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DIELECTRIC RESONATOR REFLECTARRAY ANTENNA IN KU-BAND NUR IZYANI BINTI DZULKIPLI A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Engineering (Electrical) Faculty of Electrical Engineering Universiti Teknologi Malaysia JULY 2014

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DIELECTRIC RESONATOR REFLECTARRAY ANTENNA IN

KU-BAND

NUR IZYANI BINTI DZULKIPLI

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Engineering (Electrical)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

JULY 2014

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Specially dedicated to muslim brothers and sisters around the world, may be benefits

to the community.

For family, lectures and friends,

thanks for support, teach, guide and pray for me.

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iv

ACKNOWLEDGEMENT

Alhamdulillah, Praise to Allah S.W.T for His blessing and guidance that has

inspired me through this project which was able to be completed within the required

time and gain enormous knowledge that is useful for the future undertaking.

I would like to gratitude to my supervisor and co-supervisor, Dr Mohd Haizal

Jamaluddin and Dr. Mohd Fairus MohdYusoff for their support, guidance, advice

and willingness to help me in completing my master project.

I would also like to thank all the WCC staffs for their valuable support and

discussion during my master. A special thanks to Mr Norhafizul Ismail for their help

in to use the facilities to measure the performance of the antenna.

I also want to dedicate my appreciation to my entire colleague for all the help

and assistance during my project especially to Libriati Zadarsti, Aminiril Anisah,

Suhanis Sufian, Raihan Zulkefly, Wan Azza Zainol Rashid, Nur Shazwani, and all

my beloved sisters.

I also want to give special appreciation my family for their support through

my study here in UTM. I would thanks to my parents, Dzulkipli bin Othman,

Mahani Rowi and Samisah Samad for all the love their gives to me, pray, moral

support along my study.

Alhamdulillah, I have managed to complete the project and gained valuable

knowledge and experience during that time. May Allah S.W.T repay all their

kindness and bless all of us. AMIN

.

.

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v

ABSTRACT

Direct broadcasting satellite has become a vital system in satellite

communication globally especially for digital broadcasting purposes. Currently, a

parabolic antenna is normally used for this application, however the advantages of

reflectarray which is flat in shape and possibility for beam steering capability make

the reflectarray antenna is one of the interesting topic to be studied. At the current

time, many reflectarrays are based on microstrip technology. Nevertheless, at high

frequency the conductor loss is high and the antenna efficiency will be reduced. An

interesting solution is to use dielectric resonator antennas (DRAs) as the reflectarray

elements. In facts, DRA can give low loss and high bandwidth. In this thesis, firstly

four different slots with alphabets underneath the rectangular DRA have been

investigated as unit-cell for reflectarray. A new structure of rectangular DRA with C-

shaped slot unit-cell has been proposed which can give high phase range (321.9o)

and low loss (0.3685o). This structure is then being validated experimentally in Ku-

Band. Next, the mutual coupling effects between unit-cell in the reflectarray are

studied and a simulation technique based on Finite Different Time Domain (FDTD)

is proposed. By doing so, this simulation technique is most suitable to predict the

actual reflectarray radiation pattern. Finally, the reflectarray antenna composed of 24

x 24 unit-cells based on DRA with C-shaped slot is proposed at 12 GHz.

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ABSTRAK

Penyiaran satelit langsung telah menjadi satu sistem yang penting dalam

komunikasi satelit global terutamanya untuk tujuan penyiaran digital. Pada masa ini,

penggunaannya menggunakan antena parabola, namun kelebihan reflectarray dalam

bentuk yang rata dan kemungkinan untuk keupayaan stereng rasuk membuat antena

reflectarray adalah salah satu topik yang menarik untuk dikaji. Pada masa kini,

banyak reflectarray adalah berdasarkan kepada teknologi mikrostrip. Walau

bagaimanapun, pada frekuensi tinggi, kehilangan konduktor adalah tinggi dan

kecekapan antena akan dikurangkan. Satu penyelesaian yang menarik adalah dengan

menggunakan antena resonator dielektrik (DRA) sebagai elemen reflectarray.

Malahan, DRA boleh memberi kerugian yang rendah dan jalur lebar yang tinggi.

Dalam tesis ini, untuk langkah awal, empat lubang yang berbeza dengan bentuk

huruf direka bentuk di bawah DRA segi empat tepat telah disiasat sebagai unit-sel

untuk reflectarray. Satu struktur baru DRA segi empat tepat dengan berbentuk

lubang-C unit-sel telah dicadangkan, di mana ia boleh memberi pelbagai fasa yang

tinggi (321.9o) dan kerugian yang rendah (0.3685

o). Struktur ini kemudiannya yang

disahkan secara eksperimen di Ku-Band. Seterusnya, kesan gandingan bersama

antara unit-sel dalam reflectarray dikaji dan teknik simulasi berdasarkan Finite

Different Time Domain (FDTD) dicadangkan. Dengan berbuat demikian, teknik

simulasi ini adalah yang paling sesuai digunakan untuk meramal corak sinaran

reflectarray sebenar. Akhir sekali, antena reflectarray yang terdiri daripada 24 x 24

unit-sel berdasarkan DRA dengan berbentuk lubang-C adalah dicadangkan pada 12

GHz.

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TABLES OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF ABREVIATIONS xvii

LIST OF SYMBOLS xviii

LIST OF APPENDICES xix

1 INTRODUCTION

1.1. Introduction

1.2. Problem Statement

1.3. Objectives of The Research

1.4. Scope of The Research

1.5. Organization of the Thesis

1

3

4

4

5

2 LITERATURE REVIEW

2.1. Introduction

2.1.1 Principle of Reflectarray Antenna

2.1.2 Microstrip Antenna

2.2 Dielectric Resonator Antenna

2.2.1. DRA Feeding Technique

8

8

13

15

17

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viii

2.2.1.1 Microstrip Line Coupled to

Dielectric Resonator Antenna

2.2.1.2 Probe Coupled to Dielectric

Resonator Antenna

2.2.1.3 Slot-Loaded/ Aperture-Coupled

Dielectric Resonator Antenna

2.2.1.4 DRA Reflectarray

2.3 Summary

17

18

19

21

22

3 DESIGN AND CHARACTERISATION OF

UNIT-CELL

3.1. Introduction

3.2. Basic Design Simulation

3.2.1 Defining the Boundary Condition

3.2.2 Defining Waveguide Port

3.3 S Dielectric Resonator Antenna at Ku-Band

(With Feed)

3.3.1 Dielectric Resonator Antenna Size

3.3.2 Substrate

3.4 Basic Design of Dielectric Resonator

Reflectarray Antenna

3.5 Description of the Slot-Loaded DRA (DRA

with Line Slot)

3.6 DRA with Different Alphabet Shape Slot

3.7 Comparison with the „Full-Substrate‟

Configuration

3.8 Validation of DRA and Full-Substrate

Structure

3.8.1 Fabrication and Measurement Setup

3.8.2 Results and Discussion

3.9 Summary

23

24

24

25

25

26

27

29

32

34

39

42

42

45

48

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4 STUDY OF MUTUAL COUPLING EFFECT IN

REFLECTARRAY ENVIRONMENT

4.1. Introduction

4.2. Simulation Approaches Proposed Antenna

Structure

4.2.1. FDTD Floquet

4.2.2. „Isolated element‟ approach

4.2.3. Neighbouring element

4.2.4. Simulation comparisons between

different approaches

4.3. Concept and definition

4.4. Coupling effects from several neighbouring

unit-cells on the phase variation

4.4.1. Identical unit-cells

4.4.2. Non Identical unit-cells

4.5. Prediction of overall DRA reflectarray

4.6. Summary

50

51

51

52

53

53

55

56

57

58

63

67

5 DESIGN AND CHARACTERISATION OF DRA

REFLECTARRAY

5.1 Introduction

5.2 General Overview of DRA Reflectarray

5.3 Antenna Design

5.3.1 DRA unit-cell

5.3.2 Horn Antenna

5.3.3 Antenna Array

5.4 Overall DRA Reflectarray

5.4.1 Simplified calculation

5.5 Summary

68

68

69

69

71

73

76

77

78

6 CONCLUSIONS AND RECOMMENDATIONS

6.1 Summary

6.2 Future work

79

80

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REFERENCES 82

Appendices A-E 86

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LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 Resonance frequency and return loss for different

dimension of DRA 27

3.2 Simulation result of different substrate thickness 29

3.3 Parameters of basic structure design of single unit-cell 30

3.4 Summary- Selection of alphabet shape slot 38

4.1 Gain and directivity of DRA reflectarray at 30 GHz 67

5.1 Design specification of single unit-cell 70

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Photo of parabolic reflect array for space

applications 2

1.2 Flow chart of whole project 6

2.1 Combination of (a) reflector antenna and (b) array

antenna which produces (c) reflectarray antenna 9

2.2 Process of a unit-cell model for reflectarray

element 10

2.3 Principle of a reflectarray antenna with

compensation of different paths 11

2.4 Phase delay variation of unit-cell 12

2.5 Various types of printed reflectarray antenna (a)

patch (b) slot and (c) stub 13

2.6 Techniques to reduce backward radiation, (a)

bottom conducting plate and (b) slot apertures

directly in the patch 14

2.7 Rectangular dielectric resonator antenna (a)

truncated dielectric waveguide and (b) DRA on

ground plane 15

2.8 Microstrip line coupled to the dielectric resonator

antenna (a) side coupling and (b) direct coupling 18

2.9 Probe coupled to the dielectric resonator antenna

(a) probe adjacent to the DRA and (b) probe

embedded to DRA 18

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2.10 Dielectric resonator antenna coupled to a

microstrip-fed slot in the ground plane [29] 20

2.11 Return loss for slot coupled to dielectric resonator

antenna (a) Ls = 3.33cm, (b) Ls = 2.67cm, (c) Ls =

2.33cm and (d) Ls = 2cm [29]. 20

2.12 DRA with metallic strip on the top 22

3.1 Boundary condition setting in CST MWS 24

3.2 Basic rectangular DRA (a) 3D view, (b) top view

and (c) side view 26

3.3 Simulation result for different dimensions of DRA

(a) 8 x 8 x 2 mm3, (b) 9 x 9 x 3 mm3 and (c) 10 x

10 x 2 mm3

27

3.4 Simulation result for different material of substrate 28

3.5 Basic structure of dielectric resonator reflectarray

antenna 30

3.6 Reflection coefficient of the basic structure of

dielectric resonator reflectarray antenna for a

single unit-cell (a) amplitude of S11 and (b) phase

of S11 31

3.7 Single unit-cell of dielectric resonator reflectarray

antenna loaded with line slot (a) 3D view and (b)

side view 32

3.8 Reflection coefficient of DRA reflectarray with

line slot (a) phase of S11 and (b) amplitude of S11 33

3.9 Four different shape slots (a) H-shape, (b) U-

shape, (c) C-shape and (d) E-shape 34

3.10 Phase of S11 versus length of slot a for (a) a/b =

1.25 mm, (b) a/b = 1.5 mm and (c) a/b = 1.75 mm 36

3.11 Reflection coefficient of different shape at 12 GHz

(a) phase of S11 and (b) amplitude of S11 37

3.12 3D view of the full substrate 39

3.13 Reflection amplitude (a) square DRA and (b) full

substrate 40

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3.14 Reflection coefficient of square DRA and full

substrate (a) amplitude of S11 and (b) phase of S11 41

3.15 Measurement setup 43

3.16 Geometry of dual unit-cell (a) illustration of dual

unit-cell, (b) dual unit-cell with different size of

slot and (c) dual unit-cell without DRA, square

DRA and full substrate 44

3.17 Reflection coefficient of dual unit-cell (a)

simulation result forsquare DRA, (b) measurement

result for square DRA, (c) simulation result for full

substrate and (d) measurement for full substrate. 47

3.18 Reflection phase of (a) square DRA and (b) full

substrate 48

4.1 Floquet simulation approach (a) infinite periodic

element (b) Floquet boundary condition 52

4.2 Isolated element approach. 52

4.3 Neighbouring element approach 53

4.4 DRA unit-cell structure [61] 54

4.5 Phase variation of each approach 54

4.6 Mutual coupling between two unit-cells. 55

4.7 Illustration of mutual coupling effect based on the

neighbouring-element approach and quasi-Floquet

approach 56

4.8 Phase variation comparison between quasi-Floquet

and Floquet. 57

4.9 Geometry arrangement of identical unit-cells (a)

strip length = 0.7 mm (b) strip length = 1.4 mm (c)

strip length = 2.1 mm 58

4.10 Phase variation of identical unit-cell for different

strip length. 58

4.11 Four cases for different geometry arrangements of

non-identical cells 59

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xv

4.12 Phase variation comparison of non-identical and -

illuminated unit-cells in E-plane 60

4.13 Phase variation comparison of non-identical and

non-illuminated unit-cells in H-plane 61

4.14 Geometry arrangement of non-identical and

illuminated unit-cells in E-plane case 62

4.15 Phase variation comparison of non-identical and

illuminated unit-cells in E-plane case. 62

4.16 Phase variation comparison of two non-identical

configuration and illuminated unit-cells in E-plane

case. 63

4.17 Measured vs. simulated radiation pattern for array

factor concept and neighbouring-element method;

(a) E-plane co-polar (b) H-plane co-polar. 65

4.18 The illustration to the concept of the coupling

effect for each unit-cell in the DRA reflectarray

layout. 66

5.1 Overall design of DRA reflectarray 69

5.2 Single unit-cell with C-shape slot loaded to the

DRA 70

5.3 Radiation pattern of DRA unit-cell using FDTD

with slot length = 5 mm 71

5.4 Illustration of horn antenna 72

5.5 Radiation pattern of horn antenna at 12 GHz for E-

plane and H-plane 72

5.6 Illustration for horn antenna located in E-plane 73

5.7 Colour plot of phase at each unit-cell (in degree) 74

5.8 Procedure to determine the length of the slot at

each unit-cell based on the phase at unit-cell 75

5.9 Conversion of Фcell (m,n) to slot length 75

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5.10 Illustration of final layout. 75

5.11 Radiation pattern of 24 x 24 cells reflectarray 78

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LIST OF ABBREVIATION

cm - Centimeter

CST MWS - Computer Simulation Technology Microwave Studio

dB - Decibel

dBi - Decibels with respect to isotropic

DBS - Direct Boardcast Satellite

DRA - Dielectric Resonator Antenna

E-plane - Electric Plane

FDTD - Finite Different Time Domain

FR-4 - Flame Retardant-4

GHz - Gigahertz

H-Plane - Magnetizing Field

MATLAB - Matrix Laboratory

mm - Milimeter

PEC - Perfect Electric Conductor

PMC - Perfect Magnetic Conductor

PTFE - Polytetrafluoroethylene

RT-Duroid - Rogers

TE - Transverse Electromagnetic

TM - Transverse Magnetic

TEM - Transverse Electromagnetic Mode

VNA - Vector Network Analyser

WR - Waveguide Rectangular

WGS - Waveguide simulator

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LIST OF SYMBOLS

o - Degree

- Disturbance factor

s - Distance between the microstripline and DRA

E

- Electric field

f - Frequency

S - Incident wave

Ls - Length of the slot

Ω - Ohm

- Permittivity

Ф - Phase

π - Phi

fo - resonant frequency

C - Speed of light

S11 - S-parameter from port one for a signal incident on port one

θ - Theta

n

- Unit vector normal

λ - Wavelength

k0 - wave number

kx, ky, kz - wavenumber along x, y and z directions

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A List of Author‟s Publication 86

B Calculation of DRA Size 89

C Overall Radiation using FDTD 91

D WR-90 DATASHEET 101

E Layout of Array Antenna 104

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CHAPTER 1

INTRODUCTION

1.1 Introduction

In the era of information technology, the utilization of satellite

communication that is designed originally for sending telephone, radio,

television and other signals across the country and around the world has

become more popular recently. Nowadays, the major source of revenue for

satellite communication industry is the television satellite broadcasting.

Television satellite is able to deliver a few signals of large bandwidth to

many receivers and becomes a more precise match for the capabilities of

geosynchronous communication satellite. One of the technology that is used

for Direct-To-Home satellite television service is Direct Broadcast Satellite

(DBS).

As the name implies, DBS is a system that distributes television

signals by broadcasting directly from satellite to end-user. The ability of DBS

is to deliver hundreds of television channels and confidential information to

millions of people around the world without being connected to the wires.

In order to receive DBS, subscriber antennas should possess high gain

characteristic [1]. Conventionally, in order to have high gain characteristic

antennas, most of the antennas often used parabolic reflector, which is

generally bulky in size and large in mass. As a solution, reflectarray antenna

has been developed extensively to accomplish the requirement of the mission

of DBS. This new type of antenna was presented in the early 1960s [2].

Reflectarray antenna is the suitable choice for space applications such as

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2

earth remote sensing and space exploration [3]. It is because this type of

antenna is able to reradiate and scatter the incident field with electrical phases

that is required to form a planar phase front in the far-field distance [4]. In

addition, reflectarray antenna can be designed to fulfill all the typical

requirements of a transmitted and received DBS antenna that provides the

electrical requirements [5]. The reflectarray antenna design for DBS has been

presented in literature [5, 6].

There are a lot of advantages using reflectarray antenna. One of the

advantages is the ability to achieve very good efficiency for a large aperture.

However, the use of metal waveguides in the reflectarray antenna leads to a

large and bulky structure, and the antenna is mostly languished in the

literature for many years [7].

Figure 1.1: Photo of parabolic reflect array for space applications [4].

Basically, reflectarray antenna is a combination of the features of

phased array antenna and reflector antenna. Then in the early 1960s, the first

concept of reflectarray antenna was introduced in the waveguide reflectarray.

The capability of achieving co-phasal reradiated far-field beams has been

demonstrated. However, the antenna is still bulky and heavy because it

operates at relatively low microwave frequencies.

As time goes on, in the late 1980s and early 1990s, printed

(microstrip) antenna was developed [8]. With advantages such easy

deployment in space, reducing cost production, low weight, flatness and

flexible electrical performance in terms of feeding, polarization control, beam

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steering, amplification and multiple beam capability, a lot of researchers have

contributed to this field. Nevertheless, for microstrip reflectarray at

millimeter-waves, the efficiency of the antenna may be reduced significantly

and the conductor loss becomes severe. Based on all these facts, the author

has been motivated to propose a new design of reflectarray antenna.

The new reflectarray antenna design consists of dielectric resonator

antenna (DRA) unit-cell loaded with alphabet shape slot. Due to the

interesting features of DRA such as low loss, broad bandwidth small mutual

coupling effect and higher radiation efficiency, thus DRA has become the

main subject of the study. Meanwhile, in order to excites the magnetic fields

in the DRA [9], alphabet shape slot is loaded as the main frequency tunable

for the DRA. Alphabet shape slot is chosen due to the various geometries.

1.2 Problem Statement

Most long distance wireless communication such as DBS requires

high gain antenna operation. Conventionally, it has to rely on the parabolic

reflector antenna. However, most of the structure of parabolic reflectors

caused the antenna difficult to be implemented, especially at higher

microwave. This is due to the specific parabolic curve [4]. Designing the

reflector antenna in a specific parabolic antenna has led to the antenna being

slow and has narrow angle beam scanning. Furthermore, the large number of

amplifiers and complicated beamformer are needed in the feed network,

which makes the phased array antenna becomes very expensive. As an

alternative, reflectarray antenna has been proposed in this thesis, which is

much simpler and has reliable folding mechanism due to the flat structure [4].

The features of reflectarray antenna have shown that the viability of

this technology are able to transmit and received space antenna for

telecommunications and broadcasting [5]. Recently, many investigation of

reflectarray antenna are based on microstrip design [8, 10, 11]. The unit-cell

of microstrip reflectarray will be controlled to provide higher efficiency for

very large aperture. It can also has its main beam designed to tilt at a large

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4

angle from its broadside direction. Nevertheless, at high frequencies, the

conductor loss of microstrip reflectarray becomes severe [12]. In addition,

the mutual coupling effect of microstrip element that printed on the substrate

becomes noteworthy [13]. Due to this drawback, this thesis proposes a new

reflectarray antenna based on DRA. DRA is an interesting element that can

provide low loss and high bandwidth compared to microstrip antenna.

In order to design the overall antenna, the reflectarray environment

from the non-identical unit-cells is considered. This is due to the different

phase shift at each unit-cell. Unfortunately, most of the approach in the unit-

cell analysis has been carried out for the single unit-cell [11, 14] which

assumes that all unit-cell in the array is identical which is not true in reality.

Therefore, the mutual coupling effects between the unit-cell in the

reflectarray antenna are studied.

1.3 Objectives of the Research

The objectives of this research are:

1) To design, fabricate and test a new unit-cell based on DRA that can give

high phase range approximate to 360˚ or more.

2) To design a reflectarray antenna that is based on DRA.

3) To investigate a new simulation technique based on Finite Different

Time Domain (FDTD) that can analyse mutual coupling effect and

predict the overall radiation pattern of reflectarray.

1.4 Scopes of the Research

In order to fulfill the objectives of the study, this project involves with

designing a new unit-cell based on a rectangular DRA as the reflectarray

element. A slot has been loaded underneath the unit-cell that acts as the

tuning parameter to control the phase of the reflection coefficient. Four

different alphabet shape slots have been investigated in order to have a large

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phase range. The large achievable phase range and low loss (insertion loss

less than 1 dB) will be the main goal to design a better performance of the

reflectarray element. The unit-cell will be designed at 12 GHz for DBS. The

design is simulated using commercial CST software. Meanwhile, the

fabrication and measurement have been carried out using WR 90 waveguide.

This thesis also studies the disturbance phenomena inside the

structure, which is called mutual coupling effect. The simulation technique to

analyse the mutual coupling effect in reflectarray environment is based on

FDTD, which includes the coupling effect from the actual neighbouring unit-

cell. A new method based on FDTD is introduced to predict the radiation

pattern of the overall DRA reflectarray.

Finally, the whole reflectarray antenna with 24 x 24 elements is

designed and simulated. This DRA reflectarray is designed at broadside

radiation.

1.5 Organization of the Thesis

Basically, in this thesis, the flow of the whole project is present in

Figure 1.2 below:

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Figure 1.2: Flow chart of whole project

This thesis is organized into four main chapters and one final chapter

for the conclusion. The flow of each chapter is briefly described in the

following paragraphs.

Chapter 1 presents the general introduction of this research. This

includes the background study of the reflectarray antenna and the problem

occurs in the development of reflectarray element that gives the motivation

for further study this research. In addition, the objectives need to be achieved

and the scopes of the research have been determined in order to design the

new unit-cell of the reflectarray antenna.

Chapter 2 presents a basic literature review that is related to the

design. This gives an overview about the history of the development of the

reflectarray antenna since its invention. The development has shown that the

reflectarray antenna becomes popular in the current research field. This

includes the usage of printed microstrip reflectarray antenna that has been

produced in various forms to achieve the best performance in designing

reflectarray antenna. This chapter also explains the concept, most significant

features, advantages and disadvantages of the reflectarray element followed

by the DRA that will be used to design as a new unit-cell reflectarray

antenna.

The third chapter focuses on designing the new unit-cell in the

simulation and fabrication process. The steps taken have been discussed,

END

Design an element of dielectric

resonator antenna reflectarray

loaded with alphabet shape slot

Study mutual coupling effect

Design and simulate DRA

reflectarray antenna

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including the determination of size of DRA, the waveguide port setting,

defining the boundary condition and the inter-element spacing. In order to

have a better performance in designing the reflectarray antenna, four different

alphabet shape slots have been investigated and discussed in this chapter. In

the end, the best unit-cell is selected as the reflectarray element. In addition, a

„full substrate‟ has been introduced to investigate the operating principle of

the proposed unit-cell.

The fourth chapter discusses about the mutual coupling effects in the

reflectarray environment. It is found that the nearest neighbouring unit-cell in

E-plane has a large mutual coupling effect compared to the neighbouring

unit-cell located at H-plane. A simulation technique based on FDTD has been

proposed to predict the overall radiation pattern of the reflectarray. A

reflectarray prototype that operates at 30 GHz [15] has been chosen as the

benchmark. A good agreement between simulation and measurement results

has been discussed in this chapter.

The fifth chapter discusses the overall design of DRA reflectarray

antenna. This also includes the horn antenna design and the procedure to

define the dimensions of each unit-cell of the DRA reflectarray. The overall

conclusion is given in the last section of the thesis.

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