, click  Plot.
Compare the resulting VSWR plot to Figure 4.