Modeling Printed Antennas Using The Matlab Antenna Toolbox

Wajih IqbalClemson UniversityAdvisor: Dr. Martin

Outline

Background Integral equations and method of

moments overview Formulating the antenna model LP patch antenna Future work

Background

Graduate students usually use Ansoft HFSS for antenna modeling

Too complicated and expensive for undergrads

A much easier and user-friendly code has been developed by Makarov (Worcester Polytechnic Institute) called the Matlab Antenna Toolbox (MAT)

Background (cont’d)

The code is based on method of moments and is limited to about 7000 unknowns

The code is reasonably precise for simple printed antennas

I have modeled and studied 15 different antenna structures

Integral Equations and Method of Moments Overview

Statement of an Electromagnetic Boundary Condition

Consider an incident wave (with no z variation i.e. 2D problem)

5

E Exs

xi 0 on strip

Perfectly conductingthin strip

- w

ix

w

y

Ei

90 - i

i

Formulation of an Integral Equation

E xk

d

dxk J x H k x x dxx

s

w

wbg bg c hbg FHG

IKJ

z4

2

22

02

E Exs

xi 0 on strip

E E exi i i jk x i

0 sincos e j

,s ix xE E x w w

The Electric Field Integral Equation

4

20

2

kk J x H k x x dx

w

w

RST zbg c hbg

UVW

zd

dx

d

dxJ x H k x x dx E x x w w

w

w

xibg c h bg b gbg

02 ,

The current on the strip is the unknown to be determined. The unknownquantity is under the integral sign.

J w J w b g bg0

Solution of Integral Equations (MoM)

Step 1: Approximate unknown (surface current) by means of a finite sum of N known functions each with an unknown coefficient.

1

( )N

n nn

I

J r f r

Three Major Steps

UVW

zd

dx

d

dxJ x H k x x dx E x x w w

w

w

xibg c h bg b gbg

02 ,

Solution of Integral Equations (MoM)

Step 2: Substitute the approximation (Step 1) into the IE and establish a well-conditioned system of linear equations by enforcing the resulting equations over N subintervals which are within the interval where a solution is desired

1

( )N

n nn

I

J r f r

4

20

2

kk J x H k x x dx

w

w

RST zbg c hbg

(substitute and apply testing function)

1 11 2 12 3 13 4 14 1

1 21 2 22 3 23 4 24 2

1 31 2 32 3 33 4 34 3

1 41 2 42 3 43 4 44 4

for subinterval 1

for subinterval 2

for subinterval 3

for subinterval 4

i

i

i

i

J Z J Z J Z J Z E

J Z J Z J Z J Z E

J Z J Z J Z J Z E

J Z J Z J Z J Z E

J Z E m Nn mn mi

n

N

, , , ,1 2

1

Solution of Integral Equations (MoM)

Step 3: Solve the N by N linear system of equations from step 2 and thereby obtain values for the coefficients.

11 12 13 14 1 1

21 22 23 24 2 2

31 32 33 44 3 3

41 42 43 44 4 4

i

i

i

i

Z Z Z Z J E

Z Z Z Z J E

Z Z Z Z J E

Z Z Z Z J E

Z J Emn n mi

1

11 12 13 141 1

21 22 23 242 2

31 32 33 443 3

41 42 43 444 4

i

i

i

i

Z Z Z ZJ E

Z Z Z ZJ E

Z Z Z ZJ E

Z Z Z ZJ E

1 in mn mJ Z E

Once we have found J(r) we can find all the radiation properties of the antenna

Why Printed Antennas?

Printed antennas are low-profile planar structures that utilize printed circuit board (PCB) technology

They are compact, low cost, easy to manufacture and suitable for integration with electronic systems

Multi-band operation can also be achieved by integrating several coupled printed antenna elements of different lengths and geometries on the same PCB

Dimension can be smaller with higher dielectric GPS, Radar, Satellite communication, Military, cell

phones, and wireless laptops

Execution Flow Chart

Create 2D geometry

Create 3D geometry and feed

Patch Ground Plane

Feeding Probe

MoM Calculations

4

20

2

kk J x H k x x dx

w

w

RST zbg c hbg

UVW

zd

dx

d

dxJ x H k x x dx E x x w w

w

w

xibg c h bg b gbg

02 ,

J Z E m Nn mn mi

n

N

, , , ,1 2

1

1

( )N

n nn

I

J r f r

Z J Emn n mi

Input impedance/Return loss

Near field and far field properties

-0.02-0.01

00.01

0.02

-0.03

-0.02

-0.01

0

0.01

0.02

0.0300.511.5

x 10-3

xy

z

Patch Ground Plane

Feeding Probe

Formulating the Antenna Model

Design:

Dielectric

View with Dielectric

View without Dielectric

•Linearly polarized patch antenna •Patch is 30x40mm •Ground plane is 50x60mm•Substrate has εr = 2.55

Side View

Patch

Ground Plane

Feeding Probe

2-D Mesh Projection

Feed point

Patch

Ground plane

Volume Mesh Generation

Layer(s) properties

Substrate structure

Ground plane

Vertical metal faces

Feeding points

Patch

3D model ready!

Properties of the Patch Antenna

4800 unknowns took 1.5 hours for 50 frequency points (65sec for each point)

Input Impedance

Solid line – Matlab

Dotted line – Ansoft HFSS

Resonance

Properties of the Patch Antenna

Return Loss

2.93 GHz 2.99 GHz

2.96 GHz

2.99 2.932%

2.96Bandwidth

Far Field Properties

Directivity (xz-plane)

Co-polar dominates

At 2.96GHz

Front to back ratio is about 10dB

Far Field Properties

Total Directivity (dB) 3D Directivity

The maximum directivity is approximately 7.4 dB at zenith

Near Field Properties

z-Directed Electric Fieldx-Directed Electric Field

xy

y-Directed Electric Field

Near Field Properties

Surface Current Distribution (x-directed)Surface Current Distribution (y-directed)Surface Current Distribution (z-directed)

Future Work

Simulate more multiband antennas accordingly with future wireless communication needs

Incorporate the genetic algorithm with the code for antenna optimization

After convergence studies construct and test a multiband antenna in the spherical near field chamber

Acknowledgements

Dr. Anthony Martin

Dr. Daniel Noneaker

Dr. Xiao-Bang Xu

Michael Frye

Questions

? ? ? ? ? ? ? ?