Modeling Printed Antennas Using
The Matlab Antenna Toolbox
Wajih Iqbal
Clemson University
Advisor: Dr. Martin
Outline
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

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Background
Integral equations and method of
moments overview
Formulating the antenna model
LP patch antenna
Future work
Background

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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)
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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
y

P e rfec tly condu c ting
th in s tr ip
90 - 



E
Consider an incident
wave (with no z
variation i.e. 2D
problem)
Exs  Exi  0
i

-w
i
i
i
x
w
on strip
5
Formulation of an Integral Equation
E E 0
s
x
i
x
F
d
E bg
x  G
4k H
dx

s
x
2
z
I
 k J J bg
x  H bgc
k x  x h
dx 
K
w
2
2
on strip
w
e
E  E sin  e
i
x
i
0
E  E
s
x
i
x
i
2
0
jk x cos  i
j
x   w, w
The Electric Field Integral Equation
z
R
bg
k
J bg
x H c
k x  x h
dx 
S
4k T
d
U
bg
J bg
x H c
k x  x h
dx  V
 E bg
x x b
 w, wg
dx 
W

w
2
w
d

dx
z
w
w
2
0
2
i
x
0
b g bg
J w  J w  0
The current on the strip is the unknown to be determined. The unknown
quantity is under the integral sign.
Solution of Integral Equations (MoM)
Three Major Steps

Step 1: Approximate unknown (surface current) by
means of a finite sum of N known functions each with an
unknown coefficient.
N
J  r    I nf n (r )
n 1
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

J1Z11  J 2 Z12J r J3 Z13I f J(r4)Z14  E1i for subinterval 1
N

n 1
n n
J1Z 21  J 2 Z 22  J 3 Z 23 (substitute
J 4 Z 24  and
E2i for
subinterval
2
apply
testing function)
z
z
dJ Z d E for
U
R
bg
bg
J
Z

J
Z

J
Z

subinterval
J bg
x H c
k x  x h
dx  V
3E bg
x
k
J bg
x H c
k x  x h
dx  
S
dx
dx 
4k T
W

w
w
2
1
w
31
20
2
32
3
33
4
34
w
i
3
2
0
J1Z 41  J 2 Z 42  J 3 Z 43  J 4 Z 44  E4i for subinterval 4
N

n 1
J n Zmn  Emi ,
m  1,2,, N
i
x
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.
i

Z
J

E
 J n mn  Zmnn   m 
1
 J1 Z
 11  ZZ1112
 J  Z  ZZ
 2  21  2122
 J3 Z 31  ZZ3132
  Z  Z
 J 4  41  Z 4142
ZZ1213
ZZ2223
ZZ3233
ZZ4243
1
ii
J
Z13
Z



E



E

14
1
14
11 
  J   i i
E
Z 23
24  Z 24
2

  E2 2
i
i




Z33
J

E

Z
E3 3
44
3
44
    i i
J 44
ZZ43
44  Z
4  
EE4 4
Once we have found J(r) we can find all the radiation
properties of the antenna
Why Printed Antennas?
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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
d

dx
w
w
2
w
z
w
z
R
k
J bg
x  H bgc
k x  x h
dx 
S
4k T
d
U E bg
J bg
x  H bgc
k x  x h
dx  V
dx 
W x x bw, wg

2
2
0
Feeding
Probe
i
x
0
N
J  r    I nf n (r )
MoM Calculations
n 1
N
Input impedance/
Return loss

n 1
J n Zmn  Emi ,
m  1,2,, N
Patch
Zmn J n  Emi
Near field and far
field properties
Ground
Plane
Formulating the Antenna Model
Feeding Probe
Design:
•Linearly polarized patch
antenna
•Patch is 30x40mm
•Ground plane is 50x60mm
•Substrate has εr = 2.55
Patch
Ground Plane
-3
z
x 10
View without Dielectric
1.5
1
0.5
0
0.03
0.02
0.01
0.02
0
Dielectric
Patch
0.01
-0.01
-0.01
-0.02
y
Feeding Probe
0
-0.03
-0.02
View with Dielectric
x
Side View
Ground Plane
2-D Mesh Projection
Patch
Feed point
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
Input Impedance
4800 unknowns took 1.5 hours for 50
frequency points (65sec for each point)
Solid line –
Matlab
Dotted line –
Ansoft HFSS
Resonance
Properties of the Patch Antenna
Return Loss
2.99 GHz
2.93 GHz
2.96 GHz
Bandwidth 
2.99  2.93
 2%
2.96
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 Field
y-Directed
x-Directed
y
x
Near Field Properties
Surface Current Distribution (z-directed)
(x-directed)
(y-directed)
Future Work
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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
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