Microstrip Patch Antenna

The microstrip patch antenna is used in a wide range of applications because it is easy to design and fabricate. The antenna is attractive due to its low-profile conformal design, relatively low cost, and very narrow bandwidth. This example uses an inset feeding strategy that does not need any additional matching parts.

Figure 1: Microstrip patch antenna. The model consists of a PEC ground plane, a 50 Ω microstrip line fed by a lumped port, a region of free space, and a perfectly matched layer (PML) domain.

Model Definition

Feeding a patch antenna from the edge leads to a very high input impedance, causing an undesirable impedance mismatch if a conventional 50 Ω line is directly connected. One solution to this problem is to use a matching network of quarter-wave transformers between the feed point of the 50 Ω line and the patch. However, this approach has two drawbacks. First, the quarter-wave transformers would be realized as microstrip lines that would have to extend beyond the patch antenna, significantly increasing the overall structure size. Second, these microstrip lines should have a high characteristic impedance and thus would have to be narrower than a possible width for fabrication. Therefore, a better approach is desired.

This example uses a different feed point for the patch antenna to improve matching between the 50 Ω feed and the antenna. It is known that the antenna impedance is higher than 50 Ω if fed from the edge, and lower if fed from the center. Therefore, an optimum feed point exists between the center and the edge. The matching strategy is shown in Figure 2. A 50 Ω microstrip line, fed from the end, extends into the patch antenna structure. The width of the cutout region, W, is chosen to be large enough so that there is minimal coupling between the antenna and the microstrip, but not so large as to significantly affect the antenna characteristics. The length of the microstrip line, L, is chosen to minimize the reflected power, S11. These optimal dimensions can be found via a parametric sweep; this example only treats the final design.

Figure 2: The matching strategy between a 50 Ω line and a patch antenna. A microstrip line of length L extends into a slot of with W cut into the patch antenna.

Results and Discussion

The norm of the electric field inside the antenna substrate is described in Figure 3 where an arrow plot of the electric field is included. The direction of the arrows indicate the dominant polarization in the direction of maximum radiation-the antenna boresight. Figure 4 shows the radiation pattern in the E-plane and H-plane. The E-plane is defined by the direction of the dominant antenna polarization and the H-plane is the plane the magnetic field is mainly polarized in. 3D far-field radiation pattern is visualized in Figure 5 showing the directive beam pattern due to the ground plane that blocks the radiation toward the bottom side. The calculated antenna directivity is greater than 6.9 dB. With the choice of feed point used in this example, the S11 parameter is better than −10 dB, and the front-to-back ratio in the radiation pattern is more than 15 dB. The frequency response evaluated with 100 kHz resolution is plotted in Figure 7. The −10 dB S11 bandwidth is wider than 10 MHz.

Figure 3: The norm of the electric field is stronger along the radiation edges. Arrow plot shows the dominant direction of polarization of the electric field at the antenna boresight.

Figure 4: Far-field radiation pattern (gain in dBi) at E-plane and H-plane. Because of the bottom ground plane, the radiation pattern is directed toward the top.

Figure 5: 3D Far-field radiation pattern is directed toward the top. The directivity can be evaluated when plotting the 3D far-field pattern.

Figure 6: An isosurface plot visualizes the decay of the field amplitude.

Figure 7: This S-parameter (S11) plot shows that the antenna impedance is matched to 50 Ω around 1.575 GHz.

The 3D full-wave simulation for an antenna array is memory intensive. By using an asymptotic approach such as multiplying the far-field of a single antenna with a uniform array factor, the radiation pattern of an antenna array can be evaluated quickly. Note that this method does not include the coupling among array elements. The 3D uniform array factor function is available under from the postprocessing context menu when a Far-Field Calculation feature is defined in the physics interface:

af3(nx, ny, nz, dx, dy, dz, alphax, alphay, alphaz)

where nx, ny, and nz are the number of elements along the x-, y-, and z-axis, respectively. The arguments dx, dy, and dz are the distances between array elements in terms of wavelength. alphax, alphay, and alphaz are the phase progression in radians. The gain evaluation of a virtual 8-by-8 antenna array in dB scale (Figure 8) uses the following expression:

emw.gaindBEfar+20*log10(emw.af3(8,8,1,0.48,0.48,0,0,0,0))+10*log10(1/64)

Since it is dB scale, the multiplication of the array factor represents a summation in the expression.

Table 1: Input arguments of array factor operator for an 8-by-8 Array.
Parameter	Description	Argument	unit
nx	Number of elements along x-axis	8	Dimensionless
ny	Number of elements along y-axis	8	Dimensionless
nz	Number of elements along z-axis	1	Dimensionless
dx	Distance between array elements along x-axis	0.48	Wavelength
dy	Distance between array elements along y-axis	0.48	Wavelength
dz	Distance between array elements along z-axis	0	Wavelength
alphax	Phase progression along x-axis	0	Radian
alphay	Phase progression along y-axis	0	Radian
alphaz	Phase progression along z-axis	0	Radian

It assumes that the array is excited by a single input uniform distribution network, so the input power needs to be scaled by a factor 10*log10(1/total number of elements). The direction of the main beam can be steered by defining nonzero phase progression in the uniform array factor. The maximum radiation direction of the array factor along the x-axis is defined by the angle θ from the x-axis in the phase progression using

Figure 9 includes three plots to show the evolution of the antenna radiation pattern from a single antenna to a synthesized antenna array via the uniform array factor:

The gain of the single microstrip patch antenna.

The radiation pattern of the uniform array factor configured to have the maximum radiation at 60 degrees from the x-axis by setting the value of alphax as in Table 2.

The gain of the 8-by-8 microstrip patch antenna array, using the array factor defined above.

Table 2: Input arguments of array factor operator to steer the beam.
Argument	Value	unit
alphax	-2pi0.48*cos(pi/3)	Radian

Figure 8: The far-field radiation pattern of a virtual 8-by-8 microstrip patch antenna array.

Figure 9: The single patch antenna gain, 8-by-8 uniform array factor, 8-by-8 microstrip patch antenna array gain plotted in dB-scale.

Notes About the COMSOL Implementation

This example also uses the Adaptive Frequency Sweep study step based on a model order reduction technique, asymptotic waveform evaluation (AWE) to compute the frequency response of the antenna with a fine frequency resolution. This approach is faster than a regular frequency sweep performed in a Frequency Domain study using the same fine frequency resolution, but the analysis is computationally intensive, and it may require more than 5 GB of RAM when running the Adaptive Frequency Sweep.

RF_Module/Antenna_Arrays/microstrip_patch_antenna_inset

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

In the window, under click .

In the window for , locate the section.

In the text field, type 1.575[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
d	60[mil]	0.001524 m	Substrate thickness
w_line	3.2[mm]	0.0032 m	50 ohm line width
w_patch	53[mm]	0.053 m	Patch width
l_patch	52[mm]	0.052 m	Patch length
w_stub	7[mm]	0.007 m	Tuning stub width
l_stub	15.5[mm]	0.0155 m	Tuning stub length
w_sub	100[mm]	0.1 m	Substrate width
l_sub	100[mm]	0.1 m	Substrate length

Here mil refers to the unit milliinch, that is 1 mil = 0.0254 mm.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

First, create the substrate block.

Substrate

In the toolbar, click

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

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

In the text field, type l_sub.

In the text field, type d.

Locate the section. From the list, choose .

Click

Now add the patch antenna.

Patch

In the toolbar, click

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

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

In the text field, type l_patch.

In the text field, type d.

Locate the section. From the list, choose .

Click

Create impedance matching parts and a 50Ω feed line.

Stub

In the toolbar, click

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

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

In the text field, type l_stub.

In the text field, type d.

Locate the section. From the list, choose .

In the text field, type w_stub/2+w_line/2.

In the text field, type l_stub/2-l_patch/2.

Click

Copy 1 (copy1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type -w_stub-w_line.

Click

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the objects and only.

Click

Choose wireframe rendering to get a better view of the interior parts.

Click the

button in the toolbar.

Continue with the surrounding air and the PML regions.

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_sub.

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


Layer name	Thickness (mm)
Layer 1	l_sub/5

Click

Click the

button in the toolbar.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–4 and 8–11 only.

These are all of the outermost domains of the sphere.

In the window for , locate the section.

From the list, choose .

Suppress some domains and boundaries. This helps to see the interior parts when setting up the physics and reviewing the mesh.

Hide for Physics 1

In the window, right-click and choose .

Select Domains 2 and 9 only.

Hide for Physics 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 10 and 33 only.

Hidden domains and boundaries can be shown by pressing the , , or button in the Graphic Window toolbar.

Before creating the materials for the model, specify the physics. Using this information, the software can detect which material properties are needed.

Electromagnetic Waves, Frequency Domain (emw)

Perfect Electric Conductor 2

In the window, under right-click and choose .

Select Boundaries 15, 20, and 21 only.

Lumped Port 1

In the toolbar, click

and choose .

Click the

button in the toolbar.

Select Boundary 26 only.

For the first port, wave excitation is by default.

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 in the window toolbar.

In the toolbar, click

to close the window.

Materials

Substrate

In the window, under right-click and choose .

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

Select Domains 6 and 7 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	3.38	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 .

Study 1

In the toolbar, click

Results

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Locate the section. From the list, choose .

Selection 1

Right-click and choose .

Select Domains 6 and 7 only.

Electric Field (emw)

In the window, click .

In the window for , locate the section.

Clear the check box.

Arrow Volume 1

Right-click and choose .

In the toolbar, click

In the window, click .

In the window for , locate the section.

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

Find the subsection. In the text field, type 31.

Locate the section. From the list, choose .

Selection 1

Right-click and choose .

Select Domain 5 only.

Color Expression 1

In the window, right-click and choose .

In the window for , locate the section.

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

In the toolbar, click

Strong electric fields are observed on the radiating edges. See Figure 3 and check the dominant polarization at the boresight.

2D Far Field (emw)

In the window, click .

In the window for , click to expand the section.

From the list, choose .

In the text area, type Far-field gain, dBi.

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. Find the subsection. In the text field, type 0.

In the text field, type 1.

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

In the text field, type 0.

Click to expand the section. From the list, choose .

In the table, enter the following settings:


Legends
E-plane

Radiation Pattern 2

Right-click and choose .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

In the text field, type -1.

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

In the text field, type 0.

Click to expand the section. Find the subsection. From the list, choose .

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


Legends
H-plane

In the toolbar, click

This is the far-field gain patterns on the E- and H-plane (Figure 4). The E- and H-plane of a linearly polarized antenna are defined by the dominant polarization at the boresight. The E-plane includes the main polarization that is Ey in this model while the H-plane is perpendicular to the main polarization.

Radiation Pattern 1

The default 3D far-field plot evaluates the norm of electric far field that is calculated from the near field using the Stratton-Chu formula. When the 3D far-field is visualized and is on, it also calculates the maximum directivity of an antenna. The default for is set to emw.normEfar^2, since antenna directivity is defined by the maximum radiation intensity, that is, the maximum power density per unit solid angle. The directivity calculation is used not only for electromagnetics but also for other physics such as acoustics, where the has a different input expression. The calculated maximum directivity value for the microstrip patch antenna is around 6.9 dB.

Annotation 1

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

In the text field, type Maximum directivity: 6.9 dB.

Locate the section. In the text field, type 1.71.

The location is set based on the maximum value of normEfar at the antenna boresight.

Locate the section. From the list, choose .

Select the check box.

In the toolbar, click

Compare the 3D far-field radiation pattern plot with Figure 5.

Inspect the input matching property (S11) at the simulated frequency.

3D Plot Group 4

In the window, expand the node.

Right-click and choose .

Isosurface 1

In the window, right-click and choose .

In the window for , locate the section.

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

Locate the section. In the text field, type 20.

Selection 1

Right-click and choose .

Select Domains 5–7 only.

Filter 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type x>0.

In the toolbar, click

Figure 6 shows the above isosurface plot.

Note that the following simulation requires more than 5 GB RAM.

In order to have the S-parameter plot of the microstrip patch antenna with a fine frequency resolution, analyze the model using based on asymptotic waveform evaluation (AWE). When a device presents a slowly varying frequency response, the AWE provides a much faster solution time when running the simulation on many frequency points compared to regular frequency sweeps.

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, under click .

In the window for , locate the section.

Click

In the dialog box, type Lumped port 1 in the text field.

Click .

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 2

In the window, click .

In the window for , locate the section.

Clear the check box.

Step 1: Adaptive Frequency Sweep

In the window, under click .

In the window for , locate the section.

In the text field, type range(1.545[GHz],100[kHz],1.605[GHz]).

A slowly varying scalar value curve works well for AWE expressions. For one-port devices like antennas, a trivial AWE expression is S11. However, if the frequency response of the AWE expression contains an infinite gradient — the case for the S11 value of an antenna, with excellent impedance matching at a single frequency point — the simulation will take longer to complete. If the loss from the antenna is negligible, an alternative expression such as sqrt(1-abs(comp1.emw.S11)^2) may work well and reduce the computation time. When is set to in the study settings, sqrt(1-abs(comp1.emw.S11)^2) is used automatically for one-port devices.

Because such a fine frequency step generates a memory-intensive solution, the model file size will increase tremendously when it is saved. When only the frequency response of port related variables are of interest, it is not necessary to store all of the field solutions. By selecting the check box in the section, we can control the part of the model on which the computed solution is saved. We only add the selection containing these boundaries where the port variables are calculated. The lumped port size is typically very small compared to the entire modeling domain, and the saved file size with the fine frequency step is more or less that of the regular discrete frequency sweep model when only the solutions on the lumped port boundaries are stored.

Locate the section. Find the subsection. From the list, choose .

Under , click

In the dialog box, select in the list.

Click .

It is necessary to include the lumped port boundaries to calculate S-parameters. By choosing only the lumped port boundaries for settings, it is possible to reduce the size of a model file a lot.

In the toolbar, click

Results

S-parameter, Asymptotic Waveform Evaluation

In the toolbar, click

and choose .

In the window for , type S-parameter, Asymptotic Waveform Evaluation in the text field.

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

In the text area, type Adaptive Frequency Sweep, Microstrip Patch Antenna.

Locate the section. From the list, choose .

Global 1

Right-click and choose .

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

In the toolbar, click

Review the S-parameter plot in Figure 7.

The following instructions are for quick evaluation of the far-field radiation pattern of an antenna array using the uniform array factor operator.

3D Far Field, Virtual Array

In the toolbar, click

and choose .

In the window for , type 3D Far Field, Virtual Array in the text field.

Locate the section. Select the check box.

Radiation Pattern 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type emw.gaindBEfar+20*log10(emw.af3(8,8,1,0.48,0.48,0,0,0,0))+10*log10(1/64).

See the Results and Discussion part for the usage of the uniform array factor operator af3.

Select the check box.

In the associated text field, type -30.

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

In the text field, type 180.

Locate the section. From the list, choose .

In the toolbar, click

The far-field radiation pattern of a virtual 8x8 microstrip patch antenna array is plotted in Figure 8.

2D Far Field Gain (dB), Virtual Array

In the toolbar, click

and choose .

In the window for , type 2D Far Field Gain (dB), Virtual Array in the text field.

Locate the section. From the list, choose .

In the text area, type 8x8 Microstrip Patch Antenna Array.

Locate the section. Select the check box.

In the text field, type -15.

In the text field, type 25.

Locate the section. From the list, choose .

Radiation Pattern 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type emw.gaindBEfar.

Locate the section. Find the subsection. In the text field, type 360.

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

In the text field, type 0.

Locate the section. Select the check box.

From the list, choose .

In the table, enter the following settings:


Legends
Single patch antenna gain

In the toolbar, click

Radiation Pattern 2

Right-click and choose .

In the window for , locate the section.

In the text field, type 20*log10(emw.af3(8,8,1,0.48,0.48,0,-2*pi*0.48*cos(pi/3),0,0))+10*log10(1/64).

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


Legends
8x8 uniform array factor

In the toolbar, click

Radiation Pattern 3

Right-click and choose .

In the window for , locate the section.

In the text field, type emw.gaindBEfar+20*log10(emw.af3(8,8,1,0.48,0.48,0,-2*pi*0.48*cos(pi/3),0,0))+10*log10(1/64).

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


Legends
8x8 patch antenna array gain

In the toolbar, click

See Figure 9 for the dB-scaled gain of the virtual 8x8 microstrip patch antenna array. It is plotted with the uniform array factor which has the maximum radiation at 60 degrees from the x-axis.