Design & Optimisation of a PIFA Antenna using Genetic Algorithms

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Design Optimisation of a PIFA Antenna using
Genetic Algorithms
Mphil / PhD Project

• Ameerudden M. Riyad
• Prof. H.C.S. Rughooputh

Electronics Communication Engineering
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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.

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Agenda

• Problem Formulation
• Process Overview
• PIFA Modelling
• FDTD Implementation
• GA Optimisation
• Simulation Results
• Future Work

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Problem Formulation

• 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.

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Process Overview
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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
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PIFA Modelling

• 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.

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

Modelling Techniques
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FDTD Implementation

• 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.

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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
  Maxwells 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
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FDTD Implementation

• 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
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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
• ? is 2pf 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.
• t 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

Fig 3. Excitation Gaussian Pulse
Source Excitation
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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, S11 which is the reflection
  coefficient, can be evaluated and consequently
  the VSWR is calculated as
• 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
Performance Evaluation
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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
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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
Working principles
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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
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GA Optimisation
Fig. 6. Population string known as chromosome
GA experimentation
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GA Optimisation
Fig. 7. Conventional GA vs. Clustered GA
GA experimentation
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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.

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Simulation

• Simulation was carried out initially on different
  absorbing boundary conditions (Higdon, Dispersed,
  Murs) as well as without any absorbing boundary
  condition.
• Following are the simulation results

Absorbing Boundary Condition Simulation
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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 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

Fig 8. FDTD Mesh Size
FDTD mesh size
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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 Murs 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 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.

Fig 9. Top and Side views of PIFA to be modelled
PIFA Modelled
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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
Fig 11. E-field Propagation
Frequency Range
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Results
GA Outcome
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Future Work
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Thank you

• 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.9095, 2000.