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.