Transcript Design and Optimisation of a PIFA Antenna using Genetic

Mphil / PhD Project
Design & Optimisation of a
PIFA Antenna using
Genetic Algorithms
Ameerudden M. Riyad
Prof. H.C.S. Rughooputh
Electronics & Communication Engineering

Nowadays, the development of mobile communications and the miniaturization of radio
frequency transceivers are experiencing an exponential growth, hence increasing the need for
small and low profile antennas. As a result, new antennas have to be developed to provide
larger bandwidth and this, within small dimensions. The challenge which arises is that the gain
and bandwidth performances of an antenna are directly related to its dimensions. The objective
is to find the best geometry and structure giving best performance while maintain the overall
size of the antenna small.

This project presents the optimisation of a Planar Inverted-F Antenna (PIFA) in order to achieve
an optimal bandwidth in the 2 GHz band. Two optimisation techniques based upon Genetic
Algorithms (GA), namely the Binary Coded GA (BCGA) and Real-Coded GA (RCGA) have been
experimented.
The optimisation process has been enhanced by using a Hybrid Genetic
Algorithm by Clustering.
During the optimisation process, the different PIFA models are
evaluated using the finite-difference time domain (FDTD) method - a technique belonging to
the general class of differential time domain numerical modelling methods.
Abstract
Design & Optimisation of a PIFA using GA
2

Problem Formulation

Process Overview

PIFA Modelling

FDTD Implementation

GA Optimisation

Simulation & Results

Future Work
Agenda
Design & Optimisation of a PIFA using GA
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
The introduction of cellular communications and mobile satellite technology has led to a
growing awareness of the vital role wireless systems are playing in communication networks.

With the advent of the third and nowadays fourth generation of the mobile systems and the
Universal Mobile Telecommunication System (UMTS), efficient antenna design has been the
target of many engineers during the past recent years.

The engineer nowadays must therefore develop highly-efficient and low profile antennas
which can be mounted on hand-held transceivers

The objective of this project is to optimise the bandwidth of a PIFA antenna while keeping its
overall size small.
Problem Formulation
Design & Optimisation of a PIFA using GA
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PIFA
Modelling
Antenna
Evaluation
Performance
Optimisation
Process Overview
Design & Optimisation of a PIFA using GA
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
The increase in the capacity and quality of the new services provided by mobile
communications and wireless applications requires the development of new antennas with
wider bandwidths. At the same time, due to the miniaturisation of the transceivers, the
antennas should have small dimensions, low profile and the possibility to be embedded in the
terminals. In this context, PIFA antennas are able to respond to such demands.

Its conventional geometry, that is, the simple PIFA is shown in Fig. 1 below.
Radiating
Plate
Ground
Plate
Feeding
wire
Circuit
Plate
y
Feeding
wire
h
x
h
Circuit
Plate
x
Fig 1. Geometry of a simple PIFA
PIFA Modelling
Geometry of PIFA to be modelled
Design & Optimisation of a PIFA using GA
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
In the design process, electric and magnetic fields have to be analysed in order to evaluate the
performance of the antenna. Various techniques exist for the analysis of electromagnetic fields
and microwave propagation.

To gain a better-detailed understanding of electromagnetic interaction and fields, numerical
simulation techniques are favoured against approximate analysis methodologies.

Empirical methods require much time and money while a simple model is more flexible and
easy to implement.


A simple virtual model can be more flexible and much cheaper.
To account for the electromagnetic propagation in space, a variety of three-dimensional fullwave methods are available.
FEM
Finite
Element
Method
TLM
FDTD
Transmission
Line Matrix
Finite
Difference
Time Domain
PIFA Modelling
Modelling Techniques
Design & Optimisation of a PIFA using GA
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
Finite-Difference Time Domain (FDTD) is a popular and among the most widely used
electromagnetic numerical modelling technique. It is based on the Finite-Difference
Method (FDM), developed by A. Thom in the 1920s.
FDTD Space
•FDTD starts by
discretising a 3D
space into
rectangular cells,
which are called
Yee Lattice.
•To represent the
discrete space into
a high-level
programming
language, arrays
must be used.
•3D Space and Cell
size have to be
defined.
Absorbing Boundary
Conditions
Source Excitation
•To solve for
unbounded
boundaries in a
finite computation
space, an auxiliary
boundary
condition must be
introduced to
effectively absorb
all
electromagnetic
energy impinging
on these
boundaries.
FDTD Evaluation
•Physical source
models need to be
introduced in the
system to excite
the fields for
accurate full wave
analysis.
•The Voltage
Standing Wave
Ratio (VSWR) is
the key to
obtaining the
bandwidth of the
PIFA and thus, the
key to achieve the
objective of this
project.
•VSWR is
calculated for
several
frequencies in the
2GHz band,
ranging from
1.9GHz to 2.5GHz.
FDTD Implementation
Design & Optimisation of a PIFA using GA
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
The Yee lattice is specially designed to solve vector electromagnetic field problems on a
rectilinear grid. The grid is assumed to be uniformly spaced, with each cell having edge lengths
∆x, ∆y and ∆z. Fig. 2 shows the positions of fields within a Yee cell.

Every E component is surrounded by four circulating H components. Likewise, every H
component is surrounded by four circulating E components. In this way, the curl operations in
Maxwell’s equations can be performed efficiently. Equations below are called the FDTD field
advance equations or the Yee field advance equations
Ey
Ex
n  12
Hx
Hz
i, j, k   H nx i, j, k   t  E z i, j  1, k   E z i, j, k 

1
2
 
Ex

Ey
Ez
Hy
Ez
Ez
Hx
Hy
Ez
Hx
E
n
x
i, j, k    E
z
Ey
Hz
Ex
Ex
x
n 1
x
y
FDTD Implementation
t  E

 

n
y
n
y

i, j, k  1  E i, j, k 
n
y


z
 H n  12 i, j  1 , k   H n  12 i, j  1 , k 
z
2
2

i, j, k     z
y



1
1
 H n  2 i, j , k  1   H n  2 i, j, k  1 
y
y
2
2

 
z




'
Ey
Fig 2. An FDTD cell or Yee cell showing the positions of
electric and magnetic field components
n
where  

 eq
t
2
'
 eq

t
2
and  
'
t
1

 eq
2
FDTD Space
Design & Optimisation of a PIFA using GA
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
The solution space is normally infinite since some problems require that one or more of the
boundaries to be unbounded. For practical, purposes, in order to implement FDTD, the spatial
domain must be limited in size because it is impossible for any computer to store all fields in the
entire solution space if the spatial domain is unbounded.

Various absorbing boundary conditions (ABC) have been used for truncating the FDTD mesh in
this project.
Mur’s
Liao’s
One of the most
popular ABCs was
developed by Mur
[15], based on the
Enquist-Majda
formulation [6]. It
uses the
electromagnetic wave
equation to estimate
the magnitude and
propagation direction
of the fields near the
outer boundary and
calculates the fields
along this boundary.
PML
Higdon
This technique
interpolates the fields
in space and time,
using a Newton
backward-difference
polynomial. The
numerical prediction
of Liao’s ABC is usually
one order of
magnitude better
than that of the
second-order Mur’s.
The Higdon Boundary
Operator is very
advantageous since it
involves normal
derivative only. It
produces higher levels
of absorption over
multiple angles, and
has the same degree
of accuracy as the
second-order Mur
with added flexibility
of broadening the
absorption band
More recently,
Berenger invented a
more sophisticated
ABC, called the
Perfectly Matched
Layer (PML)
technique. This
technique artificially
creates a non-physical
absorbing medium
(PML medium)
adjacent to the outer
boundary of the FDTD
space
FDTD Implementation
Absorbing Boundary Conditions
Design & Optimisation of a PIFA using GA
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
To excite the PIFA with a wide range of frequencies, a Gaussian pulse implemented as soft
source is used as the excitation source. This excitation is given by the equation:
E t   cos ot  e

t2
2 2
where
ω is 2πf and f is the frequency of the pulse
t is [(N ) – to] and N is the number of time steps
∆t is the time step
to is the time at which the pulse reaches the peak value of 1.
τ controls the width of the pulse

The Gaussian excitation has some variable parameters
which should be adjusted to fit in the situation where
the excitation is being used.

Fig. 3 illustrates the excitation pulse which is used to
feed the antenna
FDTD Implementation
E vs. N
Fig 3. Excitation Gaussian Pulse
Source Excitation
Design & Optimisation of a PIFA using GA
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
The Voltage Standing Wave Ratio (VSWR) is the key to obtaining the bandwidth of the PIFA and
thus, the key to achieve the objective of this project. In order to obtain the VSWR, the input
impedance of the PIFA has first to be determined.

Using the input impedance, a scattering parameter, S11 which is the reflection coefficient, can
be evaluated and consequently the VSWR is calculated as
VSWR 

1  S11
1  S11
VSWR is calculated for several frequencies in the
2GHz band, ranging from 1.9GHz to 2.5GHz.
A graph of VSWR against frequencies can be
plotted to observe the parabolic shape of the
curve. The performance of the antenna is then
evaluated by determining the bandwidth from
the range of frequencies where the VSWR is
less than 2 (Fig. 4).
Fig 4. Graph of VSWR vs. Frequency
FDTD Implementation
Performance Evaluation
Design & Optimisation of a PIFA using GA
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
GA is a very powerful search and optimisation tool which works differently compared to
classical search and optimisation methods. GA is nowadays being increasingly applied to various
optimising problems owing to its wide applicability, ease of use and global perspective.

As the name suggests, genetic algorithms borrow its working principle from natural genetics.
Genetic algorithms (GAs) are stochastic global search and optimisation methods that mimic the
metaphor of natural biological evolution. GAs operate on a population of potential solutions
applying the principle of survival of the fittest to produce successively better approximations to
a solution.

At each generation of a GA, a new set of approximations is created by the process of selecting
individuals according to their level of fitness in the problem domain and reproducing them
using operators borrowed from natural genetics.

This process leads to the evolution of populations of individuals that are better suited to their
environment than the individuals from which they were created, just as in natural adaptation.
GA Optimisation
Genetic Algorithms Concept
Design & Optimisation of a PIFA using GA
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
Genetic Algorithms is applied to the whole FDTD process which acts as the main component for
the fitness evaluation.

GA begins its search with a random set of solutions, analyses the solutions and selects the best
ones to afterwards converge to the optimal solution, which will result to the best bandwidth
performance.
Begin


The working principle of GAs is very different
from that of most of classical optimisation
techniques. GA is an iterative optimisation
procedure. Instead of working with a
single solution in each iteration, a GA
works with a number of solutions, known
as a population, in each iteration.
A flowchart of the working principle of a
simple GA is shown in Fig. 5.
Initialise population
Gen = 0
Evaluation
Assign fitness
Condition
satisfied?
Gen = Gen + 1
Yes
Reproduction
Stop
GA Optimisation
No
Crossover
Mutation
Fig 5. Working principles of a simple GA process
Working principles
Design & Optimisation of a PIFA using GA
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
In this project, the set of solutions was first coded in binary string structures and BinaryCoded GA was used for this purpose. Then Real-Coded GA was used for improvement in
convergence and precision to the optimal solution. The GA was then modified to a hybrid
version using Clustering technique.
BCGA
RCGA
In the Binary-Coded GA
(BCGA), the basic block
of the genetic
algorithm is the
chromosome.
Each chromosome is
composed of genes
described as a binary
sequence of zeros and
ones.
Each gene is associated
with a parameter to be
optimized.
Clustering
Real coded GA (RCGA)
represents parameters
without coding, which
makes representation of
the solutions very close to
the natural formulation of
many problems.
Real-world optimization
problems often involve a
number of characteristics,
which make them difficult
to solve up to a required
level of satisfaction
GA can sometimes get
stuck on sub optimal
solution without any
progress to the real
optimal solution.
One of the possible
solution to this problem is
to maintain a population
size as large as possible.
However, maintaining
large population involve
high cost to evaluate each
individual. Therefore to
reduce the cost of
evaluation and accelerate
the convergence the
Hybrid Clustering GA is
applied in this work
GA Optimisation
GA optimisation techniques
Design & Optimisation of a PIFA using GA
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•The population strings are represented as shown in Fig. 6 below:
Binary-Coded
GA
X 1 X2
X3 X4
fx
fz
X5
h
Fig. 6. Population string known as chromosome
•where Xi is a binary digit (0 or 1) and i taking values from 1 to 5. As illustrated in Fig.
3, the first 2 bits represent the parameter fx, the next 2 bits the parameter fz and the
last bit the height h of the radiating plate.
•Each string is decoded, mapped and evaluated. The evaluation process involves the
FDTD method mentioned earlier.
•After experimenting the BCGA, RCGA was experimented to compare the convergence
and precision of the optimization process
Real-Coded GA
•In RCGA, decision variables are used directly to form chromosome-like structure.
Chromosome represents a solution and population is a collection of such solutions.
The operators modify the population of the solution to create new one.
•For implementing the RCGA in order to solve problems developed in this model, the
following basic components are considered: Parameters of GA, Representation of
chromosomes, Initialization of chromosomes, Evaluation of fitness function, Selection
process, Genetic operators like crossover and mutation .
GA Optimisation
GA experimentation
Design & Optimisation of a PIFA using GA
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• Clustering is a simple method of grouping the population into several small groups,
called as clusters. Fig. 7 illustrates the concept behind the conventional GA and the
modified clustered GA.
Conventional GA
Clustering
GA
Clustered GA
Fig. 7. Conventional GA vs. Clustered GA
• The algorithm evaluates only one representative for each cluster. The fitness of other
individuals are estimated from the representatives’ fitness. Using this method, large
population can be maintained with relatively less evaluation cost. One of the
important factors to take into consideration for clustering is the similarity measure.
This is commonly achieved using distance measures such as Euclidean distance, City
block distance and Minkowski distance .
• There exist other clustering techniques namely the Hierarchical clustering, Overlapping
clustering and Partitional clustering. A hybrid GA with clustering based on the k-means
algorithms [11] from Partional clustering had been used in the presented work
because of its applicability and flexibility of specifying the number of clusters required
GA Optimisation
GA experimentation
Design & Optimisation of a PIFA using GA
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
In this project, MATLAB has been opted for the simulation owing to its distinct advantages over other
programming language for scientific purposes.

MATLAB proved to be suitable for the simulation although the processing time is a little more than in C
or C++. MATLAB facilitated the plotting of three-dimensional graphs and debugging of the program is
done easily

The computer program is written according to the FDTD algorithm by following all the conditions
necessary for convergence of solutions. To be more flexible, the parameters, such as the solution
space, frequency of excitation, number of time steps and others defined at the beginning of the
computer program may be modified at will without affecting the running of the simulation.

A series of tests were carried out throughout the work to check whether the implementation of the
FDTD was good enough to evaluate the performance of the PIFA. These tests were carried out using
different boundary conditions, different excitation pulses and different computational space size.
Simulation
Design & Optimisation of a PIFA using GA
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
Simulation was carried out initially on different absorbing boundary conditions (Higdon,
Dispersed, Mur’s) as well as without any absorbing boundary condition.

Following are the simulation results:
Without
Higdon
Dispersed
Mur’s
.
.
.
High peaks at the
boundaries
Good absorption of the
fields
Good absorption
reflection of the waves at
the boundary causes
stationary waves resulting
to small standing waves
inside the FDTD space
Not enough significant
attenuation
Provides reflectionless
boundary over broad
spectrum
Does not require
knowledge fields adjacent
to the cells
Does not perform well at
low frequency & Large
computational time
Achieves minimal in
computational cost and
memory requirement
Simulation
Absorbing Boundary Condition Simulation
Design & Optimisation of a PIFA using GA
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
The FDTD mesh size has to be defined large enough for the waves to propagate smoothly. A very large
mesh size would obviously give better approximation of the fields propagation since the reflection
from the boundaries would be very far from the source (if the source is located in the vicinity of the
centre of the FDTD space). However, a very large mesh size would automatically increase the
simulation time considerably.

The ground plate and the radiating plate
are assumed to be infinitely thin perfect
conductors and their conductivity has been
set to infinity in the FDTD model, that is,
they have been considered as PEC walls in
the FDTD algorithm.
FDTD
computational
space
Radiating plate
50cells
Ground plate

In this work, the FDTD mesh size was set to
approximately 20 cells away, in all direction,
from the PIFA to be modelled. Thus, within
90 time steps, the fields may propagate with
a minimum of reflection from the boundaries
and the simulation took approximately 24hrs
to display a single value of the VSWR on a
Pentium 4, 1.86GHz computer and took more
than 3 days on a slightly less powerful machine
Simulation
7ce
13c
ells
lls
ells
11c
ells
25c
70cells
60cells
Fig 8. FDTD Mesh Size
FDTD mesh size
Design & Optimisation of a PIFA using GA
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
The PIFA was excited using a Gaussian waveform of frequency ranging from 1.9 GHz to 2.5 GHz
and the boundary condition used was the Mur’s second order ABC.
FDTD space
boundary
Ground plate
FDTD space
boundary
Feeding point
Radiating plate
Feeding line
11 cells
Radiating plate
60 cells
13 cells
7
cells
Circuit plate
fx
fz
h
50 cells
11 cells
25 cells
25 cells
70 cells
Ground plate
70 cells
Fig 9. Top and Side views of PIFA to be modelled

The figures show the top and side views of the PIFA which the FDTD algorithm evaluated. The
feeding point, that is, the source location can be varied by adjusting the parameters fx and fz.
The height of the radiating plate from the ground plate may be varied by changing the value of
the parameter ‘h’. The variation of the height is quite small (approximately 2mm) since the idea
of the project is to maximise the bandwidth of the PIFA while keeping the overall dimensions
constant.
Results
PIFA Modelled
Design & Optimisation of a PIFA using GA
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
The frequency range of interest is from 1.9 GHz to 2.5 GHz and graphs of the VSWR against the
frequencies were plotted in order to calculate the bandwidth of the PIFA.

It is noteworthy that the smaller is the frequency interval for simulation, the smoother is the
graph. Owing to very large simulation time for a single value of VSWR, the frequency interval
was taken as 0.1 GHz to obtain the corresponding value of VSWR. the bandwidth obtained is
approximately 420 MHz.
Fig 10. Graph of VSWR vs Frequency
Fig 11. E-field Propagation
Results
Frequency Range
Design & Optimisation of a PIFA using GA
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BCGA
RCGA
The Binary Coded GA has proved to
be a very good optimising tool and if
used properly, it may serve to solve
various problems of search and
optimisation.
Classical optimising methods would
take much longer time to find the
optimal solution as compared to the
Binary GA method.
However, the optimisation does not
always converge to the optimal
solution and sometimes get diverted
to some other sub-optimal solution.
Clustering
The Real Coded GA has been chosen
as the alternative for Binary Coded
GA. The most important feature of
the RCGA has been observed to be
the capacity to exploit local
continuities.
Owing to the user of real
parameters in RCGA, large domains
for the variables can be used as
opposed to BCGA implementations
where increasing the domain would
decrease the precision.
The Hybrid GA by clustering, on the
other hand, has shown to converge
faster to the optimal solution.
Population size could be increase
without affecting the performance
of the optimisation using the Hybrid
GA by clustering.
The convergence looks similar to the
RCGA but performance is much
better because of the FDTD
evaluation of only the
representatives of each cluster.
Results
GA Outcome
Design & Optimisation of a PIFA using GA
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FDTD Improvement
• During the FDTD simulation process, it has been observed that processor was
highly overloaded owing to the large computational space and complexity of
the field calculation. Consequently, the processing of the FDTD was very bulky
and consumed a considerable amount of processing time throughout the
whole optimisation system. One of the future works would involve improving
the FDTD process through code and logic optimisation. Another approach
would imply approximating the FDTD process through other simplified models
achieving the same results.
GA Improvement
• In this work, we have formulated and solved a bandwidth problem for the
PIFA antenna. However, in Binary-Coded GA or Real-Coded GA, a difficulty
regarding the boundaries of the decision variables was encountered. The
optimisation sometimes converge wrongly or take very long to converge to
the optimal solution. As part of the future work, the GA has to be analysed
thoroughly and improvements identified. Few of the approaches would be:
Redefining combination of operators and Hybrid merging of GA techniques.
Future Work
Design & Optimisation of a PIFA using GA
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Main References

Pinho, P.T., Pereira, J. R., "Design of a PIFA antenna using FDTD and Genetic Algorithms", Proc IEEE AP-S/URSI International Symp.,
Boston, United States, Vol. 4, pp. 700 - 703, July, 2001.

Rashid A. Bhatti, Mingoo Choi, JangHwan Choi, and Seong Ook Park, “Design and Evaluation of a PIFA Array for MIMO-Enabled
Portable Wireless Communication Devices”, IEEE Antenna and Propagation Symposium 2008, San Diego, America, July 5-12, 2008.

Y. Gao, X. Chen, Zhinong Ying, and C. Parini, “Design and performance investigation of a dual-element PIFA array at 2.5 GHz for
MIMO terminals”, IEEE Transactions on Antennas and Propagation, vol. 55, no. 12, 2007.

K. Deb. “Optimization for engineering design: Algorithms and examples”, Prentice-Hall, Delhi, 1995.

Gedney and Maloney, “Finite Difference Time Domain modeling and applications”, FDTD Short Course, Mar. 1997.

D. Y. Su, D.-M. Fu, and D. Yu, "Genetic Algorithms and Method of Moments for the Design of Pifas", Progress In Electromagnetics
Research Letters, Vol. 1, 9-18, 2008.

Maulik U. and Bandyopadhyay S., “Genetic algorithm-based clustering technique”, Journal of Pattern Recognition Society, 1999.

Seront, G. and Bersini, H., "A new GA-local search hybrid for continuous optimization based on multi level single linkage
clustering," Proc. of GECCO-2000, pp.90~95, 2000.
Thanks to the Tertiary Education Commission (TEC) of Mauritius for sponsoring my post graduate
research work at the University of Mauritius.
Thank you…
Design & Optimisation of a PIFA using GA
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