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Journal of Communication, Navigation and Signal Processing (July 2012) Vol. 1, No.2, pp. 46-48
46
Microstrip Patch Antenna analysis using PML-
FDTD Technique
Ravi Durbha1, P.Chandrasekhar2 1Senior RF Engineer, Ananya SIP Technologies Pvt Ltd, Hyderabad-500005
ravidurbha@gmail.com 2 Head, Department of ECE
College of Engineering, Osmania University, Hyderabad-500007 sekharpaidi@yahoo.com
Abstract-The objective of this paper is to model
Electromagnetic wave propagation in Microstrip
Line fed Patch Antenna, using Perfect Matched
Layer (PML) Finite-Difference Time-Domain
(FDTD) algorithm developed in MATLAB. The
approach is validated by comparing the results
with those obtained using commercially available
software like Agilent ADS-Momentum.
Keywords: Maxwell’s Equations, Patch Antenna,
Electromagnetic Modeling, PML Method.
1. INTRODUCTION A Microstrip Antenna is a low-profile, low gain,
narrow bandwidth antenna that has number of applications and advantages over other antennas.
They play an important role in modern wireless
communication systems and as well as in many
defense applications. These antennas are small in
size, conformal to given structure, and require simple
and inexpensive modern printed circuit technology to
manufacture. Several electromagnetic techniques
have been proposed analyze these structures for
various electrical parameters like bandwidth, return
loss, beamwidth, and gain. An efficient and simple
method has been implemented in this paper to obtain
some of the afore mentioned characteristics for
microstrip line fed patch antenna using time domain
differential equation based solver/boundary
condition.
2. DESIGN OF PATCH ANTENNA The geometry of the considered antenna is given
below:
Figure1 shows the geometry of the Patch Antenna
operating at 7.5GHz. The rectangular patch has
dimensions of 50mm X 59mm, the quarter wave
transformer has dimensions of 28.2 mm X 0.95mm
and the 50 ohms input port has dimensions 5mm X
2.4mm are printed on a grounded substrate of
thickness (h) 0.794 mm, relative permittivity (ε) 2.2
and size 90 mm X 70 mm. The values of thickness
(h), relative permittivity (ε) and resonant frequency
are fixed previously while length and width of patch
antenna and feed line are determined using
transmission line model.
Figure: 1 Geometry of the patch Antenna
The following equations are employed in calculating
the dimensions of the antenna structure [1].
Width of the Patch Antenna is calculated by:
21
2
1rε
2
λw (1)
Effective permittivity is calculated as:
21
w
h121
2
1r
2
1reff (2)
Fringe length is given by:
8.0h
w258.0
eff
264.0h
w3.0
eff
412.0h
L (3)
W1
W3
W2
L1
L
2
L3
W4
Ravi Durbha and P.Chandrasekhar
47
Effective length of the Patch antenna is given by
L2Leff
L (4)
The actual length of the patch is given by:
L 2
eff2
L Δε
λ (5)
Table 1: Values of the Design Parameters
Parameter Dimensions (mm)
L1 50.0
W1 59.0
L2 28.2
W2 0.95
L3 5.0
W3 2.4
W4 3.0
3. ELECTROMAGNETIC MODELING Berenger proposed a technique which worked equally
well for all frequencies and angles of incidence [2].
The idea of PML is to add a highly damping layer
around the computational domain. To prevent
reflections at the boundary region between the PML
and the computational domain are perfectly matched.
Two media are said to be perfectly matched if a wave
can travel across the boundary between them without
any of its components being reflected.
Figure-2 EM Field Distribution in Patch Antenna
structure using PML-FDTD Technique
In order to correctly model the thickness of the
substrate, Δz is chosen so that three nodes exactly
match the thickness. The dimensions of the antenna,
Δx and Δy are chosen such that the antenna fits
exactly in integral number of nodes. The space steps
used are Δx = 0.389mm, Δy = 0.4mm, and Δz = 0.265mm. The antenna is thus 38Δx X 63Δy, and the
reference plane for port 1 is chosen 8Δy from the
edge of the FDTD wall. The line width of antenna
feed is modeled as 6Δx. An 8 cell PML is used and
the total mesh dimensions are 100 X 110 X 14 in x, y,
and z directions respectively. The time-step used is Δt
= 0.441 Picoseconds, Gaussian half-width is T = 15
Picoseconds and time delay to is set to 3T so that the
Gaussian will start at approximately zero. The circuit
shown in figure-2 is constructed on Rogers RT
Duriod substrate with εr=2.2 and no appreciable loss
term.
The excitation pulse that is used for the simulation is given as:
2
wt
ott
exp(t)z
E (6)
The system is excited by adding equation (6)
to all the Ez components under the feed line strip in
the source plane. The idea is to generate a TEM wave
under the strip which has a Gaussian time signature.
Source Waveforms One of the considerations for the source waveform construction is the spectrum of the
frequency components of the waveform. A temporal
waveform is the sum of time-harmonic waveforms
with a spectrum of frequencies that can be obtained
using Fourier transform.
A source waveform should be chosen such
that its frequency spectrum includes all the
frequencies of interest for the simulation, and should
have a smooth turn-on and turn-off to minimize the
undesired effects of high-frequency components.
Some of the multiple frequency waveforms used are a
Gaussian pulse, differentiated Gaussian pulse, and
cosine modulated Gaussian pulse [4]. Figure 3 shows
the plot of most commonly used waveforms in FDTD
simulation developed using MATLAB software.
Figure-3 Waveforms Most Commonly used in FDTD
Algorithm
Estimation of S-Parameters
The objective of estimating S11 is just to
sample the incident wave. Since we know the
-8 -6 -4 -2 0 2 4 6 8-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time (sec)
Magnitude
Gaussian
Differentiated Gaussian
Modulated Gaussian
Microstrip Patch Antenna analysis using PML-FDTD Technique
48
1 2 3 4 5 6 7 8 90 10
-20
-15
-10
-5
-25
0
freq, GHz
dB
(S(1
,1))
Readout
m1
m1freq=dB(S(1,1))=-23.96
7.47GHz
incident and reflected waves at the terminal plane, S11
can be found out as follows [3]:
(f)inc
E
(f)ref
E
(f)inc
V
(f)ref
V
11S
(7)
(f)}inc
FT{H
(f)}ref
FT{H
(f)inc
H
(f)ref
H
(f)11
S
(8)
11
S10log(dB)11
S (9)
Reflection coefficient measurements implementing
PML-FDTD and Agilent ADS-Momentum are shown
in Figures 3 and 4 respectively.
Figure-4 Reflection Coefficient of the Patch Antenna
using PML-FDTD
Figure-5 Reflection Coefficient of Patch Antenna
using ADS-Momentum
Table-2 Comparison of Results
Parameter PML-FDTD ADS-
Momentum
Frequency 7.45GHz 7.47GHz
Return loss -22.91dB -23.96dB
Bandwidth 172MHz 180MHz
4. CONCLUSION From the results obtained it is concluded that the time
domain differential equation based Maxwell’s
equation solver provides results which replicate the
results obtained using MOM method which forms
the mathematical background of Agilent ADS-
Momentum.
REFERENCES
[1] C.A.Balanis, “Antenna Theory Analysis and
Design”, 3rd
edition, John Wiley and Sons, 2005
[2] J.P.Berenger, “A Perfectly matched layer for the
absorption of Electromagnetic waves”, Journal of
Computational Physics Vol-114, page 195-200,
1994.
[3] Allen Taflove and S.C.Hagness, “Computational
Electrodynamics: The Finite Difference Time
Domain Method, 2nd
ed. Artech House, 2000
[4] Atef Elsherbeni and Veysel Demir, “FDTD
Method for Electromagnetics with MATLAB
Simulations”, SciTech Publishing Inc., 2009
Ravi Durbha received B.Sc
(Instrumentation) from Osmania University in 2002, AMIETE
(E&T) from IETE New Delhi in
2007 and M.Eng from College of
Engineering, Osmania University
in 2011. From 2007 to 2009 he was employed as
Antenna Design Engineer with ACD
Communications Pvt Ltd., Hyderabad. From Jan-
2012 he is with Ananya SIP Technologies Pvt Ltd
as Senior RF Engineer designing Phased Array
Antennas for E.W Applications. His research
interests include Microstrip Circuits, MICs,
Phased Array Antennas, and Electromagnetic
Modeling of Antennas.
P. Chandra Sekhar received
M.Tech from JNTU Hyderabad
in 1999, PhD from Osmania University in 2009. He was Post
Doctoral Fellow at Department of
Systems Engineering, Shizuoka
University, Japan 2009-10. His
primary research interests include Development
of new algorithms to study Interconnects & EM
effects in VLSI circuits, Design of Parallel
computational Systems, VLSI/VHDL based High
Performance Integrated Circuits, and
Computational Electromagnetics.