PIFA Antenna using

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Oct 23, 2013 (3 years and 10 months ago)

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Design &
Optimisation

of a
PIFA Antenna using

Genetic Algorithms

Ameerudden M. Riyad

Prof. H.C.S. Rughooputh


Electronics & Communication Engineering

Mphil / PhD Project

Abstract


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
.

2

Desi gn & Opti mi sati on of a PIFA usi ng GA

Agenda



Problem Formulation



Process Overview



PIFA Modelling



FDTD Implementation



GA Optimisation



Simulation & Results



Future Work

Desi gn & Opti mi sati on of a PIFA usi ng GA

3

Problem Formulation


The objective of this project is to optimise the bandwidth of a PIFA antenna while keeping its
overall size small.


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


4

Desi gn & Opti mi sati on of a PIFA usi ng GA

Process Overview

PIFA
Modelling

Antenna
Evaluation

Performance
Optimisation

5

Desi gn & Opti mi sati on of a PIFA usi ng GA

PIFA Modelling


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
.

Fig 1. Geometry of a simple PIFA

Geometry of PIFA to be modelled

6

Desi gn & Opti mi sati on of a PIFA usi ng GA


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
.





To

account

for

the

electromagnetic

propagation

in

space,

a

variety

of

three
-
dimensional

full
-
wave

methods

are

available
.


Modelling Techniques

7

Desi gn & Opti mi sati on of a PIFA usi ng GA


A simple virtual model can be more flexible and much cheaper.

Finite
Element
Method

FEM

Transmission
Line Matrix

TLM

Finite
Difference
Time Domain

FDTD

PIFA Modelling


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

1920
s
.




8

Desi gn & Opti mi sati on of a PIFA usi ng GA

FDTD Space


FDTD starts by
di screti sing

a 3D
space i nto
rectangul ar cel l s,
whi ch are cal l ed
Yee Latti ce.


To represent the
di screte space i nto
a hi gh
-
l evel
programmi ng
l anguage, arrays
must be used.


3D Space and Cel l
si ze have to be
defi ned.

Absorbi ng Boundary
Condi ti ons


To sol ve for
unbounded
boundari es i n a
fi ni te computati on
space, an auxi l iary
boundary
condi ti on must be
i ntroduced to
effecti vel y absorb
al l
el ectromagneti c
energy i mpi ngi ng
on these
boundari es.

Source Exci tati on


Physi cal source
model s need to be
i ntroduced i n the
system to exci te
the fi el ds for
accurate ful l wave
anal ysis.

FDTD Eval uati on


The Vol tage
Standi ng Wave
Rati o (VSWR) i s
the key to
obtai ni ng the
bandwi dth of the
PIFA and thus, the
key to achi eve the
objecti ve of thi s
project.


VSWR i s
cal cul ated for
several
frequenci es i n the
2GHz band,
rangi ng from
1.9GHz to 2.5GHz.

FDTD Implementation

FDTD Implementation


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


Fig 2.
An FDTD cell or Yee cell showing the positions of
electric and magnetic field components

FDTD Space

9

Desi gn & Opti mi sati on of a PIFA usi ng GA


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
.


Absorbing Boundary Conditions

10

Desi gn & Opti mi sati on of a PIFA usi ng GA

One of the most
popul ar ABCs was
devel oped by
Mur

[15], based on the
Enqui st
-
Majda

formul ati on [6]. It
uses the
el ectromagneti c wave
equati on to esti mate
the magni tude and
propagati on di recti on
of the fi el ds near the
outer boundary and
cal cul ates the fi el ds
al ong thi s boundary.

Mur’s

Thi s techni que
i nterpol ates the fi el ds
i n space and ti me,
usi ng a Newton
backward
-
di fference
pol ynomi al. The
numeri cal predi cti on
of
Li ao’s

ABC i s usually
one order of
magni tude better
than that of the
second
-
order
Mur’s
.

Liao’s

The Hi gdon Boundary
Operator i s very
advantageous si nce i t
i nvol ves normal
deri vati ve onl y. It
produces hi gher l evel s
of absorpti on over
mul ti pl e angl es, and
has the same degree
of accuracy as the
second
-
order
Mur

wi th added fl exi bi l ity
of broadeni ng the
absorpti on band

Higdon

More recentl y,
Berenger

i nvented a
more sophi sti cated
ABC, cal l ed the
Perfectl y Matched
Layer (PML)
techni que. Thi s
techni que arti fi ci ally
creates a non
-
physi cal
absorbi ng medi um
(PML medi um)
adjacent to the outer
boundary of the FDTD
space

PML

FDTD Implementation


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
:





where


ω

is
2
π
f

and
f

is the frequency of the pulse


t

is
[(
N

)


t
o
] and
N

is the number of time steps



t

is the time step


t
o

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



Source Excitation

11

Desi gn & Opti mi sati on of a PIFA usi ng GA

FDTD Implementation

Fig 3. Excitation Gaussian Pulse

E vs. N

FDTD Implementation


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,

S
11

which

is

the

reflection

coefficient,

can

be

evaluated

and

consequently

the

VSWR

is

calculated

as





VSWR

is

calculated

for

several

frequencies

in

the



2
GHz

band,

ranging

from

1
.
9
GHz

to

2
.
5
GHz
.



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

Performance Evaluation

12

Desi gn & Opti mi sati on of a PIFA usi ng GA

GA Optimisation


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
.



Genetic Algorithms Concept

13

Desi gn & Opti mi sati on of a PIFA usi ng GA

GA Optimisation


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
.



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
.

Fig 5. Working principles of a simple GA process

14

Desi gn & Opti mi sati on of a PIFA usi ng GA

Begin

Initialise population

Crossover

Mutation

Reproduction

Evaluation

Assign fitness

Stop

Gen = Gen + 1

Gen = 0

Yes

No

Condition
satisfied?

Working principles

GA Optimisation


In

this

project,

the

set

of

solutions

was

first

coded

in

binary

string

structures

and

Binary
-
Coded

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
.

GA optimisation techniques

15

Desi gn & Opti mi sati on of a PIFA usi ng GA

In the Bi nary
-
Coded GA
(BCGA), the basi c bl ock
of the geneti c
al gori thm i s the
chromosome.

Each chromosome i s
composed of genes
descri bed as a bi nary
sequence of zeros and
ones.

Each gene i s associated
wi th a parameter to be
opti mi zed.

BCGA

Real coded GA (RCGA)
represents parameters
wi thout coding, which
makes representation of
the solutions very cl ose to
the natural formulation of
many problems.

Real
-
world optimization
probl ems often i nvolve a
number of characteristics,
whi ch make them difficult
to sol ve up to a required
l evel of satisfaction

RCGA

GA can sometimes get
stuck on sub optimal
sol ution wi thout any
progress to the real
opti mal solution.

One of the possible
sol ution to this problem is
to mai ntain a population
si ze as l arge as possible.
However, maintaining
l arge population i nvolve
hi gh cost to evaluate each
i ndividual. Therefore to
reduce the cost of
eval uation and accelerate
the convergence the
Hybri d Cl ustering GA i s
applied i n this work

Clustering

GA Optimisation

GA experimentation

16

Desi gn & Opti mi sati on of a PIFA usi ng GA


The population strings are represented as shown in Fig. 6 below:







where X
i

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
f
x
, the next 2 bits the parameter
f
z

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.

Binary
-
Coded
GA


After experimenting the BCGA, RCGA was experimented to compare the convergence
and precision of the optimization process


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 .

Real
-
Coded GA

f
x

f
z

h


X
1

X
2

X
3

X
4

X
5

Fig. 6. Population string known as chromosome

GA Optimisation

GA experimentation

17

Desi gn & Opti mi sati on of a PIFA usi ng GA


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.












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

Clustering
GA

Fig. 7. Conventional GA vs. Clustered GA

Simulation


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
.



18

Desi gn & Opti mi sati on of a PIFA usi ng GA










Hi gh peaks at the
boundari es

refl ecti on of the waves at
the boundary causes
stati onary waves resul ti ng
to smal l standing waves
i nsi de the FDTD space

Wi thout

.









Good absorpti on of the
fi el ds

Not enough si gni fi cant
attenuati on

Hi gdon

.









Good absorpti on

Does not requi re
knowl edge fi el ds adjacent
to the cel l s

Does not perform wel l at
l ow frequency & Large
computati onal ti me

Dispersed

.









Provi des
refl ecti onl ess

boundary over broad
spectrum

Achi eves mi ni mal i n
computati onal cost and
memory requi rement

Mur’s


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
:

Absorbing Boundary Condition Simulation

19

Desi gn & Opti mi sati on of a PIFA usi ng GA

Simulation

Simulation


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
.



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

24
hrs


to

display

a

single

value

of

the

VSWR

on

a



Pentium

4
,

1
.
86
GHz

computer

and

took

more



than

3

days

on

a

slightly

less

powerful

machine


Fig 8. FDTD Mesh Size

FDTD mesh size

20

Desi gn & Opti mi sati on of a PIFA usi ng GA

Results


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
.













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

f
x

and

f
z
.

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

2
mm)

since

the

idea

of

the

project

is

to

maximise

the

bandwidth

of

the

PIFA

while

keeping

the

overall

dimensions

constant
.


Fig 9. Top and Side views of PIFA to be modelled

PIFA Modelled

21

Desi gn & Opti mi sati on of a PIFA usi ng GA

Results


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

Frequency Range

22

Desi gn & Opti mi sati on of a PIFA usi ng GA

Fig 11. E
-
field Propagation











The Bi nary Coded GA has proved to
be a very good opti mi si ng tool and i f
used properl y, i t may serve to sol ve
vari ous probl ems of search and
opti mi sati on.

Cl assical opti mi sing methods woul d
take much l onger ti me to fi nd the
opti mal sol uti on as compared to the
Bi nary GA method.

However, the opti mi sati on does not
al ways converge to the opti mal
sol uti on and someti mes get di verted
to some other sub
-
opti mal sol uti on.

BCGA











The Real Coded GA has been chosen
as the al ternati ve for Bi nary Coded
GA. The most i mportant feature of
the RCGA has been observed to be
the capaci ty to expl oi t l ocal
conti nui ti es.

Owi ng to the user of real
parameters i n RCGA, l arge domai ns
for the vari ables can be used as
opposed to BCGA i mpl ementati ons
where i ncreasi ng the domai n woul d
decrease the preci si on.

RCGA











The Hybri d GA by cl usteri ng, on the
other hand, has shown to converge
faster to the opti mal sol uti on.
Popul ati on si ze coul d be i ncrease
wi thout affecti ng the performance
of the opti mi sati on usi ng the Hybri d
GA by cl usteri ng.

The convergence l ooks si mi l ar to the
RCGA but performance i s much
better because of the FDTD
eval uati on of onl y the
representati ves of each cl uster.

Cl ustering

GA Outcome

23

Desi gn & Opti mi sati on of a PIFA usi ng GA

Results

Future Work


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
.

FDTD 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
.

GA Improvement

24

Desi gn & Opti mi sati on of a PIFA usi ng GA

Thank you…

Desi gn & Opti mi sati on of a PIFA usi ng GA

25

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
.