COMSOL 6.4 - Fast Numerical Modeling of a Conical Horn Lens Antenna

Fast Numerical Modeling of a Conical Horn Lens Antenna

An axisymmetric 3D structure such as a conical horn antenna can be simulated in a fast and efficient way using only its 2D layout. In this example, the antenna radiation and matching characteristics are computed very quickly with respect to the dominant TE mode from the given circular waveguide by simulating the 2D axisymmetric geometry of an 3D antenna structure.

Figure 1: 3D model of the conical horn lens antenna from a 2D axisymmetric model.

Model Definition

The model consists of a conical metallic horn and a Polytetrafluoroethylene (PTFE) dielectric lens surrounded by an air domain. The outer part of the air domain truncated by perfectly matched layers (PML) that absorb the strong radiation from the horn aperture. All metal surfaces are assumed lossless, and so are modeled as perfect electric conductors (PEC). The lens material is also assumed lossless and configured as PTFE material with a low dielectric constant (εr = 2.1) to avoid unwanted sudden refractive index change between the air and the dielectric.

One end of the circular waveguide is excited with a predefined TE1 mode circular port boundary condition and the other end is connected to the conical horn, which is open to the air domain. The combination of azimuthal mode index and the circular port mode index in a 2D axisymmetric model is compatible with the predefined circular port mode index of a 3D model. The TE11 mode cutoff frequency of a circular waveguide with radius 10 mm is approximately 8.8 GHz, which is calculated by

where c0 is the speed of light, p′nm are the roots of the derivative of the Bessel functions Jn(x), m and n are the mode indices, and a is the radius of a waveguide. The value of p′11 is approximately 1.841. The operating frequency of the antenna is necessarily higher than the waveguide cutoff frequency.

The circular port boundary condition is placed on the interior boundary where the reflection and transmission characteristics are computed automatically in terms of S-parameters. The interior port boundary with PEC backing for one-way excitation requires the slit condition. The port orientation is specified to define the inward direction for the S-parameter calculation.

Results and Discussion

Figure 2 shows that the excited wave from the circular waveguide is traveling via the conical horn structure, confined via the dielectric lens, and generates a very directive radiation pattern. The radiation pattern is visualized in dB scale to get a better view of its sidelobes. The first sidelobe is about 22 dB lower than the main radiation lobe. The far-field radiation pattern in Figure 2 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 3.

Figure 2: 3D far-field radiation pattern in dB, visualized with the grid above the lens. The E-field norm is focused gradually toward the center.

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

RF_Module/Antennas/conical_horn_lens_antenna

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.

Click

Browse to the model’s Application Libraries folder and double-click the file conical_horn_lens_antenna_parameters.txt.

First load the geometric parameters. Then calculate the cutoff frequency fc to ensure that a higher value is chosen for the simulation frequency f0.

In the table, enter the following settings:


Name	Expression	Value	Description
fc	1.841*c_const/2/pi/r1	8.784E9 1/s	Cutoff frequency
f0	1.2*fc	1.0541E10 1/s	Frequency

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

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.

In the window, under click .

In the window for , locate the section.

In the text field, type f0.

Geometry 1

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type hl*2.

In the text field, type 180.

Locate the section. In the text field, type 0.05.

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	c_const/f0

Click

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 wl.

Locate the section. In the text field, type -wl.

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	hl*cos(angle)
r1+hl*sin(angle)	hl*cos(angle)

Polygon 2 (pol2)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


r (m)	z (m)
r1	0
r1+hl*sin(angle)	hl*cos(angle)
r1+hl*sin(angle)+ht	hl*cos(angle)
r1+ht	0

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type ht.

In the text field, type wl.

Locate the section. In the text field, type r1.

In the text field, type -wl.

Parametric Curve 1 (pc1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type max_para.

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

In the text field, type -(s^2)*hlens/(max_para/1[m])^2.

Locate the section. In the text field, type hl*cos(angle)+hlens+0.01.

Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type max_para.

In the text field, type 0.01.

Locate the section. In the text field, type hl*cos(angle).

In the toolbar, click

In the window, click .

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1 and 7 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Dielectric

In the window, under right-click and choose .

In the window for , type Dielectric in the text field.

Select Domains 5 and 6 only.

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	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

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

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 14–19 and 21 only.

Port 1

In the toolbar, click

and choose .

Select Boundary 4 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Select the checkbox.

From the list, choose .

Click .

Far-Field Domain 1

In the toolbar, click

and choose .

Mesh 1

In the toolbar, click

In the window, under click .

Study 1

Step 1: Frequency Domain

In the toolbar, click

Results

Electric Field (emw)

Visualize the model domains except for the perfectly matched layers.

Study 1/Solution 1 (sol1)

In the window, expand the > node, then click .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Domains 2–6, 8, and 9 only.

Surface 1

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type emw.Er.

Click to expand the section. Select the checkbox.

In the text field, type -1500.

In the text field, type 1500.

Contour 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 30.

Locate the section. Clear the checkbox.

In the toolbar, click

The real parts of the Er and E-field norm contour shows that the wave is propagating toward the horn aperture and focused by the dielectric lens.

Radiation Pattern 1

Apply a finer angular resolution to get a better plot of the radiation pattern.

In the window, expand the node, then click .

In the window for , locate the section.

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

In the text field, type 0.

In the toolbar, click

3D Far Field, Gain (emw)

Add surface plots of the antenna body and lens, and show them together with the 3D far-field radiation pattern.

Radiation Pattern 1

In the window, expand the > node, then click .

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

Locate the section. In the text field, type emw.normdBEfar/400.

This reduces the size of the 3D far-field radiation pattern.

Clear the checkbox.

Click in the upper-right corner of the section. From the menu, choose > > > .

Locate the section. Find the subsection. In the text field, type 90.

Locate the section. From the list, choose .

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

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 Domains 8 and 9 only.

Revolution 2D 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click to expand the section. In the text field, type -90.

In the text field, type 270.

Study 1/Solution 1 (4) (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 5 and 6 only.

Revolution 2D 3

In the toolbar, click

and choose .

In the window for , 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. From the list, choose .

Clear the checkbox.

Surface 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the toolbar, click

Transformation 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 0.17.

In the toolbar, click

Click the

button in the toolbar.

This plot should reproduce Figure 2. The far-field radiation pattern plotted above 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.

3D TE11 Mode Pattern

In the toolbar, click

In the window for , type 3D TE11 Mode Pattern in the text field.

Locate the section. From the list, choose .

Locate the section. Select the checkbox.

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 90.

In the text field, type 90.

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.

Locate the section. From the list, choose .

In the toolbar, click

Compare the plot with Figure 3.

Click the

button in the toolbar.

In the dialog, select > in the tree.

In the tree, select the checkbox for the node > .

Click .

When plotting a far-field radiation pattern, it may take a long time due to the finer resolution. The plotting time can be reviewed from the information section.

Port Probe

Finish by inspecting the S-parameter.