COMSOL 6.3 - Monopole Antenna Array

It is possible to shape the radiation pattern and steer the beam from an antenna array by controlling the relative phases and magnitudes of the input signal. This example shows how to design an active electronically scanned array (AESA) using arithmetic phase progression on each antenna element.

Figure 1: 4 × 1 monopole antenna array on a substrate.

Model Definition

This example (Figure 1) simulates four quarter-wave monopole antenna mounted on a dielectric substrate. Each antenna is fed by a coaxial lumped port and the outer conductor of each coaxial feed is connected to the ground plane on the bottom of the dielectric (εr = 3.38) substrate. The space between the inner and outer conductor of the coaxial cable is filled with Teflon. The distance between the antenna elements is 0.47 wavelength in free space compromising a relatively high gain and low sidelobes as well as preventing unwanted grating lobes. Metallic circles are patterned on the top of the substrate and connected to the each monopole radiator part. These circular patches compensate the inductance caused by the monopole design and provide a reasonable impedance matching to the reference impedance 50 Ω. All metal parts are modeled as perfect electric conductor (PEC). The antenna is modeled in a spherical air domain. The air domain is truncated with the Perfectly Matched Layers (PMLs) to absorb the radiated fields from the array structure.

All domains except the PMLs are meshed by a tetrahedral mesh with maximum element size of five elements per wavelength so that the wave is well resolved. The monopole radiators and coaxial cables are meshed more finely to provide good resolution of the curved surfaces. The PMLs are swept with a total of five elements along the absorbing direction.

First, only the rightmost antenna element is excited while the rest of elements are terminated with 50 Ω to show a relatively low gain radiation pattern and distortion from the coupling with passive elements. Then, all elements are excited with the same magnitude and arithmetic phase variation (0, α, 2α, 3α) with the unit phase α as in Table 1 to generate a higher gain and scannable radiation pattern.

Table 1: Excited phase variation on each antenna element in degree.
Unit phase	Lumped port1	Lumped Port2	Lumped port3	Lumped port4
-90	0	-90	-180	-270
-45	0	-45	-90	-135
0	0	0	0	0
45	0	45	90	135
90	0	90	180	270

Results and Discussion

The maximum range of the default electric field norm plot is adjusted to emphasize the near field around the monopole radiators in Figure 2. Though only one antenna is excited, the electric fields coupled to other antenna elements are observed, too. The 3D far-field pattern in Figure 3 is distorted compared to that of a typical monopole antenna due to the coupling and asymmetric ground plane configuration to the excited antenna.

When all antenna elements are excited at the same time (Figure 4), the radiation pattern is more directive. While the unit phase α is parametrically swept from -90 to 90 degrees, the direction of maximum radiation is changing gradually.

Figure 2: The strongest electric fields are observed around the excited monopole antenna. The plot also shows that the excited energy is coupled to other antennas elements.

Figure 3: The distorted radiation pattern is generated due to the coupling to the passive antenna elements.

Figure 4: Each antenna element shows a strong field distribution around the monopole radiator.

The direction of maximum radiation is normal to the equiphase plane, so the radiation pattern is tilted to the direction of the faster antenna element in terms of phase. This is the basic idea of a phased array which can steer the beam toward a desired direction; See Figure 5.

Figure 5: 3D far-field radiation pattern while the unit phase variation is changing from -90 to 90 degrees in 45 degree steps.

RF_Module/Antenna_Arrays/monopole_antenna_array

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

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 2.4[GHz].

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
spacing	c_const/2.4[GHz]*0.47	0.058709 m	Array spacing
ph	60[deg]	1.0472 rad	Array phase progression

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

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 180.

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


Layer name	Thickness (mm)
Layer 1	30

Block 1 (blk1)

In the toolbar, click

Click the

button in the toolbar.

In the window for , locate the section.

In the text field, type 60.

In the text field, type 240.

In the text field, type 5.

Locate the section. In the text field, type -30.

In the text field, type -120.

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.5.

In the text field, type 41.

Locate the section. In the text field, type -1.5*spacing.

In the text field, type -5.

Cylinder 2 (cyl2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2.35.

In the text field, type 5.

Locate the section. In the text field, type -1.5*spacing.

In the text field, type -5.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 5.

Click

Work Plane 1 (wp1) > Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 5.5.

Locate the section. In the text field, type -1.5*spacing.

Array 1 (arr1)

In the window, right-click and choose > .

Select the objects , , and only.

In the window for , locate the section.

In the text field, type 4.

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

Click

The finished geometry should look like this.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–4 and 23–26 only.

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

Select Domains 1–10 and 23–26 only.

These are all domains except the monopole radiators and center conductor of the coaxial feeds. By removing from the model domain, PEC conditions are applied by default on the boundaries of the removed domains.

Perfect Electric Conductor 2

In the toolbar, click

and choose .

Select Boundaries 15, 18–23, 26, 27, 30, 31, 34, 35, 85, 92, 93, 100, 109, 116, 117, and 124 only.

You can do this most easily by copying the text ’15, 18–23, 26, 27, 30, 31, 34, 35, 85, 92, 93, 100, 109, 116, 117, and 124’, clicking in the selection box, and then pressing , or by using the Paste Selection dialog box.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 24 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Click the

button in the toolbar.

Far-Field Domain 1

In the toolbar, click

and choose .

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

Material 2 (mat2)

In the window, under right-click and choose .

Select Domain 6 only.

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	3.38	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)

Right-click and choose .

Select Domains 7–10 only.

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	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