wideband balun phd

DESIGN AND IMPLEMENTATION OF WIDEBAND

BALUNS FOR ARCHIMEDEAN SPIRAL ANTENNAS

A THESIS SUBMITTED TO

THE SCIENCE AND ENGINEERING FACULTY

OF QUEENSLAND UNIVERSITY OF TECHNOLOGY

IN FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OFENGINEERING

N7064047

KALYANY VINAYAGAMOORTHY

Science and Engineering Faculty

Queensland University of Technology

August 2011

To my family

i

Abstract

The demand for high-speed data services for portable devicehas become a driving force

for development of advanced broadband access technologies. Despite recent advances

in broadband wireless technologies, there remain a number of critical issues to be

resolved. One of the major concerns is the implementation ofcompact antennas that

can operate in a wide frequency band.

Spiral antenna has been used extensively for broadband applications due to its pla-

nar structure, wide bandwidth characteristics and circular polarisation. However, the

practical implementation of spiral antennas is challengedby its high input characteristic

impedance, relatively low gain and the need for balanced feeding structures. Further

development of wideband balanced feeding structures for spiral antennas with matching

impedance capabilities remain a need. This thesis proposesthree wideband feeding sys-

tems for spiral antennas which are compatible with widebandarray antenna geometries.

First, a novel tapered geometry is proposed for a symmetric coplanar waveguide

(CPW) to coplanar strip line (CPS) wideband balun. This balun can achieve the un-

balanced to balanced transformation while matching the high input impedance of the

antenna to a reference impedance of 50Ω. The discontinuity between CPW and CPS

is accommodated by using a radial stub and bond wires. The bandwidth of the balun is

improved by appropriately tapering the CPW line instead of using a stepped impedance

transformer. Next, the tapered design is applied to an asymmetric CPW to propose a

novel asymmetric CPW to CPS wideband balun. The use of asymmetric CPW does

away with the discontinuities between CPW and CPS without having to use a radial

stub or bond wires.

Finally, a tapered microstrip line to parallel striplines balun is proposed. The balun

consists of two sections. One section is the parallel striplines which are connected to

iii

the antenna, with the impedance of balanced line equal to theantenna input impedance.

The other section consists of a microstrip line where the width of the ground plane is

gradually reduced to eventually resemble a parallel stripline. The taper accomplishes the

mode and impedance transformation. This balun has significantly improved bandwidth

characteristics.

Characteristics of proposed feeding structures are measured in a back-to-back con-

figuration and compared to simulated results. The simulatedand measured results show

the tapered microstrip to parallel striplines balun to havemore than three octaves of

bandwidth.

The tapered microstrip line to parallel striplines balun isintegrated with a single

Archimedean spiral antenna and with an array of spiral antennas. The performance

of the integrated structures is simulated with the aid of electromagnetic simulation

software, and results are compared to measurements. The back-to-back microstrip to

parallel strip balun has a return loss of better than 10 dB over a wide bandwidth from

1.75 to 15 GHz. The performance of the microstrip to parallelstrip balun was validated

with the spiral antennas. The results show the balun to be an effective mean of feeding

network with a low profile and wide bandwidth (2.5 to 15 GHz) for balanced spiral

antennas.

iv

Keywords

Frequency Independent Antennas; Archimedean spiral antenna; WAVES; Coplanar Waveg-

uide; Coplanar Striplines; Wideband balun; Microstrip lines; Parallel striplines

v

Acknowledgments

Throughout the research for my Master’s degree at QUT, I havereceived an enormous

amount of support from various people and institutions. First and foremost, I would

like to thank my supervisors, Dr Dhammika Jayalath and Dr Jacob Coetzee for their

constant encouragement, valuable guidance, insights, andtechnical contributions. My

sincere appreciation and gratitude goes to Dr Dhammika Jayalath who has been a won-

derful mentor. Special thanks to CST MWS simulation software supporter, Dr Frank

Demming-Janssen, for his enormous help relating to CST simulation. I appreciate every

effort made by the laboratory technician, Mr Frank Mate, whohas helped me to conduct

the antenna measurements at S block, Level 13. My thanks alsogoes to Mr Brian Jeffery

from the IT Help Desk for the CST software simulation and license updates. I would

like to express my gratitude to the staff members of the research portfolio office, Science

and Engineering Faculty including Ms Elaine Reyes, Ms Diane Kolometiz and Ms Judy

Liu who have supported by creating and stimulating a positive learning environment.

I would like to express my appreciation for the financial support I have received from

QUT in the form of a Postgraduate Research Scholarship. Last but not least I would like

to thank my family for their enormous support and motivationthroughout this personal

journey. This has been a great learning journey for me. While this study is the result

of my work during my Masters program, it would not have been actualized without the

help, guidance and motivation of all the people I have mentioned above.

vii

Table of Contents

Abstract iii

Keywords v

Acknowledgments vii

Table of Contents ix

Nomenclature xiii

List of Figures xv

List of Tables xxi

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Fundamental Properties of Wideband Antennas 5

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Antenna Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Radiation Pattern . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2 Isotropic, Directional, and Omni-directional patterns . . . . . . 9

ix

2.2.3 Antenna Directivity, Gain and Radiation Efficiency . . .. . . . 10

2.2.4 Radiation Intensity . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.5 Impedance of the antenna . . . . . . . . . . . . . . . . . . . . 11

2.2.6 Beam Width . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.7 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.8 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Wideband antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Frequency Independent Antennas . . . . . . . . . . . . . . . . 17

2.3.2 Log-Periodic Antenna . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 Sinuous Antenna . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Spiral Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Equiangular Spiral antenna . . . . . . . . . . . . . . . . . . . . 24

2.4.2 The Archimedean Spiral Antenna . . . . . . . . . . . . . . . . 24

2.4.3 Wideband Arrays Antenna . . . . . . . . . . . . . . . . . . . . 29

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Feeding Systems for Wideband antennas 33

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 General Balun Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Wideband Baluns Configuration . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Quarter-Wave Coaxial Balun . . . . . . . . . . . . . . . . . . . 36

3.3.2 Bazooka Balun . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.3 Tapered Balun . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.4 Marchand Balun . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.5 Double-Y Balun . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.6 Wideband CPW to CPS Balun . . . . . . . . . . . . . . . . . . 42

3.3.7 CPW to CPS Marchand Balun . . . . . . . . . . . . . . . . . . 43

x

3.3.8 CPW to CPS Double-Y Balun . . . . . . . . . . . . . . . . . . 44

3.3.9 CPW to CPS Chebyshev Balun . . . . . . . . . . . . . . . . . 45

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Design and Analysis of Wideband Baluns 49

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Design Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2.1 Coplanar Waveguide (CPW) . . . . . . . . . . . . . . . . . . . 50

4.2.2 Asymmetric CPW . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.3 Coplanar stripline (CPS) . . . . . . . . . . . . . . . . . . . . . 53

4.2.4 Microstrip line . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2.5 Asymmetric Parallel stripline . . . . . . . . . . . . . . . . . . 55

4.2.6 Taper Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Design of CPW to CPS wideband baluns . . . . . . . . . . . . . . . . . 60

4.3.1 Proposed CPW to CPS Balun . . . . . . . . . . . . . . . . . . 61

4.3.2 Back-to-back CPW to CPS balun . . . . . . . . . . . . . . . . 64

4.3.3 Proposed Asymmetric CPW to CPS Balun . . . . . . . . . . . 66

4.3.4 Back-to-back asymmetric CPW to CPS Balun . . . . . . . . . . 70

4.4 Design of tapered Microstrip to Parallel Striplines Balun . . . . . . . . 74

4.4.1 Tapered Microstrip lines . . . . . . . . . . . . . . . . . . . . . 74

4.4.2 Proposed Microstrip to Parallel Striplines Balun . . . .. . . . . 76

4.4.3 Back-to-back Microstrip to Parallel Striplines Balun .. . . . . 79

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5 Integration of Wideband Balun with Spiral Antennas 83

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.2 Performance of a Two-arm Archimedean Spiral Antenna . . .. . . . . 84

5.2.1 Design of a Single Spiral Antenna . . . . . . . . . . . . . . . . 84

xi

5.2.2 Performance of Large Spiral Antenna without Balun . . . .. . 86

5.2.3 Performance of Small Spiral Antenna without Balun . . . .. . 87

5.3 Integration of the Spiral Antenna with Balun . . . . . . . . . . .. . . . 87

5.3.1 Performance of the Large Spiral Antenna with Balun . . . .. . 88

5.3.2 Performance of the Small Spiral Antenna with Balun . . . .. . 101

5.4 Array of Archimedean Spiral Antennas . . . . . . . . . . . . . . . .. 106

5.4.1 Theory of WAVES Array Geometry . . . . . . . . . . . . . . . 106

5.4.2 Linear Antenna Array . . . . . . . . . . . . . . . . . . . . . . 107

5.4.3 Radiation pattern of the linear antenna array . . . . . . . .. . . 109

5.4.4 Planar Antenna Array . . . . . . . . . . . . . . . . . . . . . . 112

5.4.5 Radiation pattern of the planar antenna array . . . . . . . .. . 112

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6 Conclusion and Recommendations 121

6.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.2 Recommendations for Future Directions . . . . . . . . . . . . . . .. . 124

A Appendix : MATLAB code 127

A.1 HECKEN MATLAB code for symmetric CPW Design . . . . . . . . . 127

A.2 HECKEN MATLAB code for an Asymmetric CPW Design . . . . . . . 135

References 143

xii

Nomenclature

Abbreviations

3G-LTE 3 Generation Long-Term Evolution

ADS Advanced Design System

BW BandWidth

CR Cognitive Radio

CST Computer Simulation Technology

DAA Detect and Avoid

DBS Discreet Broadcast television Systems

EBG Electromagnetic Band Gap

EIRP Effective Isotropic Radiated Power

EM Electromagnetic

FCC Federal Communications Commission

FNBW First Null Beam Width

HPBW Half power Beam Width

ITU International Telecommunication Union

LDC Low Duty Cycle

LHCP Left Hand side Circular Polarization

MIC Microwave Integrated Circuits

MIMO multiple Input and Multiple Output

MMIC Monolithic Microwave Integrated Circuits

MoM Advanced Design System

xiii

RHCP Right Hand side Circular Polarization

SNR Signal to Noise Ratio

TEM Transverse Electromagnetic

VSWR Voltage Standing Wave Ratio

WAVES Wideband Array antenna with Variable Elements Size

WLAN Wide Local Area Networks

xiv

List of Figures

2.1 Two-dimensional normalised patterns . . . . . . . . . . . . . . .. . . 7

2.2 Radiation lobes and beamwidths of an antenna pattern . . . .. . . . . . 8

2.3 Omni-directional antenna pattern [1]. . . . . . . . . . . . . . .. . . . . 9

2.4 Antenna in transmitting mode [1]. . . . . . . . . . . . . . . . . . . .. 11

2.5 A two port network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.6 Three and two-dimensional patterns . . . . . . . . . . . . . . . . .. . 13

2.7 Rotation of a plane electromagnetic wave . . . . . . . . . . . . . .. . 14

2.8 Geometry of a logarithmically periodic antenna [2] . . . .. . . . . . . 18

2.9 Geometry of a sinuous antenna . . . . . . . . . . . . . . . . . . . . . . 19

2.10 EBG structure with spiral antenna [3]. . . . . . . . . . . . . . . .. . . 22

2.11 Geometry of an equiangular spiral antenna . . . . . . . . . . .. . . . . 24

2.12 Archimedean spiral antenna structure . . . . . . . . . . . . . .. . . . 27

2.13 Current vectors and radiating zone on two-arm spiral antenna . . . . . . 27

2.14 The geometry of WAVES with two different size elements .. . . . . . 31

3.1 The unbalanced and balanced transmission lines . . . . . . .. . . . . . 34

3.2 Balanced antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 A schematic for unbalanced to balanced transformation .. . . . . . . . 35

3.4 An unbalanced coaxial cable . . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Representation of a Quarter-Wave Coaxial Balun [1]. . . . . . .. . . . 37

3.6 Representation of a Bazooka Balun . . . . . . . . . . . . . . . . . . . . 38

xv

3.7 Representation of a Tapered Balun . . . . . . . . . . . . . . . . . . . . 39

3.8 Equivalent circuit for a Marchand balun [4]. . . . . . . . . . .. . . . . 40

3.9 Microstrip to slotline etched Marchand balun [4]. . . . . .. . . . . . . 40

3.10 Stripline to slotline balun with a radial stub . . . . . . . .. . . . . . . 41

3.11 Equivalent circuit for a double-Y balun [4]. . . . . . . . . .. . . . . . 42

3.12 CPW to CPS Marchand balun [4]. . . . . . . . . . . . . . . . . . . . . 43

3.13 CPW to CPS double-Y balun [4]. . . . . . . . . . . . . . . . . . . . . . 44

3.14 CPW to CPS Chebyshev balun . . . . . . . . . . . . . . . . . . . . . . 46

4.1 Geometry of CPW transmission line . . . . . . . . . . . . . . . . . . . 50

4.2 Block view of CPW transmission line . . . . . . . . . . . . . . . . . . 51

4.3 Asymmetric CPW transmission line . . . . . . . . . . . . . . . . . . . 52

4.4 The CPS transmission line . . . . . . . . . . . . . . . . . . . . . . . . 53

4.5 Geometry of microstripline structure . . . . . . . . . . . . . . .. . . . 54

4.6 Balanced parallel strips transmission line . . . . . . . . . . .. . . . . . 55

4.7 Asymmetric parallel strips transmission line . . . . . . . .. . . . . . . 55

4.8 Geometry of a dispersive tapered transmission line . . . .. . . . . . . 57

4.9 The typical impedance profile . . . . . . . . . . . . . . . . . . . . . . 58

4.10 A back-to-back Chebyshev wideband balun [5] . . . . . . . . . .. . . 60

4.11 Dimensions of the transmissions (Units : Millimetres). . . . . . . . . . 61

4.12 The impedance profile for the tapered CPW . . . . . . . . . . . . . .. 62

4.13 The dimensions for the tapered CPW . . . . . . . . . . . . . . . . . . .63

4.14 Simulated S-parameters results for single CPW to CPS balun . . . . . . 64

4.15 The back-to-back symmetric CPW to CPS wideband balun . . . .. . . 64

4.16 Comparison of S-parameters for back-to-back baluns . . .. . . . . . . 65

4.17 The surface current in symmetric CPW to CPS wideband balun. . . . . 65

4.18 Simulated S-parameters for back-to-back balun . . . . . .. . . . . . . 66

xvi

4.19 A single asymmetric CPW to CPS Wideband balun . . . . . . . . . . .67

4.20 Configuration of the asymmetric CPW to CPS balun . . . . . . . . . .68

4.21 The impedance and dimensions profile for asymmetric CPW .. . . . . 69

4.22 Simulated S-parameters results for ACPW to CPS balun . . . .. . . . 69

4.23 The back-to-back asymmetric CPW to CPS wideband balun . . .. . . 70

4.24 Comparison of S-parameters for symmetric asymmetric baluns . . . . . 71

4.25 The surface current in asymmetric CPW to CPS Wideband balun . . . . 71

4.26 Simulated and measured results for back-to-back asymmetric balun . . 72

4.27 ACPW to CPS balun measurement with a network analyser . . . .. . . 73

4.28 Measured and simulated S-parameters for ACPW to CPS balun. . . . . 73

4.29 Tapered microstrip transmission line . . . . . . . . . . . . . .. . . . . 74

4.30 A single microstrip to parallel striplines balun . . . . .. . . . . . . . . 75

4.31 Configuration of a tapered microstrip to parallel strip lines . . . . . . . 77

4.32 Simulated S-parameters results of a single balun . . . . .. . . . . . . . 78

4.33 Back-to-back connection of the balun . . . . . . . . . . . . . . . .. . 79

4.34 Surface current distribution of the microstrip to parallel striplines balun 80

4.35 Configuration of the microstrip to parallel striplines balun . . . . . . . . 80

4.36 Measured and simulated S-parameters results for balun. . . . . . . . . 81

5.1 Geometry of the two-arm Archimedean spiral antenna . . . .. . . . . . 85

5.2 Simulated return loss for large spiral with the discreteport . . . . . . . 86

5.3 Simulated return loss for small spiral with discrete port . . . . . . . . . 87

5.4 Configuration of the microstrip taper balun with a SMA connector . . . 89

5.5 The connection between inner spiral arms and balun . . . . .. . . . . . 89

5.6 The measurement set up for large spiral . . . . . . . . . . . . . . .. . 90

5.7 Simulated 3D directivity radiation patterns of the large spiral . . . . . . 90

5.8 E-plane directivity radiation patterns for large spiral . . . . . . . . . . . 91

xvii

5.9 H-plane directivity radiation patterns for large spiral . . . . . . . . . . . 92

5.10 Large spiral antenna radiation measurements set up . . .. . . . . . . . 93

5.11 Measured and simulated radiation patterns for the large spiral . . . . . . 94

5.12 Measurement set up for the large spiral in the anechoic chamber . . . . 95

5.13 Measured and simulated radiation patterns for the large spiral . . . . . . 96

5.14 Gain measurement for the large spiral with the horn antenna . . . . . . 97

5.15 HPBW calculation of the large spiral antenna in E-plane at 5 GHz . . . 98

5.16 Measured and simulated gain of the large spiral antenna. . . . . . . . . 99

5.17 Gain measurement for the two identical horns . . . . . . . . .. . . . . 100

5.18 Measured and simulated results for the small spiral . . .. . . . . . . . 101

5.19 E-plane directivity radiation patterns for the small spiral . . . . . . . . . 102

5.20 H-plane directivity radiation patterns for the small spiral . . . . . . . . 103

5.21 Measured and simulated gain of the small spiral antenna. . . . . . . . 104

5.22 Measured and simulated radiation patterns for the small spiral . . . . . 105

5.23 Basic geometry of WAVES . . . . . . . . . . . . . . . . . . . . . . . . 106

5.24 The linear antenna array . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.25 Simulated VSWR for the linear antenna array . . . . . . . . . . .. . . 108

5.26 Simulated S-parameters for the linear antenna array . .. . . . . . . . . 109

5.27 E-plane radiation patterns for the linear array . . . . . .. . . . . . . . 110

5.28 H-plane radiation patterns for the linear array . . . . . .. . . . . . . . 111

5.29 Simulated gain of the linear antenna array . . . . . . . . . . .. . . . . 111

5.30 The planar antenna array . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.31 Configuration of the 8-elements array with baluns . . . . . .. . . . . . 113

5.32 Planar array set up with a power divider . . . . . . . . . . . . . .. . . 113

5.33 Measured and simulated S-parameters results for planar array . . . . . . 114

5.34 3D radiation patterns of the planar antenna array at 5 GHz . . . . . . . 114

5.35 Grating lobes and side lobes for the planar antenna array . . . . . . . . 115

xviii

5.36 Directivity radiation patterns of the planar array . . .. . . . . . . . . . 116

5.37 Gain of the planar antenna array . . . . . . . . . . . . . . . . . . . .. 117

5.38 Measured and simulated radiation patterns for the planar array . . . . . 118

xix

List of Tables

3.1 The comparison of the above baluns . . . . . . . . . . . . . . . . . . .48

4.1 The dimensions of the tapered CPW and CPS transitions . . . . .. . . 63

4.2 The dimensions of asymmetric CPW and CPS Balun . . . . . . . . . . 67

4.3 The dimensions of Microstrip to Parallel Striplines Balun . . . . . . . . 78

5.1 The dimensions of the spiral antenna . . . . . . . . . . . . . . . . .. . 85

5.2 HPBW of the large spiral antenna in E and H-plane . . . . . . . . .. . 97

5.3 Measured gain data for the large spiral antenna . . . . . . . .. . . . . 98

5.4 HPBW of the small spiral antenna in E and H-plane . . . . . . . . .. . 102

5.5 Measured gain data for the small spiral antenna . . . . . . . .. . . . . 103

5.6 HPBW of the linear antenna array in E and H-plane . . . . . . . . .. . 109

5.7 HPBW of the planar antenna array in E and H-plane . . . . . . . . .. . 115

5.8 Measured gain data for planar antenna array . . . . . . . . . . .. . . . 116

6.1 The comparison of proposed baluns . . . . . . . . . . . . . . . . . . .123

6.2 The comparison of the spiral antenna with the proposed balun . . . . . 124

xxi

Chapter 1

Introduction

1.1 Motivation

Wireless communication technologies continue to evolve and expand at a phenomenal

pace. Third-generation long term evolution (3G-LTE) systems, Cognitive Radio (CR)

technologies for efficient use of the spectrum, and wirelessbroadband connectivity

to mobile users have been major focuses of recent research and standardization ef-

forts. These broadband networks provide integrated packet-oriented transmission of

text, graphics, voice, image, video, and computer data overpoint-to-point links as well

as in broadcast mode. Most of these systems provide broadband services and operate in

different frequency bands.

Many wireless applications thus require low cost and compact size [6] wideband

antennas. Wideband antennas are widely used in many applications such as ground

penetrating radars, tracking, sensing and imaging, multiple input and multiple output

(MIMO) and diversity operations [7], [8], short pulse radarfor automotive and robotics

applications [9], [10].

The spiral antenna is a wideband antenna with low profile and circular polarization.

The frequency band of a spiral antenna depends only on the physical dimension of

the antenna. However, spiral antennas require balanced feed structures and the input

impedance of the spiral antenna can also vary from 140-200Ω. Most standard feeders

such as coaxial cables are unbalanced with 50Ω input impedance. Therefore, balanced

feeding structures which can also perform the impedance transformation are needed for

spiral antennas.

1

2 CHAPTER 1. INTRODUCTION

Spiral antennas also have a low gain. Therefore, arrays of elements are used to

overcome these issues. However, the wideband characteristics of spiral antennas are

compromised in the array environment. Furthermore, array bandwidth is limited by

the individual antenna elements at the lower frequency and the emergence of grating

lobes are formed due to the inter-element spacing at higher frequency. Reference [11]

introduced a method of resolving the above problem. It is called wideband array with

variable element sizes (WAVES).

Another important problem affecting the antenna performance is selecting a proper

wideband feed network. The previous research study on WAVESidentified issues with

the feed of the array elements, since the wideband characteristic of the antenna depends

on a proper feed network which has to have a sufficiently largebandwidth. The balun

provides not only balanced fields but also impedance matching to the antenna.

Different kinds of balun have been developed over the past decades [4], [12], [13],

[14]. From 1994, several CPW to CPS wideband balun have been reported [15], [16].

However, these baluns are band limited and are unable to be used in this research.

The main objective of this research work is to design a wideband balun for spiral

antennas with a compact design. In this research, two new CPW to CPS wideband

balun are proposed. It is a modified version of the balun proposed in [5] with a wider

bandwidth. In addition, another wideband balun is proposedto further improve the

bandwidth. It is called tapered microstrip line to parallelstriplines balun. The microstrip

to parallel striplines balun is used as an optimum feed network for a single and array of

spiral antennas. All these designs are done using CST MWS simulator and simulated

results are validated with measured results.

1.2 Contributions

Through the research work of the thesis several major contributions have been made

to the field of wireless communications. In this section a summary of these major

contributions are presented.

• A comprehensive review of theory, principles and techniques of antennas and

wideband baluns are presented

1.3. ORGANIZATION 3

• A novel tapered geometry for a symmetric CPW to CPS wideband balun with a

stub to accommodate the discontinuity between CPW and CPS is proposed.

• An asymmetric CPW to CPS wideband balun with a novel tapered design is

proposed

• A tapered microstrip to parallel striplines balun with new tapered design is pro-

posed

• Wideband baluns are tested with various spiral antenna configurations

This thesis presents the results of a more comprehensive characterisation of planar

back-to-back CPW to CPS balun configuration, planar microstrip to parallel striplines

configuration and two different antenna arrays based on WAVES concept. The electro-

magnetic simulations and measurement characterization ofarray with WAVES concept

and feed network provide an understanding of their capabilities and limitations.

The optimum single wideband balun is selected from the results and integrated with

a single two-arm Archimedean spiral antenna and array of two-arm Archimedean spiral

antennas. The EM simulations in CST MWS are used to design the wideband balun

and antenna array and to illustrate the operation of the WAVES array with a proper feed

network. The WAVES array with a wideband balun is able to achieve full coverage over

more than two octaves.

1.3 Organization

This thesis is organised into six chapters. Chapter 2 contains a review of previous

work related to wideband antenna, different types of wideband antennas and antenna

wideband properties such as radiation patterns, gain, polarization, impedance and band-

width. Spiral antennas which belong to the family of frequency independent antenna,

are selected to achieve wideband characteristics. This spiral antenna maintains almost

circular polarization, consistent gain and input impedance over wide bandwidths. Two-

arm Archimedean spiral antenna is used in the design for reducing the amount of anten-

nas necessary to cover a wide frequency range of operation. Furthermore, the wideband

array with variable element sizes (WAVES) techniques is illustrated to a limited degree.

4 CHAPTER 1. INTRODUCTION

A broad overview of balun theory and standard designs are given in Chapter 3. Some

of the more common etched transition designs are discussed,which includes the etched

Marchand balun and the double-Y balun. The operation of the CPW to CPS balun is

discussed in detail.

Chapter 4 consists of three proposed taper feed networks withwideband character-

istics. The coplanar feed networks are simulated to investigate the back-to-back balun

performance when changing the gap width of CPW, length of CPS and with and without

radial stub with an aid of EM simulation (CST MWS). Furthermore, asymmetric CPW

is employed to remove the discontinuities between CPW and CPS.In addition, tapered

microstrip to parallel striplines balun is proposed to improve the bandwidth further. All

these designs are simulated in back-to-back configuration using CST MWS simulator

and the simulated results are validated with measured results.

The two-arm Archimedean array of spiral antennas design with wideband array

with variable element sizes (WAVES) techniques is constructed and integrated with a

proposed wideband balun feed network which is described in Chapter 5. The wideband

performance of a single spiral antenna with tapered microstrip to parallel striplines balun

is compared with an array of spirals. The research results focused on gain and radiation

patterns measurements in order to characterise their performance as electrically small

antennas. Chapter 6 concludes the thesis by summarising the main contributions of this

study and recommendations for future work.

Chapter 2

Fundamental Properties of Wideband

Antennas

2.1 Introduction

This research study provides an overview of broadband antennas, focusing specifically

on the concept of spiral antenna arrays with different element sizes. The performance

of the antenna is determined by antenna parameters such as radiation patterns, gain,

impedance, polarization and bandwidth of the antenna. Thischapter describes all these

antenna parameters and the related equations for the antenna design in detail.

Different types of broadband antennas such as log periodic antennas, sinuous anten-

nas and spiral antennas are also examined in Section 2.3. Major focus of this research is

the development of new feeding structures for the two-arm Archimedean spiral anten-

nas. Due to easy implementation with balanced devices, and wideband characteristics

the Archimedean spiral antenna was selected as a proposed antenna. A single spiral

antenna exhibits a low gain than the spiral antenna array. The antenna array is therefore

proposed with the wideband balun to achieve a broad bandwidth and high gain. An

investigation of arrays of Archimedean spiral antennas is given in Section 2.4.2. The

main argument presented in this section suggests that wideband array with variable

element sizes (WAVES) of Archimedean spiral antenna have broad bandwidth compared

to a single element and it eliminates the grating lobes at higher frequencies.

5

6 CHAPTER 2. FUNDAMENTAL PROPERTIES OF WIDEBAND ANTENNAS

2.2 Antenna Properties

Important antenna parameters to be considered for widebandantenna designs include

impedance matching, bandwidth, radiation patterns, gain,directivity and radiation effi-

ciency. These parameters are almost constant in the narrow band antenna, but can vary

significantly in wideband antennas. These important antenna parameters are described

in detail below.

2.2.1 Radiation Pattern

An antenna radiation pattern is defined as a graphical representation or a mathematical

function of the radiation properties of the antenna as a function of space coordinates.

It is mostly determined in the far field region and is represented as a function of the

directional coordinates. Radiation properties include density, radiation intensity, field

strength, directivity phase or polarization. A trace of thereceived electric (magnetic)

field at a constant radius is called the amplitude field pattern.

On the other hand, a graph of the spatial variation of the power density along a

constant radius is called an amplitude power pattern. The field and power patterns are

often normalized with respect to their maximum value, yielding normalized field and

power patterns [1].

The power pattern is usually plotted on a logarithmic scale or more commonly in

decibels (dB). For an antenna, the field pattern (in linear scale) typically represents

a plot of the magnitude of the electric or magnetic field as a function of the angular

space; the power pattern (in linear scale) typically represents a plot of the square of the

magnitude of the electric or magnetic field as a function of the angular space. The power

pattern in (dB) represents the magnitude of the electric or magnitude field, in decibels,

as a function of the angular space.

It can be illustrated in this way. The two-dimensional normalized field pattern (plot-

ted in linear scale), power pattern (plotted in linear scale), and power pattern (plotted on

a logarithmic dB scale) of a 10-element linear antenna arrayof isotropic sources, with

2.2. ANTENNA PROPERTIES 7

a spacing ofd = 0.25λ between the elements, are shown in Figure 2.1. The plus and

minus sign indicate the relative polarization of the amplitude between the various lobes,

which change as the nulls are crossed. The half power (-3 dB) point is indicated relative

to the maximum value of the pattern in the following cases. Figure 2.1(a) shows the

half power of the field patterns at 0.707 value of its maximum.Half power of the power

pattern is (in linear scale) at its 0.5 value of its maximum asshown in Figure 2.1(b) and

power pattern (in dB scale) is at -3 dB value of its maximum as shown in Figure 2.1(c).

All three patterns yield the same angular separation between the two half-power points,

38.64o, on their respective patterns, referred to as Half Power BeamWidth (HPBW) as

illustrated in Figure 2.1.

(a) Field Pattern (b) Power Pattern(in linear scale)

(c) Power Pattern(in dB)

Figure 2.1: Two-dimensional normalised field pattern (linear scale),power pattern(linear scale), and power pattern (in dB) [1].


Radiation patterns have different parts which are referred to as lobes as shown in

Figure 2.2. They are major, minor, side and back lobes. A radiation lobe is a portion of

the radiation pattern bounded by regions of relatively weakradiation intensity.

(a)

(b)

Figure 2.2: (a) Radiation lobes and beamwidths of an antenna pattern (b)Linear plot ofpower pattern and its associated lobes and beamwidths [1].

Figure 2.2(a) shows a symmetrical three-dimensional polarpattern with a number

of radiation lobes. A major lobe is defined as the radiation lobe containing the direction

of maximum radiation. In Figure 2.2 the major lobe is pointing in theθ = 0 direction.

A minor lobeis any lobe except a major lobe. In Figure 2.2(a) and Figure 2.2(b), all the

lobes with the exception of the major can be classified as minor lobes. Aside lobeis a


radiation lobe in any direction other than the intended lobe. A back lobeis a radiation

lobe whose axis makes an angle of approximately 180o with respect to the beam of an

antenna.

2.2.2 Isotropic, Directional, and Omni-directional patterns

An isotropic radiator is a lossless antenna having equal radiation in all directions. The

directive properties of actual antennas are expressed witha reference to isotropic an-

tenna, although it is ideal and not physically realisable. Adirectional antenna is one

having the property of radiating or receiving electromagnetic waves more effectively in

some directions than in others. When maximum directivity is significantly greater than

that of a half-wave dipole, it is called directional antenna.

Figure 2.3 shows an omni-directional pattern where a pattern is non-directional in

the azimuth plane (f(ϕ), θ = π/2) and directional in the elevation plane (g(θ), ϕ =

constant). It is a special type of a directional pattern [1].An antenna’s radiation property

can be described in three common radiation patterns.

Figure 2.3: Omni-directional antenna pattern [1].

• Isotropic- A hypothetical lossless antenna having equal radiation inall directions.

It is only applicable for an ideal antenna and is often taken as a reference for

expressing the directivity properties of actual antennas.


• Directional - An antenna having the property of radiating or receiving electro-

magnetic waves more effectively in some direction than in others. Maximum

directivity of this antenna is significantly greater than that of a half wave dipole.

• Omni-directional- An antenna having an essentially non-directional patternin a

given plane and a directional pattern in any orthogonal plane.

2.2.3 Antenna Directivity, Gain and Radiation Efficiency

Directivity D is defined as the ratio of the radiation intensityU in a given direction from

the antenna to the radiation intensity averaged over all direction. The average radiation

intensity is equal to the total power radiated by the antenna(Prad) divided by4π. So the

directivity can be calculated by:

D =U

U0

=4πU

Prad

(2.1)

If not specified, antenna directivity implies its maximum value, i.e.D0.

D0 =U |max

U0

=4πUmax

Prad

(2.2)

Antenna gainG is closely related to the directivity, but it takes into account the radiation

efficiencyerad of the antenna as well as its directional properties, as given by:

G = eradD (2.3)

Radiation efficiency (erad) is determined by the ratio of the radiated power,Prad to the

input power at the terminals of the antenna,Pin.

erad =Prad

Pin

=G

D(2.4)

2.2.4 Radiation Intensity

It is defined as the power radiated from an antenna per unit solid angle. The radiation

intensity is a far-field parameter, and it can be obtained by simply multiplying the


radiation density by the square of the distance. It is given in the mathematical form

as follows:

U = r2Wrad (2.5)

whereU is the radiation intensity (W/ unit solid angle) andWrad is the radiation density

(W/m2).

2.2.5 Impedance of the antenna

Antenna input impedance is defined as the ratio of the voltageto current at the input

terminals a-b of the antenna with no load attached, as shown in Figure 2.4. The input

impedance of the antenna is given in the equation (2.6).

Figure 2.4: Antenna in transmitting mode [1].

ZA = RA + jXA (2.6)

where,

ZA - antenna impedance at terminals a-b (ohms)

RA - antenna resistance at terminals a-b (ohms)

XA - antenna reactance at terminals a-b (ohms)


Figure 2.5: A two port network

The S-parameters definition for the two port network is givenin the following

matrix:

b1 = S11a1 + S12a2b2 = S21a1 + S22a2 (2.7)

where the independent variablesa1 anda2 are normalised incident voltage waves andb1

andb2 are normalised reflected voltages.

S11 - input reflection coefficient

S22 - output reflection coefficient

S12 - reverse transmission gain

S21 - forward transmission gain

Reference [17] states that the input impedance of the antennais largely determined

by the characteristic impedance of the feeding transmission line. Reference [18], [19]

and [20] pointed out that the input impedance of an antenna iseffected by the line

width, the distance between the lines, the dielectric constant and the substrate thickness.

Reference [21] developed the 2-port measurements techniques to measure the input

impedance of the spiral antenna using the following equation:

Zin = 2Z01 + S11 − S12

1− S11 + S12

(2.8)

whereZ0 = 50Ω


2.2.6 Beam Width

The beam width of an antenna pattern is defined as the angular separation between

two identical points on opposite sides of the pattern maximum. Two most widely

used beam widths are the Half-Power Beam Width (HPBW) and the First-Null Beam

Width (FNBW). HPBW is defined by IEEE as: “In a plane containing the direction of

the maximum of a beam, the angle between the two directions inwhich the radiation

intensity is one-half value of the beam” [1]. FNBW is defined asthe angular separation

between the first nulls of the pattern. Figure 2.6 shows both the HPBW and FNBW.

However, in practice, the term beam width usually refers to the HPBW.

The beam width of antenna is a very important figure of merit and it is often used

with the side lobe level. When the beam width decreases, the side lobe increases

and vice versa. Moreover, the beam width of the antenna is also used to describe

the resolution capabilities of the antenna to distinguish between two adjacent radiating

sources or radar targets. The most common resolution criterion states that the resolution

capability of an antenna to distinguish between two sourcesis equal to half the First-

Null Beam Width (FNBW/2) which is usually used to approximate the HPBW [22],

[23].

(a) (b)

Figure 2.6: Three and two-dimensional power patterns (in linear scale) of U(ϑ) =cos2(ϑ) cos3(ϑ) [1].

2.2.7 Polarization

The polarization of an electromagnetic wave is defined as theorientation of the electric

field vector and this vector is perpendicular to both the direction of travel and the


magnetic field vector. It is determined by the physical structure of the antenna and by its

orientation. The polarization is described by the geometric figure traced by the electric

field vector upon a stationary plane perpendicular to the direction of propagation, as the

wave travels through that plane. An electromagnetic wave isfrequently composed of

two orthogonal componentsEx andEy, as shown in Figure 2.7. This figure shows a

typical trace as a function of time.

The geometric figure traced by the sum of the electric field vectors over time is,

in general, an ellipse and the field is said to be ellipticallypolarized. Under certain

conditions the ellipse may break into a straight line, in which case the polarization is

called linear; and a circle, in which case the polarization is called circular. The figure of

the electric field can be traced in a clockwise or counter-clockwise direction. Clockwise

rotation of the electric-field vector is defined as a right-hand polarization and counter-

clockwise as left-hand polarization.

(a) (b)

Figure 2.7: Rotation of a plane electromagnetic wave and its polarization ellipse atz = 0 as a function of time [1].

Spiral antennas radiate right-hand polarization to one side and left-hand polarization

to the other side. The radiating currents along the arms are travelling wave currents and

their paths are clockwise when considered from one side and counter-clockwise when

considered from the other side. The radiated field from thesetravelling currents will also


rotate in the same direction as the exciting current. Therefore, the fields will be Left-

Hand Circular Polarization (LHCP) for clockwise orientationof arms and Right-Hand

Circular Polarization (RHCP) for counter-clockwise orientation of arms.

Linear Polarization : Linear Polarization is specified as a special case of Elliptical

Polarization and a time-harmonic wave is linearly polarized at a given point in space

if the electric field (or magnetic field) vector at that point is always oriented along the

same straight line at every instant of time. This is achievedif the field vector possesses

only one component, or two orthogonal linear components that are in time phase or 180o

(or multiples of 180o) out of phase.

Circular Polarization : It is defined that the electric field (or magnetic field) vector

traces a circle as a function of time at a given point in space.It is achieved if the field

vector possesses all of the characteristics such as:

• The field must have two orthogonal linear components, and

• The two components must have same magnitude, and

• The two components must have a time-phase difference of odd multiples of 90o.

The sense of rotation is always determined by rotating the phase-leading component

toward the phase-lagging component and observing the field rotation as the wave is

viewed as it travels away from the observer. If the rotation is clockwise, the wave

is right-hand (or clockwise) circularly polarized; if the rotation is counter-clockwise,

the wave is left-hand (or counter-clockwise) circularly polarized. The rotation of the

phase-leading component toward the phase-lagging component should be done along

the angular separation between the two components that is less than 180o. Phases equal

to or greater than 0o and less than 180o should be considered leading whereas those

equal to or greater than 180o and less than 360o should be considered lagging.

Elliptical polarization : A time-harmonic wave is elliptically polarized if the tip

of the field vector (electric or magnetic) traces an elliptical locus in space. At various

instants of time the field vector changes continuously with time in such a manner as to

describe an elliptical locus. It is right-hand (clockwise)elliptically polarized if the field


vector rotates clockwise, and it is left-hand (counter-clockwise) elliptically polarized if

the field vector of the ellipse rotates counter-clockwise. The necessary and sufficient

conditions to accomplish this are if the field vector (electric or magnetic) possesses all

of the following:

• The field must have two orthogonal linear components

• The two components can be of the same or different magnitude

• If the two components are not of the same magnitude, the time-phase difference

between the two components must not be 0o or multiples of 180o (because it will

then be linear)

• If the two components are of the same magnitude, the time-phase difference

between the two components must not be odd multiples of 90o (because it will

then be circular).

2.2.8 Bandwidth

Bandwidth is the main characteristic of the wideband antenna. The bandwidth can

be considered to be the range of frequencies, on either side of the centre frequency,

where the antenna characteristics are within an acceptablevalue. The bandwidth can be

described in terms of percentage of the centre frequency,fC , of the band.

BW =fH − fL

fC× 100 = 2

fH − fLfH + fL

× 100 (2.9)

wherefH is the highest frequency in the band andfL is the lowest frequency in the

band. The centre frequency can is calculated from:

fC =fH + fL

2(2.10)

For broadband antennas, the bandwidth can also be expressedas the ratio of the highest

frequency to the lower frequency, where the antenna performance is acceptable. It is

given by:

BW =fHfL

(2.11)

2.3. WIDEBAND ANTENNAS 17

2.3 Wideband antennas

Wideband antennas are an essential part of wireless communication systems. Extensive

research has been conducted on various types of antennas, ranging from simple wire

antennas to planar antennas. However, it is necessary to select an antenna with a

compact size and wideband characteristics for wideband applications. Some wideband

antennas were examined and spiral antennas, which belong tofrequency independent

antennas, are selected as best candidates in this project due to its planar structure, low

profile, wide bandwidth characteristics, and circular polarization.

2.3.1 Frequency Independent Antennas

Frequency independent antennas are antennas whose radiation pattern, impedance and

polarization remain unchanged over a large bandwidth [24],[25]. Frequency indepen-

dent antennas exist in several configurations such as equiangular, sinuous and Archimedean

[26]. Frequency independent antenna can be completely defined by angles. The general

formula for their shape is given by the equation (2.12) and itwas taken from [27].

ρ = ea(φ+φ0)F (θ) (2.12)

whereρ, θ andφ are the usual spherical coordinates,a andφ0 are constants andF (θ) is

any function ofθ .

Frequency independent antennas provide uniform electrical characteristics over a

wide frequency band. However, frequency independent antennas have broad radiation

patterns and low gain in general, which is not suitable for some applications. This

problem can be resolved by using an array of frequency independent antenna elements.

The wideband characteristics of the frequency independentelement are lost in the array

environment even as the above method allows for pattern control and higher gains.

2.3.2 Log-Periodic Antenna

Reference [2] introduced the log-periodic antenna which haswideband frequency char-

acteristics. There are three basic design principles that embody the logarithmically


periodic antenna whose properties vary periodically with the logarithm of the frequency.

The first one is the angle concept. In this design concept, thegeometry of the antenna

structure is completely described by angles rather than lengths. The second principle is

that the input impedance of an antenna is frequency independent [27]. Therefore, it is

a frequency independent antenna. The third principle is to design the antenna structure

where its electrical properties repeat periodically with the logarithm of the frequency.

Figure 2.8: Geometry of a logarithmically periodic antenna [2]

The geometry of the logarithmically periodic antenna structure is shown in Figure 2.8.

The radii of the log-periodic antenna,Rn , rn are slots radii andβ is a subtended angle.

The geometric of the antenna is defined by the following equation (2.13), where the

radiusRn−1, Rn, Rn+1 form a geometric sequence of terms.

τ =Rn

Rn+1

(2.13)

The same geometric ratio can be derived with the radiusrn−1, rn, rn+1 which forms a

similar sequence. The successive slot lengths and distances are in the common ratio,

M :

M =rnRn

=lnLn

(2.14)

Reference [28] performed an extensive study on the performance of this antenna as a

function ofα, β, τ andM . In general, the logarithmically periodic antennas have planar

2.4. SPIRAL ANTENNA 19

and conical structure and this antenna has linear polarization.

2.3.3 Sinuous Antenna

Reference [29] invented the sinuous antenna in 1982 (shown inFigure 2.9). It is also

a frequency independent antenna and has wideband characteristics and dual linear and

dual circular polarization with low profile geometry. As shown in Figure 2.9, it is a

four-arm self-complementary structure with input impedance of 188.5Ω (based on self-

complementary antenna theory) over its bandwidth of operation in free space. However,

[30] suggests that it has lower impedance in measurements than the theoretical value.

In addition, [30] investigated that the substrate materialhas considerable influence on

the characteristics of the sinuous antenna. Most of the applications require an uni-

Figure 2.9: Geometry of a sinuous antenna

directional radiation pattern with low profile antennas, but the sinuous antenna has a

bi-directional radiation pattern. In order to produce a unidirectional radiation pattern,

the sinuous antenna is backed by a ground plane. However, theground plane changes

the antenna impedance greatly over the operation band.

2.4 Spiral Antenna

Spiral antennas also belong to the class of antennas known asfrequency independent

antennas. The bandwidth of the spiral antenna can reach up to40:1 for both the input


impedance and the radiation pattern. The smallest and largest circumference of the

spiral structure determine their respective upper and lower cut-off frequencies.

Most of the previous research on spiral antennas was based onexperiment and the

band theory. Band theory is defined by the spiral antenna operating in the region where

the circumference of the spiral is equal to a wavelength.

If the antenna have frequency independent characteristics, its surface is described

by following equation [27]:

r = F (θ, φ) = eaφf(θ) (2.15)

where,

a =1

K

dK

dC(2.16)

whereK is a factor is used to lowering the operating frequency of theoriginal frequency

by a factorK andC is the rotation angle. The derivation off(θ) (completely arbitrary

function) in equation 2.15:

df(θ)

dθ= f ′(θ) = Aδ

π

2− θ

(2.17)

whereA is a constant andδ is the Derac delta function. The reduced form of equation

(2.15) using equation 2.17is given as follows:

r = ρ =

Aeaφ θ = π2

0 elsewhere

(2.18)

whereA is the starting point of the curve whenφ = 0, and it gives logarithmic spiral

curve.

In most cases, a spiral antenna consists of a thin metal foil spiral pattern etched on

a substrate fed from the centre. Spiral antennas radiate bi-directionally. However, most

of the applications require unidirectional radiation characteristics as well as having low

profile. It can be resolved by adding a lossy cavity to the spiral antenna, backed by

conductor, or adding absorbing materials. It absorbs the back radiation from the spiral

providing for a wide bandwidth by reducing the reflection from ground plane.


The lossy cavity improves the low frequency impedance behaviour and axial ratio

of the spiral by reducing reflections from the end of the each arm of the spiral. Further-

more, [31] showed that in order to reduce the reflected currents from the arm ends of the

unbalanced-mode Archimedean spiral antenna, a ring-shaped absorbent material may

be applied to the cavity. It also absorbs the back radiation from the spiral giving a large

pattern bandwidth by reducing the reflection from the groundplane that causes pattern

nulls [32], [33]. However, lossy cavity creates gain reduction due losses. Moreover,

lossy cavity gives extra depth and weight to the antenna. Without backing, spiral

antennas have bidirectional radiation, which is not desirable. Therefore, conductor

backed spiral antennas have been used in many applications to get an unidirectional

radiation [34].

Reference [35], [36] and [37] showed that the conductor backed spiral antenna,

where a metal ground plane is used as a conductor, has a 1:2:1 circular polarization

bandwidth and to reflect unwanted power in order to get unidirectional path. However,

in conductor backed spiral antenna, the conductor will reflect the radiated fields that

enter the cavity. However, the reflected fields will destroy the forward travelling fields

of the spiral antenna if the cavity depth (d) is smaller than a wavelength.

Another method to get unidirectional pattern in spiral antenna is adding absorbing

materials. In absorbing material backed spiral antenna, the reflected fields from the cav-

ity will be attenuated. Therefore, spiral antenna can have its wideband characteristics.

One of the absorbing materials is a chip resistor which is used in a microstrip spiral

antenna structure. The usage of microwave absorbing material is not approved for some

applications due to the reduced gain. Reference [37] used three metal plates inside the

hollow metal cavity to improve the bandwidth of the spiral antenna. However, a hollow

metal cavity reflects the wave into the spiral and degrading the antenna performance,

particularly at the low frequency. Thus, resistive loads were added at the end of each

of the spiral arms to overcome the above problem. Moreover, it reduces the reflection

from the end of each arm and improved the low frequency Voltage Standing Wave Ratio

(VSWR) and axial ratio.

Reference [38] investigated that the standing wave is appeared when the thickness of

the substrate becomes thinner and it disrupts the radiationpatterns. Furthermore, stand-

ing wave deteriorates the impedance matching and radiationpatterns when the distance


between the spiral antenna and the ground plane is less thanλ/2. The thin thickness of

the substrate reduced the gain at lower frequencies. Reference [39] therefore proposed

a method to remove the standing wave by loading the antenna with chip resistors and

it was placed inside the substrate. However, the resistive loading was not enough to

remove the standing waves of higher frequencies. Thus, it was replaced along the spiral

antenna. However, it made undesirable effects and much power was dissipated in the

loads.

Size of the spiral antenna is another issue that has been considered for many years.

One way to reduce the size is through material loading. However, it can be a problem

in some applications due to material loss and weight. Therefore, slow wave spiral

techniques were developed to overcome the problems inherent in material loading. A

slow wave spiral is produced by adding some type of high frequency profile, such as

a zigzag or sine wave, to spiral antenna and increasing the circumference of the spiral

antenna, such as the square spiral. Reference [40] assert that antenna size can be reduced

by choosing a small starting angleφstart (Given in Section 2.4.2) while keeping the

spiral constant unchanged.

Figure 2.10: EBG structure with spiral antenna [3].

Reference [3] presented the implementation of electromagnetic band gap (EBG)

structures with an inherently wide band Archimedean spiralantenna (discussed in Sec-

tion 2.4.2)and they concluded that utilization of an EBG structure offers an antenna

height reduction of more than 69%, including thickness of the EBG structure (shown


in Figure 2.10). However, changing the antenna height from bottom plane makes a

variation to the antenna characteristics. Therefore, antenna height cannot be made

extremely small without additional measures to reduce the variation in the antenna char-

acteristics [41]. The electrical antenna height (Hant/ λ) decreases when the frequency

decreases and the spiral becomes strong due to the reflected EM fields impinging on

it. The current along the conducting spiral arms are affected by these reflected EM

fields. The impinging EM fields can become weaker by increasing antenna height

which increases the electrical antenna height. However, itis not possible for low profile

antennas. Therefore, [42] proposed a method to use a ring shaped strip absorber to

remove the EM fields reflected from the bottom of the cavity. Furthermore, ring shaped

strip absorber was reduced to arc shaped strip absorber by considering the size of the

antenna. Reference [19] suggests that thick dielectric, lowdielectric constant (ǫr) , and

low insertion loss is always desired for broadband purposesand increased efficiency.

In addition, slow wave techniques are employed to move the radiation zone closer

to the centre of the spiral for a specific wavelength. As a result, this reduces the velocity

of propagation along the length of the spiral, which reducesthe low frequency cut-off of

the spiral providing for size reduction. Reference [41] argues that when the length of the

longitudinal direction of the antenna decreases, the operation bandwidth of the antenna

increases. Furthermore, the low frequency cut-off can be reduced by terminating the

end of each arm of the spiral with resistive loads to remove the reflections from the end

of the spiral. However, it reduces the efficiency and gain.

Spiral antennas are classified into several types; square spiral, star spiral, Archimedean

spiral, and equiangular spiral. The square spiral antenna has the same advantage as cir-

cular Archimedean spiral antenna at the lower frequencies.However, the square spiral

geometry seems to be less frequency independent at high frequencies [43]. A star spiral

provides as much size reduction same as the square spiral andit allows tighter array

packing that the square spiral does not [44]. However, one ofthe major disadvantages of

the star and square spiral antenna is its dispersive behaviour. Archimedean spiral is the

most popular configuration due to its wide bandwidth and allowing tighter array spacing.

The equiangular planar spiral antennas have similar characteristics to the Archimedean

spiral.


2.4.1 Equiangular Spiral antenna

The equiangular spiral antenna’s surface is described by angles and its performance

would be independent of frequency [45]. Figure 2.11 shows the equiangular spiral curve

which is derived from the equation (2.19). The total length of spiral is given in the

Figure 2.11: Geometry of an equiangular spiral antenna

following equation:

L =

∫ ρ1

ρ0

[

ρ2(

dφ

dρ

)2

+ 1

]1/2

dρ = (ρ1 − ρ0)

√

1 +1

a2(2.19)

and

ρ = keaφ′

(2.20)

whereA is a constant,ρ andφ are the conventional polar coordinates,a and k are

positive constants.

2.4.2 The Archimedean Spiral Antenna

The Archimedean spiral antenna has been widely used for several applications such as

air borne applications, wireless communications, UWB communications, satellite com-

munications, radio navigations, biological medicine, andradar [20]. The Archimedean


spiral antenna was developed by E.M.Tuner [46]. It can be easily constructed using

printed circuit techniques. Since the spacing between adjacent arms of the Archimedean

spiral antenna is specified by a constant and not an angle, it cannot be considered as a

truly frequency independent antenna. It is classified as a quasi-frequency independent

antenna [39]. Planar Archimedean spiral antenna is widely used due to its low profile,

light weight, high efficiency, circular polarization, stable impedance characteristics, and

broad bandwidth [20].

Cavity backed Archimedean spiral antennas are used to obtaina single main beam

and mostly have a 90o half power beam width, VSWR of2 : 1 (VSWR is defined in

equation (2.21)) and a boresight axial ratio with a circularpolarization, where having

maximum radiated power, of 1:1 over a bandwidth of 10:1.

V SWR =1 + ρ

1− ρ(2.21)

whereρ is the magnitude of reflection coefficient (|Γ|).

Archimedean spiral antenna radiates circularly polarizedwave in bidirectionally

normal to the antenna plane in free space [20]. However, [39]noted that the character-

istic of unidirectional radiation is always required in theapplication of ultra-wideband

spiral antenna. An Archimedean spiral antenna is backed by ametal ground plane,

an absorbing cavity and shallow cavity (as described in Section 2.4) to achieve unidi-

rectional patterns [39], [34] [20] and [41]. However, absorbing cavity decreases the

gain of the antenna by 3 dB, and adding a reflector reduces the impedance and the

axial ratio. However, antenna backed by an extremely shallow cavity has a variation

in input impedance at low frequencies due to the reflection ofEM fields at the bottom

of the cavity. Reference [47] suggested that grating lobes occur in the radiation pattern

of a broadband antenna array and it can be reduced by selecting a suitable spacing of

elements.

The author in [46] conducted experiments and obtained almost a constant input

impedance and circular polarization over a wide beamwidth for a broad range of fre-

quencies (2 to 18 GHz) by winding a long straight wire dipole into an Archimedean spi-

ral shape. IffH andfL represent the upper and lower frequencies of operation for which


satisfactory performance is obtained, then a broadband antenna can be characterised as

having the impedance and radiation patterns of the antenna remaining constant over an

octave (fH / fL= 2) or more. The Archimedean spiral antenna tends to produceradiation

patterns and an input impedance which change smoothly with frequency.

The Archimedean spiral antenna has extremely wide bandwidth and its two arms

are linearly proportional to the polar angle. The slot type Archimedean spiral is the

dual of the strip type Archimedean spiral. Thin film widebandwidth planar antenna

applications of 3D Monolithic Microwave Integrated Circuits (MMIC) use slot type

spiral.

A dual arm is obtained by duplicating the single arm along thenormal axis with

180o rotation. Dual arm spiral antenna has symmetrical radiation pattern and better

axial ratio compared to a single arm spiral antenna [48]. It requires a balanced feeding

due to its balanced structure. Therefore, authors in [48] used a balun to obtain balanced

structure from unbalanced source and it transforms the characteristic impedance of a

transmission line to input impedance of the antenna.

Figure 2.12 shows the single arm and two-arm Archimedean spiral antenna. The

circular Archimedean spiral antenna produces a smooth change when the current adjusts

with frequency. The two-arm Archimedean spiral antenna radiates from a region where

the circumference of the spiral is approximately equal to one wavelength. This region

is called an active region of spiral. Each arms of the spiral is fed 180o out of phase, so

when the circumference of the spiral is one wavelength, the currents at complementary

or opposite points on each arms of the spiral, add in phase in the far field. Reference

[39] investigated that maximum radiation is obtained when the diameter of the antenna

is equal toλ/π, as a result, the current is in phase on the two arms of the antenna.

The current on opposite arms, shown by arrows in Figure 2.13(a) (feed in the centre)

and Figure 2.13(b) (feeding from outside), as current vectors, are spatially in phase

because the arms in the centre, which extend in opposite directions, are fed in anti-phase.

Therefore, the position A and position B (in Figure 2.13(a))have in phase currents. If

the arm length between A and B’ is half a wave length then the current at position B’

is in phase with B. Thus, radiation occurs at a circumference of one wavelength of the

spiral antenna. It is called band theory for spiral antenna [49], [47].


(a) Two-arm Archimedean spiral (b) Single-arm Archimedean spiral

Figure 2.12: Archimedean spiral antenna structure

Figure 2.13: Current vectors and radiating zone on two-arm spiral antenna with (a)Feeding in the center and (b) Feeding from outside [49]

The size of the antenna is computed from the lowest and the highest frequency of

the operating frequency range [39]. The low frequency operating point of the spiral is

determined theoretically by the outer radiusr2 and is given by:

fL =c0

2πr2√ǫeff

(2.22)

The high frequency operating point is based on the inner radiusr1, giving:

fH =c0

2πr1√ǫeff

(2.23)


where c0 is the propagation velocity in free space andǫeff is the effective relative

dielectric constant.

Theory of Archimedean Spiral Antenna

A self-complementary single element two-arm Archimedean spiral antenna is shown in

Figure 2.12(a). A spiral antenna is self-complementary if the metal and air regions of

the antenna are equal. The input impedance of a self-complementary antenna can be

found using Babinet’s principle, giving:

ZmetalZair =η2

4(2.24)

whereη is the characteristic impedance of the medium surrounding the antenna. For

a self-complementary Archimedean spiral antenna in free space, the input impedance

should be:

Z0 =η02

= 188.5Ω (2.25)

Each arm of an Archimedean spiral is linearly proportional to the winding angle,φ and

is described by the following relationships [24].

r = r0φ+ r1 (2.26)

and

r = r0 (φ− π) + r1 (2.27)

wherer1 is the inner radius of the spiral. The proportionality constant is determined

from the width of each arm,w, and the spacing between each turn,s, which for a self-

complementary spiral is given by [50].

r0 =s+ w

π=

2w

π(2.28)

The strip width of each arm can be found from the following equation:

s =(r2 − r1)

2N− w = w (2.29)


wherer1, r2 are inner and outer radii of the spiral respectively.

Another way of defining spiral arms in relation to the angle, is given in [42]. An

Archimedean spiral antenna has two arms A and B with strip widthw and it is symmetric

with respect to the centre. The arm A is defined by radial distance given as follows:

r = aspφw (2.30)

whereasp is the arm growth constant of the spiral antenna, andφw is the winding angle

which ranging fromφstart to φend radians.

The arm B can be obtained by rotating arm A by 180o around the centre. Reference

[42] suggests that the antenna circumference which is defined by 2πrmax (wherermax

= asp φend) must be chosen to be larger than one wavelength at the lowestdesign

frequency, taking the active region at this frequency into consideration.

Frequency independent antennas typically have broad radiation patterns and low

gain, which is not suitable for some applications. An array of frequency indepen-

dent antenna can overcome this limitation. However, wideband characteristics of the

frequency independent element are lost in the array environment. The author in [27]

obtained the radiation patterns for an Archimedean spiral similar to the spiral as a series

of semicircles.

2.4.3 Wideband Arrays Antenna

There are some applications which require a higher number ofantennas such as commu-

nication services, satellite navigation services, and conventional broadcasting services.

An array of spiral antennas is a promising candidate for use in mobile systems with

coverage of multiple services over broad frequency band [49]. A wideband array can

offer significant advantages over individual wideband antennas. Some of the advantages

are increased gain, greater control over the radiation pattern including the ability to

electronically steer the beam, and the possibility of realization on a conformal structure

[3]. However, wideband arrays are affected by inter-element spacing. Small inter-

element spacing is desirable, but the minimum spacing is limited by antenna element


size and mutual coupling effects. Mutual coupling effects are weaker in the E-plane

and inter-element distances may not become too small in the transversal direction (H-

plane) to avoid the far field pattern distortion [51]. When thefrequency of operation is

increased, the inter-element spacing also increases in terms of wavelength, and grating

lobes appear when the spacing between elements approach onewavelength. Conse-

quently, the array bandwidth is limited by the formation of the grating lobes at the upper

frequency and element size at the lower frequency. There arethree main techniques to

increase array bandwidth: unequal array spacing, shared apertures, and non-rectangular

array geometries. Reference [11] investigated the effect ofvarious unequal spacing

schemes, such as logarithmic spacing and non-monotonically increasing spacing. They

found that in comparison with equally spaced arrays, fewer elements are required for a

preferred bandwidth, and grating lobes are replaced by sidelobes. Reference [36] and

[52] introduced theoretical models for designing and analysing unequally or randomly

spaced arrays. Reference [36] showed that using Poisson’s sum formula and a new class

of unequally spaced arrays with a desired radiation patterncould be designed. Reference

[52] used a probabilistic approach and found that a side lobelevel is closely linked to the

number of elements in the array, but weakly connected to aperture size. Reference [53]

suggested that the side lobes of an unequally spaced array could be reduced by spacing

perturbation. The previous section dealt mainly with increasing array bandwidth using

unequally spaced antenna elements of uniform size. The nextsection describes the

effect of unequal space on wideband antenna array with variable element sizes.

Wideband arrays Antenna with Variable Element Sizes (WAVES) Concept

Reference [32] presented the concept and theory of a widebandarray with variable

element sizes (WAVES) in 1985 along with a basic feasibilitystudy. Reference [31]

extended work presented in [32] and built and measured an eight element planar WAVES

array. The WAVES theory, a linear WAVES array, and Shively’splanar WAVES ar-

ray will be reviewed in this section. A two-octave, eight element, planar array of

Archimedean spirals was built and tested in [31] and [32]. The planar array was mea-

sured along the diagonal where a triangular lattice and amplitude taper improved the

radiation pattern performance of the array. The smaller spiral elements are switched


on when the grating lobe due to the larger elements become toolarge. All of the

previous work on WAVES was based on array theory predictionsand measurements

of the Shively eight-element, planar array. Reference [54] stacked three different size

Figure 2.14: The geometry of WAVES with two different size elements

Archimedean spirals in layers, thus creating a three dimensional array of spirals. The

array was successfully operated over a two octave bandwidthand the blockage due to the

partial overlap of elements from different layers of the array was found to be minimal.

They used three main ideas in the WAVES array designs. Those are as follows:

1. Elements which operate well with a small electrical perimeter at the lowest op-

erating frequency, and maintain that performance over one or more octaves, are

required

2. Different element sizes, one size of element for each octave are used. The lower

octave elements should thus be twice as large in radius as thenext octave elements

3. An array architecture which interleaves the different sized elements must be se-

lected.

Antenna array can be made as unequally spaced array which canreduce the side lobe

level of the antenna array. Since elements of an array interact with each other and

transfer power to neighbouring elements of the array, mutual coupling is a main concern


in array patterns. Mutual coupling will change both the driving point impedance and the

radiation patterns compared to a case where there is no coupling. Furthermore, it usually

degrades the performance of the array. One solution is to space the elements far enough

apart. Reference [55] used the method of moments (MoM) in Advanced Design System

(ADS) software to compute the mutual coupling of arrays. Mutual coupling is lower

at high frequencies, since the electrical distance betweenelements is greater. Another

approach is to use S-parameters to determine the amount of mutual coupling.

2.5 Summary

Fundamental theory of antennas and the previous work related to the spiral antenna

and its wideband properties are outlined in the literature review. Wideband antenna

properties such as radiation patterns, gain, impedance, beam width, polarization and

bandwidth, are discussed in detail. Different types of broadband antennas are pre-

sented in Section 2.3. This chapter highlights that planar spiral antenna is the most

popular broadband antenna because of its frequency independent characteristics. It

further analyses the effect of a single element on the bandwidth of an antenna. The

Section 2.4.3 reviews multiple elements and their effect onthe bandwidth of antennas.

Array techniques with WAVES concept for spiral antenna are also presented. Later

work using a 2-octaves planar WAVES circular Archimedean spiral showed that it is

possible to achieve an even wider bandwidth. However, for these antennas, a gap exists

in the 2-octaves coverage. It can be resolved with a proper balanced feeding network

with a suitable impedance transformation, which determines the antenna bandwidth.

The following chapter investigates some existing widebandfeeding systems suitable for

spiral antennas.

Chapter 3

Feeding Systems for Wideband antennas

3.1 Introduction

Readily available transmission lines such as coaxial cablesare inexpensive and have a

50Ω characteristics impedance. When these cables are used to feed balanced structures

such as Archimedean spiral antennas, researchers are presented with two problems. The

first problem is the impedance mismatch. Coaxial cable with 50Ω needs to feed the

Archimedean spiral antenna with a high input impedance (120-200Ω). This mismatch

increases the reflection coefficient significantly, making the feed unacceptable. The sec-

ond problem is that the coaxial cable has an unbalanced structure and the spiral antenna

has a balanced structure. These unbalanced feeding structures and antenna structures

are shown in Figure 3.1(a) and Figure 3.2 respectively. Therefore, awideband balun is

needed to ensure the unbalanced to balanced transformationand that the impedance is

matched. Properly designed balun can provide the unbalanced to balance transition and

required impedance transformation as shown in Figure 3.3.

Proper operation of the spiral antenna requires that the operating currents on the

arms of the spiral must be of equal amplitude and opposite phase. Signals are converted

between an unbalanced circuit structure and a balanced circuit structure (Figure 3.1(b))

by balun devices, as shown in Figure 3.3 and these signals have same magnitude but

180o phase difference in balun circuit structure. Thus a wideband balun can insure

33

34 CHAPTER 3. FEEDING SYSTEMS FOR WIDEBAND ANTENNAS

(a)

(b)

Figure 3.1: The transmission lines (a) Unbalanced transmission lines(b) Balancedtransmission lines

Figure 3.2: Balanced antennas

3.1. INTRODUCTION 35

Figure 3.3: A schematic for unbalanced to balanced transformation

the required balanced conditions are met. There are severaltypes of balun transitions

that have been suggested with various degrees of success. The coplanar versions of the

traditional Marchand balun is the best known transition andit uses quarter wavelength

segments [4], [14]. The conventional quarter wave structure can be replaced by using LC

combination of lumped elements [56]. These two transitionshave accurately predictable

band pass characteristics with moderate bandwidths, limited by the resonant structures.

Reference [12] used the double-Y balun with four resonant stubs to achieve a rel-

atively wideband pass band with a compact design. A high permittivity substrate with

very small gap sizes (in the order of 50µm) gives good bandwidth properties but it is not

achievable. Some other designs do not benefit from a finite open circuit structure usually

because only limited bandwidth is required [56], [57] and [58]. Larger bandwidths can

be achieved but require very small etched gap sizes (of less than 100µm) to operate

effectively.

This chapter presents the general balun theory and introduces some of the exiting

wideband balun structures [16]. In many cases the most convenient type of coplanar

line is coplanar strip line, which is inherently a balanced line and can be used to feed

balanced devices and antennas. Coplanar waveguide, on the other hand, is unbalanced

and can be directly connected to unbalanced coaxial cable. Therefore, this combina-

tion of CPW to CPS balun can make the transition from an unbalanced to balanced

transformation effectively.


3.2 General Balun Theory

Many Electromagnetic (EM) devices are integrated with balun circuits which can trans-

form an unbalanced form of transmission line (eg: coaxial cable, microstrip line and

CPW) to a balanced form of transmission line (eg: slot line, parallel strip line and CPS).

Moreover, the antenna’s radiation pattern changes if the currents in the driven element of

a balanced antenna are not equal and opposite. Because of that, spiral antennas, mixers,

hybrids, couplers, dipole antennas and notch antenna require balanced feeds. Apart

from simply being a transition from one transmission line toanother, a good balun also

stops unwanted radio frequency (RF) current from flowing in the outer conductor of a

coaxial cable, as shown in Figure 3.4.

Figure 3.4: An unbalanced coaxial cable

3.3 Wideband Baluns Configuration

High frequency applications require wideband balun for broadband performance. This

section discusses some of the commonly used wideband balunsin detail with specific

emphasis on their etched implementations.

3.3.1 Quarter-Wave Coaxial Balun

A simple form of balun is a quarter-wave coaxial balun or folded balun which is rela-

tively easy to construct [1]. As shown in Figure 3.5, a foldedbalun can be constructed

3.3. WIDEBAND BALUNS CONFIGURATION 37

using an extra piece of coaxial cable which is connected between the feeding coaxial

cable and the antenna side which is connected to the inner conductor of the feed. This

extra cable should be a quarter of a wave length long. Combination of this cable with

the outer of the main transmission line forms another transmission line. Though, it is

short circuited at the connection point so that it transforms to infinite parallel impedance

at the antenna input. Therefore, this type of balun has no effect on the input impedance.

Furthermore, the quarter wavelength line induces another current on the outside of the

outer conductor, which cancels the unbalanced currents. Because of that, there is no

current on the outside of the cable below the connection point. However, this balun has

narrow bandwidth and cannot be used for wideband applications.

Figure 3.5: Representation of a Quarter-Wave Coaxial Balun [1].

3.3.2 Bazooka Balun

Another, similar type of balun is shown in Figure 3.6, referred to usually as a bazooka

balun. It uses a quarter-wave in length metal sleeve, and is shortened at one end,

encapsulating the coaxial line. The input impedance at the open end of the quarter-

wave length transmission line is large. As a result, the amount of current flow on the

outside surface of the outer conductor can become choked andthe system will be nearly

balanced. Although, this type of balun works effectively athigh frequency (higher than

1 GHz) , some high frequencies studies have shown that it might not be as effective


as generally accepted [59]. Bazooka balun also does not have asufficiently wider

bandwidth.

Figure 3.6: Representation of a Bazooka Balun

3.3.3 Tapered Balun

Tapered balun is formed by symmetrically tapering the unbalanced coaxial cable to a

balanced transmission line over several wave lengths. As shown in the Figure 3.7, this

can be done by cutting the outer conductor of the coaxial cable on an angle, which then

leaves the thin cut end to form a parallel transmission line with the extended centre

conductor [35]. The tapered balun was used in [39] and it was constructed from semi-

rigid 50 Ω coaxial cable. The outer conductor of the coaxial cable is stripped away

until the outer conductor has the same diameter as the inner conductor. The results

of this improved feed design could eliminate the feedline reflections that could cause

pattern degradation. A number of wideband antennas including TEM horns and Vivaldi

antennas use this tapered balun to feed the antenna. However, this balun is electrically

long to achieve good balance results. For example, the taperneed to be at least1m

long for proper operation at 500 MHz. So it is far too long for practical use. Due

to the above issue, certain applications have used these balun with the total length,

which is less than one wavelength. However, the reduced squint and cross-polarization

performance is acceptable. In general, the tapered balun with manageable length has


Figure 3.7: Representation of a Tapered Balun

considerably poorer balance performance than other types of commonly used baluns,

e.g. the Marchand balun, which will be discussed in the next section.

3.3.4 Marchand Balun

High frequency antenna applications commonly use this balun as a feed network to

achieve a broad bandwidth. Figure 3.8 shows the equivalent circuits for a Marchand

balun [60]. Commercially available wideband spiral antennas use this balun as feed

network. Moreover, these baluns are generally implementedin its second or third

order form by using coaxial cable inside a metal cavity whichcontrols the relative

impedance and the centre frequency. The bandwidth of standard antennas with the

Marchand balun can achieve more than a 9:1. Axial ratio levels are generally below 1.5

dB at the radiation pattern peak over the full frequency range. The above result shows

that it has better performance than those obtained by similar spirals with inline tapered

baluns. Marchand balun have also been successfully implemented in etched form with

microstrip line as an input in [4], [14]. These etched balun,which were introduced in

1960 were used to feed a spiral antenna over an octave frequency band. The advantages

of the etched form are that it is cheap and less complex to realize some of the higher

impedances needed in the design. However, the bandwidth of this etched version is not

as high as those of the coaxial versions. These balun consistof microstrip lines as input


Figure 3.8: Equivalent circuit for a Marchand balun [4].

Figure 3.9: Microstrip to slotline etched Marchand balun [4].


and slot lines as output, as shown in Figure 3.9, which rapidly tapered into a coplanar

strip line for easy connection to the spiral antenna. The bandwidth of the etched balun

can be improved with different types of terminating structures. The etched balun with

square termination were implemented and it showed that a maximum usable bandwidth

of about 4:1 [53]. Different combinations of square, circular and radial termination have

been studied in [54] and [55]. A radial strip line stub and a circular slot line cavity are the

most common combination in use nowadays, as shown in Figure 3.10. The maximum

bandwidth of these combinations is about 6:1.

Figure 3.10: Stripline to slotline balun with a radial stub and circularcavity

3.3.5 Double-Y Balun

Another type of wideband balun is double-Y balun and it is readily etchable. A number

of papers have been written about its design and performanceeven though it is not as

widely used as the Marchand baluns. Reference [23] describesthe operation of balun

and its equivalent network is shown in Figure 3.11. A double-Y balun has 6 ports,

where three of the ports are balanced, and the other three ports are unbalanced with

alterations around the centre of the structure. Balance can be achieved by uncoupling

each two opposite ports and matching the other four ports, where the junction effects

are neglected. Opposite pairs of balanced and unbalanced lines are chosen to have

opposite reflection coefficients. A balanced signal is obtained when the input signal on


Figure 3.11: Equivalent circuit for a double-Y balun [4].

an unbalanced port is equally divided between the other fourports. According to this

basic theory for the double-Y balun, it should exhibit all pass characteristics. However,

in practical applications, the balun shows a low-pass or even band pass characteristics.

Finally, it has some advantages over the Marchand balun. Even though, it is more

complex, it can be etched with good repeatability. The double-Y balun are capable

of achieving more than 6:1 bandwidth. However, it has small etching tolerances and

good high frequency performance can be achieved by using high permittivity substrates.

Therefore, it is difficult to use in some application being dealt with in this project.

3.3.6 Wideband CPW to CPS Balun

The previous two sections examined different types of baluns and some general exam-

ples. This section presents three types of balun which can beimplemented using CPW

to CPS configuration. The CPS is the most useful form to feed the etched antennas

such as dipoles [16], bow-tie [56], and notch or Vivaldi antennas [61], [62]. Moreover,

CPW and CPS are mostly used in the monolithic microwave integrated circuits (MMIC)

device due to their easy fabrication and easy integration with active devices.

Reference [51] uses different types of wideband balun such asprinted Marchand and

double -Y balun for transition from microstrip to slot line to cover several frequency

octaves. The CPS consists of two parallel metallic strips next to each other, with a small


gap in between. These configurations make an easy connectionwith an antenna. Also

these two parameters (strip width and gap) determine the characteristic impedance of the

transmission line. Since the feed structure and the etched antenna both are uniplanar,

it gives better results in antenna radiation pattern parameters such as axial ratios, cross

polarization. In addition, it is cheap and easier to manufacture.

The CPW, on the other hand, is an unbalanced transmission lineand uniplanar

version of the microstrip transmission line types. It is used as an input of balun structure.

It consists of a centre metallic strip, with a large ground strip on each side of it on

the same side of the dielectric substrate. These two parameters such as centre strip

width and the gap size determine the characteristic impedance of the CPW transmission

line. Since CPW automatically provides itself to easy integration with coaxial cable and

connectors, it is used as an input of balun and cannot directly be used to feed symmetric

etched antenna. Therefore, CPW to CPS balun needs to feed the antenna.

3.3.7 CPW to CPS Marchand Balun

This section discusses the implementation of Marchand balun in the CPW to CPS

form. Figure 3.12 shows an example of such an implementation. The CPW with the

Figure 3.12: CPW to CPS Marchand balun [4].

characteristics impedance 50Ω and the CPS with 70Ω was implemented on the top


of the alumina with 0.636 mm thickness [4]. The bandwidth of this configuration was

2.7:1, but there was a high loss in pass band due to the fact that transmission lines start

to radiate when the open or short circuits are electrically longer than 45o. Due to the

effects of radiation, it has a smaller bandwidth than the calculated one. Furthermore,

the CPW to CPS balun performance seems to be worse than its microstrip to slot line

counterpart and the maximum available bandwidth is no more than 3:1. Thus CPW to

CPS Marchand balun as shown in Figure 3.12 is rarely used in practice.

3.3.8 CPW to CPS Double-Y Balun

The basic configuration of double-Y balun and the microstripto slot line implementation

is examined in Section 3.3.5. The configuration of CPW to CPS double-Y balun [12] is

shown in Figure 3.13. Even though, the double-Y balun has allpass band characteristics

theoretically, the microstrip to slot line version shows band pass characteristics only over

a 6:1 bandwidth. Therefore, the CPW to CPS version is proposed in [12] to resolve the

Figure 3.13: CPW to CPS double-Y balun [4].

above problem. One of the advantages of this configuration isthat it can be implemented

in open and short circuits. Thus, the frequency range is not limited by the finite open

as in the previous case. The above configuration has true low pass characteristics with

the upper frequency which is limited by the minimum gap width. The baluns in [4] and

[12] are well matched from DC in practicality and have good performance over a wide


bandwidth. The upper frequency limit is 6 GHz by using the minimum gap size of 50

µm and it goes up to 13.5 GHz with the gap size of 20µm. The above balun also cannot

be used for some applications due to the transmission line radiation problems like the

Marchand balun, but apparently to a lesser degree. The balunwas unable to perform

as well at lower frequencies as its matching would indicate [13]. The magnitude and

phase balance of the balun is tested using a test circuit overthe full frequency range.

Although, the balun have a good matching from DC to 13.5 GHz, the imbalance at the

lower frequencies is very large.

The CPW to CPS double-Y balun shows that it has the capability ofachieving very

wide bandwidth. However, it requires small etched gap sizesto achieve the required

bandwidth.

3.3.9 CPW to CPS Chebyshev Balun

The basic balun structure used for this research work is firstintroduced by [5] as shown

in Figure 3.14 which is a modified version of the balun structure shown in [15]. It

consists of a CPW, a CPS and a radial stub. It uses a single open circuit element to

accomplish the transformation and is inherently inline. Itis tested in a back to back

configuration and then used to feed an etched dipole antenna.The CPW and CPS

are only used to connect the sender or receiver and the antenna, so balun is critical

to obtaining transformation between unbalanced and balanced mode. The CPW to CPS

single element balun can be divided into three sections. Thefirst section of the balun is

CPW and it is fed directly from a coax cable and CPW have the same value for good

match and almost always chosen as 50Ω. The second section of the balun is CPS and

its characteristics impedance is not similar to CPW. The characteristic impedance of

CPS should be equal to or nearly equal to antenna input impedances for a good match.

However, it is not easy to implement 50Ω CPS in practice without using very small gap

sizes (for example: gap size =1 mm ). Thus, an impedance transformation section has

been implemented between CPW and CPS sections.

The wideband balun gives not only a balanced transmission but also an impedance

matching between antenna and the transmission lines with low insertion loss and wide-

band width. Figure 3.14 shows that the CPW to CPS balun is designed to transform the


Figure 3.14: CPW to CPS Chebyshev balun

unbalanced CPW feed line to a balanced CPS feed line with radialstub [15]. They have

applied a Chebyshev impedance transformer to transform the impedance of the CPW

from 50 to 80Ω. This wideband transition from the CPW to CPS is accomplished with

a radial stub, which forces the currents to flow between the two CPS lines. In some

applications, a circular stub is used instead of a radial stub. However, [5] proves that a

radial stub yields a better solution with lower insertion loss and a better reflection coef-

ficient throughout the operating frequency band. However, the bandwidth of wideband

balun proposed by [5] is only 0.1 to 3.45 GHz.

Many other broadband transitions developed for CPW to CPS can be found in the

open literature. Reference [16] presents a wideband CPW to CPS transition with a

bandwidth from 0.45 to 5 GHz. Furthermore, [15] proposes a CPWto CPS back-to-

back transition with the bandwidth ranging from 0.4 to 3.6 GHz. To realize broadband

transition researchers have used the radial stub and CPW taper. However, the above

structures are band limited and have a discontinuity at the end of CPW transmission lines

which introduces additional reactance that may degrade itsperformance. Therefore, the

next chapter presents new planar back-to-back wideband balun transition designs using

near optimum impedance tapering method to achieve higher bandwidth than stated here.

3.4. SUMMARY 47

3.4 Summary

The previous works related to the wideband balun feeding configurations are outlined in

this chapter. It includes Marchand baluns, double-Y balunsand CPW to CPS wideband

baluns. But Marchand baluns and double-Y baluns are band limited and cannot be used

in wideband applications. Table 6.1 compares the baluns presented in this chapter. The

modified versions of [5] are presented in the next chapter to obtain a large bandwidth

(from 3.53 to 15 GHz) and to be compatible with the requirements of broadband spiral

antennas and antenna arrays.


Table 3.1: The comparison of the above baluns

Types ofBalun

Bandwidth Advantages Disadvantages

Quarter-wavecoaxialbalun

- The quarter wavelength lineinduces another current onthe outside of the outerconductor, which cancelsthe unbalanced current

Narrow bandwidth

Bazookabalun

- Works effectively at highfrequency (higher than 1GHz)

Narrow bandwidth

Taperedbalun

- Eliminate the feedline re-flections that could causepattern degradation

electrically long toachieve good balanceresults

Marchandbalun

9:1 It can be implemented inetched form and it is cheapand less complex to re-alize some of the higherimpedances needed in thedesign

Narrow bandwidth

Double-Ybalun

> 6:1 Shows a low-pass or evenband pass characteristics,and small etching toler-ances, and good high fre-quency performance can beachieved by using highpermittivity substrates

More complex than theMarchand balun

CPWto CPSMarc-handbalun

2.7:1 - High loss in pass bandand narrow bandwidth

CPWto CPSDouble-Ybalun

DC to 13.5 GHz It can be implemented inopen and short circuits, andwell matched from DC inpracticality, and have goodperformance over a widebandwidth

Cannot be used forsome applications dueto the transmission lineradiation problems

CPWto CPSCheby-shevbalun

0.1 to 3.45 GHz Give balanced transmissionand impedance matchingbetween the antenna and thetransmission lines

Band limited and havea discontinuity at theend of the transmissionlines (CPW), which in-troduces additional re-actance that may de-grade its performance

Chapter 4

Design and Analysis of Wideband Baluns

4.1 Introduction

Different kinds of baluns have been developed over the past decades [60], [63]. Bal-

anced mixers and printed antenna using planar baluns implemented in stripline have

been reported. Currently, balanced antenna applications focus on baluns which have pla-

nar and compact structures. The wideband characteristics of the antenna are dependent

on a proper feed network with sufficiently broad bandwidth. The wideband balun feed

network and its applications were reviewed in Chapter 3, Section 3.3. However, those

wideband baluns have limited bandwidth which makes them unsuitable for wideband

applications. Therefore, this project proposes new designs for wideband feed networks

for spiral antennas. Since 1995, several CPW to CPS transitionhave been reported.

Reference [15] introduced a wideband balun to feed a spiral antenna with a return loss

better than 10 dB over wide bandwidth from DC to 3.7 GHz. Reference [5] proposed a

coplanar waveguide to coplanar stripline transition whichis a modified version of [15],

and with a return loss better than 10 dB in back-to-back configuration from DC to 3.85

GHz. In this thesis, a tapered coplanar waveguide is utilized to realize a wideband balun

(bandwidth : 3.53 to 15 GHz). Two different tapered CPW designs are presented for

CPW to CPS wideband balun implementation. In addition, a new tapered microstrip to

parallel striplines wideband feed network covering three octaves of bandwidth is also

developed.

49

50 CHAPTER 4. DESIGN AND ANALYSIS OF WIDEBAND BALUNS

Each of the three balanced wideband feed configurations weresimulated using CST

MWS 2011 simulator and validated with measured results. All measurements were

conducted at the RF Lab, Level 13 of S Block, Queensland University of Technology,

Gardens Point campus, using two different network analysers. In the next section,

design formulas for the characteristic impedance of the basic structures used in the balun

designs are presented.

4.2 Design Formulas

4.2.1 Coplanar Waveguide (CPW)

CPW has three conductors having two grounds in the same plane of the centre con-

ductor, as shown in Figure 4.1. These ground planes do not require plated through-

holes to a plane on the other side of the substrate. It reducesthe coupling effects

and allows for easy inclusion of series and shunt elements. It is widely used in circuit

elements and as interconnecting lines since microwave integrated circuits are basically

coplanar in structure. Reference [64] presented closed formanalytical formulas for the

Figure 4.1: Geometry of CPW transmission line

characteristic impedance of a typical CPW. It is given by the following relations, under

the assumption that the metal thicknesst ≈ 0:

ZCPW =30π√ǫeff

K ′(k1)

K(k1)(4.1)

4.2. DESIGN FORMULAS 51

Figure 4.2: Block view of CPW transmission line

K(k) is the complete elliptic function of the first kind,K ′(k) =K(k′), wherek′2=1−k2.

The complete elliptic function of the first kindK(k) is approximated by, [65]:

K(k)/K(k′) =

π

ln2(1+

√k′)

(1−√k′)

0≤ k ≤ 1√2

1

π ln[2(1+

√k)]

(1−√k)

1√2≤ k ≤ 1

(4.2)

ǫeff = 1 +ǫr − 1

2.K(k2)

K ′(k2)

K ′(k1)

K(k1)(4.3)

k1 =a

b(4.4)

k2 =sinh(πat

4h)

sinh(πbt4h)

(4.5)

at = a+1.25t

π

[

1 + ln

(

4πa

t

)]

(4.6)

bt = b− 1.25t

π

[

1 + ln

(

4πa

t

)]

(4.7)

The parameterb should be selected to be less thanλ/2 to prevent propagation of higher

order modes.

4.2.2 Asymmetric CPW

The asymmetric CPW is a modified conventional CPW in which gaps between the

signal strip and the ground strip are not equal, as shown in Figure 4.3. This allows for


Figure 4.3: Asymmetric CPW transmission line

the evaluation of the actual characteristic impedance of asymmetric CPW. Analytical

equation for asymmetric CPW from [66] is given as follows:

Z0 =30π√ǫeff

K ′(k1)

K(k1)(4.8)

where,

k1 =0.5a[1 + α(0.5a+ d1)]

0.5a+ d1α√0.5a

(4.9)

k2 =wA(1 + α1wB)

wB + α1wA2

(4.10)

wA = sinh(πa

4h

)

(4.11)

wB = sinh

(

π(a/2 + d1)

2h

)

(4.12)

wE = − sinh

(

π(a/2 + d2)

2h

)

(4.13)

α =d1d2 + 0.5a(d1 + d2)±

√

d1d2(a+ d1)(a+ d2)√0.5a(d1 − d2)

(4.14)

α1 =1

wB + wE

[

−1− wBwE

wA2

±√

(

wB2

wA2− 1

)(

wE2

wA2− 1

)

]

(4.15)

It is assumed that the ground plane is infinitely wide and strips have negligible

thickness in this model of asymmetric coplanar waveguide. As shown in Figure 4.3,

the CPW is an unbalanced structure and easy to integrate with an SMA connector.

However, it cannot be integrated with a spiral antenna. The objective of this project is

to derive a balun configuration with high characteristic impedances to feed the array of


spiral antennas, which has high input impedances. Since a spiral antenna is a balanced

structure, it needs a balanced feed. Therefore, CPS is used toconnect the balanced

antenna.

4.2.3 Coplanar stripline (CPS)

Coplanar stripline consists of a signal strip and ground plane on the top of the substrate,

as shown in Figure 4.4. The width of the strip line and height of the substrate determine

the characteristic impedance of the line. The characteristic impedance for CPS is given

(a) (b)

Figure 4.4: (a) Top view of the CPS transmission line (b) Side view of the CPStransmission line

by [67],

ZCPS =120π√ǫeff1

K(k0)

K ′(k0)(4.16)

where,

k =tanh

(

πg2h

)

tanh(

π(s+g)2h

) (4.17)

k0 =g

s+ g(4.18)

k′0 =

√

1− k20 (4.19)

ǫeff1 = 1 + (ǫr − 1) q (4.20)


q =1

2

K(k′)

K(k)

K(k0)

K(k′0)

(4.21)

4.2.4 Microstrip line

The microstrip line consists of a narrow signal strip and an infinite ground plane sepa-

rated by a dielectric material. The geometry of the microstrip line is shown in Figure

4.5. The characteristic impedance of the line depends on thewidth of the signal strip

along with the height and the dielectric constant of the substrate [1]. The characteristic

impedance for microstrip line is defined as following equation [68]:

Figure 4.5: Geometry of microstripline structure

Z0 =

60√ǫeff

ln(8hw+ w

4h) w/h<1

120π√ǫeff [w/h+1.393+0.667 ln(w/h+1.444)]

w/h> 1

(4.22)

and

ǫeff =ǫr + 1

2+

ǫr − 1

2

1√

1 + 12h/w(4.23)

whereǫeff is an effective dielectric constant,w is a width of the signal strip, andh is a

height of the dielectric material.


4.2.5 Asymmetric Parallel stripline

Parallel stripline is mostly combined with a tapered microstrip line to transform the

impedance from an unbalanced device to a balanced structure. It consists of two parallel

strips separated with a dielectric substrate, as shown in Figure 4.6.

Figure 4.6: Balanced parallel strips transmission line (a) Block view ofbalancedparallel striplines (b) Cross section of parallel striplines

Figure 4.7: Transversal cut to compute the characteristic impedance of Asymmetricparallel stripline [69]


The characteristic impedance and the effective dielectricconstant for the asymmetric

parallel strip, as shown in Figure 4.7are given [69]:

ǫeff =

K(ϑ′)K(ϑ)

+ ǫrK(α′)K(α)

K(ϑ′)K(ϑ)

+ K(α′)K(α)

(4.24)

Z0 =60π

√eeff

(

K(ϑ′)K(ϑ)

+ K(α′)K(α)

) (4.25)

whereK(λ) is the complete elliptical integral.

K(λ) =

∫ π/2

0

dx√

1− λ2 sin2 x(4.26)

ϑ =

(

πb

2∆

)

(4.27)

ϑ′ =√1− ϑ2 (4.28)

α =

√

2(xa + xb)

(1 + xb)(1 + xa)(4.29)

α′ =√1− α2 (4.30)

xa = cosh(aπ

h

)

, xb = cosh

(

bπ

h

)

(4.31)

where2b is the width of the top strip line and the value of∆ is chosen to be 20h.

4.2.6 Taper Design

As mentioned in Section 4.2.2, CPW can easily be integrated with a SMA connector,

while CPS, being a balanced transmission line, is suited for spiral antenna. The CPW

should have the impedance of the SMA connector (Z0 = 50Ω) and CPS should have the

impedance of the spiral antenna (ZL > 50Ω). A gradual change of impedance between

the CPW and CPS is therefore required, as shown in Figure 4.8. CPWtapers were

constructed to connect CPS transmission lines of different characteristic impedances

which undergo a gradual change of size and/or form in the direction of propagation. The

tapered sections gradually transform the fields from the CPW to CPS lines, and should

accomplish this transformation with little loss due to reflection. Three different tapered


Figure 4.8: Geometry of a dispersive tapered transmission line

line methods are used to design the tapered transmission line: optimum Chebyshev

taper; exponential taper; and Hecken taper. Reference [70] described the design of a

continuous TEM transmission line taper in which has an optimum Chebyshev frequency

response, but which requires impedance steps at the taper ends, as shown in Figure

4.9(a) . As a result, [71] proposed a near-optimum matching section which avoids

the impedance steps and yields tapers only fractionally longer than the optimum taper.

However, both these impedance matching techniques treat the analysis and synthesis of

transmission line tapers supporting only TEM modes and witha constant propagation

along the taper. The design of near-optimum tapers in non-TEM dispersive media has

been described [72], [73]. The taper do not have any discontinuities and the propagation

constant varies along the length of the taper.

References [74], [75] presented a theory for the synthesis ofa near optimum dis-

persive tapered transmission line without the disadvantage of discontinuities. Typical

impedance profile of the near optimum matching section is shown in Figure 4.9(b). The

impedance steps have been avoided by utilizing a generalized Fourier transform pair

with a modified Chebyshev frequency response. The taper is only slightly longer than

the optimum taper with equal bandwidth.

Taper Design Procedure

The following equations and design procedure were used to design the CPW impedance

taper [74]. Given a maximum reflection ripple level in the pass bandRL in dB, the


(a) (b)

Figure 4.9: The typical impedance profile (a) Chebyshev taper (b) The near optimumtaper

maximum reflection coefficient magnitude is given by:

ρmax = 10(−RL/20) (4.32)

ǫmax =ρmax

12ln(ZL/Z0)

(4.33)

Substituting the calculated value forǫmax in equation (4.34) then yields the parame-

terB.

ǫmax =

∣

∣

∣

∣

0.217234B

sinh(B)

∣

∣

∣

∣

(4.34)

Minimum value ofπu, yields that:

πu = πu0 =√B2 + 6.520694 (4.35)

The taper impedance profile can be obtained using equation (4.37):

ln[Z(θ)/Z0] =1

2ln(ZL/Z0) +

1

2ln(ZL/Z0)G[B, 2θ/πu0] (4.36)

where,

−πu0

2≤ θ ≤ πu0

2


θ =

∫ 0

z

β0(τ)dτ − πu0/2 (4.37)

And the transcendental functionG may be approximated using Cloete’s [76] method,

where,

G(B, ξ) =B

sinh(B)

k=0∑

∞

akbk (4.38)

a0 = 1 ak =B2

4k2ak−1

b0 = ξ bk =ξ(1−ξ2)+2kbk−1

2k+1

ln[Z(θ)/Z0] =1

2ln(ZL/Z0)[1 +

2θ

πu0

] (4.39)

where,

−πu0

2≤ θ ≤ πu0

2

The design procedure for a matching section using this near optimum method taper is

summarized in the following steps [74]:

1. ρmax is calculated in terms of the given ripple levelRL using equation (4.32)

2. Using equation (4.33), the value ofǫmax is calculated for a givenZ0 andZL

3. The parameters B andu0 are computed from equation (4.34) and (4.35) respec-

tively. The termsu0 then represents the electrical length of the taper at the

specified cut off frequency,f0

4. Using∆Z = λ0/N , is calculated, whereN was chosen arbitrarily depending on

the required accuracy of the design. A value ofN ≥ 50 is recommended

5. Z(θ) is calculated using equation (4.36) and (4.38). After set the value ofz as 0

andθ as(−πu0)/2

6. A suitable synthesis scheme has been used to obtain the corresponding physical

parameter or dimension of the transmission line in order to realize the required

impedance level


7. Using an analysis technique,β0(z) for transmission line with dimension as calcu-

lated in the previous step is obtained

8. Equation (4.37) is approximated over the interval [z,z +∆z] by replacingθ with

θ +∆zβ0(z) and z is replaced withz +∆z

9. Steps5 to 8 are repeated untilθ ≥ −πu0/2

4.3 Design of CPW to CPS wideband baluns

The coplanar waveguide feed network consists of a balun which properly connects a

balanced coplanar strip line (CPS) to an unbalanced coplanarwaveguide (CPW), and

uses radial stub and bond wires to accomplish this. The inputof a wideband balun

is connected with a SMA connector and the output is connectedto the spiral antenna.

The CPW to CPS wideband balun is designed to achieve the unbalanced to a balanced

transformation and impedance matching.

A new wideband balun configuration was proposed. It is a modified version of [5],

shown in a back-to-back configuration in Figure 4.10.

Figure 4.10: A back-to-back Chebyshev wideband balun [5]

The CPW to CPS transformation is accomplished with a wideband radial stub which

entices current to flow on the two CPS lines. Bond wires were added on the upper

CPW ground strip to suppress the generation of unwanted non-CPW modes and ensure

4.3. DESIGN OF CPW TO CPS WIDEBAND BALUNS 61

that the potential on both ground planes are equal. The bond wires were chosen to

be very thin and to be located as close as possible to discontinuities to achieve the

high frequency performance. However, this discontinuity produces unwanted mode

excitation and reactance, which degrade the performance ofthe balun. The discontinuity

at the CPW end in the wideband balun of [5] were removed in this new wideband balun

configuration by tapering the CPW section using a near optimummethod as illustrated

in the next section.

In this part, a symmetric CPW to CPS balun is presented. Figure 4.10 shows a

stepped CPW to CPS balun. When a CPW is joined to a CPS line, a step discontinuity

between the CPW ground plane and the CPS lines exists. A taperedCPW is introduced

in the next section to achieve a smooth transition and a good match between the two

lines.

4.3.1 Proposed CPW to CPS Balun

The proposed CPW to CPS balun consists of the three parts : a tapered CPW section

(parameters - centre strip width and gap size), radial stub (parameters - length and

angle), and CPS (parameters - strip width and gap size), as shown in Figure 4.11).

The wideband balun is designed in back-to back configurationand ultimately, the per-

formance of the new balun will be compared to the stepped transition in Figure 4.10. In

Figure 4.11: Dimensions of the transmissions (Units : Millimetres)


[5], the CPS impedance was selected asZCPS = 80Ω. In this design, the same value of

ZCPS = 80Ω was used. The input impedance of the balun was chosen as 50Ω (ZSMA =

ZCPW ). As shown in Figure 4.11, a radial stub with a radius 6 mm and an angle of 45o

is etched at the end of the CPW. This helps to entice the currentto flow on the CPS lines.

In [5], two bond wires with a diameter of 0.15 mm are located near the discontinuity

plane to ensure proper operation of the balun.

The impedance matching transformer is optimized for impedance matching between

SMA connector (50Ω) and CPS (80Ω). Since the characteristic impedance of the CPS

(ZCPS = 80Ω) is higher than the CPW input impedance (ZCPW =50Ω), an exponential

tapered matching transformer is used in the CPW section. Figure 4.12 and shows a

taper profile for the CPW impedances with different value ofl indicating the length of

the profile. The CPW dimensions (signal strip width and gap sizes) for impedance from

50 to 80Ω were derived using the procedures provided in Section 4.2.6.

Figure 4.12: The impedance profile for the tapered CPW

The following parameters were selected in the taper design.RL = -20 dB, N=100,

f0 = 0.5 GHz,Z0 = 50 Ω, For an example:ZL = 80 Ω using taper design procedure

and the equation given in Section 4.2.6, CPW impedance profilewas determined using

MATLAB (coding was given in Appendix A), as shown in Figure 4.12. For a known

impedance value and length of profile, parametersa andb were derived from the taper

profile graph, as shown in Figure 4.13.


For an example: as indicated in Figure 4.13, for an impedanceZ = 60Ω, the position

along the taper is 19.5 mm. The parametersa andb are obtained asa = 3.07 mm and

b = 5.65 mm. The CPS dimensions (gap size and strip width) for 80Ω characteristic

Figure 4.13: The dimensions for the tapered CPW

impedance were derived from equation (4.16). The radial stub parameters (radius = 6

mm and angle = 45o) were taken from [5]. The optimized dimensions of the transition

are listed in Table 4.1. The balun configuration was constructed on RT Rogers 6010

substrate with a thickness ofh = 0.635 mm and a relative dielectric constantǫr = 10.2.

The size of the prototype is 22 x 42 mm. A single balun structure was simulated in

CST MWS 2011 considering a terminatorRL = 80Ω at the end of the CPS. Figure 4.14

shows the simulation results of the return loss for the CPW to CPS transition balun. As

shown in Figure 4.14, the return loss better than 10 dB is from0.2 to 4 GHz.

Table 4.1: The dimensions of the tapered CPW and CPS transitions

selectedImpedance fromCPW taper Profile(Ω)

50 55 60 65 70 75 80 ZCPS

strip width (mm) 3.28 3.2 3.07 2.96 2.81 2.63 2.53 3.6

gap width (mm) 0.86 1.04 1.29 1.47 1.71 1.98 2.13 1.7

position along thelength (mm)

0 13.5 19.5 22.5 25.5 28.5 30 12


Figure 4.14: Simulated S-parameters results for single symmetric CPW toCPSWideband balun

4.3.2 Back-to-back CPW to CPS balun

In order to check the performance of the balun, it was tested in back-to-back configura-

tion. This configuration facilitates the measurement of thereturn loss and insertion loss

without the necessity of loads. The Figure 4.15 illustratesthe back-to-back CPW to CPS

Figure 4.15: The back-to-back symmetric CPW to CPS wideband balun

configuration. The performance of this balun is compared to the stepped Chebyshev

wideband balun (Figure 4.16). It can be seen that the taperedCPW to CPS balun has

better wideband performance than the stepped Chebyshev balun. The tapered CPW

helps to improve the bandwidth of the balun.


(a) (b)

Figure 4.16: Simulated S-parameters for back-to-back symmetric and Chebyshevwideband balun (a) Return Loss (b) Insertion Loss

Figure 4.17 illustrates the surface current distribution on the back to back balun,

which aids understanding and working of the balun. In addition, this figure shows

the sections of high current density, shown in red colour. Itcan be seen that currents

are evenly distributed on each side of the centre conductor between this centre strip

and ground planes of the CPW part. The radial stub and bond wires succeeded in

transforming these currents from CPW to the balanced CPS line,where currents are

more evenly distributed on the edges between the two conducting striplines.

Figure 4.17: The surface current in symmetric CPW to CPS wideband balun


Figure 4.18: Simulated S-parameters for back-to-back symmetric wideband balun

The S-parameters for the back-to-back CPW to CPS are given in Figure 4.18. It

shows a return loss better than 10 dB from 0.6 to 3.5 GHz. Additionally, the 2 dB back-

to-back insertion loss is achieved from 1 to 3.5 GHz. However, the bandwidth is rather

narrow. It can therefore not be used in some applications which need more than two

octaves of bandwidth, including the problem being dealt with in this project.

4.3.3 Proposed Asymmetric CPW to CPS Balun

This section presents a high performance wideband balun with a new configuration. It

is a modified version of a symmetric CPW to CPS balun. An asymmetric coplanar

waveguide without radial stub helps to achieve better bandwidth than the previous

symmetric example. A single asymmetric CPW to CPS transition is shown in the Figure

4.19. The same tapering technique was applied to the asymmetric CPW section. An

unequal space at the end of the CPW helps to eliminate the current at the open end

without using the radial stub in asymmetric CPW to CPS balun configuration. Figure

4.20 shows the top and side view of asymmetric CPW to CPS balun. The balun consists

of tapered asymmetric coplanar waveguide and coplanar striplines, as shown in Figure

4.19. The terminating impedance at the CPS end was in this caseselected asZCPS =

100Ω . The dimensions of the asymmetric CPW were derived from the equations in

Section 4.2.2. Same tapered procedure was applied for asymmetric CPW part.


Figure 4.19: A single asymmetric CPW to CPS Wideband balun

For example: consider impedance ofZL = 80 Ω , position along the taper is 9.6

mm, as shown in Figure 4.21(a). The dimensions of the ACPW (d1, d2 and a) for

corresponding length can be derived from the dimension graph given in Figure 4.21(b).

The CPS dimensions for 100Ω characteristic impedance were derived from equation

(4.16). The optimized dimensions of the transition are listed in Table 4.2.

Table 4.2: The dimensions of asymmetric CPW and CPS Balun

SelectedImpedancefromACPWtaperProfile (Ω)

50 55 60 65 70 75 80 85 90 100

strip width[a(mm)]

2.6 2.5 2.4 2.3 2.21 2.1 1.99 1.9 1.8 1.63

small gapwidth[d1(mm)]

0.69 0.78 0.87 0.97 1.05 1.16 1.25 1.33 1.43 1.58

large gapwidth[d2(mm)]

0.691 1.04 1.42 1.83 2.12 2.6 2.94 3.3 3.67 4.29

positionalong thelength(mm)

0 1.8 3.6 5.4 6.6 8.4 9.6 10.8 12 13.8


(a)

(b)

Figure 4.20: (a) Configuration of the asymmetric CPW to CPS balun with SMAconnector (b) Side view of the balun


The single balun configuration is simulated with an aid of CST MWS 2011 simu-

lator. The simulated result for S-parameters is shown in Figure 4.22, where port 1 is

normalized to 50Ω while port 2 is connected to load with an impedance of 100Ω. It

shows that a return loss is better than 10 dB from 2 to 10 GHz.

(a) (b)

Figure 4.21: (a) The impedance profile for asymmetric CPW (b) The dimensions forasymmetric CPW

Figure 4.22: Simulated S-parameters results for single asymmetric CPW to CPSWideband balun (where port 1= 50Ω and port 2 = 100Ω)


4.3.4 Back-to-back asymmetric CPW to CPS Balun

Figure 4.23 illustrates the back-to-back asymmetric CPW to CPS configuration. In order

to check the performance of the balun, it was tested in back-to-back configuration. Thus,

it is easy to measure the return loss and insertion loss without the necessity of loads.

The circuit simulation was accomplished with an aid of CST simulator. This balun is

Figure 4.23: The back-to-back asymmetric CPW to CPS wideband balun

compared with symmetric CPW to CPS wideband balun. Figure 4.24shows the return

loss and insertion loss for those two baluns. It can be seen that the asymmetric CPW to

CPS balun have better wideband performance than the symmetric example. Figure 4.25

illustrates the surface current distribution on the back-to-back balun. The high current

densities are shown in red colour. The current is evenly distributed on each side of the

centre conductor and the ground planes in the CPW part. The unequal space at the end

of the asymmetric CPW helps to transform these currents from CPW to the balanced

CPS line, where currents are more evenly distributed on the edges between the two

conducting strip lines (see Figure 4.25).

The S-parameters results for the back-to-back asymmetric CPW to CPS are given

in Figure 4.26 and it shows that the return loss better than 10dB is from 1.75 GHz to

higher than 15 GHz. Additionally, the 3 dB back-to-back insertion loss is achieved from

2.5 GHz to higher than 15 GHz. From the S-parameter results, it is evident that it can

achieve more than two octaves of bandwidth. Therefore, thisstructure can be used in


(a) (b)

Figure 4.24: Comparison of simulated S-parameters for back-to-back symmetric andasymmetric CPW to CPS wideband balun (a) Return Loss (b) Insertion Loss

Figure 4.25: The surface current in asymmetric CPW to CPS Wideband balun


ultra wideband applications. The simulated results of the back-to-back configuration

were verified with measured results.

(a) (b)

Figure 4.26: Simulated and measured S-parameters results for back-to-backasymmetric CPW to CPS wideband balun (50 to 100Ω) with RT-Rogers 6010 substratematerial (a) Return Loss (b) Insertion Loss

Figure 4.26 shows the simulated and experimental return loss and insertion loss

results for the back-to-back asymmetric CPW to CPS wideband balun. In this design,

measured results of insertion loss for ACPW to CPS is high due tohigh dielectric

material. The same back-to-back ACPW to CSP balun was constructed on RT-duroid

5880 substrate withǫr = 2.2 and heighth = 1.5748 mm. The simulated results for back-

to-back ACPW to CPS with the impedance of 50 to 188Ω is shown in Figure 4.28. The

simulated results for 50 to 188Ω have return loss better than 10 dB from 1.6 GHz to

15 GHz. However, the measured result for insertion loss has some variation with the

simulated one (shown in Figure 4.28). From the measured results, the bandwidth for the

asymmetric CPW to CPS balun is 3.53 to 15 GHz. This structure cantherefore not be

used as a wideband balun due to the limited bandwidth. The bandwidth achieved by an

asymmetric CPW to CPS may be adequate in some applications, butthere are situations

where greater bandwidth is required. The next section presents a tapered microstrip

lines to parallel striplines balun with improved frequencyperformance.


(a) (b)

Figure 4.27: Back-to-back asymmetric CPW to CPS balun measurement with a networkanalyser (a) Design of the back-to-back ACPW to CPS wideband balun (b) Balun witha Rohde Schwarz ZVL Network Analyser

(a) (b)

Figure 4.28: Measured and simulated S-parameters for back-to-back asymmetric CPWto CPS balun with RT-duroid 5880 substrate material (50 to 188Ω) (a) Return loss (b)Insertion loss


4.4 Design of tapered Microstrip to Parallel Striplines Balun

Impedance transformation and matching are required in balanced devices to obtain

maximum power transfer between the source and load. For spiral antenna, the feed

network consists of tapered microstrip transmission line and parallel strip lines. Refer-

ence [77] proposed a microstrip tapered balun as a feed network for a low profile planar

dipole antenna. It consists of microstrip line where groundplane is tapered to form an

overlapped parallel stripline.

4.4.1 Tapered Microstrip lines

An exponential tapered microstrip structure helps to design a microstrip to parallel

striplines balun. The tapered microstrip structure consists of a tapered strip printed

on the substrate and an infinite ground plane on the other sideof the substrate. The

Figure 4.29: Tapered microstrip transmission line (a) Cross section (b)z- dependentconfiguration of strip conductor [78].

tapered microstrip line uses as an impedance transformer tomatch line impedanceZ1

to a load of impedanceZ2 as shown in Figure 4.29. The characteristic impedance of the

tapered microstrip configuration is given in the following equation [78]:

Z = η/(C0(w/h)/ǫ0)√

ǫeff (w/h, 0) (4.40)

4.4. DESIGN OF TAPERED MICROSTRIP TO PARALLEL STRIPLINES BALUN 75

whereη =√

µ0/ǫ0 denotes the intrinsic impedance of free space,ǫeff (z, w) denotes

the effective permittivity, andC0(w/h) is the line capacitance per unit length for the

case ofǫr = 1 and shape ratiow/h .

In reference [79], following approximate formula forC0(w/h)/ǫr was presented for

the case of 0.1≤w/h≤ 0.7 : C0(w/h)/ǫr = 0.4109 +√

5.940w/h+ 0.4631(4.41)And

an approximate formula forǫeff (w/h, 0) is:

ǫeff (w/h, 0) = 4.5 + 1.832e0.9282 logA− 0.3367 logA2

− 0.3189 logA3 − 0.0615 logA

(4.42)

where,

A = log w

4.4h

(4.43)

The tapered microstrip line is usually used as an impedance transformer. However, in

this project, the tapered microstrip line is used to form a balun with parallel striplines.

The broadband impedance matching properties of the balun are obtained by utilizing a

continuous transmission line taper with its characteristic impedance changing smoothly

fromZ1 (impedance at port 1) toZ2 (impedance at port 2), as shown in Figure 4.30. The

Figure 4.30: A single microstrip to parallel striplines balun

smooth transition from a microstrip line to a parallel stripline operates as a balun, shown


in Figure 4.30. When a microstrip line is joined to a parallel stripline, there is a step

discontinuity between the ground plane of the microstrip line and the bottom parallel

striplines. Furthermore, a step discontinuity exists between the top strip conductors

of these two lines. Therefore, a transmission line taper is applied to both the top and

bottom conductors to achieve a good match between the two lines [80].

4.4.2 Proposed Microstrip to Parallel Striplines Balun

The synthesis of a tapered microstrip transmission line to create a wideband microstrip

to parallel striplines balun is described. The tapered balun has two sections: the parallel

lines which connect with the antenna where the impedance of parallel lines is equal to

the antenna input impedance (188Ω); and an another section which actually performs

the mode transformation (see Figure 4.30).

Starting with a specific microstrip widthws (ws = w1, with an impedance of 50Ω,

the ground plane width is found using parameters sweep method in CST. This procedure

was repeated up to the parallel strip lines impedance (188Ω).

Example I:Z0 = 50Ω, ws was found from equation (4.22) in Section 4.2.4. wherew/h

>1 (ws = 4.8 ,h = 1.5748 mm)

Example II:for known value ofws = 1.76, the impedance of the microstrip line was

found using equation (4.22). wherew/h > 1 (ws = 1.76 ,h = 1.5748 mm). Using

impedance of the line and width of signal strip, width of ground plane was found with

an aid of parameter sweep method in CST.

Example III: for known value ofws = 0.92, the impedance of the microstrip line

was found from the equation (4.22). wherews/h < 1 (ws = 0.92 ,h = 1.5748 mm) and

ground width was obtained from parameter sweep method.

The widths of the top and bottom conductors change graduallycorresponding to the

line impedances, as shown in Figure 4.31. The top strip widthchanges from 4.8 mm

(ZM = 50Ω) to 0.88 mm (ZS = 188Ω) and the ground plane changes from 18 mm to

0.88 mm. The length of each profile (t1 to t8) was calculated from equation (4.45).


Figure 4.31: Configuration of a tapered microstrip to parallel strip lines with SMAconnector

The characteristic impedances of microstrip line and parallel striplines are 50Ω and

188Ω respectively. The exponential taper has the form:

Z1(z) = Z0eaz (4.44)

0 ≤ z ≤ L

and

a =1

Lln

ZL

Z0

(4.45)

where,z is a position along the length,L is a total length of the taper,Z1 is an output

impedance of the transmission line, andZ0 is an input impedance of the transmission

line (50Ω). Table 4.3 shows the width of microstrip and ground plane for different

frequencies. Once the width has been calculated, these lines are connected together.

Using these dimensions for microstrip lines and parallel strip lines, the balun was

constructed on RT-duroid 5880 substrate with a thickness ofh = 1.5748 mm and a

relative dielectric constantǫr = 2.2 and simulated in CST. The return loss and insertion

loss for single balun is given in Figure 4.32. These results show that the balun has a

wider bandwidth than asymmetric CPW to CPS balun.


Table 4.3: The dimensions of Microstrip to Parallel Striplines Balun

selected Impedancefrom microstrip linetaper profile (Ω)

50 70 90 110 150 170 188 ZS

Top Strip width (mm)(w1 to w8)

4.8 2.6 1.76 1.2 1.1 0.92 0.88 0.88

Ground width (mm)(w′

1) to (w′8)

18 16 7 2 1.8 0.98 0.88 0.88

Position along thelength (mm) (t1 to t8)

5 12.7 22.2 29.8 41.5 46.2 50 55

(a)

(b)

Figure 4.32: (a) Simulated S-parameters results of a single balun (b) Smith chart forthe input impedance (normalized at 50Ω)


4.4.3 Back-to-back Microstrip to Parallel Striplines Balun

The geometry of microstrip to parallel striplines balun is presented in Figure 4.31 and

the dimension of the each part is listed in Table 4.3. Two balun structures were joined at

the balanced port in a back-to-back configuration to validate the balun performance (see

Figure 4.33). The balun structure was constructed on the substrate, as shown in Figure

(a) (b)

Figure 4.33: Back-to-back connection of the tapered microstrip to parallel striplinesbalun (a) Top View (b) Bottom View

4.35. It was simulated in back-to-back configuration.The simulated results are shown in

Figure 4.36. The return loss is better than 10 dB from 1.5 to 15GHz and insertion loss

is less than 0.5 dB for frequencies from 2 to 15 GHz.

The simulated surface current distribution for different frequencies of the microstrip

to parallel striplines balun is shown in Figure 4.34. It can be seen that the distribu-

tion of current on the parallel striplines are symmetrical for the frequency bandwidth.

Furthermore, it shows that balun operates well in field matching between the coaxial

transmission line to parallel striplines. The microstrip to parallel striplines balun

exhibits wideband performance from 1.75 to 15 GHz with an insertion loss of 3 dB

and a return loss of better than 10 dB (as shown in Figure 4.36)for the back-to-back

transition.

This balun gives good performance over more than two octavesof bandwidth and

can therefore be used to excite spiral antennas. Good agreement is observed between


Figure 4.34: Surface current distribution at 2.5 GHz of the microstrip to parallelstripline balun

(a) (b)

Figure 4.35: Configuration of the microstrip to parallel striplines balun with SMAconnector (a) Top View and Bottom View (b) Back-to-back balun with NetworkAnalyser

4.5. SUMMARY 81

Figure 4.36: Measured and simulated S-parameters results for back-to-back Microstripto parallel striplines balun

simulation and measurement results (Figure 4.36). The difference between the sets

of results is due to soldering a SMA connector with a printed circuit board, and the

difficulty in aligning two conductors (bottom and top layersof the balun) on opposite

sides of the printed circuits boards.

4.5 Summary

In this chapter, three novel types of tapered wideband baluntransitions were designed,

analysed and examined. First, a tapered geometry was proposed for a symmetric CPW

to CPS wideband balun. The tapered CPW was used to improve the bandwidth of

the symmetric CPW balun. The discontinuity between the CPW andthe CPS was

accommodated by using a radial stub and bond wires. However,the bandwidth achieved

by this balun is 0.6 to 3.5 GHz and it is not suitable for the proposed spiral antenna in

this thesis. The asymmetric CPW to CPS balun was proposed as a second wideband

balun. The same tapered design was applied to the asymmetricCPW. The tapered

asymmetric CPW helps to remove the discontinuity between theCPW and the CPS

without having to use a radial stub or bond wires. The bandwidth of the asymmetric

CPW to CPS balun is 9 to 15 GHz (for RT-Rogers as a substrate material) and 3.53 to 15

GHz (for RT-duroid as a substrate material). However, it wasnot used with the proposed


spiral antenna due to the limited bandwidth. Therefore, a tapered microstrip to parallel

striplines balun was proposed as a third wideband balun. A transmission taper was

applied to the both conductors of the microstrip line (bottom and top conductors) and

widths of the conductors were gradually reduced to eventually resemble with the parallel

striplines. The measured results showed that the back-to-back microstrip to parallel

striplines balun has a wide bandwidth of 1.75 to 15 GHz. Each of the three wideband

balun configuration were simulated with the aid of CST MWS and validated with the

measured results. Good agreement between the measured results and the simulated one

showed that the microstrip to parallel striplines balun is suitable for the proposed spiral

antenna. The following chapter will outline the performance of the microstrip to parallel

striplines balun integrated with the spiral antennas.

Chapter 5

Integration of Wideband Balun with Spiral

Antennas

5.1 Introduction

Recently, there has been an increasing demand for integratedand low profile antenna

structures in different types of the industries [81], [82].The size of the structure affects

the bandwidth and gain of the antenna. Therefore, it is a challenging task to miniaturise

antenna capable of providing a wide bandwidth and acceptable gain. The spiral antenna

maintains nearly circular polarization, consistent gain and input impedance over wide

bandwidths. Frequency independent antennas typically have stable radiation patterns

but low gain, which makes them unsuitable for some applications. This chapter in-

troduces an array of spiral antennas for high gain and pattern control. However, the

wideband characteristics of the spiral elements are lost inan array environment. The

spacing between two antennas limits the array bandwidth to avalue which is less than

that of a single antenna. The spacing problem in spiral arrays has been resolved with the

wideband array with variable element sizes (WAVES) techniques discussed in Chapter

2. Due to its unique shape, the two-arm Archimedean spiral antenna works very well as

an element in a WAVES array.

The objective of this chapter is to demonstrate the widebandoperation of spiral an-

tennas integrated with a proposed wideband balun. In Chapter4, a microstrip to parallel

striplines wideband balun was proposed. Simulated and measured results showed that

83

84 CHAPTER 5. INTEGRATION OF BALUN WITH SPIRAL ANTENNAS

it has wideband characteristics and can be used with the wideband antennas. This balun

is integrated with the two-arm Archimedean spiral antenna configuration discussed in

Section 5.3 and spiral array configuration discussed in Section 5.4.

This chapter presents the results of electromagnetic and circuit level simulations

performed to investigate the performance of the single antenna and the antenna array

with the proposed wideband balun.

Radiation performance of an array with eight-element is alsosimulated and pre-

sented. These results are validated with experimental results. All the experiments were

conducted at the RF Laboratory of the Queensland University of Technology.

5.2 Performance of a Two-arm Archimedean Spiral Antenna

5.2.1 Design of a Single Spiral Antenna

In this section, an implementation of a two-arm circular Archimedean spiral antenna

integrated on one side of a substrate and an infinite ground plane on the other side is

presented. This substrate helps to reduce the physical sizeof the antenna structure. The

spiral antenna design parameters are taken from [31] are given in Table 5.1 .

Two different sized antennas are designed and used to construct arrays of spirals.

The parameters include spacing between the turnss, width of armw, inner radiusr1,

and outer radiusr2, as shown in Figure 5.1. The inner radius is measured from centre

of the spiral to the centre of the first turn while the outer radius is measured from centre

of the spiral to the centre of the outer most turn. These parameters can be derived from

equation (5.1). For a self-complementary structure, the spacing between adjacent arms

s and width of the armsw are equal and can be calculated from equation (5.1):

s = w =r2 − r14N

(5.1)

whereN is the number of turns.

The lowest frequency of operation occurs when the total arm length is comparable to

a wavelength. The lower frequency of this design is 1.69 GHz.The inner radius for the

large spiral antenna and the small spiral antenna are 0.86 mmand 0.83 mm, respectively.

5.2. PERFORMANCE OF A TWO-ARM ARCHIMEDEAN SPIRAL ANTENNA85

Figure 5.1: Geometry of the two-arm Archimedean spiral antenna

The lower cut-off frequency and higher cut-off frequency ofthe large and small spiral

antenna are derived from equation (5.2) and (5.3). For the large spiral antenna, the

corresponding results arefL = 1.69 GHz andfH = 55.5 GHz. From these equations,

the lower and higher cut-off frequencies of the small spiralantenna are 3.37 GHz and

57.5 GHz, respectively. The physical size of the two-arm spiral antenna increases as the

lower cut-off frequency is decreased.

fL =c

2πr2(5.2)

fH =c

2πr1(5.3)

wherec is the speed of the light.

The input impedance of the spiral antenna depends on the inner radius of the spiral.

When the inner radius of the spiral is equal to the strip width,the real part of the

impedance is 188Ω. When the inner radius is smaller than the arm width, the real

Table 5.1: The dimensions of the spiral antenna

spiral antenna r1 [mm] w [mm] s [mm] r2 [mm] N

Large Spiral (built on RT-duroid)

0.86 0.86 0.86 28.3 8

Small Spiral (built on RT-duroid)

0.83 0.83 0.83 14.15 4


part of the input impedance is less than 188Ω, and when the inner radius is larger than

the arm width, the real part of the input impedance is greaterthan 188Ω [83].

The next section presents the performance of a single spiralantenna without and

with balun feed network. The simulated results clearly demonstrate the influence of the

balun feed network on the wideband characteristics of the antenna.

5.2.2 Performance of Large Spiral Antenna without Balun

The layout of the large spiral antenna connected with a discrete port, is shown in Figure

5.2(a). In the absence of a balun structure, the two strips atthe centre of the spiral

antenna are first fed with a delta gap voltage source (discrete port in CST MWS) during

the simulations. The simulated return loss of the large spiral antenna at the feed point is

illustrated in Figure 5.2(b). The simulation result confirms that the large spiral antenna

has good wideband properties from 2.0 to 15 GHz. Note that thereflection coefficient

is normalised toR = 188Ω. Thus, if a balun is used, it should achieve impedance

matching from 50 to 188Ω.

(a) (b)

Figure 5.2: (a) Large spiral with the discrete port in CST (b) Simulated return loss fora large spiral antenna

5.3. INTEGRATION OF THE SPIRAL ANTENNA WITH BALUN 87

5.2.3 Performance of Small Spiral Antenna without Balun

The layout of the small spiral antenna connected to a discrete port is shown in Figure

5.3(a), and the dimension of the structure is defined in Table5.1. The simulated result

of the return loss is illustrated in Figure 5.3(b). It can be seen that a 10 dB return loss

bandwidth from 4 GHz to 15 GHz is obtained.

(a) (b)

Figure 5.3: (a) Small spiral with discrete port (b) Simulated return loss for the smallspiral antenna

From the S-parameter results, both spiral structures have wideband characteristics

and can be integrated with the proposed wideband balun to improve bandwidth of

these antennas further. In the next section, the microstripto parallel striplines balun

is integrated with the same antenna geometries as a feed network.

5.3 Integration of the Spiral Antenna with Balun

The two-arm Archimedean spiral antenna is a balanced antenna with wideband char-

acteristics. Therefore, the feeding system needs to have a balun with wideband char-

acteristics. The microstrip to parallel striplines balun is suitable for implementation as

feeding system for the two-arm Archimedean spiral antenna.


5.3.1 Performance of the Large Spiral Antenna with Balun

The large spiral antenna with the same dimensions as given inTable 5.1 is used. The

proposed microstrip to parallel striplines balun was used to excite the antennas. Two-

arm Archimedean spiral antenna is a self-complementary spiral antenna, where inner

radius is equal to strip width. The input impedance of both antennas is therefore 188Ω.

A microstrip to parallel striplines balun was optimized to provide impedance matching

between 50Ω and 188Ω.

The microstrip to parallel striplines transition consistsof a microstrip line where

the ground plane is tapered and overlapped with a parallel stripline, as shown in Figure

5.4. The unbalanced part (A-A’) is connected with the coaxial cable and balanced part

(B-B’) is connected with the spiral inner arms. Simulation andexperimental results

for this balun showed that it has a wider frequency bandwidththan the asymmetric

CPW to CPS balun. It was therefore preferred to excite the arrayof spiral antenna.

Figure 5.5(a) illustrates the connection of inner spiral arms with microstrip to parallel

striplines balun. Figure 5.5(b) shows that the overall dimension for the proposed large

spiral antenna connected with the proposed balun, is 60 mm x 60 mm x 52 mm or 0.34

λL x 0.34λL x 0.29λL, whereλL is the wavelength of the large spiral at lower cut-off

frequency fL = 1.69 GHz.

The antenna was connected with a network analyser (Rohde Schwarz ZVL Vector

Network Analyser with frequency range from 9 kHz to 15 GHz), as shown in Figure

5.6(a) for the measurement of the return loss. The simulatedS-parameters result for the

large spiral antenna as given in Figure 5.6(b). The simulated return loss shows that the

antenna has a good impedance matching over the entire frequency range. The antenna

operates well between 2.5 to 15 GHz with return loss better than 10 dB. The simulated

results of the large antenna are compared with the measured results as shown in Figure

5.6(b). The measured 10 dB return loss bandwidth is between 2.26 to 15 GHz. However,

the measured results differ from the simulations due to the improper connection between

the spiral antenna and the balun, and the losses from the SMA connector and the balun.

The 3D directivity radiation pattern of the large spiral antenna at frequency of 8 GHz

is presented in Figure 5.7. High radiation (directivity) ismarked in red, and the green

colour for lower radiation.


Figure 5.4: Configuration of the microstrip taper balun with a SMA connector

(a) (b)

Figure 5.5: (a) The connection between inner spiral arms and striplines of the balun(b) The photograph of the large spiral antenna with the microstrip to parallel striplinesbalun


(a) (b)

Figure 5.6: (a) A single large spiral antenna measurement set up (b) Measured andsimulated results of the large spiral antenna with the balun

Figure 5.7: Simulated 3D directivity radiation patterns of the large spiral


The electric field is a function ofθ and it is measured in x-y plane (φ = 0o). Figure

5.8 and Figure 5.9 show the simulated directivity radiationpatterns of the large spiral

antenna for the selected frequencies in both the E and H-plane, respectively. The co-

polarized radiation patterns are symmetrical with respectto the boresight (θ = 180o)

and have a maximum value atθ = 180o in both the E and H-plane.

Figure 5.8: Simulated E-plane (φ = 0o) directivity radiation patterns for the large spiralantenna at 2.5, 5, 10 and 15 GHz

It can be seen from the results presented in Figure 5.8 that the cross-polarization

of the large spiral antenna increases with frequency. This is because of the vertical

feed network which produces a large amount of leakage radiation to the back side

of the antenna at high frequencies. The thickness of the substrate material with a

low dielectric constant (in this caseǫr = 2.2) can also produce higher order modes

which deteriorates the radiations of the antenna [84]. As a result, the cross-polarization


component, especially in H-plane, is increased significantly, as depicted in Figure 5.9.

Reflectors or absorbing materials, can be used to suppress thecross-polarization of the

antenna. However, it was not used in the measurement set up due to the vertical feed

network.

Figure 5.9: Simulated H-plane (φ = 90o) directivity radiation patterns for the largespiral antenna at 2.5, 5, 10 and 15 GHz

Two different antenna measurements for single antennas were conducted. First,

antenna radiation measurement set up with a Yagi antenna (used as a receiver and

frequency range from 0.25 to 2.4 GHz) is illustrated in Figure 5.10. A signal generator

(frequency range from 0.1 to 4 GHz) is connected with the transmitter antenna and a

spectrum analyser (frequency range: 0.1 to 22 GHz) is connected with the receiver. A


transmitter antenna position controller is used to change the height of the transmitter

antenna and the position rotator is used to change the angle (E-plane radiation measure-

ments) from 0 to 360o.

Figure 5.10: Large spiral antenna radiation measurements set up with the signalgenerator and the spectrum analyser

The measured radiation patterns at frequencies of 1.02, 1.5, 2 and 2.4 GHz, are

given in Figure 5.11. The measured radiation patterns show that the antenna has a good

wideband characteristic when it is connected with the microstrip to parallel striplines

balun. The measured and simulated results show that the spiral antenna experienced

more reflections from the ground plane and the surrounding objects. It can also be

noticed that the receiver antenna has multiple dipoles, as shown in Figure 5.10. The

radiation pattern of the spiral at 2.4 GHz, has more fluctuations when the E-plane is


changing from 0 to 360o (see Figure 5.11). Therefore, the single antenna as a transmitter

(or receiver) is used to obtain smooth radiation patterns.

Figure 5.11: Measured and simulated radiation patterns for the large spiral antenna at1.02, 1.5, 2 and 2.4 GHz

Secondly, the large spiral was set up with a horn antenna (as atransmitter, frequency

range: 1 to 18 GHz) to measure the radiation patterns at different frequencies of 2, 4, 6,

8, 10, 12, 13 and 15 GHz in the anechoic chamber at the RF lab (measurement set up

is shown in Figure 5.12). The measured results are compared with the simulated results

in Figure 5.13. The measurements were taken for each 30o increment in both the E and

H-plane. The measured results are quite similar to the simulated values. However, the

measurement set up was subject to external reflections whichcan affect the radiation

pattern significantly.


Figure 5.12: Measurement set up for the large spiral in the anechoic chamber

The measured gain of the single spiral antenna was conductedwith a network anal-

yser (frequency range from 9 kHz to 15 GHz) and two identical horn antennas (with

the model DRH-0118 double-ridged horn with Serial Number 104A092 and frequency

range from 1-18 GHz). The following procedure illustrates the gain measurements of

the antennas.

• Two identical horn antennas were aligned with each other as shown in Figure

5.17(a). The received power of the reference horn antenna (Pref ) was measured

(S21 in dB) with known gain (Gref )

• Reference horn antenna was replaced with a single spiral antenna (see Figure

5.14) and the received power of the antenna under test (spiral antenna) was mea-

sured from the network analyser (consider as (PAUT ))

• The difference between the two received powers is the difference between the

antenna gains.

Measured data is given in Table 5.3 for different frequencies. Gain of spiral antenna

was calculated from the following equation:

GAUT (dB) = Gref(dB) +∆dB (5.4)

where,

∆dB = PAUT (dB) − Pref(dB) (5.5)


Figure 5.13: Measured and simulated radiation patterns for the large spiral antenna at2, 4, 6, 8, 10, 12, 13 and 15 GHz


(a) (b)

(c) (d)

Figure 5.14: Gain measurement for the large spiral with the horn antennaTable 5.2: HPBW of the large spiral antenna in E and H-plane

Frequency / (GHz) HPBW at E-plane (o ) HPBW at H-plane (o )

2.5 75 71.6

5.0 96.2 55.3

10 36.2 37.2

15 30.6 33.0

The simulated HPBW for the large spiral antenna is given in Table 5.2. The values

for the HPBW are decreasing as frequency increases. The gain of the antenna there-

fore is increasing with the frequency. The HPBW calculation is illustrated in Figure

5.15. The HPBW is calculated from the difference between the angle of the maximum


Figure 5.15: HPBW calculation of the large spiral antenna in E-plane at 5 GHz

Table 5.3: Measured gain data for the large spiral antenna

Frequency / (GHz) Gref (dB) ∆dB GAUT (dB)

2 6.55 -2.55 4.0

4 8.26 -3.16 5.1

6 8.55 -1.75 6.8

8 11.69 -3.84 7.85

10 11.32 -3.87 7.45

12 9.95 -3.0 6.95

13 11.14 -3.44 7.7

15 12.42 -4.92 7.5


radiated power (208.4o) and the angle of the following half radiated power (143.5o).

The simulated gain of the large spiral antenna was compared with the measured

values. However, the measured gain differs from the simulation as shown in Figure

5.16, due to the transmitter (horn antenna) which has not thesame polarization (linear

polarization) as the receiver (spiral antenna has a circular polarization). It is shown

Figure 5.16: Measured and simulated gain of the large spiral antenna with respect tothe boresight (θ = 0o)

in Figure 5.17, where the measured power changed dramatically when an antenna was

rotated by45o or 90o. For circularly polarized antennas, radiation patterns are usually

taken with a rotating linearly polarized reference antenna. Even though this linear polar-

ization source works with circular polarization, it is better to have the same polarization

antenna as a receiver to get a maximum received power.

Results from the return loss, radiation pattern and gain showthat the large spiral

antenna operates well in frequency band from 2.5 to 15 GHz andit is a good candidate

for an element in an array structure able to achieve more thantwo octaves bandwidth.


(a) (b)

(c) (d)

(e) (f)

Figure 5.17: Gain measurement for the two identical horn antennas (a) Receiver hornantenna aligned with the transmitter in 0o (b) S21 for the 0o aligned horn antenna (c)Receiver horn antenna aligned with the transmitter in 45o (d) S21 for the 45o alignedhorn antenna (e) Receiver horn antenna aligned with the transmitter in 90o (b) S21 forthe 90o aligned horn antenna


5.3.2 Performance of the Small Spiral Antenna with Balun

The dimensions of the small spiral antenna were obtained from the Table 5.1. It was also

integrated with the proposed balun as shown in Figure 5.18(a). The overall dimension

for the proposed small spiral antenna is 30 mm x 30 mm x 52 mm or 0.34λL x 0.34λL

x 0.58λL, whereλL is the wavelength of small spiral at the lower frequency (fL = 3.37

GHz).

The results of the simulated S-parameters for small spiral antenna is shown in Figure

5.18(b). The simulated 10 dB return loss bandwidth of the small spiral antenna is from

4 to 15 GHz and measured bandwidth is from 3 to 15 GHz.

(a) (b)

Figure 5.18: (a) The photograph of the small spiral antenna with balun (b) Measuredand simulated results for the small spiral antenna

The radiation patterns for the small spiral antenna were simulated at frequencies of

3, 5, 10 and 15 GHz in E and H-plane (Figure 5.19 and Figure 5.20). It shows that the

small spiral antenna has a maximum co-polarization at boresight (θ = 0o) in both E and

H-plane. However, unexpected cross-polarization is high for otherθ values due to the

vertical feed network.

The small spiral antenna gain was measured using the same procedure as given

in Section 5.3.1. Table 5.5 shows measured gain of the small spiral antenna. These

measurements were compared with the simulated results, as shown in Figure 5.21. It

shows significant discrepancies.


Figure 5.19: Simulated E-plane (φ = 0o) directivity radiation patterns of the smallspiral antenna at 3, 5, 10 and 15 GHz

Table 5.4: HPBW of the small spiral antenna in E and H-plane

Frequency / (GHz) HPBW E-plane (o) HPBW H-plane (o)

2.5 216.3 343.9

5.0 80.6 120.3

10 42.0 42.1

15 100.5 33.7


Figure 5.20: Simulated H-plane (φ = 90o) directivity radiation patterns for the smallspiral antenna at 3, 5, 10 and 15 GHz

Table 5.5: Measured gain data for the small spiral antenna


2 6.55 -5.05 1.5

4 8.26 -5.46 2.8

6 8.55 -5.15 3.4

8 11.69 -5.69 6.0

10 11.32 -5.39 5.93

12 9.95 -4.45 5.5

13 11.14 -4.89 6.25

15 12.42 -6.32 6.10


Figure 5.21: Measured and simulated gain of the small spiral antenna

The radiation patterns of the small spiral was measured withthe horn antenna as

receiver (frequency range: 1 to 18 GHz) are given in Figure 5.22. It can be seen that the

maximum radiation was occurred atθ = 180o (at boresight). In addition, the measured

results agree with simulated values.


Figure 5.22: Measured and simulated radiation patterns for the small spiral antenna at2, 4, 6, 8, 10, 12, 13 and 15 GHz


5.4 Array of Archimedean Spiral Antennas

Section 5.3 discussed the single spiral antenna and its wideband characteristics. How-

ever, the single spiral antenna has low gain which is not suitable for some applications.

Thus, an array of Archimedean spiral antenna is demonstrated in this section in an

attempt to improve the gain. Wideband array with variable element sizes techniques

(WAVES) were applied to reduce the grating lobes level. The proposed wideband balun

was integrated with the antenna array to achieve wideband antenna performances.

5.4.1 Theory of WAVES Array Geometry

The concept of WAVES was presented in Chapter 2. As shown in Figure 5.23, the larger

antenna elements are used to cover the first octave of bandwidth. When the grating

Figure 5.23: Basic geometry of WAVES

lobe appears at frequencies approaching the point whereS1∼=λ, the smaller antenna

is switched on and all three elements are used to cover the next octave of bandwidth.

Typically, it is desirable for the inter-element spacing tobe between 0.5λ andλ. This

leads to a larger element spacing of:

S1 =λ1

2(5.6)

whereλ1 is the low frequency cut-off for the larger element. From Figure 5.23, the

larger spacing is also given by

S1 = 2S2 > D1 +D2 (5.7)

5.4. ARRAY OF ARCHIMEDEAN SPIRAL ANTENNAS 107

and

D1 = 2D2 (5.8)

whereS2 is the spacing between a larger and smaller element and the diameters of the

larger and smaller elements are given byD1 andD2 , respectively. An Archimedean

spiral antenna was chosen for the WAVES array since the larger element is required

to cover a minimum of two octaves of bandwidth and its diameter is required to scale

proportionally with frequency [50].

5.4.2 Linear Antenna Array

The linear WAVES array of spirals was demonstrated with three spiral elements with

array elements placed on thex axis with a uniform spacingd, as shown in Figure 5.24.

The array was shown to have a performance gap between 2.5 GHz where the first grating

lobe appears and 4 GHz where the smaller, second octave elements becomes active. The

two-arm circular Archimedean spiral antenna with the wideband balun was designed to

eliminate the performance gap in feeding system in [83]. Figure 5.24 shows that the

spirals 2 and 3 have same size and the diameter of the spiral 1 is half that of the spiral

2.

Figure 5.24: The linear antenna array

The spacing between the elements (S1 andS2) were calculated from equation (5.6)

and (5.7) to maintain minimum element spacing. The parameters of the large and small

spiral are presented in Table 5.1. The lower and higher cut-off frequencies can be


obtained from the equation (5.2) and (5.3) respectively, where outer and inner circum-

ference of the spiral equal to one wavelength. Theoretically, the large spiral operates

from 1.69 to 55.5 GHz and the small spiral from 3.37 to 57.5 GHz.

Figure 5.25 shows the VSWR performance of the array of 3 elements (The relation

between VSWR and|S11| was given in Chapter 2, Section 2.4.2). Array is designed to

operate from 2.5 to 15 GHz. The simulated VSWR for only large elements is shown in

Figure 5.25(a) with a VSWR less than 2 from 2.5 GHz. In this case, only large elements

(Spiral 2 and Spiral 3) are active and having identical performance. The lower cut-off

frequency for large element is 2.5 GHz, which is 48% above thefrequency derived from

the theory. The VSWR for large and small elements are given in Figure 5.25(b), where

all three elements are active. The small element has a lower cut-off frequency at 4 GHz,

which is 19% above the frequency derived from the theory. These results show that,

the lower cut-off frequencies for both spiral antennas are higher than predicted. This

problem can be addressed with the unique slow wave spiral to increase the diameter of

the spiral elements.

(a) (b)

Figure 5.25: Simulated VSWR for the linear antenna array (a) Only large spirals areactive (b) All elements are active

The S-parameters for the linear array elements are shown in Figure 5.26. It can be

seen that the mutual coupling (given by|S12| and|S13|) is quite low, lower than about

20 dB from 3 GHz.


Figure 5.26: Simulated S-parameters for the linear antenna array

5.4.3 Radiation pattern of the linear antenna array

Other most important parameters in antenna design are the far field radiation patterns.

They are shown for the linear array in Figure 5.27. The basic principle behind the

WAVES theory can be seen that the grating lobes are eliminated when smaller elements

become active. The simulated radiation patterns (directivity of the antenna array) are

shown in Figure 5.27 at frequencies of 2.5, 5, 10 and 15 GHz in Eand H-plane.

The cross-polarization (LHPC in this right hand wound spiral) in Figure 5.27 is high

due to the spiral antenna back radiation and vertical feed network but the co-polarization

(RHCP) in Figure 5.28 is higher than cross-polarization. The addition of a reflector

could eliminate the back radiation. Table 5.6 shows the HPBW in E and H-plane. The

values for HPBW are decreasing with frequency. The gain of thelinear antenna array

therefore is increasing with frequency.

Table 5.6: HPBW of the linear antenna array in E and H-plane


2.5 60.4 175.6

5.0 32.6 49.0

10 16.8 33.9

15 5.4 28.5


Figure 5.27: Simulated E-plane (φ = 0o) directivity radiation patterns for linear antennaarray at 2.5, 5, 10 and 15 GHz


Figure 5.28: Simulated H-plane (φ = 90o) directivity radiation patterns for the linearantenna array at 2.5, 5, 10 and 15 GHz

Figure 5.29: Simulated gain of the linear antenna array


5.4.4 Planar Antenna Array

Section 5.4.2 demonstrated the operation of the linear array integrated with the wide-

band balun. This linear array was extended to a planar array.The geometry of the

planar array is shown in Figure 5.30. The dimensions of the spirals were derived from

Table 5.1. The element spacing was selected to be less thanλ/2 ( fL - lower cut-off

frequency). The planar array with 8-elements was designed and simulated in CST. The

Figure 5.30: The planar antenna array

array structure was constructed on the RT-duroid 5880 with adielectric constantǫr =

2.2 and height ofh of 1.5748 mm. Each array element in the structure was integrated

with the single microstrip to parallel striplines balun. The array structure was simulated

with a 3 dB power divider to split the power to each port equally (see Figure 5.32). The

simulated return loss for the planar antenna array is shown in Figure 5.33. It confirms

the effective operation of the planar antenna array integrated with the proposed balun

has a wide bandwidth and it is from 2.1 to 15 GHz.

5.4.5 Radiation pattern of the planar antenna array

The simulated 3D radiation patterns of the planar array at frequency of 5 GHz is illus-

trated in Figure 5.34. It shows that more back radiation occurred at 5 GHz in red colour.

It can be removed with a reflector-backed by a spiral antenna.However, a ground plane

or absorbing materials is not used as a reflector in this design, due to the geometry of

the proposed feed network.


(a) (b)

Figure 5.31: Configuration of the 8-elements array with baluns (a)Top view (b) Sideview

(a) (b)

Figure 5.32: Planar array set up with a power divider (a) Set up with 3 dB powerdividers in CST (b) Set up with 6 dB power divider with the Network Analyser


Figure 5.33: Measured and simulated S-parameters results for the planar antenna array

Figure 5.34: 3D radiation patterns of the planar antenna array at 5 GHz


The appearance of grating lobes, as shown in Figure 5.35 is anunwanted peak in the

array environment. Reference [31] used the amplitude distribution between the elements

to reduce the level of grating lobes. The amplitude distribution was set to 1:2:2:2:1,

when all the elements were radiating.

Figure 5.35: Grating lobes and side lobes for the planar antenna array atthe frequencyof 4 GHz

The simulated radiation patterns for both E and H-plane are shown in Figure 5.36 for

four different frequencies 2.5, 5, 10 and 15 GHz respectively. It shows that an unequal

amplitude distribution have an influence on grating lobes. The grating lobes level was

not changed at high frequencies. It can be reduced with an unequal power and phase

distribution without affecting the array performance.

Table 5.7 shows the HPBW in E and H-plane at frequencies of 2.5,5, 10 and 15 GHz.

The HPBW decreases as frequency increases. The gain of the antenna is therefore high

at high frequencies.

Table 5.7: HPBW of the planar antenna array in E and H-plane


2.5 41.2 47.6

5.0 15.0 50.5

10 13.5 26.4

15 20.3 10.4


Figure 5.36: Simulated directivity radiation patterns (φ = 0o) of the planar antennaarray equal and unequal amplitude distribution at 2.5, 5, 10and 15 GHz

Table 5.8: Measured gain data for planar antenna array


2 6.55 -0.67 5.88

4 8.26 -0.48 7.78

6 8.55 0.73 9.28

8 11.69 0.35 12.04

10 11.32 -0.45 10.87

12 9.95 -0.48 9.47

13 11.14 0.09 11.23

15 12.42 0.6 13.02


The gain of the planar antenna array is given in Figure 5.37. The simulated and

measured gain results for single and antenna array show thatarray of spirals have higher

gain than the single element with frequency increases. The measured gain of the planar

antenna array is shown in Table 5.8. The measured boresight gain should be similar to

the simulated value, but the measurements show some variation. It can be also seen that

it has a higher gain than the single spiral antenna.

Figure 5.37: Gain of the planar antenna array

Radiation measurements for the planar array antenna were performed with the horn

antenna as a receiver. The same radiation procedure as the large spiral antenna was used

in the planar array antenna. The measured and simulated radiation patterns of the planar

array are presented in Figure 5.38 at different frequenciesto give an idea about their

frequency characteristics.

The results for return loss, radiation patterns and gain obtained for the antenna array

show that the array has generally better wideband performance when compared to the

single spiral. In addition, the proposed balun is capable ofmaintaining the wideband

performance of the spiral antenna.


Figure 5.38: Measured and simulated radiation patterns for the planar antenna array at2, 4, 6, 8, 10, 12, 13 and 15 GHz

5.5. SUMMARY 119

5.5 Summary

The simulation and measurement results of a single spiral antenna and the wideband

array with variable element sizes integrated with the proposed balun were presented in

this chapter. Two different sized spiral antennas were selected. These antenna were

simulated without the balun (in CST discrete port) and with the proposed balun. The

simulated and measured results showed that the spiral antenna with the balun has a

wide bandwidth from 2 to 15 GHz for the large spiral antenna, and 3.5 to 15 GHz for

the small spiral antenna. In addition, the wideband characteristics (radiation pattern

and gain) of the spiral antenna with the balun were simulatedand compared with the

measured results. The directivity radiation pattern of thespirals in both E and H-plane

were simulated. In both cases, spiral antennas have a maximum directivity radiation at

boresight (θ = 0o). The radiation patterns of the each spiral antenna were measured

with the help of the horn antenna (transmitter) at differentfrequencies. The measured

radiation pattern of the both spirals have a good agreement with the simulated results.

These both spiral were used to form the linear and planar antenna array. The sim-

ulated gain of the linear antenna array showed that the arrayantenna has a higher gain

than the single spiral antenna. The HPBW is also used to prove that the gain of the

linear antenna array and it increased at higher frequency. The planar array with the

proposed balun was simulated with the aid of CST MWS, and measured results for the

return loss showed that the bandwidth of the planar array is 2.10 - 15 GHz. The planar

array was arranged with the amplitude distribution of 1:2:2:2:1 to suppress grating lobes.

However, the directivity radiation patterns of the planar antenna array showed that the

grating lobes of the array were not changed at higher frequencies. The measured gain

and radiation patterns of the planar antenna array had some variation with the simulated

results. The radiation measurement errors were due to the array not being perfectly

centred during azimuth rotation. However, the proposed antenna array generally showed

better performance in terms of return loss, radiation patterns and gain when compared

to the single spiral antenna.

Chapter 6

Conclusion and Recommendations

In this final chapter the results and contributions of the thesis are summarised. Some

recommendations for future research work are also presented. During the first part of the

thesis a comprehensive literature search of antenna designand broadband antenna tech-

nologies are presented. Special attention is given to the bandwidth and the characteristic

impedance of the antenna. Existing wideband feeding structures are also discussed in

detail. In the second part of the thesis, design procedures for three new wideband balun

structures and test results of balun and spiral antenna integration are presented.

6.1 Contributions

This thesis proposes three different types of wideband feeding systems: a tapered sym-

metric CPW to CPS balun, a tapered asymmetric CPW to CPS balun and tapered

Microstrip to parallel striplines balun. Summary of major contributions of the thesis

is presented below.

• A comprehensive review of theory, principles and techniques of antennas and

wideband baluns are presented.

121

122 CHAPTER 6. CONCLUSION AND RECOMMENDATIONS

• A novel tapered geometry for a symmetric coplanar waveguide(CPW) to coplanar

strip line (CPS) wideband balun with a stub to accommodate thediscontinuity

between CPW and CPS is proposed. The bandwidth of the wideband balun is

improved by tapering symmetric CPW, stub and bond wires.

• An asymmetric CPW to CPS wideband balun with a novel tapered design is

proposed by applying the new tapering procedure. Asymmetric CPW to CPS

wideband balun has wider bandwidth compared to the symmetric CPW to CPS

wideband balun. This balun consists of asymmetric CPW to remove the disconti-

nuities between CPW and CPS without using a radial stub or bond wires.

• A tapered microstrip to parallel striplines balun with new tapered design is pro-

posed. This configuration can further improve the bandwidth. The simulated and

measured results show that tapered microstrip to parallel striplines balun has more

than three octaves of bandwidth and it is chosen as the preferred feeding structure

for wideband antenna array.

• Tapered microstrip to parallel striplines wideband balun is integrated and tested

with various spiral antenna configurations

All the proposed feeding structures are simulated and measured in a back-to-back con-

figuration before integrating with spiral antenna structures. These balun structures have

following characteristics:

• Impedance transforming between the coaxial cable and the spiral antennas

• Field matching between an unbalanced transmission line to abalanced transmis-

sion line

• Planar structure and easy to integrate with the planar balanced structures

Although the CPW to CPS baluns have above characteristics, it cannot be used with

the array of spiral antennas due to its insufficient bandwidth. The microstrip to parallel

striplines balun operates more than two octaves of bandwidth and is therefore preferred

as the optimum wideband balun feed for spiral antennas. Table 6.1 shows the compari-

son of proposed baluns.

6.1. CONTRIBUTIONS 123

Table 6.1: The comparison of proposed baluns

Proposedbaluns

Impedance bandwidth (GHz)Bandwidth in ratio Volume (mm3 )

SymmetricCPW to CPS

0.6 - 3.5 5.8 : 1 42 x 20 x 0.67

AsymmetricCPW to CPSusing RTRogers

9 - 15 1.7 : 1 36 x 20 x 0.67

AsymmetricCPW toCPS usingRT-duroid

3.53 - 15 4.2 : 1 62 x 20 x 0.67

Microstripto parallelstriplines

1.75 - 15 8.6 : 1 55 x 18 x 1.61

Moreover, this thesis investigated the integrated wideband performance of the spiral

antennas with the proposed microstrip to parallel striplines balun. Array of two-arm

Archimedean spiral antennas with variable element sizes are integrated with the balun

tested. The spiral antenna array used for testing has the following properties:

• More than two octaves of bandwidth having a return loss less than 10 dB in the

frequency range of 2.5 to 15 GHz)

• Improved gain in the array environment compared to a single element

• Reduced grating lobes level in the array environment with an unequal amplitude

distribution and small element spacing (< λ/2)

First, a single Archimedean spiral antenna is integrated with proposed microstrip to

parallel striplines balun and tested. The measured and simulated results prove that the

proposed balun can be integrated with spiral antennas efficiently. Next, spiral antennas

with two different dimensions are used to construct an eightelements array with WAVES

techniques. The element spacing are chosen to be less than half a wavelength at the

lower operating frequency of each element to reduce the grating lobes and to increase

the operating bandwidth of the array [31]. An unequal amplitude distribution is also

used to reduce the grating lobe level.


Table 6.2: The comparison of the spiral antenna with the proposed balun

Spiral anten-nas

Impedance bandwidth (GHz)Bandwidth in ratio Volume (mm3 )

Large Spiral 2.26 - 15 7.5 : 1 60 x 60 x 52

Small Spiral 3.0 - 15 4.3 : 1 30 x 30 x 52

Array of Spi-ral

2.1 - 15 7.1 : 1 200 x 200 x 1.61

The bandwidth of the single element and array of spiral is given in Table 6.2. The

directivity radiation patterns for a single spiral and an array of spirals are simulated and

measured at different frequencies. The results show that the amplitude distribution has

more effect on the grating lobes. Simulated and measured results of the single and array

of spiral antennas integrated with the proposed wideband balun show that the integrated

structure can operate in a bandwidth spanning more than two octaves. (two octaves :

fL=2.5 GHz andfH= 10 GHz).

6.2 Recommendations for Future Directions

Therefore, some recommendations for future directions arepresented below.

• The results of the proposed asymmetric CPW to CPS balun show that it has

high insertion loss at high frequencies used with high dielectric constant and thin

material. The insertion loss could be reduced with a low dielectric constant and

thick substrate material.

• Measured microstrip to parallel striplines balun also differs from the simulated

insertion loss results. It could be resolved by properly aligning the two layers at

the centre on the printed circuit boards. Proper soldering could also improve the

results.

• Spiral antennas have bidirectional radiation patterns. Therefore, the use of a

reflector can produce unidirectional patterns. The feed network is perpendicular

to the back side of the antenna. Better results may be obtainedby having an

absorber behind the antenna array to reduce radiation from feed region.

6.2. RECOMMENDATIONS FOR FUTURE DIRECTIONS 125

• Grating lobes are unwanted peak values in the radiation patterns of the array

environment. This is reduced by maintaining an element spacing of less than

one wavelength and by using an unequal amplitude distribution. However, the

results show that grating lobes level was still present at high frequencies. It is

necessary to use some techniques such as unequal power and phase distribution

to reduce the grating lobes level without affecting the performance of the array.

• The lower cut-off frequency for the antenna array is 2.5 GHz.It can be reduced

with a larger diameter of the spiral or slow wave star spiral antenna with a low

profile.

• The bandwidth of the antenna array can be improved to more than two octaves by

increasing the number of the spirals (for example: 3-octaves bandwidth requires

three different sized spirals). The size of the third element should be half of the

second.

• Self-complementary spirals have high characteristic input impedance (188Ω).

Due to the high impedance of the spiral, output impedance of the striplines is

also high. Consequently, the width of the stripline is very small which makes it

difficult to integrate with the spiral arms. For 188Ω characteristic impedance, the

stripline has a width of 0.88 mm. However, actual input impedance of the spiral

is reduced by the presence of the substrate. Spiral antenna input impedance can

also be reduced by selecting the inner radius of the spiral arm to be smaller than

the spiral arm width.

• In the radiation measurements of the array, an 8-way power divider is used to split

the power to each port. Ports connected to small spirals, were connected with 6 dB

attenuator to suppress the power by half. However, the simulations in CST were

conducted using only 3 dB power dividers. Results from the CST could therefore

not be compared directly with the measured results due to thedifferences in power

levels. To validate results, each port of an actual power divider output should be

measured.

Appendix A

Appendix : MATLAB code

A.1 HECKEN MATLAB code for symmetric CPW Design

MATLAB script Hecken taper for symmetric Coplanar waveguide

clear all;

Z0=50;

Z2=50;

Zl=80;

RL=40;

f0=0.5e9;

lam0=2.998e8/f0;

dz=lam0/100;

er = 10.2; % dielectric constant of the substrate

h = 0.635e-3; % height of the substrate

t = 35e-6; % thickness of the metal

b = 0.69e-3; % gap size of the CPW

a = 3e-3; % strip width of the CPW

global emax

127

128 APPENDIX A. APPENDIX : MATLAB CODE

rhomax=10ˆ(-RL/20);

emax=rhomax/0.5/log(Zl/Z0);

if emax > 0.217234

B=0;

piu0=fzero(@getpiu0,[0.001 2.55356]);

else

B = fzero(@getb,[0.001 10]);

piu0=sqrt(Bˆ2+6.520694);

end

B

piu0

pause;

z=0;

theta=-piu0/2;

i=1;

while theta < piu0/2

if emax > 0.217234

Z=Z0* exp(0.5 * log(Zl/Z0) * (1+2 * theta/piu0));

else

Z=Z0* exp(0.5 * log(Zl/Z0)+0.5 * log(Zl/Z0)

* gfunc(B,2 * theta/piu0));

end

if Z2 < 188.5

at=a+(1.25 * t/pi) * (1+log(4 * pi * a/t));

bt=b-(1.25 * t/pi) * (1+log(4 * pi * a/t));

k=a/b;

ka=sqrt(1-kˆ2);

kt=at/bt;

A.1. HECKEN MATLAB CODE FOR SYMMETRIC CPW DESIGN 129

kta=sqrt(1-ktˆ2);

k1=sinh(pi * at/4/h)/sinh(pi * bt/4/h);

k1a=sqrt(1-k1ˆ2);

eeff=1+((er-1)/2) * (kfunc(k1,k1a)/kfunc(k,ka))

eefft=eeff-(eeff-1)/((b-1)/2/0.7/t * kfunc(k,ka)+1)

Z2 = ceil(abs(30 * pi/sqrt(eefft)/kfunc(kt,kta)))

beta=2 * pi/lam0;

data_matrix(i,1) = z;

data_matrix(i,2) = Z;

data_matrix(i,3) = beta;

data_matrix(i,4) = Z2;

data_matrix(i,5) = b;

data_matrix(i,6) = a;

z=z+dz;

if b < 19e-3

b= b+0.2e-3;

else

a= a-0.2e-3;

end

end

i=i+1;

theta=theta+dz * beta;

end

data_mat = transpose(data_matrix);

length = size(data_mat,2)

pause;

figure(1)

hold on

plot(data_mat(1,1:length), data_mat(2,1:length),’r’);


plot(data_mat(1,1:length), data_mat(3,1:length),’g’);

plot(data_mat(5,1:length), data_mat(4,1:length),’b’);

plot(data_mat(6,1:length), data_mat(4,1:length),’c’);

title(’Impedance profile’)

legend(’Z’,’Beta’,’b’,’a’);

%axis([2.375,2.625,-40,0]);

xlabel(’Distance z (m),b a’);

ylabel(’Z (Ohm)’);

hold off

save symmetricCPW.txt data_matrix -ASCII

%******************* geta function **********************

function dimfunc = geta(a)

%function to iterate to determine dimension a

global dims

er = dims(1);

h = dims(2);

t = dims(3);

b = dims(4);

Z0 = dims(5);

at=a+1.25 * t/pi * (1+log(4 * pi * a/t));

bt=b-1.25 * t/pi * (1+log(4 * pi * a/t));

k=a/b;

ka=sqrt(1-kˆ2);

kt=at/bt;

kta=sqrt(1-ktˆ2);


k1a=sqrt(1-k1ˆ2);

eeff=1+(er-1)/2 * kfunc(k1,k1a)/kfunc(k,ka);

eefft=eeff-(eeff-1)/((b-1)/2/0.7/t * kfunc(k,ka)+1);

dimfunc = 30 * pi/sqrt(eefft)/kfunc(kt,kta)-Z0;


end

%**************************** getb function **************

function bfunc = getb(b)

%function to iterate to determine B

global emax

bfunc = abs(0.217234 * b/((exp(b)-exp(-b))/2))-emax;

end

%************************ getpiu0 function ****************

function pfunc = getpiu0(piu0)

%function to iterate to determine B

global emax

pfunc = sin(piu0)/piu0-emax;

end

%*********************** gfunc function ******************

function g=gfunc(b,xi)

% Hecken transition function

k=0;

ak=1;

bk=xi;

g=b/((exp(b)-exp(-b))/2) * ak * bk;

for k = 1:12

ak=bˆ2/4/kˆ2 * ak;

bk=(xi * (1-xiˆ2)ˆk+2 * k* bk)/(2 * k+1);

g=g+b/((exp(b)-exp(-b))/2) * ak * bk;

end

%******************* kfunc function **********************

function krat=kfunc(k,kdash)

% K(k)/K(k’)


if k < 0.5

krat=pi/log(2 * (1+sqrt(kdash))/(1-sqrt(kdash)));

else

krat=1/pi * log(2 * (1+sqrt(k))/(1-sqrt(k)));

end

%********************************************************

%******* MATLAB CODE for CPS impedance calculation *******

clear all;

%Z0=50;

%Zl=180;

%RL=30;

w=2.7;

g=1.3;

er=10.2;

h=0.635e-3;

t=35e-6;

l1= (exp(pi * g/2 * h) - exp(-pi * g/2 * h))/2;

%l2=(exp(pi * g/2 * h) + exp(-pi * g/2 * h))/2;

m1= (exp(pi * (w+g)/2 * h)-exp(-pi * (w+g)/2 * h))/2;

%m2=(exp(pi * (w+g)/2 * h)+exp(-pi * (w+g)/2 * h))/2;

k=(l1)/(m1);

kdash= sqrt(1-(kˆ2));

%Specify diemnsions of circuit board

%k=(tanh(pi * g/2 * h))/(tanh(pi * (s+g)/2 * h))


k0= g/(g+w);

k0dash=sqrt(1-k0ˆ2);

q=0.5 * kfunc(k0,k0dash)/kfunc(k,kdash);

eff=1+(er-1) * q

Z0= (120 * pi/sqrt(eff)) * kfunc(k0,k0dash)

% output from symmetric impedance taper: symmetric.txt

[z] [Z] Beta [a] [b]

0.00 50.00 80.42 3.28 5.00

1.50 50.13 80.36 3.27 5.01

3.00 50.32 80.29 3.27 5.02

4.50 50.59 80.18 3.27 5.04

6.00 50.96 80.03 3.26 5.06

7.50 51.42 79.85 3.25 5.09

8.99 52.01 79.62 3.24 5.12

10.49 52.73 79.35 3.23 5.17

11.99 53.59 79.02 3.22 5.22

13.49 54.62 78.65 3.20 5.28

14.99 55.81 78.23 3.17 5.36

16.49 57.19 77.76 3.14 5.44

17.99 58.76 77.24 3.11 5.54

19.49 60.53 76.69 3.07 5.65

20.99 62.51 76.10 3.02 5.77

22.49 64.71 75.48 2.96 5.91

23.98 67.13 74.85 2.89 6.05

25.48 69.78 74.20 2.81 6.22

26.98 72.66 73.56 2.73 6.39

28.48 75.75 72.92 2.63 6.58

29.98 79.07 72.31 2.53 6.79

31.48 82.61 71.72 2.42 7.01

32.98 86.34 71.17 2.30 7.24

34.48 90.27 70.65 2.17 7.48


35.98 94.38 70.18 2.04 7.73

37.48 98.66 69.76 1.91 7.99

38.97 103.07 69.38 1.77 8.27

40.47 107.60 69.05 1.64 8.54

41.97 112.21 68.77 1.51 8.83

43.47 116.90 68.53 1.38 9.12

44.97 121.61 68.32 1.26 9.41

46.47 126.31 68.16 1.15 9.70

47.97 130.98 68.02 1.04 9.98

49.47 135.58 67.91 0.95 10.27

50.97 140.06 67.83 0.86 10.54

52.47 144.40 67.77 0.78 10.81

53.96 148.56 67.72 0.71 11.07

55.46 152.52 67.68 0.65 11.31

56.96 156.24 67.66 0.60 11.54

58.46 159.70 67.65 0.55 11.75

59.96 162.89 67.64 0.51 11.95

61.46 165.80 67.64 0.47 12.13

62.96 168.41 67.64 0.44 12.29

64.46 170.72 67.65 0.42 12.43

65.96 172.75 67.66 0.40 12.55

67.46 174.49 67.66 0.38 12.66

68.95 175.96 67.67 0.36 12.75

70.45 177.17 67.68 0.35 12.83

71.95 178.15 67.68 0.34 12.89

73.45 178.92 67.69 0.34 12.93

74.95 179.50 67.69 0.33 12.97

76.45 179.91 67.70 0.33 12.99

%******************************************************

A.2. HECKEN MATLAB CODE FOR AN ASYMMETRIC CPW DESIGN 135

A.2 HECKEN MATLAB code for an Asymmetric CPW Design

% MATLAB CODE for Asymmetric CPW taper

% MATLAB script Hecken taper

clear all;

Z0=50;

Zl=200;

RL=20;

f0=2e9;

lam0=2.998e8/f0;

dz=lam0/250;

%Specify diemnsions of circuit board

er=2.2; % dielectric constant of the substrate

h=1.5748e-3; % height of the substrate

t=35e-6; % thickness of the metal

d1min=0.690e-3; % minimum small gap size of the CPW

d2min=0.691e-3; % minimum large gap size of the CPW

d1max=3e-3; %maximum small gap size of the CPW

d2max=10e-3; %maximum large gap size of the CPW

%aguess=1e-3;

a1=0.1e-3; %minimum centre strip width of the CPW

a0=2.6e-3; %maximum centre strip width of the CPW

global emax

%global dims

rhomax=10ˆ(-RL/20);

emax=rhomax/0.5/log(Zl/Z0);


if emax > 0.217234

B=0;

piu0=fzero(@getpiu0,[0.001 2.55356]);

else

B = fzero(@getb,[0.001 10]);

piu0=sqrt(Bˆ2+6.520694);

end

%a=aguess;

z=0;

theta=-piu0/2;

i=1;

while theta < piu0/2

if emax > 0.217234

Z=Z0* exp(0.5 * log(Zl/Z0) * (1+2 * theta/piu0));

else

Z=Z0* exp(0.5 * log(Zl/Z0)+0.5 * log(Zl/Z0)

* gfunc(B,2 * theta/piu0));

end

%This is for Asymmetric Coplanar waveguide

a=(Z-Z0)/(Zl-Z0) * (a1-a0)+a0;

d1=(Z-Z0)/(Zl-Z0) * (d1max-d1min)+d1min;

d2=(Z-Z0)/(Zl-Z0) * (d2max-d2min)+d2min;

if abs(d1-d2)<1E-10

b=d1+d2+a

at=a+1.25 * t/pi * (1+log(4 * pi * a/t));

bt=b-1.25 * t/pi * (1+log(4 * pi * a/t));


k=a/b;

ka=sqrt(1-kˆ2);


k1a=sqrt(1-k1ˆ2);


else

alp=(d1 * d2+0.5 * a* (d1+d2)-sqrt(d1 * d2* (a+d1)

* (a+d2)))/((a/2)ˆ2 * (d1-d2));

k1= a/2 * (1+alp * (a/2+d1))/((a/2)+d1+alp * (a/2)ˆ2);

k1a=sqrt(1-k1ˆ2);

WA= sinh(pi/4/h * a);

WB= sinh(pi/2/h * (a/2+d1));

WE=-sinh(pi/2/h * (a/2+d2));

alp1=(WB+WE)ˆ(-1) * (-1-WB * WE/WAˆ2-sqrt((WBˆ2/WAˆ2-1)

* (WEˆ2/WAˆ2-1)));

k2=WA* (1+alp1 * WB)/(WB+alp1 * WAˆ2);

k2a=sqrt(1-k2ˆ2);

eeff=1+(er-1)/2 * kfunc(k2,k2a)/kfunc(k1,k1a);

end

beta=2 * pi * f0/2.99796e8 * sqrt(eeff);

data_matrix(i,1) = z * 1000;

data_matrix(i,2) = Z;

data_matrix(i,3) = beta;

data_matrix(i,4) = a * 1000;

%This is for Asymmetric Coplanar waveguide

data_matrix(i,5) = d1 * 1000;

data_matrix(i,6) = d2 * 1000;

data_matrix(i,1:end)


z=z+dz;

i=i+1;

theta=theta+dz * beta;

end

data_mat = transpose(data_matrix);

length = size(data_mat,2)

pause;

%figure(1)

%hold on

%plot(data_mat(1,1:length), data_mat(2,1:length),’b’);

%plot(data_mat(1,1:length), data_mat(3,1:length),’g’);

%title(’Impedance profile’)

%legend(’Z’,’Beta’);

%axis([2.375,2.625,-40,0]);

%xlabel(’Distance z (mm)’);

%ylabel(’Z (Ohm)’);

hold off

figure(2)

hold on

plot(data_mat(1,1:length), data_mat(4,1:length),’b’);

plot(data_mat(1,1:length), data_mat(5,1:length),’g’);

plot(data_mat(1,1:length), data_mat(6,1:length),’r’);

title(’Dimensions’)

legend(’a’,’d1’,’d2’);

xlabel(’Distance z (mm)’);

ylabel(’a,b (mm)’);

hold off

save asymmetricCPW.txt data_matrix -ASCII

%********************* geta function *********************

function dimfunc = geta(a)


%function to iterate to determine dimension a

global dims

er = dims(1);

h = dims(2);

t = dims(3);

d1 = dims(4);

d2=dims(5);

Z0 = dims(6);

if abs(d1-d2)<1E-10

b=d1+d2+a

at=a+1.25 * t/pi * (1+log(4 * pi * a/t));

bt=b-1.25 * t/pi * (1+log(4 * pi * a/t));

k=a/b;

ka=sqrt(1-kˆ2);


k1a=sqrt(1-k1ˆ2);


dimfunc = 30 * pi/sqrt(eeff)/kfunc(k,ka)-Z0;

else

alp=(d1 * d2+ 0.5 * a* (d1+d2)-sqrt(d1 * d2* (a+d1)

* (a+d2)))/((a/2)ˆ2 * (d1-d2));

k1= a/2 * (1+alp * (a/2+d1))/((a/2)+d1+alp * (a/2)ˆ2);

k1a=sqrt(1-k1ˆ2);

WA= sinh(pi/4/h * a);

WB= sinh(pi/2/h * (a/2+d1));

WE=-sinh(pi/2/h * (a/2+d2));

alp1=(WB+WE)ˆ(-1) * (-1-WB * WE/WAˆ2

-sqrt((WBˆ2/WAˆ2-1) * (WEˆ2/WAˆ2-1)));

k2=WA* (1+alpha1 * WB)/(WB+alp1 * WAˆ2);

k2a=sqrt(1-k2ˆ2);

eeff=1+(er-1)/2 * kfunc(k2,k2a)/kfunc(k1,k1a);


dimfunc = 30 * pi/sqrt(eeff)/kfunc(k1,k1a)-Z0;

end

end

% other functions are same as symmetric taper

%*****************************************************

%output of the Asymmetric taper: asymmetric.txt file

(z) [Z] Beta [a] [d1] [d2]

0.00 50.00 78.46 2.60 0.69 0.69

0.60 51.66 77.84 2.57 0.72 0.79

1.20 53.36 77.29 2.54 0.74 0.90

1.80 55.11 76.81 2.51 0.77 1.01

2.40 56.90 76.40 2.49 0.80 1.12

3.00 58.74 76.04 2.45 0.82 1.23

3.60 60.63 75.73 2.42 0.85 1.35

4.20 62.57 75.47 2.39 0.88 1.47

4.80 64.57 75.25 2.36 0.91 1.59

5.40 66.62 75.07 2.32 0.95 1.72

6.00 68.74 74.91 2.29 0.98 1.85

6.60 70.91 74.78 2.25 1.01 1.99

7.20 73.16 74.66 2.21 1.05 2.13

7.79 75.47 74.56 2.18 1.08 2.27

8.39 77.85 74.48 2.14 1.12 2.42

8.99 80.30 74.40 2.10 1.16 2.57

9.59 82.82 74.33 2.05 1.20 2.73

10.19 85.43 74.26 2.01 1.24 2.89

10.79 88.11 74.19 1.96 1.28 3.06

11.39 90.87 74.13 1.92 1.32 3.23

11.99 93.72 74.07 1.87 1.36 3.40

12.59 96.66 74.01 1.82 1.41 3.59

13.19 99.68 73.96 1.77 1.46 3.77

13.79 102.80 73.90 1.72 1.50 3.97

14.39 106.01 73.85 1.67 1.55 4.17


14.99 109.32 73.80 1.61 1.60 4.37

15.59 112.74 73.76 1.55 1.66 4.58

16.19 116.25 73.72 1.50 1.71 4.80

16.79 119.88 73.69 1.44 1.77 5.03

17.39 123.61 73.66 1.37 1.82 5.26

17.99 127.46 73.65 1.31 1.88 5.50

18.59 131.43 73.64 1.24 1.94 5.74

19.19 135.52 73.65 1.17 2.01 6.00

19.79 139.74 73.67 1.10 2.07 6.26

20.39 144.09 73.71 1.03 2.14 6.53

20.99 148.59 73.77 0.96 2.21 6.81

21.59 153.22 73.86 0.88 2.28 7.10

22.19 158.01 73.98 0.80 2.35 7.39

22.78 162.95 74.14 0.72 2.43 7.70

23.38 168.06 74.35 0.63 2.51 8.02

23.98 173.34 74.62 0.54 2.59 8.35

24.58 178.81 74.98 0.45 2.67 8.69

25.18 184.48 75.46 0.36 2.76 9.04

25.78 190.37 76.14 0.26 2.85 9.40

26.38 196.50 77.19 0.16 2.95 9.78

%******************************************************

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