Parabolic Reflector Antenna

A large reflector can be modeled easily with the 2D axisymmetric formulation. In this example, the radius of the reflector is greater than 20 wavelengths and the reflector is illuminated by an axial feed circular horn antenna. The simulated far-field shows a high-gain sharp beam pattern.

Figure 1: This is a 3D visualization of the parabolic reflector antenna that is solved using the 2D axisymmetric formulation.

Model Definition

Since the axial feed circular horn and parabolic reflector antenna are solids of revolution, the antenna can be simulated using the 2D axisymmetric formulation of the electromagnetic wave equation (Figure 1). This approach overcomes a general difficulty when optimizing a reflector antenna: due to its very large size in terms of wavelength, the 3D calculation is computationally intensive.

In this example, all metal surfaces are modeled as perfect electric conductors (PECs) and all domains are filled with air.

The radius of the circular horn feed waveguide is 0.01 m and the cutoff frequency of the TE11 mode is approximately 8.8 GHz. The operating frequency of the antenna should be higher than the cutoff frequency. The horn aperture radius is 0.03 m and the overall horn length is 0.06 m. A slit-conditioned circular port is assigned on the end of the waveguide to excite the antenna with the TE1m mode. The azimuthal mode number, m, is defined from the Electromagnetic Waves, Frequency Domain interface. In this example, m = 1.

The reflector is built using a 53 degree sector of a circle with a radius of 0.85 m. The reflector body is removed from the model domain and, consequently, the PEC is automatically applied to its boundary. The model domain is enclosed by perfectly matched layers (PMLs). The PMLs are thicker than that of other antenna examples in the Application Libraries since high gain and stronger propagation are expected from the reflector.

A Free Triangular mesh is used for the antenna and air domains. The maximum element size is one-fifth of the wavelength at the simulation frequency. A mapped mesh with 10 layers is used for the PMLs.

Results and Discussion

In Figure 2, the norm of the electric field is plotted in decibels with arrows indicating the direction and relative magnitude of power flow. The field from the horn antenna is reflected by the parabola and propagates in the +z direction, confined near the axis of rotation.

The 3D far-field radiation pattern is plotted with a visualization of the antenna body in Figure 3. The low gain radiation from the axial feed horn results in a very high gain pattern created by the reflector.

The far-field radiation pattern in Figure 3 is just a simple body of revolution of the 2D plot data that is useful to measure quickly the maximum gain and review the overall shape of the pattern. The effective 3D far-field radiation pattern of the antenna excited by TE11 mode can be estimated using the predefined postprocessing function, normdB3DEfar_TE11(angle), that is shown in Figure 4.

Figure 2: The norm of the electric field is plotted in decibels. The field from the horn antenna is reflected by the parabola and propagates in the +z direction.

Figure 3: The very sharp 3D far-field radiation pattern is visualized over the axial feed circular horn and parabolic reflector.

Figure 4: Effective 3D far-field radiation pattern plotted in 80 dB dynamic range using far-far field function normdB3DEfar_TE11(angle).

RF_Module/Antennas/parabolic_reflector

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
r0	0.85[m]	0.85 m	Reflector, radius
r1	0.01[m]	0.01 m	Feed horn waveguide, radius
fc	(1.841*c_const/2/pi/r1)	8.784E9 1/s	Feed horn waveguide, cutoff frequency
f0	fc*1.1	9.6625E9 1/s	Frequency
lda0	c_const/f0	0.031027 m	Wavelength
l_horn	0.028[m]	0.028 m	Horn length

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum.

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type f0.

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r1.

In the text field, type 0.06.

Polygon 1 (pol1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


r (m)	z (m)
0.01	l_horn
0.03	0
0.01	0

Click

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.9.

In the text field, type 180.

Locate the section. In the text field, type 270.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	1.5*lda0

Click

Click the

button in the toolbar.

Circle 2 (c2)

In the toolbar, click

In the window for , locate the section.

In the text field, type r0.

In the text field, type 53.

Locate the section. In the text field, type r0-0.365.

Locate the section. In the text field, type 270.

Locate the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.002

Delete Entities 1 (del1)

In the window, right-click and choose .

On the object , select Boundary 1 only.

In the window for , click

The finished geometry should look like this.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1 and 5 only.

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

Select Domains 1, 2, and 4–6 only.

The reflector body is removed from the model domain and, consequently, the PEC is automatically applied to its boundary.

In the window for , locate the section.

In the m text field, type 1.

Perfect Electric Conductor 2

In the toolbar, click

and choose .

Select Boundaries 13 and 14 only.

Port 1

In the toolbar, click

and choose .

Select Boundary 8 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Select the check box.

Click .

Scattering Boundary Condition 1

In the toolbar, click

and choose .

Select Boundaries 17 and 22 only.

Far-Field Domain 1

In the toolbar, click

and choose .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

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

Mesh 1

In the window, under right-click and choose .

Click the

button in the toolbar, a couple of times to get a better view of the meshed structure.

Study 1

In the toolbar, click

Results

Surface

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type 20*log10(emw.normE).

In the toolbar, click

Arrow Surface 1

In the window, right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

Select the check box.

In the associated text field, type 0.004.

In the toolbar, click

Click the

button in the toolbar.

Compare with the plot in Figure 2.

Radiation Pattern 1

Increase the resolution of the far field polar plot.

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 180.

Find the subsection. In the text field, type -1.

In the text field, type 0.

In the toolbar, click

Study 1/Solution 1 (2) (sol1)

In the toolbar, click

and choose .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Domains 4 and 6 only.

Revolution 2D Feed horn

In the toolbar, click

and choose .

In the window for , type Revolution 2D Feed horn in the text field.

Locate the section. From the list, choose .

Study 1/Solution 1 (3) (sol1)

In the toolbar, click

and choose .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Domain 3 only.

Revolution 2D Reflector

In the toolbar, click

and choose .

In the window for , type Revolution 2D Reflector in the text field.

Locate the section. From the list, choose .

Surface 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 1.

Locate the section. From the list, choose .

From the list, choose .

Surface 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 1.

Locate the section. From the list, choose .

From the list, choose .

Radiation Pattern 1

In the window, click .

In the window for , locate the section.

In the text field, type comp1.emw.normEfar/300.

In the toolbar, click

Table

Go to the window.

Click the

button in the toolbar.

The plotted figure describes the axial feed circular horn and parabolic reflector as well as the 3D far-field pattern as shown in Figure 3.

The 3D far-field radiation pattern plotted by default is just a simple body of revolution of the 2D plot that is useful to measure quickly the maximum gain. Using the predefined postprocessing function, it is possible to estimate an effective 3D far-field radiation pattern of the antenna that is excited by the dominant mode of the 3D model of a circular waveguide, TE11 mode.

Results

3D Plot Group 4

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the check box.

Radiation Pattern 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type emw.normdB3DEfar_TE11(angle).

Locate the section. Find the subsection. In the text field, type 180.

In the text field, type 45.

In the text field, type angle.

The far-field function contains an argument, which is given the name angle by default. For the azimuthal angle variable field in the Evaluation section, enter angle to match the function argument. Note that the name can be chosen freely as long as the function argument matches the azimuth angle variable specified in the Evaluation section. This plot would take up to several minutes.

Locate the section. From the list, choose .

In the toolbar, click

Compare the plot with Figure 4.