An investigation on the possibility for bandwidth improvement of dielectric antennas via modification of their geometry

DEGREE PROJECT IN TECHNOLOGY, SECOND CYCLE, 30 CREDITS

STOCKHOLM, SWEDEN 2020

An investigation on the possibility for bandwidth improvement of dielectric antennas via modification of their geometry

Nandan Dutta Chaudhury

KTH ROYAL INSTITUTE OF TECHNOLOGY

Author

Nandan Dutta Chaudhury <nandandc@kth.se>

School of Electrical Engineering and Computer Science KTH Royal Institute of Technology

Place for Project

Department of Antenna Technology and Electromagnetic Modelling

Fraunhofer Institute for High Frequency Physics and Radar Techniques FHR Fraunhoferstraße 20, 53343 Wachtberg

Germany

Examiner

Prof. Lars Jonsson

School of Electrical Engineering and Computer Science KTH Royal Institute of Technology

Supervisors

Andrej Konforta (Fraunhofer FHR) and Ahmad Emadeddin (KTH)

Abstract

The dielectric antenna is an interesting alternative to a metallic antenna. This is mainly due to its low manufacturing cost and the possibility to fabricate complex antenna geometry with the aid of additive manufacturing (AM). Sophisticated AM technology provides new degrees of freedom in shaping the outer and inner geometry of antennas.

This feature can be utilized to optimize various properties of antenna, such as its bandwidth, radiation pattern etc, while maintaining a compact geometry.

This master thesis investigates the possibility of improving the bandwidth of a compact dielectric antenna by modifying its geometry. Specifically, dielectric resonator antennas (DRAs) have been considered here. In this connection, two embedded cylindrical DRAs operating within 8 GHz-17 GHz frequency band have been designed and simulated using Ansys HFSS. For the first design (Design-1), a bandwidth (corresponding to reflection coefficient ≤ -10dB) of approximately 63%

has been obtained and the second design (Design-2) has a bandwidth (corresponding to reflection coefficient ≤ -10dB) of about 57%. However, in terms of radiation characteristics, the performance of Design-2 has been found to be superior compared to Design-1, mainly due to its symmetrical geometry. Furthermore, the two designs have been compared to an existing compact rectangular embedded DRA. It has been found that both Design-1 and Design-2 have comparatively wider bandwidth. With respect to the radiation characteristics, the performance of the reference antenna and Design-2 are similar. While, the radiation performance of the reference antenna is found to be better than Design-1.

Keywords

Multifunctional antenna array, AESA, Additive manufacturing, Stereolithography,

Ultra-wideband antenna, Dielectric antenna, Embedded DRA, PSF

Abstrakt

Dielektriska antenner är ett intressant alternativ till metalliska diton. Detta beror dels på lägre tillverkningskostnader men också, tack vare additiva tillverkningsmetoder, på grund av möjligheten att använda komplexa geometrier. De senaste årens framsteg inom additiv tillverkning har öppnat upp nya möjligheter vid designen av den externa och den inre geometrin hos dielektriska antenner. Detta kan utnyttjas till att optimera olika aspekter hos antennen, exempelvis bandbredd och strålningsmönster, utan att påverka de yttre måtten.

Denna avhandling studerar möjligheten att förbättra bandbredden hos dielektriska resonansantenner (DRA) genom att modifiera deras inre. Två cylindriska DRA:er, verksamma inom 8-17 GHz, har designats och simulerats i Ansys HFSS. Bandbredder om 63 % för Design-1, samt 57 % för Design-2, erhölls. Trots den första designens större bandbredd uppvisar Design-2 bättre strålningsegenskaper, främst avseende antennens strålningsmönster. De simulerade antennerna har också visat sig ha större bandbredd jämfört med en redan existerande kompakt, inbäddad DRA. Sett till strålningsegenskaper är prestandan hos Design-2 jämförbar med referensantennen, medan design ett uppvisar sämre prestanda.

Nyckelord

Multifunktionell antenngrupp, AESA, Additiv tillverkning, Stereolitografi,

Ultrabredbandig antenn, Dielektrisk antenn, Inbäddad DRA, PSF

Acknowledgements

I would like to thank Dr.Frank Weinmann for providing me the opportunity to conduct my MSc thesis at Fraunhofer Institute for High Frequency Physics and Radar Techniques FHR. I would like to thank my supervisor from Fraunhofer FHR, Andrej Konforta for mentoring me and helping me to develop professionally. I also want to thank my colleagues, Dr.Endri Stoja and Claudius Löcker for supporting me throughout my journey at Fraunhofer FHR. Furthermore, I would like to extend my gratitude to my supervisor from KTH, Ahmad Emadeddin for his guidance and feedback during the thesis.

Moreover, I want to thank Prof. Lars Jonsson, Prof. Oscar Quevedo-Teruel, Prof.

Martin Norgren, Prof. Urban Westergren and Prof. Joachim Oberhammer for their guidance in exploring the magnificent world of electromagnetism, antennas, microwaves and microsystems. Without their contributions, I couldn’t have gotten this far.

Also, I would like to thank my parents for their constant encouragement, support and inspiration during my MSc study.

Last but definitely not the least, I would like to thank my friend Jonas Olsson for

helping me prepare the Swedish version of the abstract.

Contents

1 Introduction 1

1.1 Multifunctional Aperture . . . . 1

1.2 Physical limitations of antennas . . . . 3

1.3 Wideband antenna designing principles . . . . 3

1.4 Additive manufacturing . . . . 4

1.5 A brief discussion on dielectric antennas . . . . 5

1.5.1 Dielectric rod antenna . . . . 5

1.5.2 Dielectric horn antenna . . . . 6

1.5.3 Dielectric Resonator Antenna . . . . 8

1.6 Problem description . . . . 8

1.7 Technical Specification . . . . 9

1.8 Outline . . . . 9

2 Dielectric Resonator Antenna 10 2.0.1 Hemispherical DRA . . . . 10

2.0.2 Rectangular DRA . . . . 12

2.0.3 Cylindrical DRA . . . . 15

2.1 DRA feeding techniques . . . . 21

2.2 Broadband DRA . . . . 25

2.2.1 Multiple DRAs . . . . 26

3 Ultra-wideband embedded DRA 29 3.1 Previous works . . . . 29

3.2 This work . . . . 30

3.3 Antenna geometry . . . . 31

3.3.1 Modification of effective permittivity of dielectric material using

perforations . . . . 31

CONTENTS

3.3.2 Design-1 . . . . 32

3.3.3 Design-2 . . . . 39

4 Results and discussion 47 4.1 Design-1 . . . . 47

4.1.1 Model setup in HFSS . . . . 47

4.1.2 Frequency response . . . . 48

4.1.3 Internal electric field distribution and radiation pattern . . . . 48

4.2 Design-2 . . . . 52

4.2.1 Model setup in HFSS . . . . 52

4.2.2 Frequency response . . . . 52

4.2.3 Internal electric field distribution and radiation pattern . . . . 53

5 Conclusion and future works 59 5.1 Summary and Conclusion . . . . 59

5.2 Future works . . . . 61

References 63

List of Figures

1.0.1 An airborne multifuctional RF system. Image source:[2] . . . . 2

1.5.1 Dielectric rod antenna. . . . 6

1.5.2 Dielectric horn antenna. . . . 7

2.0.1 A hemispherical DRA. . . . 11

2.0.2 Ideal radiation patterns of the hemispherical DRA. . . . 12

2.0.3 A rectangular DRA. . . . 12

2.0.4 The 2D representation of DRA on ground plane and its equivalent dielectric waveguide model. . . . 13

2.0.5 The magnetic dipole equivalent model for (from left) T E

, T E

and T E

modes. . . . 14

2.0.6 Ideal normalized far-field (dB) vs θ(deg.) plot for T E

, T E

and T E

modes. These plots have been obtained from the theoretical calculation of the far-fields of the magnetic dipole equivalent model of T E

, T E

and T E

modes. . . . 14

2.0.7 A cylindrical DRA. . . . 15

2.0.8 Internal electric field distribution of (from left) T M

, T E

and HE

modes in a cylindrical DRA. . . . 16

2.0.9 Ideal normalized far-field (dB) vs θ(deg.) plot for three different types of modes excited in a cylindrical DRA. . . . 17

2.0.10 Variation of normalized wave number and Q factor with the aspect ratio for different values of ϵ

. . . . 19

2.0.11 Internal electric field distribution of (from left) HE

, HE

and HE

of a cylindrical DRA mounted over a ground plane. . . . 20

2.0.12 Ideal normalized far-field (dB) vs θ(deg.) plot for the first three HE

modes that can be excited in a cylindrical DRA, computed using the

horizontal magnetic dipole array equivalent model. . . . 21

LIST OF FIGURES

2.1.1 Probe fed DRA. . . . 23

2.1.2 Microstrip line fed DRA. . . . 23

2.1.3 Aperture coupling. . . . 24

2.1.4 Electric field distribution and magnetic current equivalent model of aperture coupling. . . . 24

2.2.1 Examples of stacked DRA. . . . 27

2.2.2 Co-planar DRA. . . . 27

2.2.3 Embedded DRA. . . . 28

3.3.1 Square lattice. . . . 32

3.3.2 Variation of k

r and Q factor with aspect ratio(r/h) for ϵ

=9.1 and 30. 33 3.3.3 Configuration of the inner DRA with circular cross-section and its simulated frequency response (when excited using a rectangular slot feed). . . . 33

3.3.4 Configuration of the inner DRA with semi-circular cross-section and its simulated frequency response (when excited using a rectangular slot feed). . . . 34

3.3.5 Configuration of the outer DRA and its simulated frequency response (when excited using a rectangular slot feed). . . . 34

3.3.6 Top view of the perforated outer DRA. . . . 35

3.3.7 Configuration of the perforated outer DRA and its simulated frequency response (when excited using a rectangular slot feed). . . 36

3.3.8 Configuration of Design-1. . . . 37

3.3.9 Feeding structure of Design-1. . . . 38

3.3.10 Smith chart plots for Design-1 in the frequency range 8 GHz- 16 GHz. 39 3.3.11 Variation of k

r and Q factor with aspect ratio for ϵ

=6.1 and 30. . . 39

3.3.12 Configuration of the inner DRA with circular cross-section and its simulated frequency response (when excited using a rectangular slot feed). . . . 40

3.3.13 Top view of the cylindrical DRA with notches. . . . 40

3.3.14 Parametric study of the notch dimensions. . . . 41

3.3.15 Configuration of the notched inner DRA and its simulated frequency response (when excited using a rectangular slot feed). . . . 41

3.3.16 Configuration of the outer DRA and its simulated frequency response

(when excited using a rectangular slot feed). . . . 42

LIST OF FIGURES

3.3.17 Unit cell of the cubical perforation. . . . 42 3.3.18 Configuration of the perforated outer DRA and its simulated

frequency response (when excited using a rectangular slot feed). . . 43 3.3.19 Configuration of Design-2. . . . 44 3.3.20 Feeding structure of Design-2. . . . 45 3.3.21 Smith chart plots for Design-2 in the frequency range 9 GHz- 17 GHz. 46 4.1.1 Convergence plot of Design-1. . . . 48 4.1.2 Simulated reflection coefficient. . . . 49 4.1.3 Internal electric field distribution(vector) in the E plane (YZ-plane). 50 4.1.4 Normalized gain (dB) vs θ(deg.) for co and x-polarization in E and H

plane. . . . 52 4.2.1 Convergence plot of Design-2. . . . 53 4.2.2 Simulated reflection coefficient. . . . 53 4.2.3 Internal electric field distribution (vector) in the E plane (YZ-plane). 54 4.2.4 Internal electric field distribution (magnitude) in the XY-plane at Z=

height of the inner DRA. . . . 57 4.2.5 Normalized gain (dB) vs θ(deg.) for co and x-polarization in E and H

plane. . . . 58

5.2.1 Conformal 10 × 10 array. . . . 61

Acronyms

AESA active electronically scanned array AM Additive manufacturing

CNC computer numerical control

DRA dielectric resonator antenna

EMI electromagnetic interference

FDM Fused deposition modeling

PMC Perfect Magnetic Conductor

PSF Pattern Stability Factor

PML Perfectly Matched Layer

PCB printed circuit board

RF radio frequency

SLA Stereolithography

UWB ultra-wideband

Chapter 1 Introduction

Antenna is an essential device in warfare for meeting several needs such as target detection and ranging, communication, electronic warfare and spectrum monitoring.

With the evolution of modern warfare techniques, there has been a proliferation in the use of radio frequency systems which has, consequently, increased the number of antennas installed on various military platforms. Due to this expansion, several issues related to antenna have arisen, such as signal obstruction, interference, limited area availability, increased weight and increased maintenance cost. The approach implemented in the past to resolve some of these issues was, to design separate antenna arrays for each RF back-end and optimize their positions based on requirement.

Nevertheless, due to limited space availability, electromagnetic interference (EMI) considerations and cost, this strategy is deemed unacceptable. Thus, there is a need for the concept of a common aperture shared by multiple radio frequency (RF) back-end systems. A single radar that can perform activities such as surveillance, tracking and fire control simultaneously is known as multifuctional radar system. A multifuctional RF system, on the other hand, is the one which can combine the radar operation with other diverse functions such as communication, electronic counter measure, navigation aid etc [1]. Fig.1.0.1 presents a conceptual picture of an airborne multifunctional RF system.

1.1 Multifunctional Aperture

The crux of the multifunctional radar and multifunctional RF system is a multifuctional

aperture, i.e a single aperture which can be integrated with various RF back-ends

CHAPTER 1. INTRODUCTION

Figure 1.0.1: An airborne multifuctional RF system.

Image source:[2]

operating in different frequency ranges, such as the radar unit, electronic warfare

unit, spectral monitoring unit and communication unit. Therefore, the aperture

should be ultra-wideband (UWB) and it should be able to generate multiple beams

simultaneously with the capability of individual beam steering. To meet this end, active

electronically scanned array (AESA) is preferred because several transmitter-receiver

module can be interfaced with the antenna elements and simultaneous multiple radar

beams at different frequency can be generated. Several such UWB antennas proliferate

in literature for example, a broadband multifunctional spiral antenna array which

operates from 500 MHz to 2 GHz has been mentioned in [3]. In [4], a multifunctional

frequency agile circular patch antenna with polarization reconfigurability has been

demonstrated. A circularly polarized shared aperture array for C and X band operation

has also been reported in the literature [5]. A light weight, low-profile and compact

UWB phased array antenna with wide scan capability has been designed in [6]. In

[7], various optimization techniques have been discussed for the antenna mentioned

in [6]. All the antennas discussed hitherto have been designed using conventional

manufacturing techniques like computer numerical control (CNC) or printed circuit

board (PCB). Additive manufacturing (AM), on the other hand, is an interesting

alternative to conventional manufacturing techniques which offers more degrees of

freedom to the antenna designers in shaping the antenna geometry in order to optimize

various characteristics such as bandwidth, beamwidth, x-polarization level etc, for a

given volume.

CHAPTER 1. INTRODUCTION

1.2 Physical limitations of antennas

According to H.A.Wheeler, an electrically small antenna is the one whose maximum dimension is less than λ/2π, where λ is the wavelength of the electromagnetic wave radiated by the antenna [8]. These antennas are crucial for the development of compact RF systems. Wheeler, in his paper, has approximated electrically small antenna as a lumped capacitor (in case electric dipole antenna) or inductor (in case of magnetic dipole antenna) connected to a resistor representing the radiation resistance.

He found that the ratio between radiated power (radiation loss) and reactive power is limited by the size of the antenna [8]. Besides, in [9], Chu has shown that the maximum gain of an omnidirectional antenna is limited to 4a/λ, if low radiation Q factor (i.e broad bandwidth) is desired, where a is the radius of the smallest sphere that could circumscribe the antenna. Fante extended this work and derived the maximum ratio of gain to Q factor (G/Q) for directional antennas [10]. In [11], the maximum G/Q ratio for both omnidirectional and directional antennas have been recalculated and for both the cases new upper limits have been derived. The physical limitations of antenna is, in itself, a vast topic of research in electromagnetic engineering with contributions from several researchers [12–15]. Therefore, to summarize, the size of the antenna limits its gain and minimum achievable radiation Q factor (thereby limiting its maximum attainable bandwidth).

1.3 Wideband antenna designing principles

Most of the wideband antennas are designed based on one or a combination of the following principles [16]:

• Multiple resonating structures

• Angular constant structures (Frequency independent antenna)

• Traveling wave structures

• Wideband impedance matching of electrically small antenna

• Self-complementary structures

In case of Multiple resonance structures, several simple narrowband antennas

are carefully coupled which results into a single antenna with a continuous broad

CHAPTER 1. INTRODUCTION

frequency range with respect to the matching. For e.g: in patch antennas, stacked or coplanar parasitic elements are added to improve the bandwidth [17]. Rumsey’s principle states that if the shape of the antenna is invariant to physical scaling and is described only in terms of angles, then the antenna will be frequency independent [18]. The antennas designed based on this principle are known as Angular constant structures, one example of such antenna is the biconical antenna [19]. Theoretically speaking, an infinitely long angular constant antenna has an infinite bandwidth.

However in practice they are truncated which limits their operation bandwidth. The Traveling wave structure provides a smooth transition for the electromagnetic waves from guided structure to the free space [19]. In order to maintain a perfectly smooth transition, the transition structure needs to be infinitely long which is impossible in practice. Thus, the structure is truncated which, in turn, limits the bandwidth. An example of this kind of antenna is a Vivaldi antenna [20]. The dimension of the Electrically small antenna is notably smaller than its wavelength at the resonant frequency. If proper impedance matching could be achieved over a wide bandwidth, it will be possible to make it broadband. In practice, however, it is very difficult to design a wideband matching using passive elements. On way to resolve this issue is by matching the antenna using non-Foster network which consist of active devices, this is still in the research stage [21]. In case of Self-complementary antenna, the positions of metal and dielectric are interchanged forming a self- complementary structure. The log-spiral antenna is an example of self-complementary antenna. An interesting property of this kind of antenna is that, it has a constant input impedance over a wide bandwidth. Nevertheless, the radiation characteristics may not be constant throughout its operational frequency band [16]. In practice, its bandwidth is limited by the feeding structure and the size of the antenna.

1.4 Additive manufacturing

Additive manufacturing (AM) is a technique of fabricating objects by systematic

deposition of materials in layers over each. This is in sharp contrast to subtractive

manufacturing techniques (such as milling) where materials are removed in order

to fabricate various structures. With AM, structures with greater complexity and

better tolerance can be manufactured which are, otherwise, difficult to fabricate using

traditional subtractive methods. Moreover, with AM the manufacturing cost and the

CHAPTER 1. INTRODUCTION

weight can also be significantly reduced. Due to its attractive features, AM has been recently used to fabricate microwave devices [22–24].

Two widely used AM techniques are: (a) Fused deposition modeling (FDM) and (b) Stereolithography (SLA). In case of FDM, a structure is manufactured by depositing melted thermoplastic layer-by-layer. Whereas in SLA a high powered ultra-violet(UV) laser is used to selectively harden a photosensitive liquid resin to manufacture a 3D structure. SLA can also be used to manufacture 3D structures with ceramic materials by properly mixing ceramic powder with the photosensitive liquid resin. However, this technique is currently limited to certain ceramic materials only which does not absorb UV radiation significantly and offer only a slight change of refractive index with respect to the base photosensitive liquid resin. The FDM process is fast and cheap but the process has low accuracy and resolution. Although more expensive, very high resolution 3D-printing can be achieved using SLA. The minimum resolution of SLA can be as low as 10µm [25].

1.5 A brief discussion on dielectric antennas

The dielectric antenna has become an interesting alternative to the metallic antenna.

This is because of its low manufacturing cost and the possibility to fabricate complex antenna shapes using AM.

In this section some of the commonly known dielectric antennas, namely: dielectric rod antenna, dielectric horn antenna and dielectric resonator antenna will be briefly described.

1.5.1 Dielectric rod antenna

Antennas in which the electromagnetic fields follow a traveling wave pattern, instead

of standing waves, are categorized as traveling wave antenna. The traveling wave

nature of the electromagnetic fields can be achieved by carefully terminating the

antenna so that the reflection at the edge can, ideally, be eliminated. The dielectric

rod antenna, as shown in fig.1.5.1(a.), falls under the category of a traveling wave

antenna, where surface waves are excited that radiate at the discontinuities which

interrupt these waves [26]. These antennas radiate in the end-fire direction and have

a high gain over wide bandwidth which makes them an important candidate for UWB

antenna array. However, in order to radiate efficiently, its length should be sufficiently

CHAPTER 1. INTRODUCTION

long. Fig.1.5.1(b.) shows the electric field distribution on the rectangular dielectric rod antenna with metal waveguide feeding which has been simulated using CST Microwave Studio. In the figure, a strong presence of surface wave can be seen. The simulated radiation pattern of the rod antenna, is shown in fig.1.5.1(c.).

(a) Configuration of dielectric rod antenna (b) Electric field distribution (V/m)

(c) Directivity (dBi) vs θ (degrees) Figure 1.5.1: Dielectric rod antenna.

1.5.2 Dielectric horn antenna

The metallic horn antenna is widely used in the antenna engineering community due to

its high gain, wide bandwidth and easy construction. Horn antennas are often used as a

feed to the reflector antenna and lens antenna [27]. In regular arrays with rectangular

grid, the distance between each element should be less than λ/2, in order to prevent

CHAPTER 1. INTRODUCTION

grating lobes. However, due to the dimension of its cross-section, it is often difficult to place metallic horn antennas within λ/2 distance from each other in an array. Due to this limitation, it is very challenging to design a broadband array of horn antennas with wide-angle scanning capability.

(a) Configuration of dielectric horn antenna (b) Electric field distribution (V/m)

(c) Directivity (dBi) vs θ (degrees) Figure 1.5.2: Dielectric horn antenna.

For a given cutoff frequency, the dimension of the cross-section of the waveguide is dependent on the relative permitivity of the dielectric material inside it. For example, in case of the fundamental T E

mode, the dimension of the rectangular waveguide is ∝ 1/ √

ϵ

. Therefore, using a fully dielectric horn, it might be possible to reduce its cross-

section. Besides, due to the skin effect, the metallic boundary contributes to conductor

losses at high frequencies. Additionally, metallic parts significantly increase the weight

CHAPTER 1. INTRODUCTION

of the antenna. An alternative to this is, solid dielectric horn antenna. In dielectric horn, surface waves are excited which radiate at the terminal end of the horn. The total radiation of the antenna is given by superimposing the radiation at the terminal and the radiation at the feed [28]. The configuration of a dielectric horn antenna which has been designed and simulated using CST Microwave Studio is shown in fig.1.5.2(a.). Its simulated electric field distribution and radiation pattern is shown in fig.1.5.2(b.) and (c.) respectively. Similar to the dielectric rod, the length of the dielectric horn antenna should be long enough in order to make it an efficient radiator.

1.5.3 Dielectric Resonator Antenna

The dielectric resonator is an imperfect resonating structure due to the leakage of fields from its sides. When designed properly and if a low-loss material is used, then the losses in the dielectric resonator are mainly due to radiation. In this case, it forms a dielectric resonator antenna (DRA). Long, McAllister and Shen through their systematic study have demonstrated that the DRA could be used as an alternative to the commonly used low gain antennas such as microstrip patch antenna [29]. A detailed discussion on DRA will be provided in the subsequent chapter.

1.6 Problem description

Using AM, dielectric antennas with increased geometrical complexity can be manufactured. The question, whether it is possible to optimize various antenna characteristics (such as bandwidth, radiation properties etc) with the aid of AM, is of great interest. To evaluate the new possibilities, in the first step known radiator shapes need to be adapted and improved.

The main goal of this thesis is to investigate whether the bandwidth of a dielectric antenna can be improved by shaping its geometry while maintaining a compact footprint

. The antenna element is intended for UWB phased array application with wide-angle scanning capability. Therefore, in order to avoid grating lobes, the spacing between the array elements needs to be limited within λ/2, at the highest frequency of its operational bandwidth. Thus, the unit antenna element of the array should be UWB and have a compact footprint.

1

The area occupied by the antenna on the ground plane.

CHAPTER 1. INTRODUCTION

1.7 Technical Specification

This thesis focuses on designing a single antenna element which is intended for application in a multifunctional phased array antenna with wide-angle scanning capability. The antenna designed in the thesis is based on the following specifications:

Features Specifications

Frequency range of interest 8 GHz - 17 GHz (X+Ku band)

Radiation pattern Symmetrical, Unidirectional (covering the angular space -60° ≤ θ ≤ 60°)

Polarization Linear

Maximum x-polarization level -10dB (in the angular space -60° ≤ θ ≤ 60°)

Footprint λ/2 x λ/2 (wavelength corresponding to the highest frequency within operational bandwidth)

Minimum acceptable return loss 10dB (within the antenna’s operational bandwidth)

1.8 Outline

The outline of the thesis is as follows: Chapter-2 will discuss some basic ideas about DRA. There, three simple DRA shapes and three widely used feeding techniques for DRA excitation will be presented. Also, the chapter will include some techniques for designing broadband DRA. In the next chapter, Chapter-3, some previous works on embedded DRA will be presented and two embedded DRAs that have been designed for the thesis will be introduced. The simulation results will be discussed in Chapter-4.

Finally, in Chapter-5, conclusion and future work will be presented.

Chapter 2

Dielectric Resonator Antenna

The DRA, in general, is a low gain antenna and has a wide radiation pattern. With the proper choice of dielectric material and antenna geometry, its size can be significantly reduced and a broad bandwidth can be achieved. Therefore, the DRA is a promising candidate for application in a broadband phased array antenna with wide-angle scanning capability.

In the literature, there has been a proliferation of different DRA geometries in order to enhance/modify certain characteristics of the antenna such as bandwidth, beam- width, circular polarization etc [30–33]. Mostly, these complex shapes are derived from the the three basic shapes, namely, hemispherical, rectangular and cylindrical.

In the next section these three simple DRA geometries will be briefly described.

2.0.1 Hemispherical DRA

A simple hemispherical DRA with radius, r and a permittivity, ϵ

, mounted on a ground plane is shown in fig. 2.0.1. If the ground plane is a perfect electric conductor and is infinitely extended along x and y axis, the image theory can be used to replace the hemispherical DRA with an isolated spherical DRA having the same radius. Then, the results of the analysis of the resonance modes of an isolated dielectric sphere in [34]

can be directly applied in the case of hemispherical DRA. There are two kinds of modes in a spherical dielectric resonator:

• TE mode, with no radial component of the electric field (E

=0).

• TM mode, with no radial component of the magnetic field (H

=0).

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

Figure 2.0.1: A hemispherical DRA.

In case of hemispherical DRA specifically, the two interesting modes are:

• TE

: This is the lowest order mode that can be excited in a hemispherical DRA.

The far field of this mode is similar to that of a short horizontal magnetic dipole as represented by blue curve in fig.2.0.2(a.) and 2.0.2(b.)

• TM

: The radiation pattern of this mode is similar to that of a short electric monopole antenna as represented by green curve in fig. 2.0.2(a.) and 2.0.2(b.).

In case of hemispherical DRA, for a given ϵ

, its radius r determines the resonant frequency [35]. Therefore, the hemispherical DRA offers limited freedom to the antenna designers for choosing design parameters.

(a) Normalized far-field (dB) vs θ (degrees) at ϕ = 0° plane.

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(b) Normalized far-field (dB) vs θ (degrees) at ϕ = 90° plane.

Figure 2.0.2: Ideal radiation patterns of the hemispherical DRA.

2.0.2 Rectangular DRA

A rectangular DRA is defined by its width w, height h and length l as shown in fig.2.0.3. By changing the w/h and w/l ratios, which are often referred to as aspect ratios, a desired resonant frequency and bandwidth can be achieved [35]. For a fixed permittivity ϵ

, different values of aspect ratios can be chosen in order to resonate the DRA at a desired frequency. Therefore, rectangular DRA offers more design flexibility than hemispherical DRA. However, it should also be kept in mind that although with different aspect ratios, the DRA can have a fixed resonant frequency, but its operational bandwidth and gain might vary significantly.

Figure 2.0.3: A rectangular DRA.

The fields within a rectangular DRA can be approximated using the dielectric

waveguide model. According to this model, the internal fields of the DRA of height h,

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

placed over a ground plane can be computed by assuming it as a dielectric waveguide with the same cross-section but with a height of 2h, as shown in fig.2.0.4. A magnetic wall or Perfect Magnetic Conductor (PMC) boundary is assumed on the four lateral surfaces of the dielectric waveguide. Although, the PMC boundary condition is valid for high values of ϵ

, however it is a fair assumption for lower values of ϵ

as well [35].

Figure 2.0.4: The 2D representation of DRA on ground plane and its equivalent dielectric waveguide model.

An isolated rectangular waveguide can support both TE and TM modes but it is only the TE type modes which are generally excited in case of a rectangular DRA mounted on a ground plane [35]. The radiation pattern of TE modes are similar to that of an infinitesimally small magnetic dipole. A rectangular DRA can be excited in the TE

, TE

and TE

modes which radiate like magnetic dipole oriented in the x, y and z direction respectively.

For achieving a wide radiation pattern covering the angular space -90°<θ<+90°,

0°<ϕ<360°, the TE

or TE

modes are excited depending upon the orientation of the

feed. The first three TE

modes in a rectangular DRA are TE

, TE

and TE

where

the subscripts represent the field variation in the x, y and z directions respectively. The

value of δ is taken as 0 for low permittivity DRAs and is taken as 1 for DRAs with high

permittivity [35]. However, the definition of low/ high permittivity in this case is not

very precise. The equivalent magnetic dipole model is shown in fig.2.0.5, where the

outer shape of the DRA has been represented by green lines. As the DRA is excited to

the higher order modes, the number of equivalent magnetic dipoles increases, forming

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

an array as shown in the figure. The distance d between each element of the array depends upon the aspect ratio of the DRA. Due to the alternating phase of the dipoles, end-fire radiation is achieved [36]. Using the array factor method, it can be shown that as the number of element increases, i.e at higher order modes, the main beam becomes narrower and the number of side lobes increases as shown in fig.2.0.6.

Figure 2.0.5: The magnetic dipole equivalent model for (from left) T E

, T E

and T E

modes.

(a) E-plane pattern (b) H-plane pattern

Figure 2.0.6: Ideal normalized far-field (dB) vs θ(deg.) plot for T E

, T E

and T E

modes. These plots have been obtained from the theoretical calculation of the far-fields

of the magnetic dipole equivalent model of T E

, T E

and T E

modes.

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

2.0.3 Cylindrical DRA

The geometry of a cylindrical DRA is shown in fig.2.0.7. A cylindrical DRA is defined by its radius r, height h and dielectric constant ϵ

. For a fixed ϵ

of the dielectric material, the resonant frequency and the bandwidth of a cylindrical DRA depend upon its aspect ratio (r/h) [35]. Thus, a short, wide cylindrical DRA and a tall, slender cylindrical DRA can have the same resonance frequency. Therefore, the number of degrees of freedom is increased by one when compared to the hemispherical DRA. However, as in the case of rectangular DRA, having the same resonance frequency for different aspect ratios does not imply that their operational bandwidths are the same.

Figure 2.0.7: A cylindrical DRA.

A cylindrical DRA can support TE

, TM

and the Hybrid modes (HE

or EH

). The first two indices i.e, m and n denote the field variation along ϕ and ρ directions respectively of the cylindrical coordinate system. The third index, i.e, p + δ (p=0,1,2....) denotes the field variation along z direction [37]. The value of δ is taken as 0 for low permittivity DRAs and is taken as 1 for DRAs with high permittivity. Here, the definition of low/ high permittivity is not very precise. The Hybrid modes (HE

or EH

) are, essentially, a combination of TE & TM modes. They are referred to as HE mode when the E

component is dominant and EH mode if H

is dominant.

The TE

, TM

and HE

are the modes which are mostly excited in the cylindrical DRA due to their low cut-off frequency [35] [38]. The radiation patterns of the TM

and TE

modes are similar to that of a vertically oriented short electric and magnetic

monopole respectively. The HE

is the lowest order mode that radiates like a short

horizontal magnetic dipole [39]. The internal electric field distribution of the TM

,

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

TE

and HE

modes of a cylindrical DRA is shown in fig.2.0.8. The ideal radiation patterns of these modes, computed using their electric/magnetic-monopole/dipole equivalent model, is presented in fig.2.0.9. For designing antenna element for AESA, the HE type mode is preferable because the TE and TM type modes have a null at θ=0°.

Figure 2.0.8: Internal electric field distribution of (from left) T M

, T E

and HE

modes in a cylindrical DRA.

(a) T M

mode

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(b) T E

mode

(c) HE

mode

Figure 2.0.9: Ideal normalized far-field (dB) vs θ(deg.) plot for three different types of

modes excited in a cylindrical DRA.

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

There is no exact analytical field solution for cylindrical DRAs. Therefore, they are analyzed using the dielectric waveguide model, similar to the one described for the rectangular DRA in fig.2.0.4. Using the dielectric waveguide model, the ⃗ E and ⃗ H fields within the cylindrical DRA for the HE

mode are approximately given by [38]:

E

∝ J

(αρ) cos( πz 2h )

® cos(ϕ) sin(ϕ)

´

(2.1)

E

∝ ∂J

(αρ)

∂(αρ) sin( πz 2h )

® cos(ϕ) sin(ϕ)

´

(2.2)

E

∝ J

(αρ) sin( πz 2h )

® sin(ϕ) cos(ϕ)

´

(2.3)

H

∝ J

(αρ) cos( πz 2h )

® sin(ϕ) cos(ϕ)

´

(2.4)

H

∝ ∂J

(αρ)

∂(αρ) cos( πz 2h )

® cos(ϕ) sin(ϕ)

´

(2.5)

H

≈ 0 (2.6)

where h is the height of the DRA, J

(αρ) is the first order Bessel’s function of first kind and α is the first non-trivial solution of J

(α r)=0, for a given radius r of the cylindrical DRA. Depending upon the position of the feed either sin(ϕ) or cos(ϕ) can be chosen.

Based on numerical computation and curve fitting, the general expression for the normalized wave number k

r, for HE

mode and its corresponding Q factor is found to be [35],

k

r = 6.324

√ ϵ

+ 2 {0.27 + 0.36 r

2h + 0.02( r

2h )

} (2.7)

Q = 0.01007ϵ

r

h {1 + 100 · e

} (2.8) where ϵ

is the permittivity, r is the radius and h is the height of the cylindrical DRA.

The relation between k

r and resonant frequency in GHz (f

) is given by the following approximate formula,

k

r = f

· h

· (r/h)

4.7713 (2.9)

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

where h

is the height of the DRA in centimeters and r/h is the aspect ratio.

From the Q factor, the bandwidth can be calculated using the following equation:

BW = ∆f

f

= √ V SW R

− 1

V SW R

· Q (2.10)

where VSWR

is the maximum acceptable voltage standing wave ratio which is mostly taken as 2 because VSWR=2 is approximately equivalent to S

=-10dB.

Fig.2.0.10 shows the k

r and Q factor vs the aspect ratio for materials with different dielectric constants. In order to choose proper dimension and appropriate material to design a cylindrical DRA for a given bandwidth and resonant frequency requirement, the following general designing steps can be undertaken:

• Using eq.(2.10), the Q factor can be determined from the required bandwidth.

• Using the graph provided in fig.2.0.10(b.), possible values of ϵ

and r/h that fits the Q factor requirement can be quickly determined.

• Comparing both the plots in fig.2.0.10, a proper aspect ratio and dielectric material can be chosen such that it fits the resonant frequency, bandwidth and dimension requirement.

(a) Normalized wave-number vs

aspect ratio (b) Q factor vs aspect ratio

Figure 2.0.10: Variation of normalized wave number and Q factor with the aspect ratio for different values of ϵ

.

A widely applied technique for DRA bandwidth enhancement is to merge other higher

order modes with the fundamental mode. In case of a cylindrical DRA mounted on a

ground plane, the first three lower order HE type modes that can be excited are: HE

,

HE

and HE

. The modes HE

and HE

cannot be excited due to the presence

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA of the ground plane [40].

Figure 2.0.11: Internal electric field distribution of (from left) HE

, HE

and HE

of a cylindrical DRA mounted over a ground plane.

Internal electric field distributions of the three modes are shown in fig.2.0.11. Using the magnetic dipole equivalent model, it can be said that the HE

, HE

and HE

modes correspond to a linear array (with array axis along z direction) of horizontally oriented one, three and five magnetic dipoles respectively. The arrangements of magnetic dipoles are similar to the one shown for the rectangular DRA case in fig.2.0.5. The ideal radiation patterns of the HE

, HE

and HE

modes computed using the horizontal magnetic dipole array equivalent model is presented in fig.2.0.12. From the figure it can be concluded that with increase in the order of the HE

mode, the main lobe becomes narrower and the number of side lobe increases.

(a) HE

mode (b) HE

mode

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(c) HE

mode

Figure 2.0.12: Ideal normalized far-field (dB) vs θ(deg.) plot for the first three HE modes that can be excited in a cylindrical DRA, computed using the horizontal magnetic dipole array equivalent model.

2.1 DRA feeding techniques

In the previous section, a general discussion on DRAs of basic shapes was provided.

There, using the dielectric waveguide model, a simple design strategy for cylindrical DRA was mentioned. In the dielectric waveguide model, an isolated DRA mounted over an infinite ground plane is assumed. Thus, the model does not take into account the effect of the feeding mechanism used to excite the DRA. In practice, however, the selection and location of the feed play an important role in determining the kind of modes that will be actually excited. Moreover, due to mutual interaction between the feed and the DRA, the feeding structure affects the resonant frequency and Q factor.

For the sake of simplicity, the feed can be approximately modelled as an equivalent impressed electric or magnetic current on the DRA which is invariant [35]. The amount of coupling between the feed and the DRA is represented by the Greek symbol χ. In case of magnetic current source (dominant in slot feed),

χ ∝

∫

V

H ⃗

· ⃗ M dV (2.11)

where ⃗ H

is the magnetic field within the DRA, ⃗ M is the impressed equivalent magnetic current density

and V is the volume of the DRA. For electric current source

1

from Maxwell’s equation:⃗ ∇ × ⃗ E=−jωµ ⃗ H − ⃗ M

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(dominant on probe feed),

χ ∝

∫

V

E ⃗

· ⃗JdV (2.12)

Here, ⃗ E

is the inner electric field of the DRA, ⃗ J is the impressed equivalent electric current density and V is the volume of the DRA.

The feeding mechanism will have a loading effect. The external Q factor, Q

, is given by,

Q

= Q

χ (2.13)

The loaded Q factor (Q

) is given by,

Q

= 1

1 Q

+

ext

= Q

1 + χ (2.14)

where Q is the unloaded Q factor.

When χ=1, the condition is called critical coupling. In this condition maximum power is coupled between the feed and DRA. When χ > 1, the feed is said to be over coupled and for χ < 1, the feed is said to be undercoupled [35].

There are several feeding techniques which can be used to excite a DRA. Some of the widely used feeds are as follows:

• Probe feed:

Fig.2.1.1 shows a DRA mounted on ground plane and is excited by a probe feed.

The length of the probe and its position can be optimized in order to control the input impedance of the antenna. Depending upon the bandwidth and resonant frequency requirements, the coaxial probe can either be placed inside the DRA by drilling a hole or it can be placed within a close proximity to it. However, a probe placed inside the DRA has better coupling efficiency compared to the one placed close to it. Probe feeds are often used in case of low frequency DRAs where the dimension of slot feed would be too large to properly couple the fields to the DRA.

• Microstrip feed:

In this technique, a DRA can be coupled to the microstrip line by either placing it

directly above the line (known as direct coupling), as shown in fig.2.1.2(a.) or the

DRA can be placed within close proximity to the line (known as side coupling),

as shown in fig.2.1.2(b.). The coupling can be controlled by optimizing the

parameter g. Another parameter which plays an important role in the coupling is

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

Figure 2.1.1: Probe fed DRA.

the ϵ

of the DRA. Better coupling is achieved if the ϵ

of the DRA is high. One of the problems associated with this kind of feed, especially with the direct coupling, is the presence of a small air-gap between the substrate and the DRA. This air- gap affects the performance of the DRA, especially when it is operating at the millimeter wave frequencies.

(a) Direct coupling. (b) Side coupling.

Figure 2.1.2: Microstrip line fed DRA.

• Aperture coupling:

A thin rectangular slot, as shown in fig.2.1.3, is most widely used in aperture coupling. The slot length L

and slot width W

control the coupling between the feed and the DRA. The extension of the microstrip line beyond the slot by a length of L

, as shown in fig.2.1.3(b.), acts like an open stub. Therefore, the length L

can also be varied for optimizing the impedance matching [35]. Furthermore, the

bandwidth can be improved by slightly offsetting the position of the microstrip

line from the center of the slot (along the blue arrow in fig.2.1.3(a.)).

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(a) An aperture fed DRA. (b) Detailed configuration of the aperture feed.

Figure 2.1.3: Aperture coupling.

For the sake of simplicity, the slot can be considered as an equivalent magnetic current oriented along the direction of the slot length. The electric fields in the rectangular slot and the magnetic current equivalent representation of the slot is presented in fig.2.1.4(a.) and 2.1.4(b.). For optimal coupling, the slot should be placed directly below the spot where the DRA magnetic field is maximum. In case of a cylindrical DRA fed by a centrally located slot, the HE

mode can be excited.

(a) E ⃗ field distribution in the rectangular slot.

(b) The equivalent magnetic current representation of the rectangular slot.

Figure 2.1.4: Electric field distribution and magnetic current equivalent model of aperture coupling.

To determine the input impedance of a slot for a given L

and W

, various

numerical tools such as method of moment, finite element method and finite

difference time domain can be used. To this end, various commercial software

packages such as FEKO, HFSS and CST can be used to perform the numerical

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

analysis of the slot. For the simulation, the following three simple steps can be taken to calculate the initial values of L

and W

, then they can be optimized after comparing the simulation results [35]:

1. Firstly, the effective dielectric constant or ϵ

is calculated using,

ϵ

= ϵ

+ ϵ

2 (2.15)

where ϵ

is the dielectric constant of the DRA and ϵ

is the dielectric constant of the substrate.

For efficient coupling, the slot length L

should be sufficiently large but at the same time it should be small enough so that it does not resonate within the operating frequency of the DRA, which usually results in excessive power spillage beneath the ground plane . The initial value of L

for optimization can be taken as,

L

= 0.4λ

√ ϵ

(2.16)

2. To prevent large backlobe, the slot width should be narrow. Its starting value for optimization can be taken as,

W

= 0.2L

(2.17)

3. For impedance matching, the initial value of the stub length L

can be taken as,

L

= λ

4 (2.18)

where λ

is the guided wavelength.

2.2 Broadband DRA

Due to their resonant nature, DRAs inherently have narrow operational bandwidth.

However, different techniques have been mentioned in the literature which aids in increasing its bandwidth. These techniques can be broadly categorised into: (1.) Lowering the Q factor of the DRA, (2.) Using external matching network and (3.) Combining multiple DRAs [41].

A simple way to lower the Q factor of the DRA is to use a dielectric material of low ϵ

,

since, roughly speaking, Q ∝ ϵ

. However, the main problem with this technique is,

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

when a material of low ϵ

is used, the dimension of the DRA will increase for a given resonant frequency which will make the antenna bulky. This might not be preferable for applications where compact antenna is required.

External matching network is often incorporated to improve the impedance bandwidth. The main idea here is to design a wideband matching network using, for e.g, quarter-wave transformer, Chebyshev impedance networks etc to transform the input impedance of the antenna in order to match it with the source.

The third category involves the use of multiple DRAs. In this approach, two or more DRAs are designed whose resonance frequencies are close to each other, they are then combined in order to get in total a wide bandwidth. A detailed discussion of this technique will be presented in the following sub-section.

2.2.1 Multiple DRAs

The three different configurations for multiple DRAs are as follows :

• Stacked DRA:

In this approach multiple DRAs of different dimensions and/or permittivity are stacked one upon another as shown in fig.2.2.1(a.). Often a small air-gap is introduced between the resonators, as shown in fig.2.2.1(b.), in order to improve the bandwidth [42].

• Coplanar DRAs:

In certain applications where there is a strict restriction on the height of the antenna, the stacked DRA will not be feasible. In that case, the DRAs can also be positioned on the same plane. Fig.2.2.2 presents three element co-planar DRA.

The DRA elements are designed by varying their dimension and/or the ϵ

so that each element has a different resonant frequency which are close to each other.

The combined DRA has a wider bandwidth compared to the individual ones. The

main problem with this technique is, it requires large area, thereby making it

unsuitable for array applications.

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA

(a) Two element stacked DRA.

(b) Stacked DRA with air-gap.

Figure 2.2.1: Examples of stacked DRA.

Figure 2.2.2: Co-planar DRA.

• Embedded DRA:

For designing more compact broadband antenna, often two or more DRAs are

embedded within one another as shown in fig.2.2.3. Mostly, the configuration is

chosen such that ϵ

> ϵ

, as this will allow the power from the feed to efficiently

couple with the inner DRA, which will then propagate towards the low ϵ

outer

DRA and finally radiate into free-space. The embedded DRA is more compact

CHAPTER 2. DIELECTRIC RESONATOR ANTENNA than stacked and coplanar DRA.

Figure 2.2.3: Embedded DRA.

Chapter 3

Ultra-wideband embedded DRA

An antenna having a bandwidth of at least 20% is regarded as ultra-wideband [43]. Due to its compactness and broad bandwidth, the embedded DRA is one of the preferable alternatives for designing antenna elements for ultra-wideband arrays. This chapter will briefly mention some of the previous works on embedded DRAs and two new embedded DRA designs will be presented and discussed.

3.1 Previous works

One of the earlier works on embedded DRA was reported in 1997, where a cylindrical DRA with ϵ

=30.5 is inserted into a dielectric ring of same height but larger radius having an ϵ

=36.7. There, a bandwidth of around 38% was obtained [44]. In [45], a cylindrical DRA with radius=4 mm, height=2mm and ϵ

=12.3 has been inserted into a larger cylinder with radius=5.5 mm, height=6mm and ϵ

=4.1 and the resulting embedded DRA has a bandwidth over 50%. An eye-shaped embedded DRA with an inner cylinder having a diameter=4 mm, height= 2.54 mm and ϵ

=12 and the outer ellipse having a major diameter=10 mm, minor diameter=8 mm, height= 2.54 mm and ϵ

= 10.2 have been presented in [46]. The bandwidth of the resulting DRA is 28%.

A two layer embedded half-split cylindrical DRA with inner ϵ

=10.2 and outer ϵ

=2.32,

having a bandwidth of 88.25% has been reported in [47]. Although the DRA has a very

broad bandwidth, its radiation pattern gets distorted at the higher frequencies. An

embedded-stacked DRA has been designed in [48] which has a maximum bandwidth

of 68.1%.

CHAPTER 3. ULTRA-WIDEBAND EMBEDDED DRA

Often it is difficult to manufacture an embedded DRA using two different dielectric materials for the inner and outer layer. In such situation, a single material of high ϵ

can be used to construct the whole embedded DRA. The effective ϵ

of a particular layer can be reduced by creating air inclusions (i.e, perforations). Some works on perforated embedded DRA have also been reported in the literature. In [49], an embedded rectangular DRA has been designed employing a single material of ϵ

=10.2, the effective ϵ

of the outer layer has been reduced to 6.5 using cylindrical perforations. A maximum bandwidth of approximately 51% has been obtained when the DRA is fed using coaxial probe. A four layered embedded DRA with varying layer permittivities of 10.2(innermost layer), 2.93, 5.7 and 4.7(outermost layer), created by drilling cylindrical holes of different radius on a material of ϵ

=10.2 has been reported in [50]. The resulting DRA has a bandwidth of 26.7%.

3.2 This work

From the previous works on broadband embedded DRA it can be observed that, mostly, the ϵ

of the outer layer is taken to be smaller than that of the inner layer. Moreover, the designs where the contrast between the ϵ

of the outer and the inner layer is high, have a wider frequency bandwidth. One reason for this could be, the outer layer of the embedded DRA works as a transition between the high ϵ

inner layer and the free space. This, in addition to the effect of the merging of bandwidths of various modes that are excited in the embedded DRA increases the overall bandwidth of the antenna. Analysing [46] and [47] particularly, it can be fairly concluded that the overall bandwidth of the embedded DRA is broad when its individual components, i.e., the inner and the outer DRA are broadband. Therefore, for designing a broadband embedded DRA, it is preferable to start with designing the inner and outer element individually such that each element has a broad frequency bandwidth.

The basic idea for achieving a broad bandwidth in a DRA is, to reduce its radiation

Q factor without increasing the losses that lead to Ohmic power dissipation in the

antenna. In this regard, it is challenging to design a broadband DRA with high ϵ

material because the Q factor is proportional to ϵ

. However, one way to reduce the

radiation Q factor for high ϵ

material is to shape the geometry of the DRA in such a

way so that it has a low volume to surface area ratio. Lowering the volume to surface

area ratio will ensure less energy being stored within the volume of the DRA and will

CHAPTER 3. ULTRA-WIDEBAND EMBEDDED DRA

facilitate more energy to radiate through its surface [51]. This will, in turn, reduce the radiation Q factor of the DRA. Since, the radiation Q factor is proportional to the stored energy and is inversely proportional to the radiated energy. Additionally, a broadband DRA can be designed by removing materials from certain portions of the dielectric material (e.g by carving a notch). This effectively reduce the radiation Q factor of the antenna [41]. Utilizing these two techniques, two cylindrical embedded DRAs have been designed and simulated using Ansys HFSS in this thesis. The shaping has been done only on the inner layer, while a cylindrical geometry has been maintained for the outer layer. For this study, a loss less dielectric material of ϵ

=30 has been considered. Therefore, if the effects of dielectric losses are included, the efficiency of the antenna will decrease. However, it is expected that the reduction in the efficiency will be low because the dielectric materials which are used in microwave engineering generally have low value of loss tangent (tan δ). For example, the tan δ of some of the dielectric materials which are widely used for microwave applications, such as BZT (Ba

ZnTa

O

), Zirconia and Alumina are 2 × 10

, 2 × 10

and 5 × 10

respectively [52].

In the next section, the geometry of the two embedded DRA designs will be presented and in the next chapter, the simulation results will be discussed.

3.3 Antenna geometry

3.3.1 Modification of effective permittivity of dielectric material using perforations

The embedded DRA has been designed in a way such that it can be constructed monolithically, i.e by using a single material (ϵ

=30), with SLA printing. Therefore, in the outer layer, perforations have been created in order to reduce its effective permittivity. Two different techniques have been applied for designing the perforations. In the first antenna (Design-1), cylindrical perforations have been used and for the second antenna (Design-2), cubical perforations have been employed.

In order to compute the effective permittivity (ϵ

) due to the cylindrical perforations, the following approximate formula has been used [50]:

α = πr

s

, ϵ

= ϵ

(1 − α) + α (3.1)

CHAPTER 3. ULTRA-WIDEBAND EMBEDDED DRA

where α is the filling factor for square lattice, r

is the radius of the cylindrical holes, s is the spacing between two consecutive holes as shown in fig.3.3.1 and ϵ

is the permittivity of the bulk material. In case of cubical perforations, the following

Figure 3.3.1: Square lattice.

approximate design equation has been used to calculate the effective permittivity,ϵ

[53]:

ϵ

= f (ϵ

− 1) + 1 (3.2)

where f is the volume fill factor, which is the ratio between the solid volume and the total volume of the unit cell. The value of f lies between 0 (no fill) and 1 (fully filled).

The ϵ

is the permittivity of the bulk material.

3.3.2 Design-1

In the Design-1, the geometry of the inner DRA has been shaped in a way to reduce its volume to surface area ratio.

Using the techniques described in sec.2.0.3, it can be found from fig.3.3.2(a.) that for ϵ

=30, r=2.9 mm and h=6.3 mm (i.e r/h=0.46), the k

r=0.4. This gives a resonant frequency of 6.6 GHz according to eq.(2.9). However, when the DRA is simulated using HFSS, the resonance frequency is found to be shifted to 8 GHz as shown in fig.3.3.3.

The DRA has been excited using a rectangular slot feed similar to the one shown in fig.3.3.9. The shift in the resonance frequency might be due to the effect of the feeding mechanism which eq.(2.9) does not take into account. The volume to radiation surface area

ratio of this geometry is 1.18 mm. It can be seen from fig.3.3.3 that the cylindrical

1

Radiation surface area is calculated by considering only those surfaces where radiation can take