COMSOL 6.4 - Balanced Patch Antenna for 6 GHz

Patch antennas are becoming more common in wireless equipment, like wireless LAN access points, cellular phones, and GPS handheld devices. The antennas are small in size and can be manufactured with simple and cost-effective techniques. Due to the complicated relationship between the geometry of the antenna and the electromagnetic fields, it is difficult to estimate the properties of a certain antenna shape. At the early stages of antenna design, engineers can benefit a lot from using computer simulations. The changes in the shape of the patch are directly related to the changes in radiation pattern, antenna efficiency, and antenna impedance.

Balanced antennas are fed using two inputs, resulting in less disturbances on the total system through the ground. Balanced systems also provide a degree of freedom to alter antenna properties, by adjusting the phase and magnitude of the two input signals. Figure 1 shows the antenna that this example simulates.

Figure 1: A photo of the real antenna that the model extracts the properties for.

Model Definition

The patch antenna is fabricated on a printed circuit board (PCB) with a relative dielectric constant of 5.23 (Ref. 1). The entire backside is covered with copper, and the front side has a pattern as shown in Figure 2 below.

Figure 2: The patch antenna geometry is composed of a PCB board, two connectors, and a printed antenna pattern on top of the circuit board.

The coaxial connectors have an outer conductor with an inner diameter of 4 mm and a center conductor with a diameter of 1 mm. The gap between the conductors is filled with a material with a dielectric constant of 2.07, giving a characteristic impedance close to 58 Ω. The signals into the connectors have the same magnitude but are shifted 180 degrees in phase. This results in a balanced feed.

The time-harmonic nature of the signals makes it possible to solve the vector-Helmholtz equation for the electric field everywhere in the geometry,

where k0 is the wave number for free space and is defined as

All metallic objects are defined as perfect electric conductors. The antenna is placed in a spherical air domain surrounded by a Perfectly Matched Layer (PML) serving to absorb the radiation from the antenna with a minimum of reflection.

The model is run through a range of frequencies surrounding the operational frequency of 6.28 GHz.

Results and Discussion

Figure 3: The patch antenna with the electric field plotted both on its surface and on a slice through the air domain. The surrounding PML is hidden from view.

Figure 3 shows the distribution of the electric field norm on the surface of the antenna and in the air, at 6.26 GHz. Most of the energy radiates out from the central patch.

The Lumped Port boundary condition, which is applied to the coaxial cables, is mimicking a connection to a transmission line feed with a characteristic impedance, Zref. The incident voltage wave from the transmission line has an amplitude equal to V0, part of which is reflected directly at the port depending on how well Zref matches the characteristic impedance of the coaxial cable.

Under these circumstances and from each coaxial cable, the theoretical maximum power that can be produced in the antenna is achieved when the antenna impedance matches that of the coaxial cable. This power evaluates to

where V0 is the peak value of the time-harmonic applied voltage.

The antenna efficiency η is defined as the fraction of the theoretical max power that actually radiates out of the antenna:

where P1 and P2 are the net power flow through ports 1 and 2 respectively. In Figure 4 this efficiency is plotted against the frequency, showing that the optimum operating frequency is located at 6.24 GHz.

Figure 4: The antenna efficiency as a function of the frequency.

RF_Module/Antennas/patch_antenna

Notes About the COMSOL Implementation

Possible model extensions include the addition of an external circuit or a far-field computation.

Reference

1. E. Recht and S. Shiran, “A Simple Model for Characteristic Impedance of Wide Microstrip Lines for Flexible PCB,” Proceedings of IEEE EMC Symposium 2000, pp. 1010–1014, 2000.

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 highest frequency value in the specified range.

In the window, under click .

In the window for , locate the section.

In the text field, type range(6.2[GHz], 0.02[GHz], 6.3[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
V0	1[V]	1 V	Applied voltage
epsilonr_coax	2.07	2.07	Relative permittivity, coaxial cable
epsilonr_pcb	5.23	5.23	Relative permittivity, circuit board
a_coax	0.5[mm]	5E-4 m	Inner coax conductor radius
b_coax	2[mm]	0.002 m	Inner radius of outer coax conductor
Z_coax	sqrt(mu0_const/(epsilonr_coaxepsilon0_const))/(2pi)*log(b_coax/a_coax)	57.772 Ω	Cable impedance
Pmax	V0^2/(2*Z_coax)	0.0086546 W	Theoretical max power

Geometry 1

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file patch_antenna.mphbin.

Click

The imported geometry consists of the patch antenna and its connectors. Add two concentric spheres, one for the air surrounding the antenna and one for the PML.

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.06.

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


Layer name	Thickness (m)
Layer 1	0.02

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

Disable the analysis of the geometry as the remaining small geometric details are needed.

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Activate the PML in the volume covered by the outer but not the inner sphere:

Select Domains 1–4 and 13–16 only.

In the window for , locate the section.

From the list, 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

Coax Dielectric

In the window, under right-click and choose .

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

Locate the section. Click

Select the cylinders between the inner and outer conductors of the coaxial cables:

Select Domains 7 and 11 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	epsilonr_coax	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

PCB

Right-click and choose .

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

Select the PCB board:

Select Domain 9 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	epsilonr_pcb	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)

By default, the Electromagnetic Waves equation is active in all domains. However, because you represent the metal in this model as perfectly conductive boundaries, there is no need to model the interior of the contacts. Therefore, remove the metal domains from the domains selection.

In the window, under click .

In the window for , locate the section.

Click

In the dialog, type 1-5, 7, 9, 11, 13-16 in the text field.

Click .

Lumped Port 1

In the toolbar, click

and choose .

To define the first port, select the outer air/dielectric boundary on the cable facing the x direction:

Select Boundary 16 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Locate the section. In the V0 text field, type V0.

In the Zref text field, type Z_coax.

Lumped Port 2

In the toolbar, click

and choose .

The second port is the outer air/dielectric boundary on the contact facing the y direction:

Select Boundary 96 only.

In the window for , locate the section.

From the list, choose .

Locate the section. In the V0 text field, type V0.

In the θin text field, type pi.

In the Zref text field, type Z_coax.

Although you have not yet specified any conducting boundaries, there is already a Perfect Electric Conductor condition in the model. By default, it applies to all boundaries that are exterior to the active domains. It then gets overridden by any other conditions that you are applying. If you click its node in the Model Builder, you can see that it still applies to the conductors.

Perfect Electric Conductor 1

The patch and the PCB ground plane are interior to the model domain (meaning they neighbor only to domains where the equation is active) and hence need to be explicitly assigned this same condition.

Perfect Electric Conductor 2

In the toolbar, click

and choose .

Select the patch and the ground plane (bottom surface) of the PCB:

Select Boundaries 59 and 69 only.

The settings that you have made until now completely define the physics of your model. To enable postprocessing of the antenna efficiency, you need to add integral operators on the port boundaries.

Definitions

Variables 1

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
P1	0.5real(emw.Vport_1conj(emw.Iport_1))	W	Power into Port 1
P2	0.5real(emw.Vport_2conj(emw.Iport_2))	W	Power into Port 2
eff	(P1+P2)/(2*Pmax)		Antenna efficiency