Design & Optimisation of a PIFA Antenna using Genetic Algorithms

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

Problem Formulation • Process Overview • PIFA Modelling • FDTD Implementation • GA Optimisation • Simulation & Results • Future Work Agenda Design & Optimisation of a PIFA using GA

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 Problem Formulation Design & Optimisation of a PIFA using GA

Process Overview Design & Optimisation of a PIFA using GA

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. PIFA Modelling Fig 1. Geometry of a simple PIFA Geometry of PIFA to be modelled Design & Optimisation of a PIFA using 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. • A simple virtual model can be more flexible and much cheaper. PIFA Modelling Modelling Techniques Design & Optimisation of a PIFA using GA

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 Implementation Design & Optimisation of a PIFA using GA

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 FDTD Implementation Fig 2. An FDTD cell or Yee cell showing the positions of electric and magnetic field components FDTD Space Design & Optimisation of a PIFA using 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. FDTD Implementation Absorbing Boundary Conditions Design & Optimisation of a PIFA using GA

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 2πfand f is the frequency of the pulse t is [(N ) – to] and N is the number of time steps ∆tis 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 E vs. N FDTD Implementation Fig 3. Excitation Gaussian Pulse Source Excitation Design & Optimisation of a PIFA using GA

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). FDTD Implementation Fig 4. Graph of VSWR vs. Frequency Performance Evaluation Design & Optimisation of a PIFA using GA

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

Begin Initialise population Gen = 0 Evaluation Assign fitness No Condition satisfied? Gen = Gen + 1 Yes Reproduction Stop Crossover Mutation • 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. GA Optimisation Fig 5. Working principles of a simple GA process Working principles Design & Optimisation of a PIFA using GA

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 GA optimisation techniques Design & Optimisation of a PIFA using GA

X1 X2 X3 X4 X5 fx fz h Fig. 6. Population string known as chromosome GA Optimisation GA experimentation Design & Optimisation of a PIFA using GA

Fig. 7. Conventional GA vs. Clustered GA GA Optimisation GA experimentation Design & Optimisation of a PIFA using GA

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

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: Simulation Absorbing Boundary Condition Simulation Design & Optimisation of a PIFA using GA

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 Simulation Fig 8. FDTD Mesh Size FDTD mesh size Design & Optimisation of a PIFA using GA

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 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 Results PIFA Modelled Design & Optimisation of a PIFA using GA

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. Results Fig 10. Graph of VSWR vs Frequency Fig 11. E-field Propagation Frequency Range Design & Optimisation of a PIFA using GA

Results GA Outcome Design & Optimisation of a PIFA using GA

Future Work Design & Optimisation of a PIFA using GA

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, MingooChoi, JangHwanChoi, and SeongOok 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

Design & Optimisation of a PIFA Antenna using Genetic Algorithms