Models.rf.Patch Antenna

7/22/2019 Models.rf.Patch Antenna

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Solved with COMSOL Multiphysics 4.3a

2 0 1 2 C O M S O L 1 | B A L A N C E D P A T C H A N T E N N A F O R 6 G H Z

Ba l a n c e d Pa t c h An t e nna f o r 6 GH z

Introduction

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 antennashape. At the early stages of antenna design the engineer 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 1shows the antenna that this model simulates.

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


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2 | B A L A N C E D P A T C H A N T E N N A F O R 6 G H Z 2 0 1 2 C O M S O L

Model Definition

The patch antenna is fabricated on a printed circuit board (PCB) with a relativedielectric constant of 5.23 (Ref. 1). The entire backside is covered with copper, and

the front side has a pattern as shown in Figure 2below.

Figure 2: The patch antenna. The PCB is has a side length of 50 mm and a thickness of0.7 mm. The centered printed square is 10 mm by 10 mm, the smaller rectangles are5.2 mm by 3.8 mm, the thicker lines are 0.6 mm wide, and the thinner lines are 0.2 mm

by 5.2 mm.

The coaxial cables have an outer conductor with an inner diameter of 4 mm and a

center conductor with a diameter of 1mm. The gap between the conductors is filled

with a material with a dielectric constant of 2.07, giving a characteristic impedance

close to 58. There are two coaxial cables feeding the patch antenna from two sides.

In this model, the signals in the cables have the same magnitude but are shifted

180degrees in phase. This results in a balanced feed.

The entire antenna is modeled in 3D. 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 k0is the wave number for free space and is defined as

1 E( ) k

0

2rE 0=


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All metallic objects are defined as perfect electric conductors. The antenna is placed ina spherical air domain surrounded by a Perfectly Matched Layer (PML) serving to

absorb the radiation from the antenna with a minimum of reflection. You can find

detailed information about PMLs in Perfectly Matched Layers (PMLs)in the RF

Module Users Guide. In addition, a scattering boundary condition is added outside

the PML to further reduce the 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 slicethrough the air domain. The surrounding PML is hidden from view.

Figure 3shows the distribution of the electric field norm on the surface of the antenna

and in the air, at 6.26GHz. Most of the energy radiates out from the central patch.

k0

00

=
http://../rf/rf_ug_modeling.pdfhttp://../rf/rf_ug_modeling.pdf


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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 toV0, part of which is reflected directly at the port depending on how wellZrefmatches

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 V0is the peak value of the time-harmonic applied voltage.

The antenna efficiency is defined as the fraction of the theoretical max power that

actually radiates out of the antenna:

Pmax

V02

2Zref

-------------=

P

1

P2

+

2Pmax

--------------------

=


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whereP1andP2are 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 6.26GHz.

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

Model Library path: RF_Module/Antennas/patch_antenna

Notes About the COMSOL Implementation

This model uses a mesh resulting in almost 500,000 complex-valued degrees of

freedom. It therefore needs a little bit more than 2 GB of memory and should be

solved on a 64-bit platform. You can make it solve on a 32-bit computer with a coarsermesh, but the results will be less accurate.

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

computation.


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Reference

1. E. Recht and S. Shiran, A Simple Model for Characteristic Impedance of WideMicrostrip Lines for Flexible PCB, Proceedings of IEEE EMC Symposium 2000,

pp. 10101014, 2000.

Modeling Instructions

M O D E L W I Z A R D

1 Go to the Model Wizardwindow.

2 Click Next.

3 In the Add physicstree, select Radio Frequency>Electromagnetic Waves, Frequency

Domain (emw).

4 Click Next.

5 Find the Studiessubsection. In the tree, select Preset Studies>Frequency Domain.

6 Click Finish.

G E O M E T R Y 1

Import 1

1 In the Model Builderwindow, under Model 1right-click Geometry 1and choose

Import.

2 In the Importsettings window, locate the Importsection.

3 Click the Browsebutton.

4 Browse to the models Model Library folder and double-click the file

patch_antenna.mphbin.

5 Click the Importbutton.

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

1 In the Model Builderwindow, right-click Geometry 1and choose Sphere.

2 In the Spheresettings window, locate the Size and Shapesection.

3 In the Radiusedit field, type 0.04.

Sphere 2

1 Right-click Geometry 1and choose Sphere.


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2 In the Spheresettings window, locate the Size and Shapesection.

3 In the Radiusedit field, type 0.06.

4 Click the Build Allbutton.

5 Click the Wireframe Renderingbutton on the Graphics toolbar.

6 Click the Zoom Extentsbutton on the Graphics toolbar.

G L O B A L D E F I N I T I O N S

Parameters

1 In the Model Builderwindow, right-click Global Definitionsand choose Parameters.

2 In the Parameterssettings window, locate the Parameterssection.

3 In the table, enter the following settings:

M A T E R I A L S

Mater ial 1

1 In the Model Builderwindow, under Model 1right-click Materialsand choose Material.2 Right-click Material 1and choose Rename.

3 Go to the Rename Materialdialog box and type Coax Dielectricin the New name

edit field.

4 Click OK.

5 In the Materialsettings window, locate the Geometric Entity Selectionsection.

Name Expression Description

V0 1[V] Applied voltage

epsilonr_coax 2.07 Relative permittivity, coaxial

cable

epsilonr_pcb 5.23 Relative permittivity, circuit

board

a_coax 0.5[mm] Inner coax conductor radius

b_coax 2[mm] Inner radius of outer coax

conductor

Z_coax sqrt(mu0_const/

(epsilonr_coax*

epsilon0_const))/(2*pi)*log(b_coax/

a_coax)

Cable impedance

Pmax V0^2/(2*Z_coax) Theoretical max power


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6 From the Selectionlist, choose Manual.

7 Click Clear Selection.

8 Select the cylinders between the inner and outer conductors of the coaxial cables,

Domains 4 and 8 only.

9 Locate the Material Contentssection. In the table, enter the following settings:

Mater ial 2

1 In the Model Builderwindow, right-click Materialsand choose Material.

2 Right-click Material 2and choose Rename.

3 Go to the Rename Materialdialog box and type PCBin the New nameedit field.

4 Click OK.

5 Select the PCB board, Domain 6 only.

6 In the Materialsettings window, locate the Material Contentssection.


Mater ial Browser

1 In the Model Builderwindow, right-click Materialsand choose Open Material Browser.

2 In the Material Browserwindow, locate the Materialssection.

3 In the tree, select Built-In>Air.

4 Right-click and choose Add Material to Modelfrom the menu.

Air

In order to properly match the wave, the PML needs to have the same material

properties as the air domain inside it. Therefore, select both spheres surrounding the

antenna.

1 In the Model Builderwindow, under Model 1>Materialsclick Air.

Property Name Value

Relative permittivity epsilonr epsilonr_coax

Relative permeability mur 1

Electric conductivity sigma 0

Property Name Value

Relative permittivity epsilonr epsilonr_pcb

Relative permeability mur 1

Electric conductivity sigma 0


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2 Select Domains 1 and 2 only.

E L E C T R O M A G N E T I C W A V E S , F R E Q U E N C Y D O M A I NBy 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.

1 In the Model Builderwindow, under Model 1click Electromagnetic Waves, Frequency

Domain.

2 Select Domains 1, 2, 4, 6, and 8 only.

D E F I N I T I O N S

Perfectly Matched Layer 1

1 In the Model Builderwindow, under Model 1right-click Definitionsand choose

Perfectly Matched Layer.

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

Domain 1 only.

3 In the Perfectly Matched Layersettings window, locate the Geometrysection.

4 From the Typelist, choose Spherical.

E L E C T R O M A G N E T I C W A V E S , F R E Q U E N C Y D O M A I N

Scattering Boundary Condition 1

1 In the Model Builderwindow, under Model 1right-click Electromagnetic Waves,

Frequency Domainand choose Scattering Boundary Condition.

2 The scattering boundary condition applies to the spherical exterior boundaries of

your model, Boundaries 14, 103, 104, 115, and 118 only.

3 In the Scattering Boundary Conditionsettings window, locate the Scattering Boundary

Conditionsection.

4 From the Wave typelist, choose Spherical wave.

Lumped Port 1

1 In the Model Builderwindow, right-click Electromagnetic Waves, Frequency Domain

and choose Lumped Port.

2 To define the first port, select the outer air/dielectric boundary on the cable facing

thex-direction, Boundary 12 only.

3 In the Lumped Portsettings window, locate the Port Propertiessection.


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4 From the Type of portlist, choose Coaxial.

5 From the Wave excitation at this portlist, choose On.

6 In the Voltageedit field, type V0.

7 Locate the Settingssection. In theZrefedit field, type Z_coax.

Lumped Port 2

1 Right-click Electromagnetic Waves, Frequency Domainand choose Lumped Port.

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

direction, Boundary 92 only.

3 In the Lumped Portsettings window, locate the Port Propertiessection.

4 From the Type of portlist, choose Coaxial.

5 From the Wave excitation at this portlist, choose On.

6 In the Voltageedit field, type V0.

7 In the inedit field, type pi.

8 Locate the Settingssection. In theZrefedit field, type Z_coax.

Although you have not yet specified any conducting boundaries, there is already a

Perfect Electric Conductorcondition in the model. By default, it applies to all

boundaries that are exterior to the active domains. It then gets over-ridden 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 theyneighbor only to domains where the equation is active) and hence need to be explicitly

assigned this same condition.

Perfect Electric Conductor 2

1 Right-click Electromagnetic Waves, Frequency Domainand choose Perfect Electric

Conductor.

2 Select the patch and the ground plane (bottom surface) of the PCB, Boundaries 55

and 65 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.


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D E F I N I T I O N S

Variables 1

1 In the Model Builderwindow, under Model 1right-click Definitionsand choose

Variables.

2 In the Variablessettings window, locate the Variablessection.


The power that goes through each of the ports is computed from port voltage and

current. The last variable defines the efficiency as the ratio of the input power and

the theoretical maximum for each port.

M E S H 1

The default mesh settings give a mesh that is sufficiently fine in most parts of this

model, including the minimum required 2-3 second-order elements across the

thickness of the PML. However, to improve the accuracy it makes sense to use a finer

mesh where the field gradients are the steepest, that is, on the patch and the ports.

Free Tetrahedral 1

In the Model Builderwindow, under Model 1right-click Mesh 1and choose Free

Tetrahedral.

Size 1

1 In the Model Builderwindow, under Model 1>Mesh 1right-click Free Tetrahedral 1

and choose Size.

2 In the Sizesettings window, locate the Geometric Entity Selectionsection.

3 From the Geometric entity levellist, choose Boundary.

4 Select the patch and the port boundaries, Boundaries 12, 65, and 92 only.

5 Locate the Element Sizesection. Click the Custombutton.

6 Locate the Element Size Parameterssection. Select the Maximum element sizecheck

box.

7 In the associated edit field, type 1e-3.

Name Expression Description

P1 0.5*real(emw.Vport_1*

conj(emw.Iport_1))

Power into Port 1

P2 0.5*real(emw.Vport_2*

conj(emw.Iport_2))

Power into Port 2

eff (P1+P2)/(2*Pmax) Antenna efficiency


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8 Select the Minimum element sizecheck box.

9 In the associated edit field, type 1e-4.

A few edges are shorter than the default minimum mesh element size. To avoid

warning messages and to improve the mesh quality, explicitly set the minimum mesh

element size that is equal to the minimum edge length.

Size

1 In the Model Builderwindow, under Model 1>Mesh 1click Size.

2 In the Sizesettings window, locate the Element Sizesection.

3 Click the Custombutton.

4 Locate the Element Size Parameterssection. In the Minimum element sizeedit field,

type 1e-4.

S T U D Y 1

Step 1: Frequency Domain

1In the

Model Builderwindow, under

Study 1click

Step 1: Frequency Domain.

2 In the Frequency Domainsettings window, locate the Study Settingssection.

3 In the Frequenciesedit field, type range(6.2e9,0.02e9,6.3e9).

This gives you six linearly spaced frequencies between 6.2 and 6.3 GHz. If you want

to reproduce the plot in Figure 4and are prepared to let the model run for a while,

try range(6.0e9,0.01e9,6.5e9) instead.

4 In the Model Builderwindow, right-click Study 1and choose Compute.

R E S U L T S

Electric field

The default plot shows a slice plot of the electric field norm at 6.3 GHz. It is

dominated by the result near the antenna. Most of the remaining part of these model

instructions will guide you towards an informative and nice-looking plot of the local

electric field on and around the antenna. But first, take the following steps in order to

plot the antenna efficiency versus the frequency.

1D Plot Group 2

1 In the Model Builderwindow, right-click Resultsand choose 1D Plot Group.

2 In the 1D Plot Groupsettings window, locate the Titlesection.

3 From the Title typelist, choose Manual.


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4 In the Titletext area, type Efficiency.

5 Locate the Plot Settingssection. Select the x-axis labelcheck box.

6 In the associated edit field, type Frequency (Hz).

7 Right-click Results>1D Plot Group 2and choose Global.

8 In the Globalsettings window, click Replace Expressionin the upper-right corner of

the y-Axis Datasection. From the menu, choose Definitions>Antenna efficiency (eff).

9 Click to expand the Legendssection. Clear the Show legendscheck box.

10 Click the Plotbutton.

The plot has sharp edges because you solved only for 6 frequencies. See Figure 4for a

smoother version over a wider frequency range.

Data Sets

In order to prepare for the 3D plot, define selections of the domains, boundaries, andedges that you want the plot to include. As everything is included per default, you will

make these selections with the purpose of hiding what you do not select.

1 In the Model Builderwindow, under Results>Data Setsright-click Solution 1and

choose Add Selection.

2 Right-click Results>Data Sets>Solution 1>Selectionand choose Rename.


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3 Go to the Rename Selectiondialog box and type Physical Domainin the New name

edit field.

4 Click OK.

5 In the Selectionsettings window, locate the Geometric Entity Selectionsection.

6 From the Geometric entity levellist, choose Domain.

7 Click to select the Zoom Boxbutton on the Graphics toolbar.

8 Draw a box enclosing the air sphere but not the PML.

9 Go to the Selectionwindow. Locate the Geometric Scopesection and click the Add to

Selectionbutton. Verify that you have now selected Domains 2-8.

10 In the Model Builderwindow, right-click Data Setsand choose Solution.

11 Right-click Results>Data Sets>Solution 2and choose Add Selection.


13 Go to the Rename Selectiondialog box and type Physical Boundariesin the New

nameedit field.

14 Click OK.15 In the Selectionsettings window, locate the Geometric Entity Selectionsection.

16 From the Geometric entity levellist, choose Boundary.

17 Click to select the Zoom Boxbutton on the Graphics toolbar.

18 Draw a box enclosing the entire antenna but not any of the boundaries between the

air and the PML.

19 Go to the Selectionwindow. Locate the Geometric Scopesection and click the Add toSelectionbutton.

20 In the Model Builderwindow, right-click Data Setsand choose Solution.

21 Right-click Results>Data Sets>Solution 3and choose Add Selection.


23 Go to the Rename Selectiondialog box and type Physical Edgesin the New name

edit field.

24 Click OK.

25 In the Selectionsettings window, locate the Geometric Entity Selectionsection.

26 From the Geometric entity levellist, choose Edge.

27 Click to select the Select Boxbutton on the Graphics toolbar.

28 Draw a box enclosing the air sphere but not the PML.


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29 Go to the Selectionwindow. Locate the Geometric Scopesection and click the Add to

Selectionbutton.

Electric field

The plot group you just selected already contains a slice plot of the electric field norm.

Note that because it uses the data set for which you defined the domain selection, the

plot does not show up in the PML.

Delete the multislice plot and add a single slice.

1 In the Model Builderwindow, under Results>Electric fieldright-click Multisliceand

choose Delete.

2 Click Yesto confirm.

3 Right-click Electric fieldand choose Slice.

4 In the Slicesettings window, locate the Plane Datasection.

5 From the Planelist, choose zx-planes.

6 In the Planesedit field, type 1.

7 Click to expand the Rangesection. Select the Manual color rangecheck box.

8 In the Minimumedit field, type 0.

9 In the Maximumedit field, type 500.

10 Locate the Coloring and Stylesection. From the Color tablelist, choose Thermal.


You are now looking at a nicely scaled plot of the electric field norm on a slice of

your geometry, excluding the PML where it does not have any physical relevance.

12 Right-click Electric fieldand choose Surface.

13 In the Surfacesettings window, locate the Datasection.

14 From the Data setlist, choose Solution 2.


The electric field norm now also shows up on the surface of the antenna. All exterior

surfaces are hidden from view, but the edges defining the contour of the PML arestill visible.

16 In the Model Builderwindow, click Electric field.

17 In the 3D Plot Groupsettings window, locate the Plot Settingssection.

18 Clear the Plot data set edgescheck box.


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Now all edges are gone. This makes the contours of the PCB and the contacts less

prominent. To retain a sharper-looking geometry, draw your selected edges in blackwith the help of a line plot.

20 In the Model Builderwindow, right-click Electric fieldand choose Line.

21 In the Linesettings window, locate the Datasection.

22 From the Data setlist, choose Solution 3.

23 Locate the Expressionsection. In the Expressionedit field, type 1.

24 Locate the Coloring and Stylesection. From the Coloringlist, choose Uniform.25 From the Colorlist, choose Black.


27 In the Model Builderwindow, click Electric field.

28 In the 3D Plot Groupsettings window, locate the Titlesection.

29 From the Title typelist, choose Manual.

30 In the Titletext area, type Electric field norm (V/m).


32 Click the Go to Default 3D Viewbutton on the Graphics toolbar.

33 Click the Zoom Inbutton on the Graphics toolbar. Your plot should now look like

that in Figure 3.

Models.rf.Patch Antenna

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