Multi-band Microwave Antennas and Devices based on … · 2016-07-19 · a device, achieving quad-band operation between 2.5 GHz and 5.6 GHz, with a minimum radiation e ciency of

Multi-band Microwave Antennas and Devices based onGeneralized Negative-Refractive-Index Transmission Lines

by

Colan Graeme Matthew Ryan

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

© Copyright 2016 by Colan Graeme Matthew Ryan

Abstract

Multi-band Microwave Antennas and Devices based on Generalized

Negative-Refractive-Index Transmission Lines

Colan Graeme Matthew Ryan

Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

2016

Focused on the quad-band generalized negative-refractive-index transmission line (G-

NRI-TL), this thesis presents a variety of novel printed G-NRI-TL multi-band microwave

device and antenna prototypes. A dual-band coupled-line coupler, an all-pass G-NRI-TL

bridged-T circuit, a dual-band metamaterial leaky-wave antenna, and a multi-band G-

NRI-TL resonant antenna are all new developments resulting from this research. In

addition, to continue the theme of multi-band components, negative-refractive-index

transmission lines are used to create a dual-band circularly polarized transparent patch

antenna and a two-element wideband decoupled meander antenna system.

High coupling over two independently-specified frequency bands is the hallmark of

the G-NRI-TL coupler: it is 0.35λ0 long but achieves approximately −3 dB coupling

over both bands with a maximum insertion loss of 1 dB. This represents greater design

flexibility than conventional coupled-line couplers and less loss than subsequent G-NRI-

TL couplers. The single-ended bridged-T G-NRI-TL offers a metamaterial unit cell with

an all-pass magnitude response up to 8 GHz, while still preserving the quad-band phase

response of the original circuit. It is shown how the all-pass response leads to wider

bandwidths and improved matching in quad-band inverters, power dividers, and hybrid

couplers. The dual-band metamaterial leaky-wave antenna presented here was the first

to be reported in the literature, and it allows broadside radiation at both 2 GHz and

6 GHz without experiencing the broadside stopband common to conventional periodic

antennas. Likewise, the G-NRI-TL resonant antenna is the first reported instance of such

ii

a device, achieving quad-band operation between 2.5 GHz and 5.6 GHz, with a minimum

radiation efficiency of 80%.

Negative-refractive-index transmission line loading is applied to two devices: an NRI-

TL meander antenna achieves a measured 52% impedance bandwidth, while a square

patch antenna incorporates NRI-TL elements to achieve circular polarization at 2.3 GHz

and 2.7 GHz, with radiation efficiencies of 70% and 78%, respectively. Optical trans-

parency of 50% is then realized by cutting a grid through the antenna and substrate,

making the device suitable for direct integration with solar panels.

Therefore, this research provides several proof-of-concept devices to highlight the

flexibility and multi-band properties of the G-NRI-TL which extend the capabilities of

microwave transceiver systems.

iii

Dedication

To my parents

iv

Acknowledgements

I would like to thank my supervisor, Professor George Eleftheriades, for his insight and

ingenuity, as well as his patience as I developed my thesis. I always appreciated the inde-

pendence he gave me, as well as the guidance he provided in either solving problems, or in

finding the next research direction. Our meetings and informal talks were of much value

not only as I finished the thesis, but also as I prepared for the next stage of my career.

Thanks are also due to the members of my supervisory and defence committees, Sean

Hum, Costas Sarris, and Piero Triverio, who have provided valuable feedback throughout

my program.

A special thanks to Dr. Tse Chan for his technical assistance in the etching lab, his

professional advice, and for his friendship. Without his help, this thesis would not have

gone so smoothly.

I have made many close friends among my fellow graduate students. Thanks to

Mohammad, Tony, Alex, Hassan, Trevor, Jason, Neeraj, Michael, and Ayman, and all

my EM group colleagues for making my time at the University of Toronto so enjoyable.

I wish you all the best.

I would also like to acknowledge the financial support I have received from the

National Sciences and Research Council (NSERC) of Canada, the Queen Elizabeth

II/Slemon Graduate Scholarship in Science and Technology, and the University of Toronto

Department of Electrical and Computer Engineering Doctoral Completion Award.

My sister, Laurel, and brother-in-law, Michael, both know the long road to complete

a Ph.D., and have been supportive from start to finish. To my girlfriend Tara, thank

you for your encouragement and love; we’ve had big changes in the last year and you’ve

made every day of it brighter.

Finally, I thank my parents, Leonard and Kathleen. Their interest in my research

and their enthusiastic support have motivated me throughout my academic career, and

their love of learning has been my life-long inspiration. This thesis is dedicated to them.

v

Contents

1 Introduction 1

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

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 The Applicability of Periodic Analysis . . . . . . . . . . . . . . . . . . . 3

1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 The Generalized NRI-TL 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Derivation of the G-NRI-TL . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 A Qualitative Approach . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Foster Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.3 Frequency Transformations . . . . . . . . . . . . . . . . . . . . . . 16

2.3 The Modified-π G-NRI-TL Unit Cell . . . . . . . . . . . . . . . . . . . . 18

2.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Periodic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 The Printed G-NRI-TL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Beyond Four Bands with the G-NRI-TL . . . . . . . . . . . . . . . . . . 28

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 A G-NRI-TL Dual-band Leaky-Wave Antenna 35

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Prior Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Leaky-Wave Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.1 First Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

vi

3.4.2 Second Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4.3 Third (and Final) Design . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4 A Printed Dual-band Coupler with G-NRI-TLs 58

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3 G-NRI-TL Unit Cell Design . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Multiconductor Transmission Line Analysis . . . . . . . . . . . . . . . . . 62

4.5 Coupler Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . 66

4.6 Simulated Performance of Final Design . . . . . . . . . . . . . . . . . . . 68

4.7 Measured Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 An All-Pass G-NRI-TL Using a Bridged-T Circuit 77

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2 Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2.1 Lattice Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2.2 Bartlett’s Bisection Theorem . . . . . . . . . . . . . . . . . . . . . 84

5.2.3 Bridged-T Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.2.4 A Bridged-T NRI-TL . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.3 Printed Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.4 Simulated and Measured Results . . . . . . . . . . . . . . . . . . . . . . 91

5.5 Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.5.1 Impedance Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.5.2 Wilkinson Divider . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.5.3 Hybrid Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.5.4 The Same Applications with Standard G-NRI-TLs . . . . . . . . 98

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 A Wideband Metamaterial Meander-Line Antenna 102

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.2 Single Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.2.1 Antenna Layout with Metamaterial Unit Cell . . . . . . . . . . . 104

vii

6.2.2 Comparison of Conventional and Metamaterial Meander Antennas 105

6.2.3 Measured Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2.4 Comparison of Radiation Efficiency . . . . . . . . . . . . . . . . . 110

6.3 Two-Antenna System with Low Mutual Coupling . . . . . . . . . . . . . 112

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.3.2 Exciting Two Characteristic Modes on a Ground Plane . . . . . . 113

6.3.3 Simulated and Measured Results . . . . . . . . . . . . . . . . . . 117

6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7 Transparent Circularly-Polarized Antennas 124

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.3 Single-band Circularly-Polarized Transparent

Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.3.1 Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125


7.4 Dual-band Transparent Circularly-Polarized

Antenna with Metamaterial Loading . . . . . . . . . . . . . . . . . . . . 130

7.4.1 Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.4.2 Wheeler Matching Network . . . . . . . . . . . . . . . . . . . . . 132


7.5 Solar Panel Transparency Testing . . . . . . . . . . . . . . . . . . . . . . 139

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

8 Conclusion 145

8.1 Summary of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

8.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

A Multi-band Resonant G-NRI-TL Antennas 150

A.1 Dual-band G-NRI-TL Monopole Antenna . . . . . . . . . . . . . . . . . . 152

A.2 Quad-band Crossed-Dipole Antenna . . . . . . . . . . . . . . . . . . . . . 154

A.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

viii

List of Tables

3.1 Dimensions of printed LWA unit cell- version 1 . . . . . . . . . . . . . . . 38

4.1 Coupler’s printed dimensions and equivalent circuit values . . . . . . . . 62

4.2 Summary of measured and simulated results . . . . . . . . . . . . . . . . 73

5.1 Dimensions of fabricated all-pass unit cell . . . . . . . . . . . . . . . . . 91

6.1 Measured and simulated efficiency of metamaterial meander antenna . . . 111

6.2 Measured and simulated efficiency of two-antenna system . . . . . . . . . 121

7.1 Summary of results for dual-band antenna . . . . . . . . . . . . . . . . . 137

ix

List of Figures

1.1 G-NRI-TL insertion phase computed from periodic and circuit analysis . 3

2.1 Derivation of G-NRI-TL . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 G-NRI-TL principle of operation . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Foster networks for one-port impedance functions . . . . . . . . . . . . . 14

2.4 S -parameters and dispersion curve of quad-band G-NRI-TL obtained from

frequency transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Circuit schematic of G-NRI-TL unit cell . . . . . . . . . . . . . . . . . . 19

2.6 Image impedance of G-NRI-TL unit cell . . . . . . . . . . . . . . . . . . 23

2.7 Specifying insertion phase at four arbitrary frequencies . . . . . . . . . . 24

2.8 Fully-printed G-NRI-TLs in existing literature . . . . . . . . . . . . . . . 25

2.9 Circuit and diagram of fully-printed microstrip G-NRI-TL . . . . . . . . 26

2.10 Comparison of types of printed capacitor . . . . . . . . . . . . . . . . . . 27

2.11 Hex-band G-NRI-TL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.12 Hex-band G-NRI-TL alternative version . . . . . . . . . . . . . . . . . . 31

2.13 Calculated dispersion curves of hex-band G-NRI-TL . . . . . . . . . . . . 32

3.1 Operation of LWA based on G-NRI-TLs . . . . . . . . . . . . . . . . . . 36

3.2 Initial printed LWA G-NRI-TL unit cell . . . . . . . . . . . . . . . . . . 38

3.3 Comparison of LWA dispersion diagram from circuit simulation and from

full-wave analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Simulated performance of initial LWA . . . . . . . . . . . . . . . . . . . . 40

3.5 Printed G-NRI-TL unit cell for multi-layer LWA . . . . . . . . . . . . . . 41

3.6 Simulated dispersion curve and S-parameters of unit cell of multi-layer

leaky-wave antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7 Simulated S11 of full-length multi-layer LWA . . . . . . . . . . . . . . . . 43

3.8 Simulated high-band radiation patterns for multi-layer LWA . . . . . . . 44

3.9 Simulated low-band radiation patterns for multi-layer LWA . . . . . . . . 46

3.10 Dipole model of cross-polarized LWA radiation . . . . . . . . . . . . . . . 47

x

3.11 Photographs of fabricated multi-layer LWA . . . . . . . . . . . . . . . . . 48

3.12 Measured results for multi-layer LWA at upper frequency band . . . . . . 49

3.13 G-NRI-TL unit cell used in single-layer LWA . . . . . . . . . . . . . . . . 50

3.14 Single-layer LWA dispersion diagram and S11 . . . . . . . . . . . . . . . . 51

3.15 Simulated radiation patterns of single-layer LWA . . . . . . . . . . . . . 52

3.16 Simulated 3-D radiation patterns of single-layer LWA . . . . . . . . . . . 53

3.17 Leakage constant of five-cell single-layer LWA . . . . . . . . . . . . . . . 54

4.1 Illustration of dual-band MS/G-NRI-TL coupler . . . . . . . . . . . . . . 59

4.2 Dimensions of coupler’s G-NRI-TL unit cell . . . . . . . . . . . . . . . . 61

4.3 Multiconductor transmission-line model of G-NRI-TL coupler . . . . . . 63

4.4 Analytical and simulated dispersion of dual-band coupler . . . . . . . . . 66

4.5 S31 of coupler for varying cell number . . . . . . . . . . . . . . . . . . . . 67

4.6 S31 of coupler for varying cell length . . . . . . . . . . . . . . . . . . . . 68

4.7 Simulated response of dual-band coupler . . . . . . . . . . . . . . . . . . 69

4.8 Field plots of Poynting vector on coupler . . . . . . . . . . . . . . . . . . 70

4.9 Photograph of fabricated MS/G-NRI-TL coupler . . . . . . . . . . . . . . 71

4.10 Measured response of dual-band coupler . . . . . . . . . . . . . . . . . . 72

5.1 Circuit diagram of standard G-NRI-TL and its lattice equivalent . . . . . 79

5.2 Dispersion curve of lattice network . . . . . . . . . . . . . . . . . . . . . 83

5.3 Bartlett’s Bisection Theorem for T-Circuit . . . . . . . . . . . . . . . . . 84

5.4 Bartlett’s Bisection Theorem for Bridged-T Circuit . . . . . . . . . . . . 85

5.5 Steps in transforming a lattice to a bridged-T circuit . . . . . . . . . . . 86

5.6 Quad-band bridged-T circuit. . . . . . . . . . . . . . . . . . . . . . . . . 87

5.7 Dispersion curve and S-parameters of lattice network and bridged-T equiv-

alent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.8 Insertion phase of G-NRI-TL circuit as T-circuit, lattice network, and as

bridged-T circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.9 NRI-TL as bridged-T circuit . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.10 Dispersion curves of NRI-TL circuit as lattice and as bridged-T networks 90

5.11 HFSS bridged-T model and photographs of fabricated device . . . . . . . 91

5.12 Simulated and measured S-parameters of bridged-T circuit . . . . . . . . 93

5.13 Measured group delay of all-pass bridged-T unit cell . . . . . . . . . . . . 94

5.14 Simulated S11 of ideal bridged-T impedance inverter . . . . . . . . . . . . 95

5.15 Measured and simulated S11 of microstrip bridged-T impedance inverter . 96

5.16 Simulated and measured S-parameters of bridged-T Wilkinson divider . . 97

xi

5.17 Simulated and measured S-parameters of bridged-T hybrid coupler . . . . 98

5.18 Simulated S11 of impedance inverter using G-NRI-TL unit cells. . . . . . 99

5.19 Simulated S -parameters of Wilkinson divider using G-NRI-TL unit cells. 99

5.20 Simulated S -parameters of hybrid coupler using G-NRI-TL unit cells. . . 100

6.1 Principle of operation of metamaterial meander antenna . . . . . . . . . 102

6.2 Principle of operation of metamaterial meander antenna . . . . . . . . . 103

6.3 Wideband meander-line antenna . . . . . . . . . . . . . . . . . . . . . . . 105

6.4 S11 response of metamaterial and conventional meander-line antenna . . 106

6.5 Plot of surface current density on metamaterial meander antenna . . . . 107

6.6 Simulated and measured radiation patterns . . . . . . . . . . . . . . . . . 108

6.7 Illustration of effects of ground plane on radiated fields . . . . . . . . . . 110

6.8 Simulated radiation efficiency of standard and metamaterial meander an-

tenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.9 S11 of metamaterial meander antenna over extended frequency range. . . 112

6.10 Meander antenna surface current distributions for different ground plane

widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.11 Ground plane surface current distribution for two-antenna system . . . . 114

6.12 Simulated eigencurrents of two-antenna system . . . . . . . . . . . . . . 115

6.13 Eigenvalues and excitation coefficients of antenna’s characteristics modes 116

6.14 Fabricated two-antenna system . . . . . . . . . . . . . . . . . . . . . . . 117

6.15 Measured (solid lines) and simulated (dotted lines) S-parameters for two-

antenna system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.16 Correlation Coefficient of Two-Antenna System . . . . . . . . . . . . . . 119

6.17 Measured and simulated radiation patterns for two-antenna system . . . 120

7.1 Fabricated single-band antenna . . . . . . . . . . . . . . . . . . . . . . . 126

7.2 Effect of grid on CP patch antenna . . . . . . . . . . . . . . . . . . . . . 127

7.3 Single-band CP Antenna Simulated and Measured Data . . . . . . . . . . 129

7.4 Circuit model of metamaterial-loaded circularly-polarized patch antenna. 130

7.5 Dual-band CP Antenna Layout . . . . . . . . . . . . . . . . . . . . . . . 132

7.6 Modified Wheeler matching network . . . . . . . . . . . . . . . . . . . . 133

7.7 CP antenna impedance characteristics . . . . . . . . . . . . . . . . . . . 134

7.8 Dual-band CP antenna S11 . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.9 Electric field plots of dual-band CP antenna . . . . . . . . . . . . . . . . 136

7.10 Measured gain and axial ratio of dual-band CP antenna . . . . . . . . . . 138

7.11 CP antenna integration on solar panel . . . . . . . . . . . . . . . . . . . 139

xii

7.12 Measured transparency of CP antennas . . . . . . . . . . . . . . . . . . . 141

7.13 S11 of single-band CP antenna on solar panel . . . . . . . . . . . . . . . . 142

A.1 G-NRI-TL operation as resonant antenna . . . . . . . . . . . . . . . . . . 151

A.2 G-NRI-TL dual-band monopole antenna . . . . . . . . . . . . . . . . . . 152

A.3 G-NRI-TL monopole antenna simulated results . . . . . . . . . . . . . . 154

A.4 Crossed-dipole antenna and simulated S11 . . . . . . . . . . . . . . . . . 155

A.5 Electric field plots of crossed-dipole antenna . . . . . . . . . . . . . . . . 156

A.6 Crossed-dipole radiation patterns . . . . . . . . . . . . . . . . . . . . . . 157

xiii

List of Acronyms

ADS Advanced Design System by Agilent Technologies

CP Circularly Polarized

CPS Co-Planar Strip

DGS Defected Ground Structure

FEKO Feldberechnung fur Korper mit beliebiger Oberflache

G-NRI-TL Generalized-Negative-Refractive-Index Transmission Line

HFSS High-Frequency Structure Simulator by Ansoft Corporation

LH Left-Handed

LWA Leaky-Wave Antenna

MIMO Multiple-Input Multiple-Output

MM Metamaterial

mm-wave Millimetre-Wave

NRI Negative Refractive Index

PRI Positive Refractive Index

RF Radio Frequency

RH Right-Handed

SIW Substrate Integrated Waveguide

TCO Transparent Conductive Oxides

TL Transmission Line

UWB Ultra-Wideband

xiv

Chapter 1

Introduction

1.1 Motivation

Negative-refractive-index transmission lines (NRI-TLs) were introduced in [1] and have

found a wide variety of innovative uses in microwave components. Formed by a periodic

loading of a small section of conventional transmission line with a series capacitor and

a shunt inductor, these NRI-TLs produce two frequency bands where the homogeneous

metamaterial medium has an effective refractive index that is either positive or negative,

resulting in a transmission-line circuit with either phase delay (positive refractive index,

or “right-handed” propagation) or phase advance (negative refractive index, or “left-

handed” propagation) [2]. Since their first appearance, NRI-TLs have yielded broadside-

scanning leaky-wave antennas [3], small resonant antennas [4], compact and broadband

power dividers [5], printed couplers with high coupling [6], frequency-reconfigurable an-

tennas [7], and squint-free antenna arrays using negative-group delay circuits [8], to name

just a few achievements drawn solely from our own research group at the University of

Toronto.

This thesis continues the work on NRI-TLs, but also looks to apply a “higher-order”

version, called the generalized negative-refractive-index transmission line (G-NRI-TL),

first reported in [9]. This latter device follows the same approach as the NRI-TL in

loading an underlying transmission line with the appropriate circuit elements, but it now

gives access to two pairs of right- and left-hand bands, instead of just the single pair of

the NRI-TL. So, for example, a quarter-wave impedance transformer can now operate

at four frequencies as a G-NRI-TL, compared to two as an NRI-TL and just one as

a conventional transmission line. The prospects of extending the capabilities of other

microwave components are enticing, and my goal in this thesis is to develop prototype

microwave devices using printed G-NRI-TLs and NRI-TLs, and, by providing such a

1

Chapter 1. Introduction 2

“proof-of-concept” approach, to demonstrate the advantages and challenges associated

with this new metamaterial. Although design equations and guidelines are determined

wherever possible, it is expected that, as this field matures, device performance will

be improved though optimization routines and the use of more reliable manufacturing

techniques. Therefore, this research does not provide the final answer on G-NRI-TL-

based circuits, but seeks to open up that field instead.

The impetus behind this work stems from the demand for greater data rates in mobile

devices, the importance of compact and space-efficient electronics, and the desirability

of low cost, easily-produced microwave components [10]. Although these requirements

apply particularly well to consumer electronics, they are important for all types of mobile

platforms and so this thesis, in general, does not focus on any single set of applications or

communication standards. Enabling multi-band or wideband transceiver operation, the

NRI-TL and G-NRI-TL devices developed here access a greater segment of the RF spec-

trum without needing to dedicate multiple separate antennas or circuits to each operating

band. The proposed designs are all made in low-cost microstrip technology without using

any discrete elements or biasing circuitry, thus reducing component and fabrication costs.

These components not only represent an important step in improving the performance

of wireless systems, but also serve as a further demonstration of how metamaterials may

be applied to practical devices with immediate applications and benefits.

1.2 Background

A discussion of the state-of-the-art for each component created in this thesis is given

in its corresponding chapter, so this section focuses on the background of the G-NR-

TL itself. The concept was first reported in [11], and expanded upon in [12] to include

design equations which allow a desired insertion phase to be specified at four frequencies;

[13] simultaneously suggested, but did not design, the same G-NRI-TL circuit. A dual-

bandpass G-NRI-TL filter with discrete components appeared in [14], while an optically-

reconfigurable G-NRI-TL unit cell was reported in [15]. The work of [16] contained

the first instance of a fully-printed G-NRI-TL, and, although those authors proposed

its applicability in multi-band leaky-wave antennas and couplers, they did not actually

create such devices. Since I began this research, various printed versions have appeared,

implementing multi-band couplers, power dividers, and antennas [17]-[19], and these will

be discussed in detail in the next chapter. Most recently, [20] reported a tri-band G-NRI-

TL, and, although it is not interpreted as such, the approach they follow is identical to

that presented in Chapter 2 of this thesis.


1.3 The Applicability of Periodic Analysis

Although this work deals with metamaterial transmission lines, many of the devices

presented here use only a few metamaterial unit cells; they are not periodic and are not

homogeneous media with effective material parameters. Nevertheless, periodic analysis

and not conventional circuit synthesis techniques is still used in the development of

these devices, for several reasons. First, this thesis research began by investigating how

the G-NRI-TL unit cell could be used to create just such a homogeneous metamaterial

transmission line in which the insertion phase could be controlled at four independently

specified frequencies. This line of inquiry led directly to the development of the dual-

band leaky-wave antenna, a structure which cannot be described by a conventional filter

synthesis approach [21]. Secondly, the non-periodic dual-band coupler and all-pass G-

NRI-TL cell (itself a building block of a homogeneous TL) are terminated in the unit

cell’s Bloch impedance, deliberately chosen to match the system impedance of 50 Ω.

Consequently, there are theoretically no reflections at the cell edges, the structure “looks”

infinite, and periodic analysis is justified in determining the insertion phase characteristics

of a single cell. Finally, these phase characteristics of a G-NRI-TL unit cell can be

computed from either periodic analysis or a traditional circuit analysis; as long as the

unit cell is electrically small (the operating frequencies are close to the βd = 0 points),

the results from the two cases are nearly identical, as illustrated in Figure 1.1, which

shows the S21 phase truncated to the two passband frequencies of the unit cell.

2 2.5 3 3.5 4 4.5 5 5.5 6−200

−150

−100

−50

0

50

100

150

200

Frequency (GHz)

Pha

se (

deg)

↑βd=0

↑βd=0

Periodic AnalysisCircuit Analysis

Figure 1.1: G-NRI-TL unit cell insertion phase computed from periodic and standard

circuit analysis.


1.4 Contributions

The G-NRI-TL had been only recently introduced when I started my work, and this

research has yielded a variety of new multi-band metamaterial components. Five novel

devices comprise the main contributions of this thesis:

a dual-band leaky-wave antenna

a dual-band coupled-line coupler

a single-ended all-pass G-NRI-TL circuit

a two-element wideband and decoupled meander-line antenna system

a dual-band transparent circularly-polarized antenna

In addition, two more ideas for microstrip antennas based on the G-NRI-TL which would

make good candidates for further study are proposed in Appendix A. These developments

have resulted in eight journal and conference publications, and together, show the great

potential the G-NRI-TL has in creating multi-band or wideband microwave components.

The dual-band leaky-wave antenna and dual-band coupled-line coupler created as part of

my research are the first reported instances of such devices. Likewise, the all-pass G-NRI-

TL is the first to be produced as a single-ended microstrip circuit, and thus could be easily

integrated into multi-band microwave systems. Dual-band circularly-polarized antennas,

on the other hand, are widely known (see, for example, [22]-[25]); the contribution in this

case comes from the novel inclusion of metamaterial loading on the antenna, resulting

in a simple, low-profile design which can then be made transparent in anticipation of

the antenna’s integration with a satellite’s solar panel. To my knowledge, the particular

transparency technique used here is the first of its type. Finally, the application of

NRI-TL elements to a meander-line antenna produced an ultra-wideband impedance

match. While this result came about by fortuitous accident and not by design, the effort

culminated in a wideband and decoupled two-antenna system, suitable for multiple-input,

multiple-output (MIMO) communications.

1.5 Organization of Thesis

Because such a variety of components has been studied, this thesis devotes a separate

chapter to each of the items listed above; containing a background and summary of

previous work relevant to the particular device under discussion, each chapter presents


the analysis, design, and measured performance of those devices and identifies the specific

advances made over existing designs in the literature.

The dual-band leaky-wave antenna (LWA) is described in Chapter 3. This antenna

is based on a periodic arrangement of G-NRI-TL unit cells and makes use of the two

fast-wave regions to create a frequency-scanning beam over two operating bands. Like

the earlier NRI-TL LWA, this version allows radiation at broadside at two frequencies

from the fundamental microstrip mode, without experiencing the broadside stopband

common to periodic antennas operating with the higher spatial harmonics.

Chapter 4 discusses a G-NRI-TL-based dual-band coupled-line coupler. Tight cou-

pling levels are achieved at two frequencies where the “left-handed” regions of the G-

NRI-TL intersect the “right-handed” region of the isolated coupled transmission line.

Measured and simulated insertion losses are significantly smaller than those obtained by

competing multi-band G-NRI-TL couplers.

Because many microwave components require large insertion phase shifts – the 90° lines

in a hybrid coupler is one example – metamaterial TLs can offer significant size reduc-

tions, but potentially at the expense of decreasing transmission magnitude. Chapter 5

describes an all-pass microstrip G-NRI-TL which offers large single-cell phase shifts with-

out any such transmission decrease. To highlight the benefits, some sample applications

using this new approach are provided.

Chapter 6 presents a printed meander line antenna with an ultra-wideband impedance

bandwidth (i.e., a fractional bandwidth greater than 50%) achieved by loading the an-

tenna with metamaterial components. The chapter then shows how two such antennas

can be combined with low mutual coupling between them, which results in a compact

two-antenna system for implementing MIMO communications in small consumer hand-

sets.

Circularly polarized (CP) antennas are the subject of Chapter 7. Intended for use on

a microsatellite, a single-band CP patch antenna with high optical transparency is first

developed as a proof-of-concept. Then, a dual-band version of the transparent antenna is

created by incorporating NRI-TL loading onto the patch; the loading requires relatively

little patch area which permits high transparency to be maintained.

Finally, the Appendix presents two ideas for G-NRI-TL-based multi-band resonant

antennas. These antennas were never fabricated, but their simulated performance and

simple construction make them excellent candidates for further development.

In the concluding chapter, the results achieved in this thesis are summarized, the

overall usefulness of G-NRI-TL printed circuits is assessed, and some suggestions for

future research directions are given.


The thesis begins, however, with an overview of the generalized-negative-refractive-

index transmission line: Chapter 2 explains the origin of this circuit, shows how higher-

order versions are created both as lumped circuit models and as printed structures,

and provides the theory necessary to develop the multi-band antennas and microwave

components to come.


1.6 References

[1] G.V. Eleftheriades, A.K. Iyer, and P.C. Kremer, “Planar negative refractive index

media using periodically L-C loaded transmission lines,” IEEE Trans. Microw.

Theory & Techn., vol. 50, no. 12, pp. 2702-2712, December, 2002.

[2] G.V. Eleftheriades and K.G. Balmain, “Negative-refractive-index transmission-line

metamaterials” in Negative Refraction Metamaterials: Fundamental Principles and

Applications, Hoboken, NJ: John Wiley & Sons, 2005, ch. 1, pp. 19-20.

[3] A.K. Iyer and G.V. Eleftheriades, “Leaky-wave radiation from planar negative-

refractive-index transmission-line metamaterials,” in Proc. IEEE Int. Symp. An-

tennas & Propag., Monterey, CA, June, 2004, vol. 2, pp. 1411-1414.

[4] F. Qureshi, M.A. Antoniandes, and G.V. Eleftheriades, “A compact and low-profile

metamaterial ring antenna with vertical polarization,” IEEE Antennas & Wireless

Propag. Lett., vol. 4, pp. 333-336, September, 2005.

[5] M.A. Antoniades and G.V. Eleftheriades, “A broadband series power divider using

zero-degree metamaterial phase-shifting lines,” IEEE Microw. & Wireless Compo-

nent Lett., vol. 15, no. 11, pp. 808-810, November, 2005.

[6] R. Islam, F. Elek, and G.V. Eleftheriades, “Analysis of a finite length

microstrip/negative-refractive-index coupled-line coupler,” in Proc. IEEE Int.

Symp. Antennas & Propag., Washington, D.C., 2005, vol. 1B, pp. 268-271.

[7] H. Mirzaei and G.V. Eleftheriades, “A compact frequency-reconfigurable

metamaterial-inspired antenna”, IEEE Antennas & Wireless Propag. Lett., vol. 10,

pp. 1154-1157, October, 2011.

[8] H. Mirzaei and G.V. Eleftheriades, “Arbitrary-angle squint-free beamforming in

series-fed antenna arrays using non-Foster elements synthesized by negative-group-

delay networks,” IEEE Trans. Antennas & Propag., February, 2015.

[9] G.V. Eleftheriades, “Design of generalised negative-refractive-index transmission

lines for quad-band applications,” IET Microw., Antennas, & Propag. (Special Is-

sue of Metamaterials), vol. 4, pp. 977-981, February, 2010.

[10] S. Yang, C. Zhang, H.K. Pan, A.E. Fath, and V.K. Nair, “Frequency reconfigurable

antennas for multiradio wireless platforms,” IEEE Microw. Mag., vol. 10, no. 1,

pp. 66-83, January, 2009.


[11] G.V. Eleftheriades, “A generalized negative-refractive-index transmission line

(NRI-TL) metamaterial for dual-band and quad-band applications,” IEEE Microw.

& Wireless Comp. Lett., vol. 7, no. 6, pp. 415-417, June, 2007.



sue of Metamaterials), vol. 4, no. 8, pp. 977-981, August, 2010.

[13] C. Caloz and H.V. Nguyen, “Novel Broadband conventional- and dual-composite

right/left-handed (C/D-CRLH) metamaterials : properties, implementation and

double-band coupler application,” Appl. Physics A: Materials Sci. & Process., vol.

87, no. 2, May. 2007.

[14] M. Studniberg and G.V. Eleftheriades, “A dual-band bandpass filter based on

generalized negative-refractive-index transmission-lines,” IEEE Microw. & Wireless

Component Lett., vol. 19, pp. 18-20, January, 2009.

[15] D. Draskovic and D. Budimir, “Optically controlled negative refractive index trans-

mission lines,” in 3rd European Conf. on Antennas and Propagation, Berlin, 2009,

pp. 1672-1674.

[16] B.H. Chen, Y.N. Zhang, D. Wu, and K. Seo, “A novel composite right/left handed

transmission line for quad band applications,” in 11th IEEE Int. Conf. on Com-

munication Systems, Singapore, 2008, pp. 617-620.

[17] M. Duran-Sindreu, G. Siso, J. Bonache, F. Martin, “Planar multi band microwave

components based on the generalized composite right/left handed transmission line

concept,” IEEE Trans. Microw. Theory & Techn., vol. 58, no. 12, pp. 3882-3891,

December, 2010.

[18] M. Duran-Sindreu, J. Choi, J. Bonache, F. Martin, and T. Itoh, “Dual-band leaky

wave antenna with filtering capability based on extended-composite right/left-

handed transmission lines,” IEEE-MTTS Int. Microw. Symp. Dig., Seattle, WA,

June, 2013, pp. 1-4.

[19] J. Machac, M. Polivka, and K. Zemlyakov “A dual band leaky wave antenna on a

CRLH substrate integrated waveguide,” IEEE Trans. Antennas & Propag., vol. 61,

no. 7, pp. 3876-3879, July, 2013.

[20] M.A. Fouad and M.A. Abdalla, “New T generalised metamaterial negative refrac-

tive index transmission line for a compact coplanar waveguide triple band pass filter


applications,” IET Microw., Antennas, & Propag., vol. 8, no. 13, pp. 1097-1104,

October, 2014.

[21] R. Islam, “Theory and Applications of Microstrip/Negative-Refractive-Index

Transmission Line (MS/NRI-TL) Coupled-line Couplers,” Ph.D. dissertation,

Dept. of Elec. & Comp. Eng., Univ. of Toronto, Toronto, Canada, 2011.

[22] T.N. Thi, K.C. Hwang and H.B. Kim, “Dual-band circularly-polarised spidron frac-

tal microstrip patch antenna for Ku-band satellite communication applications,”

IET Electron. Lett., vol. 49, no. 7, March, 2013.

[23] A. Narbudowicz, X. L. Bao, and M. J. Ammann, “Dual-band omnidirectional cir-

cularly polarized antenna,” IEEE Trans. Antennas & Propag., vol. 61, no. 1, pp.

77-83, January, 2013.

[24] Nasimuddin, Z. N. Chen, and X. Qing, “Dual-band circularly polarized S-shaped

slotted patch antenna with a small frequency-ratio,” IEEE Trans. Antennas &

Propag., vol. 58, no. 6, pp. 2112-2115, June, 2010.

[25] S. T. Ko, B.-C. Park, and J.-H. Lee, “Dual-band circularly polarized hybrid meta-

material patch antenna,” in Proc. Asia-Pacific Microw. Conf., November, 2013,

pp. 342-344.

Chapter 2

The Generalized

Negative-Refractive-Index

Transmission Line

2.1 Introduction

Because it forms the basis for multiple devices developed in this thesis, the generalized

negative-refractive-index transmission line (G-NRI-TL) is the subject of this chapter.

First, the derivation of the G-NRI-TL circuit from Foster networks is explained and

periodic analysis is applied to this unit cell to determine its dispersion characteristics

and Bloch impedance. This chapter next addresses how a printed version of the circuit

in microstrip technology may be created and illustrates some of the associated design

challenges. Finally, higher-order G-NRI-TLs are discussed along with possible fully-

printed microstrip equivalents.

2.2 Derivation of the G-NRI-TL

2.2.1 A Qualitative Approach

The circuit model of a small 1-D section of positive-refractive-index (or “right-handed”)

transmission line (TL) is shown in Fig 2.1(a). If this circuit, or its corresponding in-

finitesimally small TL section, is repeated infinitely, the resulting periodic structure’s

behaviour can be determined from the dispersion diagram of the unit cell; the trans-

mission line in this case provides an increasing phase delay with increasing frequency.

Perhaps intuitively, the dual of the TL model in Fig 2.1(b) may be expected to yield a

10

Chapter 2. The Generalized NRI-TL 11

phase advance with increasing frequency and its dispersion diagram shows negative phase

values. There is also a lower limit on the frequency range where propagation through the

cell can occur, arising from the fact that this “left-handed” TL has the form of a high-pass

filter. Combining these two circuits produces the negative-refractive-index transmission

line of Fig 2.1(c) which has a frequency band below f0 of phase advance (corresponding

to an effective medium with a negative-refractive-index) and a frequency band above f0

of phase delay (corresponding to a positive-refractive-index) [1]. In general, these bands

are separated by a stopband at f0 as illustrated in the corresponding dispersion diagram.

The NRI-TL can be taken one step further when the dual of its series and shunt branches

is added to the circuit. The result is the G-NRI-TL of Fig 2.1(d) [2]. For this unit cell,

there are now four total propagation bands where each pair of right- and left-hand bands

is separated by stopbands at f1 and f2 and the pairs themselves are separated by another

stopband at fstop. This G-NRI-TL has many uses in creating multi-band components:

the alternating passbands and stopbands can be applied to multi-band filters, while the

characteristic of a single insertion phase (±90°, for example), has uses in a wide variety

of multi-band microwave components.


(a) (b)

(c) (d)

Figure 2.1: Equivalent circuits and dispersion diagrams of (a) right-handed TL, (b) left-

handed TL, (c) NRI-TL, and (d) G-NRI-TL.


To gain a more intuitive understanding of the G-NRI-TL operation, it is helpful

to simplify the behaviour of the equivalent circuit in the manner of Figure 2.2. To

illustrate the point, we assume all inductor (L) - capacitor (C) pairs are tuned to the

same resonant frequency ω = ωres. Below this frequency, the G-NRI-TL takes on the

form of Figure 2.2(a) and the overall circuit behaves as the well-known NRI-TL with a

pair of right- and left-hand bands as highlighted in Figure 2.2(c) (note that from this

point on, the dispersion curves are plotted over the first Brillouin zone 0 ≤ βd ≤ π only).

Above ωres we have the circuit of Figure 2.2(b) where we have the equivalent of a second

NRI-TL and a corresponding second pair of right- and left-hand bands. Visualizing the

G-NRI-TL in this way also makes it easier to increase the complexity of the circuit to

add even more bands as is done later in this chapter.

(a) (b)

(c)

Figure 2.2: G-NRI-TL operation at (a) low band and (b) high band. (c) Sample disper-

sion diagram.


2.2.2 Foster Networks

The NRI-TL and G-NRI-TL are a combination of Foster networks, canonical circuits

which realize a given immittance (impedance or admittance) function or transfer function

with a minimum number of elements (i.e., resistors, inductors, or capacitors). It may be

noted that these Foster circuits are for one-port networks, while the various TL models

of Fig 2.1 are two-port networks. However, we can equally treat the two-port equivalent

circuit of a section of a periodic structure as a one-port circuit terminated in a suitable

(i.e., Bloch) impedance, and so these Foster networks can provide a useful explanation

of the transmission-line circuits. The two general forms of Foster networks [3] are shown

in Figure 2.3.

(a)

(b)

Figure 2.3: (a) First Foster network realization of a one-port impedance function. (b) Sec-

ond Foster network realization of a one-port admittance function.

Mathematically, any realizable, lossless impedance function can be written in the

following form (where s = jω) through the use of a partial fraction expansion:

Z(s) =K0

s+K∞s+

n∑i=1

Kis

s2 + qi (2.1)


This equation represents the impedance of the same series circuit shown in Figure 2.3(a)

where the first term in equation (2.1) is a capacitor (C), the second an inductor (L), and

the third is a parallel LC circuit. An admittance may be written in an identical format:

Y (s) =K0

s+K∞s+

n∑i=1

Kis

s2 + qi(2.2)

which similarly corresponds to Figure 2.3(b).

To form the NRI-TL circuit of Fig 2.1(c), we can combine elements of the two Foster

networks. Because the NRI-TL has two propagation bands it has two βd = 0 points on

the positive frequency axis (i.e., those that are visible in that figure) and two more on the

negative frequency axis (not shown). These points correspond to the zeros of the NRI-

TL’s series and shunt impedance and admittance; for these immittance functions to be

realizable with inductive, capacitive, or resistive elements, they must have the property

that their complex roots occur in conjugate pairs [4]. The consequence is that to generate

two bands, the NRI-TL requires four circuit elements in total, with two elements in each

of its series and shunt branches. Therefore, for each branch, we can use either the first two

terms of the partial fraction expansions (the individual L and C elements) or the third

term alone. Any of the four possible combinations results in a dual-band circuit, but only

one leads to the NRI-TL of Fig 2.1(c); we could also choose to use the two tank circuits

which would result in the dual of Fig 2.1(c) and which would have a dispersion diagram

consisting of a lower PRI frequency band (phase delay) and an upper NRI frequency

band (phase advance). Each of the two remaining choices produces two PRI bands.

To create four propagation bands and form the Generalized-NRI-TL, we need a total

of eight circuit elements to produce the eight βd = 0 frequencies on the negative and

positive frequency axes. Figure 2.1(d) shows that the G-NRI-TL uses the first three

terms of equation (2.1) and equation (2.2) in its series and shunt branches, respectively;

its corresponding dispersion curve shows four bands, as expected.

Therefore, the immittance functions represented by equation (2.1) and equation (2.2)

and realized by the Foster networks of Figure 2.3 form a general way of creating multi-

band metamaterial circuits with either phase advance or phase delay properties. Ex-

tending this technique to create even higher-order G-NRI-TLs is possible and will be the

subject of a later section in this chapter.


2.2.3 Frequency Transformations

As an alternative viewpoint, the forms of either the standard or generalized NRI-TLs

can also be obtained from the well-known frequency transformations of an LC low-pass

prototype filter. For instance, the transform

jω −→ ω′cw0

∆ω

(jωω0

+ω0

jω

)(2.3)

transforms a low-pass frequency response to a band-pass response where ∆ω = ωA − ωBis the bandwidth, ω0 =

√ωAωB is the centre frequency, and ω′c is the prototype filter’s

3 dB corner frequency [4]. The impedance of the series branch of the LC filter under this

transformation can also be written in the form of equation (2.1), where

K0 =ω′cω

20

∆ω

K∞ =ω′c∆ω

K1 = q1 = 0.

(2.4)

A similar procedure is followed for the shunt branch, resulting in identical transformation

values and so the prototype’s series L is transformed to a series L and C and its shunt

C is transformed to a shunt L and C. Therefore, the LC prototype filter (identical to

Fig 2.1(a)) is transformed to the NRI-TL of Fig 2.1(c). Because the prototype filter has

source and load resistances of unity, a final step is to scale the circuit component values

according to

Z −→ R

R′Z and Y −→ G

G′Y (2.5)

where R (G) is the desired terminating resistance (conductance) and R′ (G′) is the pro-

totype resistance (conductance).

The transformation to two passbands at ω1 and ω2

jω −→ ω′c

(( ω1

∆ω1

(jωω1

+ω1

jω

))−1+( ω2

∆ω2

(jωω2

+ω2

jω

))−1)−1(2.6)

results in LC prototype impedances and admittances again expressed by equation (2.1)

and equation (2.2) but now using the terms comprising the series L and C elements and


the LC resonators with

K0 =ω′c

(Q1ω1)−1 + (Q2ω2)−1

q1 =Q1ω

21ω2 +Q2ω

22ω1

Q1ω2 +Q2ω1

K∞ =Q1Q2ω

′c

Q1ω2 +Q2ω1

K1 = K0q1

( 1

ω21

+1

ω22

)−K0 −K∞q1

(2.7)

whereQ1 =

ω1

∆ω1

Q2 =ω2

∆ω2

(2.8)

and the G-NRI-TL of Fig 2.1(c) results.

Applying this multi-passband transform not only automatically eliminates the stopbands

at f1 and f2 but also allows the centre frequencies of the two passbands to be specified

along with their approximate desired bandwidths. As an example, a two-passband cir-

cuit with ω1 = 2 GHz, ω2 = 6 GHz, ∆ω1 = ∆ω2∼= 1.1 GHz, and R = 1/G = 50 Ω is

synthesized by equations 2.5 - 2.8 and the results given in Figure 2.4. The stopbands are

closed and the passbands are indeed centred at the specified frequencies. Note that to

obtain this behaviour, the circuit should be terminated in its image impedance and so a

symmetric T-section equivalent of Figure 2.1(d) is used instead of the depicted L-section.

These transformations can provide a useful starting point to understand the circuit’s

behaviour, but in the next section, periodic analysis is applied to the G-NRI-TL unit cell

to give a more complete picture.


0 1 2 3 4 5 6 7 8−30

−20

−10

−3

0

Frequeny (GHz)

Mag

nitu

de (

dB)

S11

S21

(a)

0 20 40 60 80 100 120 140 160 1800

1

2

3

4

5

6

7

8

βd (deg)

Fre

quen

cy (

GH

z)

(b)

Figure 2.4: (a) S -parameters and (b) dispersion curve of G-NRI-TL with circuit val-

ues based upon dual-bandpass transform: LHP = 2.1 nH, CHP = 0.58 pF, LHS =

3.6 nH, CHS = 1.0 pF, LV P = 2.6 nH, CV P = 1.4 pF, LV S = 1.4 nH, and CV S =

0.85 pF.

2.3 The Modified-π G-NRI-TL Unit Cell

2.3.1 Background

A symmetric version of the G-NRI-TL circuit of Figure 2.1(d) is the basis for the meta-

material devices developed in this thesis, but instead of the T-network of [2] and [5] (and


shown in Figure 2.5(a)), the “modified-π” network as shown in Figure 2.5(b) is used.

Since a primary goal of this thesis was to create fully-printed devices that can be easily

produced, the unit cell’s equivalent circuit must be amenable to fabrication in microstrip

(or perhaps, co-planar stripline or co-planar waveguide) technology. The T-network G-

NRI-TL has one drawback in this regard: it uses four capacitors in its series branch and

it is these elements which are the most difficult to realize in a printed circuit. Derived

from a π-circuit, the “modified-π” unit cell combines the two CHP capacitors into one,

easing design complexity and reducing the overall length of the unit cell. The elements

CHS and LHS have been moved to the ends of the cell because for both full-wave simu-

lations of the G-NRI-TL and for and fabricated devices, the shunt elements cannot be

placed directly against a port; a length of TL must then extend some finite distance out

from that port and the current arrangement was thought to be a better model of such a

construction. A later section of this chapter will discuss the realization of the G-NRI-TL

as a transmission-line circuit in more detail.

(a)

(b)

Figure 2.5: Circuit schematic of G-NRI-TL unit cell as a (a) T-network, and as a (b)

modified-π network.


2.3.2 Periodic Analysis

The dispersion equation and Bloch impedance of the modified-π G-NRI-TL can be found

using the unit cell’s ABCD matrix[A B

C D

]=

[1 ZHS

0 1

][1 0

YV S + YV P 1

][1 ZHP

0 1

][1 ZHP

0 1

][1 0

YV S + YV P 1

][1 ZHS

0 1

](2.9)

where

ZHS =1− ω2LHSCHS

2jωCHSZHP =

jωLHP2(1− ω2LHPCHP )

YV S =jωCV S

2(1− ω2LV SCV S)YV P =

2(1− ω2LV PCV P )

jωLV P

(2.10)

For the purpose of calculation, the central HP element is divided to make two symmetric

halves of the circuit but appears as a single LC resonant element in any physical device.

For the symmetric cell of Figure 2.5(b), matrix element A equals D and the dispersion

equation from [7] is then

cos(βd) =A+D

2= A

= 1 + 2(ZHS + ZHP )(YV S + YV P ) + 2ZHSZHP (YV S + YV P )2(2.11)

As seen in Figure 2.1 previously, the G-NRI-TL produces two pairs of NRI- and PRI-

propagation bands, separated by a stopband at fstop. However, under certain conditions,

the stopbands which appear between the individual bands at βd = 0 (indicated by f1 and

f2) can be closed, thus allowing for a continuous transition from the NRI to PRI frequen-

cies. These conditions can be identified by determining the βd = 0 frequencies in terms

of the circuit components and then equating these expressions. From equation (2.11) we

have, first

YV S + YV P = 0. (2.12)

Therefore,jωCV S

2(1− ω2LV SCV S)+


jωLV P= 0 (2.13)


We also have

2(ZHS + ZHP )(YV S + YV P ) + 2ZHSZHP (YV S + YV P )2 = 0 (2.14)

so we get

ZHS + ZHPZHSZHP

= −(YV S + YV P )

1

ZHS+

1

ZHP= −(YV S + YV P )

2jωCHS1− ω2LHSCHS

+2(1− ω2LHPCHP )

jωLHP= −

( jωCV S2(1− ω2LV SCV S)

+2(1− ω2LV PCV P )

jωLV P

)(2.15)

We require both equation (2.13) and equation (2.15) to have the same number of roots

(corresponding to the βd = 0 points), since otherwise, we cannot equate the two and

all the stopbands cannot be closed. To meet this requirement, LV SCV S = LHSCHS.

Furthermore, to make the equations more manageable, we also set LV PCV P = LHPCHP ;

this assumption will be shown later to be justified in terms of the Bloch impedance.

Where ω2X = 1/CXLX , we have, then

ωV S = ωHS ωV P = ωHP . (2.16)

With these assumptions, equation (2.13) now becomes

4( 1

ω2V S

)( 1

ω2V P

)ω4 − ω2(4(

1

ω2V S

) + 4(1

ω2V P

) + CV SLV P ) + 4 = 0. (2.17)

Similarly, equation (2.15) is then

2(1

ω2V S

)(1

ω2V P

)(LHP + LV P )ω4 −(

2(1

ω2V S

+1

ω2V P

)(LHP + LV P )

+(2CHS + CV S/2)LHPLV P

)ω2 + 2(LHP + LV P ) = 0.

(2.18)

When we divide both equations 2.17 and 2.18 appropriately to set the coefficients of the

ω4 terms equal to 1, the coefficients of the last terms in each equation also become equal

to each other. Therefore, the roots of equations 2.17 and 2.18 will be equal when the


coefficients of the ω2 terms are equal:

CV SLV P

(ω2V Sω

2V P/4

)=(

(2CHS + CV S/2)LHPLV P

)( ω2V Sω

2V P

2(LHP + LV P )

)1

4LV SCV P=( LHPLHSCV P

+LHP

4LV SCV P

)( 1

LHP + LV P

) (2.19)

Finally, we arrive at the condition

4LV SLHP = LHSLV P (2.20)

Therefore, choosing element values that satisfy equation (2.20) and the resonance condi-

tion of equation (2.16) results in two closed stopbands. There is still a stopband at fstop

which cannot be closed with the current circuit but can be eliminated with the all-pass

version of the G-NRI-TL, a device which will be seen later as the subject of Chapter 5.

The second important parameter of the unit cell to determine is its Bloch impedance

(i.e., the impedance at the boundaries of the cell in an infinite periodic structure). How-

ever, the Bloch impedance expression can be unwieldy and a more tractable form can

be obtained from the image impedance. This image impedance at port 1 (Zi1) is the in-

put impedance when port 2 is terminated in its image impedance (Zi2), and the reverse

holds true for port 2. So, for periodic symmetric networks (where Zi1 = Zi2), the image

impedance is equivalent to the Bloch impedance. Using Figure 2.6, the network’s ABCD

matrix, and the fact that A = D for a symmetric network we can find

Zin = Zi1 =AZi1 +B

CZi1 +D

CZ2i1 +DZi1 = AZi1 +B

Zi1 =

√B

C

=

√(1 + ZHS(YV S + YV P ))(ZHS + ZHP + ZHSZHP (YV S + YV P ))

(YV S + YV P )(1 + ZHP (YV S + YV P ))

(2.21)

For frequencies close to the βd = 0 points, and for the closed-stopband condition

ωV S = ωHS, the image (or Bloch) impedance can be written as

Zi1 =

√ ((1− ω2/ω2

HS)(1− ω2/ω2HP )− CHSLHPω2

)(jωLV P (1− ω2/ω2

HS)))

4((1− ω2/ω2

HS)(1− ω2/ω2V P )− CHSLHPω2

)(jωCHS(1− ω2/ω2

HP )))(1 +

LHPLV P

)(2.22)


To obtain a frequency-independent value, we should have

LV SCV S = LHSCHS = LV PCV P = LHPCHP (2.23)

which is consistent with (although more restrictive than) the assumption made in deriving

the closed-stopband condition previously. When equation (2.20) and equation (2.23) are

met, the Bloch impedance simplifies to the constant value

Zi1 = ZB =

√LV P + LHP

4CHS(2.24)

Therefore, with the proper choice of element values, a periodic arrangement of G-NRI-

TLs can be matched to the desired system impedance.

Figure 2.6: Image impedance for modified-π G-NRI-TL.

It is also important to note that, despite the constrains of the closed stopband con-

dition, the insertion phase can still be specified at four arbitrary frequencies; the details

and design equations were reported in [6] and so will not be repeated here, but Fig-

ure 2.7 illustrates the concept. The phase shift (90°) at four frequencies (ω1=2.5 GHz,

ω2=3 GHz, ω3=4 GHz, and ω4=5 GHz) is selected, along with the Bloch impedance

(50 Ω). The figure shows the correct phase is obtained and the stopbands are closed. In

principle, the position and width of each band can be controlled independently, but for

low-frequency bands or those that are closely spaced in frequencies, the required circuit

element values may be too large to realize in a printed transmission line format.


0 45 90 135 1802

2.5

3

3.5

4

4.5

5

5.5

βd (deg)

Fre

quen

cy (

GH

z)

Figure 2.7: Specifying a 90° insertion phase at four arbitrary frequencies: ω1=2.5 GHz,

ω2=3 GHz, ω3=4 GHz, and ω4=5 GHz.

2.4 The Printed G-NRI-TL

Since it was first reported in [5] as a combination of printed and discrete components, the

G-NRI-TL has been implemented in a variety of fully-printed layouts. In the version of

[8], shown in Figure 2.8(a), defected ground structures (DGS) are employed to synthesize

the CHP and LHP elements. This layout, however, has a serious disadvantage in that the

DGS allows radiation below the ground plane which, as will be seen in the next chapter,

poses a problem when this unit cell is applied to the design of a dual-band leaky-wave

antenna. The approach of [9] also opens slots in the ground plane and results in the

relatively complicated unit cell of Figure 2.8(b) and incurs large insertion losses of up

to 4 dB; these same authors later used a substrate integrated waveguide (SIW) as the

host medium of another G-NRI-TL (Figure 2.8(c) [10]. The group of [11] uses the SIW

of Figure 2.8(d), but the drawback is that there is no clear correspondence between the

physical structure and the equivalent circuit, so tuning the SIW unit cell to achieve a

desired circuit response would be difficult. Finally, a CPW-based G-NRI-TL was reported

in [12], but again, due to the small conductor dimensions, insertion losses of 2 dB for a

single cell were observed, making it impractical for any multi-cell microwave component.


(a) (b)

(c) (d)

(e)

Figure 2.8: Fully-printed G-NRI-TLs in existing literature: (a) Chen et al in ([8]), (b)-(c)

Duran-Sindreu et al in [9] and [10], (d) Machac et al in [11], and (e) Fouad and Abdalla

in [12].

An illustration of one of the printed G-NRI-TL used in this thesis is shown in Fig-

ure 2.9 with its equivalent circuit repeated for comparison. With no slots in the ground

plane and only a single metallization layer to be patterned, this design is easier to fab-


ricate than the versions shown in Figure 2.8. The LV P elements are formed by traces

connecting to vias to the ground plane, CV S is realized by a parallel-plate capacitance to

the ground, and the host transmission line’s per-unit-length parameters account for LHS

and CV P .

(a) (b)

Figure 2.9: (a) Equivalent circuit and (b) diagram of fully-printed microstrip G-NRI-TL.

There are two main challenges in creating the printed equivalent of a desired circuit:

first, the sought-after element values themselves cannot be too large, and second, the

printed components should ideally synthesize a constant impedance value over the G-

NRI-TL device’s entire operating bandwidth. These two issues, unfortunately, are at odds

with one another since small element values lead to LH/RH band pairs that are widely

spaced in frequency, and vice-versa; smaller element values are also able to be realized by

printed components over a larger bandwidth than larger values, but this larger bandwidth

may not compensate for the increased overall band separation. Therefore, there is always

a balance between the two factors to be considered.

Since the parallel plates and meandered lines can reliably synthesize relatively large

capacitance and inductance values (up to approximately 4 pF and 5 nH, respectively, are

possible), the series interdigitated capacitors are the limiting factors in the design. One

constraint is that for large capacitances, they can have self-resonant frequencies within

the operating band of the device. Although it adds significant complexity to the design,

one possible solution is to include bonding wires between the capacitor fingers as in [13]

to short out spurious resonances. A more practical approach, however, is simply to limit


the length and number of fingers to shift self-resonances higher in frequency. In this

scenario, capacitor values of up to 1-2 pF can reliably be achieved over a bandwidth of

3-4 GHz.

Another approach to the series capacitors is to use overlapping parallel plates as

part of the main transmission line, as in done with the G-NRI-TL coupler in Chapter 4.

Figure 2.10 compares the magnitude response of a discrete 2 pF capacitor with that

of printed interdigitated and parallel-plate capacitors; at low frequencies, both types of

printed components provide a fair approximation of the ideal value, but the interdigitated

capacitor has a resonance at 5.7 GHz while its parallel-plate counterpart has the widest

bandwidth. A drawback is that the parallel-plate method requires the main signal line to

travel on two metallization layers, thereby increasing the overall fabrication complexity,

and so the interdigitated capacitor is the preferred version, if possible.

1 2 3 4 5 6−30

−25

−20

−15

−10

−5

0

S11

Mag

nitu

de (

dB)

Frequency (GHz)

Ideal capacitorInterdigitated capacitorParallel−plate capacitor

Figure 2.10: Comparison of S11 of an ideal 2 pF capacitor, a five-finger interdigitated

capacitor with length 7 mm, and a parallel-plate capacitor with an overlap length of

1.7 mm.

Selecting the dimensions of the G-NRI-TL unit cell to realize a particular set of ele-

ment values usually results in relatively good agreement between the printed transmission

line and the equivalent circuit. Although semi-analytical formulae for meander-line in-

ductors and interdigitated capacitors are available ([9], [14]), it is usually more convenient

to simulate each printed component in isolation and tune its dimensions to match the

response of the corresponding ideal L or C element. Once the individual elements are

assembled into the complete G-NRI-TL unit cell, optimization of the final structure is

done in full-wave simulation. It is generally best to limit the separation between printed


elements since the coupling between them tends to be small, but introducing long sections

of transmission line within the unit cell creates a significant deviation from the desired

frequency response. Actual comparisons between the printed circuit and the ideal circuit

model will be made when specific devices are discussed in subsequent chapters.

2.5 Beyond Four Bands with the G-NRI-TL

Section 2.2.2 showed how Foster networks can be applied to realize the dual-band NRI-TL

and quad-band G-NRI-TL. If we want to create a circuit with an even greater number of

frequency bands, we can follow the same method and simply add more pairs of resonant

elements to the series and shunt branches to increase the order of those Foster networks.

Figure 2.11(a) shows a higher-order G-NRI-TL with one extra LC pair in each series and

shunt branch and its dispersion curve is plotted in Figure 2.11(b). As expected, there are

now three pairs of right- and left-hand bands and although the closed-stopband condition

for this cell has not been derived, it could be worked out following the same approach as

in Section 2.3.2.


(a)

0 20 40 60 80 100 120 140 160 1800

1

2

3

4

5

6

7

βd (degrees)

Fre

quen

cy (

GH

z)

(b)

Figure 2.11: Hex-band G-NRI-TL from Foster networks: (a) equivalent circuit and (b)

dispersion curve. Element values are CH1 = CV 1 = 2.21 pF, LH1 = LV 1 = 3.5 nH, CH2 =

CV 2 = 2.0 pF, LH2 = LV 2 = 3.17 nH, CH3 = CV 3 = 0.96 pF, and LH3 = LV 3 = 1.5 nH.

Using the two Foster networks is not the only way to create a higher-order G-NRI-TL.

Figure 2.12(a) shows another possible hex-band unit cell which is similar to a symmetric-

π version of the quad-band G-NRI-TL, but has an extra resonator, as highlighted, in

each of the series and shunt branches. The dispersion equation for this circuit is

cos(βd) = 1 +2(ZHS + ZHP )(YV S + YV P )ZHPSYV SP

(ZHS + ZHP + ZHPS)(YHP + YV P + YV SP )(2.25)


where

ZHS =1− ω2LHSCHS

2jωCHSZHP =

jωLHP1− ω2LHPCHP

YV S =jωCV S

2(1− ω2LV SCV S)YV P =


jωLV P

ZHPS =1− ω2LHPSCHPS

2jωCHPSYV SP =

2(1− ω2LV SPCV SP )

jωLV SP

(2.26)

Therefore, the stopband frequencies (those at which βd = 0) are determined by the

frequencies where

ZHS + ZHP = 0

YV S + YV P = 0

ZHPS = 0

YV SP = 0

(2.27)

The first two conditions are identical to those of a T- or π-version of the quad-band

G-NRI-TL, as identified in [2]. The last two conditions are independent criteria relating

only to the added elements. In this case, therefore, the stopbands are closed when we

satisfy both the closed-stopband conditions of the original quad-band G-NRI-TL (i.e.,

4LV SCV P = LHSCHP , ωHP = ωV S, and ωHS = ωV P ) as well as the new condition

CV SPLV SP = LHPSCHPS.

A microstrip version of this hex-band circuit has been developed in simulation and

is shown in Figure 2.12(b). This circuit has two signal layers above a ground plane

and so requires a multi-layer board. The topmost layer is in orange and the middle

layer, implementing the added resonant elements, is in grey. The CHPS capacitor is

incorporated here using overlapping parallel plates, and the connection to the new set of

shunt elements CV SP and LV SP is made through both capacitive coupling between the

two square patches and through the LV P via which connects the two signal layers.


(a)

(b)

Figure 2.12: Alternative version of hex-band G-NRI-TL: (a) equivalent circuit and (b)

printed microstrip circuit.

Figure 2.13 compares the dispersion curves obtained from the circuit model and from

full-wave simulation in HFSS. Six bands are indeed obtained, and the correspondence

between the microstrip circuit and its equivalent model is reasonably good, although the

agreement lessens as frequency increases and the bandwidth of the printed components

is exceeded. Tuning of the cell’s geometry could be applied in HFSS to optimize the

frequency response over the entire operating band.


0 20 40 60 80 100 120 140 160 1801

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

βd (degrees)

Fre

quen

cy (

GH

z)

Circuit ModelHFSS

Figure 2.13: Calculated dispersion curves of hex-band G-NRI-TL from ideal circuit model

and from full-wave simulation in HFSS. Element values are CHS = 0.45 pF, LHS =

4.55 nH, CV S = 0.89 pF, LV S = 2.32 nH, CHP = 0.93 pF, LHP = 2.23 nH, CV P =

0.45 pF, LV P = 4.55 nH, CHPS = 0.23 pF, LHPS = 9.09 nH, CV SP = 1.82 pF, and

LV SP = 1.14 nH.

2.6 Conclusion

This chapter has discussed the development of the G-NRI-TL and has analysed its dis-

persion and impedance characteristics to derive design constraints affecting the unit cell.

A fully-printed, microstrip version of the G-NRI-TL was then presented which is superior

to competing configurations in terms of performance and ease of fabrication. Finally, two

methods of creating higher-order G-NRI-TLs were proposed, and some preliminary sim-

ulated results given. The succeeding chapters will now apply the results and observations

made here toward the design of a variety of multi-band microwave antennas and circuits.


2.7 References

[1] G. V. Eleftheriades and K. G. Balmain, “Negative-refractive-index transmission-

line metamaterials” in Negative Refraction Metamaterials: Fundamental Principles

and Applications, Hoboken, NJ: John Wiley & Sons, 2005, ch. 1, pp. 19-20.



sue of Metamaterials), vol. 4, no. 8, pp. 977-981, August, 2010.

[3] L. Weinberg, “Realization of driving-point functions: two-element-kind networks,”

in Network Analysis and Synthesis, McGraw-Hill Book Company, 1962, ch. 9,

pp. 399-403.

[4] J. Helszajn, “Frequency and impedance transformations,” in Synthesis of Lumped

Element, Distributed and Planar Filters, Berkshire, England: McGraw-Hill Book

Company (UK), 1990, ch. 12, pp. 175-184.

[5] M. Studniberg and G.V. Eleftheriades, “A dual-band bandpass filter based on

generalized negative-refractive-index transmission-lines,” IEEE Microw. & Wireless

Component Lett., vol. 19, pp. 18-20, Jan. 2009.

[6] C.G.M. Ryan and G.V. Eleftheriades, “Design of a printed dual-band coupled-

line coupler with generalised negative-refractive-index transmission lines,” IET Mi-

crow., Antennas, & Propag., vol. 6, no. 6, pp. 705-712, April, 2012.

[7] D. M. Pozar, “Microwave filters,” in Microwave Engineering, 3rd ed., Hoboken, NJ:

John Wiley & Sons, 2005, ch. 8, pp. 371-374.


transmission line for quad band applications,” in 11th IEEE Int. Conf. on Commu-

nication Systems, Singapore, 2008, pp. 617-620.

[9] M. Duran-Sindreu, G. Siso, J. Bonache, F. Martin, “Planar multi band microwave

components based on the generalized composite right/left handed transmission line

concept,” IEEE Trans. Microw. Theory & Techn., vol. 58, no. 12, pp. 3882-3891,

December, 2010.

[10] M. Duran-Sindreu, J. Choi, J. Bonache, F. Martin, and T. Itoh, “Dual-band leaky



handed transmission lines,” 2013 IEEE-MTTS Int. Microw. Symp. Dig., Seattle,

WA, June, 2013, pp. 1-4.

[11] J. Machac, M. Polivka, and K. Zemlyakov “A dual band leaky wave antenna on a

CRLH substrate integrated waveguide,” IEEE Trans. Antennas & Propag., vol. 61,

no. 7, pp. 3876-3879, July, 2013.

[12] M.A. Fouad and M.A. Abdalla, “New T generalised metamaterial negative refrac-

tive index transmission line for a compact coplanar waveguide triple band pass filter

applications,” IET Microw., Antennas, & Propag., vol. 8, no. 13, pp. 1097-1104,

October, 2014.

[13] F. Casares-Miranda, P. Otero, E. Marquest-Segura, and C. Camacho-Pealosa,

“Wire bonded interdigital capacitor,” IEEE Microw. & Wireless Component Lett.,

vol. 15, no. 10, pp. 700-702, October 2005.

[14] “Left-handed metamaterial design guide,” Ansoft Corp., Pittsburgh, PA, 2007.

Chapter 3

A Dual-band Leaky-Wave Antenna

Based on G-NRI-TLs

3.1 Introduction

The leaky-wave antenna (LWA) has several benefits: it is easily manufacturable, it can

achieve a high gain with a relatively short physical length and low profile, and matching

can usually be achieved over a broader bandwidth than with resonant array elements.

Furthermore, its single series feed is more compact and potentially less lossy than the

corporate feed network of a phased array [1]. Finally, for certain applications such as

automobile radar sensing, the beam scanning angle versus frequency of a LWA is a

desirable trait [2].

A quasi-uniform LWA based on negative-refractive-index transmission lines (NRI-

TLs) allows the fundamental n = 0 spatial harmonic to radiate and scan continuously

from backfire to endfire with no stopband formed at broadside [3]. This chapter presents

a dual-band leaky-wave antenna based on the generalized-NRI-TL (G-NRI-TL) [4]; as

seen in the previous chapter, when used as the unit cell in a periodic structure, the G-

NRI-TL has two pairs of right- and left-hand bands and so the G-NRI-TL LWA will have

two operating frequency bands over which the beam scans.

First, the operating principle behind the LWA is presented and the existing work

on dual-band LWAs is summarized. Then, three designs developed for this thesis are

explained with simulated and measured results characterizing the performance of the

different antenna versions.

35

Chapter 3. A G-NRI-TL Dual-band Leaky-Wave Antenna 36

3.2 Background

The operating principle of a leaky-wave antenna is illustrated in Figure 3.1(a). For a

beam to radiate at an angle θ, an electromagnetic wave travelling along the periodic

structure must have a propagation constant of β satisfying

θ = sin−1(β(ω)

k0

)(3.1)

where k0 is the free-space wave number [5]. Equation 3.1 represents the phase-matching

condition between the substrate supporting the guided wave and the radiated wave in

air, and requires |β| < k0, thus corresponding to a fast-wave on the structure. For

conventional periodic structures, this condition cannot be met by the n = 0 harmonic,

but from the sample dispersion curve of the G-NRI-TL in Figure 3.1(b), it is seen that

the dispersion constant β does indeed fall within the fast-wave region (shaded yellow)

over two frequency bands. Therefore, a G-NRI-TL LWA should scan from backfire to

endfire over two frequencies and have two broadside radiation points where βd = 0.

(a) (b)

Figure 3.1: (a) Leaky-wave antenna operation. (b) Fast-wave region (shaded yellow) of

leaky-wave antenna based on G-NRI-TL.

3.3 Prior Work

Although the literature in the field of leaky-wave antennas is extensive, there have been

relatively few dual-band antennas. The authors of [6] proposed that their G-NRI-TL


unit cell could be applied to dual-band LWAs but did not actually create such a device.

As we shall see, their own unit cell is not suitable since the presence of slots for their

defected ground structure (DGS) allows radiation below the plane of the antenna. The

authors of [7] also used the G-NRI-TL concept to create another dual-band LWA. In that

work, the unit cell is a substrate integrated waveguide (SIW) where radiation occurs from

slots cut in the waveguide walls. However, the matching of their antenna is poor (the

reflection coefficient reaching approximately −6 dB) and their use of tapered transitions

from the microstrip feed to the SIW input increases the overall length of the antenna.

Furthermore, there is no explicit correspondence between the SIW unit cell and the G-

NRI-TL equivalent circuit, making the analysis and optimization of that antenna more

difficult. More recently, [8] applied their own SIW G-NRI-TL unit cell (see Figure 2.8(c)),

resulting in a LWA with large scanning angle capability. Dual-band LWAs have also been

reported without using a G-NRI-TL: in [9], a ferrite-loaded waveguide LWA was combined

with a NRI-TL LWA to operate at two frequency bands (one for each mode of operation),

while in [10], two microstrip LWAs were combined to result in dual-band behaviour. The

latter case does not allow scanning to broadside or forward angles, while the former is

achieved only with a more complicated and costly approach than the printed G-NRI-TL

method of this chapter.

3.4 Leaky-Wave Antenna Design

3.4.1 First Design

The initial attempt at a dual-band leaky-wave antenna was based on the unit cell of [6]

and shown in Figure 3.2. The design starts with the unit cell and its equivalent circuit:

the values of the circuit components were chosen as LV S = 2.46 nH, CV S = 1.31 pF,

LV P = 5.7 nH, CV P = 0.57 pF, LHP = 3.1 nH, CHP = 1.04 pF, CHS = 2.39 pF, and

LHS = 1.35 nH. Selected to satisfy the closed-stopband conditions laid out in Chapter 2,

these circuit values yielded two βd = 0 points (the broadside scanning points of the LWA)

that were close enough in frequency to be obtainable from a printed circuit and two

propagation bands with a reasonably wide bandwidth. The dimensions of each isolated

component of the microstrip G-NRI-TL were then swept in HFSS to provide the best

match between the full-wave and simulated circuit results. A final parametric sweep on

the entire unit cell was then performed to compensate for any coupling effects between

the elements that were not accounted for in the circuit diagram. In particular, the

large cut-out forming the defected ground plane alters the behaviour of its surrounding


components, and for this reason, the stub and meander-line/patch combination were both

offset from the cut-out to mitigate its effect. The final parameters are given in Table 3.1.

(a) (b)

Figure 3.2: Layout of printed LWA G-NRI-TL unit cell using approach of [6]: (a) top

view and (b) bottom view.

Table 3.1: Dimensions of printed LWA unit cell- version 1

Parameter Value (mm) Parameter Value (mm)

LCell 11.2 LFinger 5.8

WTL 5 WFinger 0.3

LS 8.75 SFinger 0.2

WS 1 LCutout 16.8

WMeander 0.2 WCutout 6.5

SMeander 0.2 LTee 4.75

WPatch 3.6 STee 0.2

LPatch 4.8 WTee 0.3

VDiam 0.2

Figure 3.3 presents a comparison between the dispersion diagrams obtained from

ADS circuit simulation and from HFSS full-wave analysis which yields the necessary


ABCD parameters. Reasonably good agreement between the two sets of data is obtained

for the lower passband; discrepancies arise at higher frequencies since equivalent circuit

parameters of printed structures are relatively constant at lower frequencies but show

some variation as frequency is increased. Nevertheless, the results show that the fully-

printed unit cell possesses a pair of right-handed/left-handed transmission bands and

that both stopbands are closed.

0 20 40 60 80 100 120 140 160 1800

1

2

3

4

5

6

βd (degrees)

Fre

quen

cy (

GH

z)

Circuit modelPrinted layout

(a)

Figure 3.3: Comparison of dispersion diagram from lumped-element circuit simulation

and from printed full-wave analysis.

As shown in Figure 3.4(a), a leaky-wave antenna comprising 10 unit cells was simu-

lated in HFSS. The transmission and reflection magnitudes versus frequency are shown

in Figure 3.4(b) while Figure 3.4(c) and Figure 3.4(d) present the simulated gain versus

elevation angle in a cut along the length of the antenna at both the lower band and

upper band frequencies. At the lower band, the reflection magnitude is usually below

−10 dB from 1.3 GHz−1.9 GHz, while a narrow stopband is observed in the upper fre-

quency range at 3.7 GHz, thus indicating that further optimization is necessary in this

frequency range. However, it is also observed that the antenna does indeed scan through

broadside over both bands; the total angular range is ±30° from 1.5 GHz-1.9 GHz and

from −40° to +15° over a frequency range of 3.4 GHz-3.9 GHz. Moreover, the gain is

relatively constant over each of the frequency ranges. One drawback is that significant

radiation occurs in the bottom half of the plane; due to the large cut-outs in the ground

plane, this radiation represents wasted power and could create interference with other


components in the system. In light of this drawback, this particular approach was not

pursued further.

(a)

0 1 2 3 4 5−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Mag

nitu

de (

dB)

S21

S11

(b)

−20.3333

−20.3333

−9.1667

−9.1667

2 dB

2 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

1.5 GHz1.6 GHz1.7 GHz1.8 GHz1.9GHz

(c)

−9.0667

−9.0667

−0.53333

−0.53333

8 dB

8 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

3.4 GHz3.5 GHz3.6 GHz3.7 GHz3.8 GHz3.9GHz

(d)

Figure 3.4: (a) 10-cell LWA, (b) its simulated S11 and S21 versus frequency, and the

Gain-θ pattern in the elevation plane for (c) 1.5-1.9 GHz and (d) 3.4-3.9 GHz.


3.4.2 Second Design

The next version of the LWA, as published in [4], does not use a defected ground plane,

and so confines antenna radiation to the upper-half space. The unit cell is shown Fig-

ure 3.5(a) with its corresponding equivalent circuit in Figure 3.5(b). The series capacitors

CHS and CHP are created using overlapping parallel plates on two substrate layers and

the drawing shows the area of overlap where the bright orange is the top transmission line

(TL) and the faded orange represents the underlying TL. These two metallization layers

are separated by a 0.127 mm Rogers 5880 substrate and both are placed on a 1.57 mm

substrate of the same type; the ground is printed on the underside of this thicker layer.

The other feature to note is the orientation of the meandered line representing the LHP

element. In earlier versions of this cell, the meander ran horizontally which resulted

in strong cross-polarization from the leaky-wave antenna. As will be seen, the vertical

orientation depicted here significantly reduces cross-polarization levels.

(a) (b)

Figure 3.5: Unit cell used for multi-layer LWA: (a) diagram of microstrip G-NRI-TL and

(b) equivalent circuit.

From Figure 3.6, the unit cell shows good matching over both operating bands centred

on 2.35 GHz and 5.9 GHz and the dispersion diagram calculated from the S-parameters

indicates that both stopbands are closed. However, although a well-designed unit cell is a

good starting point, periodic analysis applied to a single unit cell does not account either


for radiation from the multi-cell leaky-wave antenna or for mutual coupling between cells,

and so it fails to predict fully the behaviour of the complete structure. A partial solution

requires modifying the unit cell’s equivalent circuit to include radiation resistances in

both the series and shunt branches. Indeed, in [11], it was shown that both resistances

need to exist (thus necessarily producing co-polarized and cross-polarized fields) for the

stopband of a LWA to be closed. Therefore, simulation of a larger radiating structure is

required to produce an acceptable LWA design.

0 20 40 60 80 100 120 140 160 1801

2

3

4

5

6

7

βd (deg)

Fre

quen

cy (

GH

z)

(a)

1 2 3 4 5 6 7−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

S21

(b)

Figure 3.6: Simulated (a) dispersion curve and (b) S-parameters of unit cell of multi-layer

leaky-wave antenna.


Instead of simulating the complete antenna, it would be beneficial to run the required

optimization on a smaller version. One approach is to simulate a five- or ten-cell segment

(which would at least partially account for antenna radiation) and then cascade these

blocks mathematically to determine the overall antenna response. Figure 3.7 shows the

simulated S11 of a 20-cell LWA calculated from the cascade of four five-cell blocks and

two ten-cell blocks, and compares them to the S11 found from a straight 20-cell full-wave

simulation. The general trend is consistent (and the stopband at approximately 5.8 GHz,

resulting from unaccounted-for radiation, is apparent in all simulations), but even the

cascade of the half-length antenna does not model the full antenna perfectly.

1 2 3 4 5 6 7−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

from 5 cell cascade

S11

from 10 cell cascade

S11

from 20 cell simulation

Figure 3.7: Simulated S11 of 20-cell multi-layer LWA, comparing the responses obtained

from a cascade of four blocks of 5 cells, two blocks of 10 cells, and a single 20-cell

simulation.

This conclusion is perhaps not surprising, since, as was found in the NRI-TL LWA

of [12], the complex propagation constant converged only after 30 cells (an electrical

length of 6λ0) were included. In this case, due to the more complicated unit cell layout,

the limits of computing resources lead to a maximum size of the LWA of 15-20 unit

cells (approximately 2λ0 at the lower band); anything larger becomes impractical to

simulate and optimize. From a practical viewpoint, therefore, if a large, high-gain LWA

is required, the best course may be fabricate a series of antennas, each with slightly

perturbed dimensions. In the case of the LWA being designed here, three main parameters

control the width of the stopband: the lengths of the two series capacitors, and the

length of the shunt patch capacitor. These components strongly influence the radiated


field patterns, and so, varying these alters the radiation resistances of the LWA unit

cell, which in turn affects the stopband and overall matching characteristics. Focusing

optimization efforts on these few dimensions reduces the number of possibilities to be

evaluated.

For the purpose of a prototype, however, a ten-cell leaky wave antenna was simulated

in HFSS with the configuration shown in Figure 3.8. The gain patterns at the upper

frequency range are also given in Figure 3.8. The beam scans through broadside almost

exactly at the frequency predicted by the dispersion diagram of Figure 3.6(a); there is a

slight drop in magnitude at broadside, likely due to the stopband which was not perfectly

closed. The orthogonal Gain-φ component is approximately −30 dB lower than the co-

polarized field, which is a direct result of orienting the LHP meander element vertically,

as explained earlier; without doing so, both gain patterns are nearly equal in magnitude.

Gainθ Gain

Φ

0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30° 0 dB

-10 dB

-20 dB

-30 dB

-40 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°

5.5 GHz5.6 GHz5.8 GHz6.0 GHz6.1 GHz

Figure 3.8: Simulated Gain-θ and Gain-φ components over the higher operating frequency

band (5.5 GHz-6.1 GHz).


The simulated co-polarized and cross-polarized gain components for the lower fre-

quency band in the elevation plane are shown in Figure 3.9(a), and it is seen that,

although the antenna’s main beam angle does scan through broadside as frequency in-

creases, the φ-component is larger than the θ component (and actually exhibits a more

uniform scanning range). The large Gain-φ values arise because current is flowing later-

ally across the microstrip line: the plot of the surface current at 2.4 GHz (in Figure 3.9(a))

shows current between the inductive shorted stub and the capacitive meander-patch

combination. At the high band, the meander-patch combination is above its resonant

frequency, thus appearing inductive, and so the current branches off into both this com-

ponent and into the inductive stub-and-via, as seen in Figure 3.8 (the vector current plot

is taken at 5.8 GHz). These currents, flowing in opposite directions, do not radiate so

strongly as they do for the low-frequency case, and so the cross-polarization is lower.

The stub-meander-patch combination in the unit cell was specifically chosen to be

anti-symmetric about the central CHPLHP element to reduce cross-polarized radiation.

To improve the polarization purity further, every second cell of the LWA was then mir-

rored about the antenna axis, as shown in Figure 3.9(b), with the goal of cancelling

the radiation from these transverse currents. As a result, the φ-component magnitude

has decreased by 20 dB, while leaving the θ-patterns unchanged. This counter-intuitive

result (for one would expect the configuration of Figure 3.9(a) to produce the lowest

cross-polarization levels) is also seen in the simple cross-polarization radiation model in

Figure 3.10(a). Four dipoles on the yz-axis are positioned corresponding to the spacing

between the LWA’s meander-patches components, and Figure 3.10(b) plots the dipoles’

E-plane radiation pattern, where 0° corresponds to broadside radiation. The alternat-

ing phase case (corresponding to the arrangement of Figure 3.9(a)) has a much larger

radiated field magnitude (and, hence, a larger cross-polarized component) than does the

“grouped-phase” case (corresponding to the mirrored arrangement).

Not shown, the high-band patterns were unaffected by this geometry change.


0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°


Gainθ

GainΦ

(a)

Gainθ

0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°0 dB

-10 dB

-20 dB

-30 dB

-40 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°

GainΦ


(b)

Figure 3.9: Simulated Gain-θ and Gain-φ components over the lower operating frequency

band (2.2 GHz-2.4 GHz) for (a) standard configuration and (b) LWA with mirrored cells.


(a)

−30

−30

−20

−20

−10

−10

0 dB

0 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

0°/0°/180°/180°0°/180°/0°/180°

(b)

Figure 3.10: (a) Dipole model of cross-polarized LWA radiation. (b) E-plane radiation

pattern of dipoles for two different excitation phase profiles.

The fabricated antenna is shown in Figure 3.11 and the measured S11 and radiation

patterns at the high band are in Figure 3.12(a) and Figure 3.12(b). The beam scans as

predicted in simulation, the cross-polarized component is very low (−30 dB compared

to the co-polarized), and reasonable matching is achieved across the band; the peak

gain is 16.0 dB. Unfortunately, the performance at the lower band was very poor with

a near-unity S11 magnitude observed. The antenna also did not display any significant

frequency scanning. One major source of error could be the fabrication tolerances of

the multilayer substrate itself. The Speedboard C prepreg (εr = 2.59, tanδ = 0.0035)

bonding layer used, while low-loss and with a permittivity close to that of Rogers 5880

(εr = 2.2, tanδ = 0.0009), has a thickness (0.05 mm) comparable to that of the top-most

layer of the antenna (0.127 mm) which was not anticipated during the design stage. This

added layer, as well as thickness variations in these multi-layer boards could result in

relatively large errors in the CHP and CHS capacitances, and smaller differences in the

transmission-line elements CV P and LHS. Since the lower operating frequency has a small

bandwidth in simulation, it is possible these errors eliminated the passband altogether.

A more sensible approach to building this antenna is to clamp or screw the two layers


together, thus avoiding the use of the adhesive altogether.

(a)

(b)

Figure 3.11: Photographs of fabricated (a) unit cell and (b) multi-layer LWA.


4 4.5 5 5.5 6 6.5 7-20

-15

-10

-5

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

0 dB

-10 dB

-20 dB

-30 dB

-40 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°


Gainθ Gain

Φ

(a)4 4.5 5 5.5 6 6.5 7

-20

-15

-10

-5

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

0 dB

-10 dB

-20 dB

-30 dB

-40 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°0 dB

-5 dB

-10 dB

-15 dB

-20 dB

0°

30°

60°

90°

120°

150°

180°

-150°

-120°

-90°

-60°

-30°


Gainθ Gain

Φ

(b)

Figure 3.12: (a) Measured S11 for 20-cell LWA. (b) Gain-θ and Gain-φ in elevation plane

over 5.5-6.1 GHz.

3.4.3 Third (and Final) Design

In light of the fabrication challenges posed by the multilayer LWA, this design simplifies

the antenna’s construction with a single metallization layer. Interdigitated capacitors

have replaced the multi-layer parallel plates, but this simpler antenna layout comes at a

price: the large number of capacitor fingers in a single unit cell, let alone in a full-length

leaky-wave antenna, make this structure very computationally intensive to analyze. For

this reason, the LWA presented here is only five cells long, but despite this truncated


length, beam scanning is still observed. Also, the LV P vias connect directly between the

trace and the ground, without any meandered stubs of earlier designs. This antenna has

not been fabricated, and so the results here are all from simulation in HFSS.

X

YZ

Figure 3.13: G-NRI-TL unit cell used in single-layer LWA.

The dispersion diagram in Figure 3.14(a) for the unit cell indicates that both stop-

bands are closed and that a broadside beam is expected at approximately 2.4 GHz and

3.9 GHz. From the simulated S11 of a five-cell LWA in Figure 3.14(b), good matching is

achieved over both bands. Finally, the radiation patterns are shown in Figure 3.15. The

beams are relatively broad due to the small size of the antenna, but the broadside points

correspond well with the dispersion diagram. Again, alternate cells are mirrored about

the longitudinal axis which reduces the cross-polarized field to −20 dB and −10 dB over

the two operating bands, respectively.


0 20 40 60 80 100 120 140 160 1801

1.5

2

2.5

3

3.5

4

4.5

5

βd (deg)

Fre

quen

cy (

GH

z)

(a)

1 2 3 4 5 6−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

(b)

Figure 3.14: (a) Dispersion diagram of unit cell and (b) simulated S11 of five-cell LWA.


LWA Renewed 5 Cell Simulated

(i.e., with IDC’s)


Gainθ Gain

Φ

(a)

3.7 GHz3.8 GHz3.9 GHz4.0 GHz4.1 GHz4.2 GHz4.3 GHz4.4 GHz

Gainθ Gain

Φ

(b)

Figure 3.15: Simulated radiation patterns for single-layer LWA. Gain-θ and Gain-φ in

elevation plane for (a) 2.4-2.6 GHz and (b) 3.7-4.4 GHz.

At the lower frequency of Figure 3.15(a), the gain is not constant over the scanning

range and decreases by nearly 9 dB for forward scanning angles, a shortcoming which

is, in part, attributable to the changing 3-D radiation pattern of the LWA. Figure 3.16

plots the 3-D radiation patterns of the unit cell across the lower frequency band between

2.4 GHz to 2.6 GHz. These patterns show that two side-beams form and most of the

power is directed away from the axis of the antenna, thereby resulting in a decreasing

gain. This changing pattern shape may be due to the “element” pattern of the LWA

(i.e., that of the unit cell), plotted in Figure 3.16(d); the pattern appears to be somewhat

monopolar (likely due to radiation from the vias, which have a significant effect on the


transmission line’s current distribution at low-band) with a null directed to the forward

scanning angles at around 45°. No such null is observed at the upper frequency band,

and so the pattern magnitude remains roughly constant there.

(a) (b)

(c) (d)

Figure 3.16: Simulated 3-D radiation patterns for single-layer LWA across lower frequency

band at (a) 2.4 GHz, (b) 2.5 GHz, and (c) 2.6 GHz. The element pattern at 2.5 GHz is

shown in (d).

The normalized leakage constant, α/k0, determines how much energy is radiated by

the antenna and is plotted in Figure 3.17, to show how this value is affected by geometry

variations in the individual unit cell components. Certain parameters, such as the length

of the LHP meander inductor (Figure 3.17(a)), have little impact on the antenna’s radi-

ation, whereas the length of the capacitive CV S patch (Figure 3.17(b)) strongly affects

performance. It is also important to note that changing one particular dimension of the

unit cell does not necessarily yield a uniform change over the entire frequency range:

varying the length of the CHP capacitive fingers (Figure 3.17(c)) between 2 mm and


2.8 mm produces a proportionally larger variation in α/k0 at the higher operating band

than at the lower, and the effect of the LV S meander length (Figure 3.17(d)) varies within

the higher frequency band itself. As mentioned earlier, the reactive circuit model of Fig-

ure 3.5(b) does not provide a complete picture of the antenna since radiation resistances

are ignored and the above discussion indicates these should actually be included with the

LV S, CV S, LHP , and CHP elements; however, due to their frequency-dependent nature,

the values of these resistances would be difficult to determine. For the purpose of an

initial design, therefore, the elements which most strongly affect the radiated fields have

been identified, so any further optimization can be focused on tuning these parameters.

2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

Frequency (GHz)

α/k 0

LHP

meander length = 5.2mm

LHP


LHP


(a)

2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (GHz)

α/k 0

CVS

length = 1mm

CVS

length = 2mm

CVS

length = 3mm

CVS

length = 4mm

(b)

2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

Frequency (GHz)

α/k 0

CHP

finger length = 1.4mm

CHP

finger length = 2mm

CHP

finger length = 2.4mm

(c)

2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

Frequency (GHz)

α/k 0

LVS


LVS


LVS


(d)

Figure 3.17: Normalized leakage constant α/k0 of the five-cell single-layer LWA for vary-

ing dimensions of the following elements: (a) LHP , (b) CV S, (c) CHP , and (d) LV S.


3.5 Conclusion

This chapter has described three different topologies of a dual-band leaky-wave antenna.

The latter two are the most promising, and while the short single-layer LWA shows good

performance, its complex unit cell makes optimization of a full-length antenna difficult.

The multi-layer version, on the other hand, can be readily analyzed and tuned with

standard EM solvers, but the physical device requires a precise alignment of the layers

as well as a mechanically robust method of connecting them.

Overall, the results confirm the possibility of dual-band leaky-wave radiation from

a G-NRI-TL antenna, but more work is needed to optimize the radiated field patterns

to yield an increased scanning range and a constant gain versus frequency over both

frequency ranges.


3.6 References

[1] K.-C. Huang and D.J. Edwards, “Multiple antennas” in Millimetre Wave Antennas

for Gigabit Wireless Communications: A Practical Guide to Design and Analysis

in a System Context, United Kingdom: John Wiley & Sons, 2008, ch. 7, pp. 184.

[2] Y. Li, Q. Xue, E. K.-N. Yung, and Y. Long, “The periodic half-width microstrip

leaky-wave antenna with a backward to forward scanning capability,” IEEE Trans.

Antennas & Propag., vol. 58, no. 3, pp. 963-966, March 2010.

[3] A.K. Iyer and G.V. Eleftheriades, “Leaky-wave radiation from planar negative-

refractive-index transmission-line metamaterials,” in Proc. IEEE Int. Symp. An-

tennas & Propag., vol. 2, Monterey, CA, June 2004, pp. 1411-1414.

[4] C.G.M. Ryan and G.V. Eleftheriades, “A dual-band leaky-wave antenna based on

generalized negative-refractive-index transmission lines,” in Proc. IEEE Int. Symp.

Antennas & Propag., Toronto, Canada, July 2010, pp. 1-4.

[5] T. Kokkinos, C.D. Sarris, and G.V. Eleftheriades, “Periodic FDTD analysis of

leaky-wave structures and applications to the analysis of negative-refractive-index

leaky-wave antennas,” IEEE Trans. Microw. Theory & Techn., vol. 54, no. 4, pp.

1619-1630, April 2006.


transmission line for quad band applications,” in Proc. 11th IEEE Singapore Int.

Conf. Comm. Systems, pp 617-620, November 2008.

[7] J. Machac and M. Polivka, “A planar leaky wave antenna operating in two fre-

quency bands,” in Proc. 43rd Eur. Microw. Conf., Nuremberg, October 2013, pp.

487-490.

[8] M. Duran-Sindreu, J. Choi, J. Bonache, F. Martn, and T. Itoh, “Dual-band leaky


handed transmission lines,” in IEEE-MTS Int. Microw. Symp. Dig., Seattle, WA,

June 2013, pp. 1-4.

[9] T. Kodera and C. Caloz, “Dual-band full-space scanning leaky-wave antenna based

on ferrite-loaded open waveguide,” IEEE Antennas & Wireless Propag. Lett., vol. 8,

pp. 1202-1205, November 2009.


[10] Y. Ding, Y. Li, H. Tan, and Y. Long, “A dual operating frequency band peri-

odic half-width microstrip leaky-wave antenna,” in Proc. Third Int. Conf. Inform.

Science & Technol., Jiangsu, China, March 2013, pp. 1339-1342.

[11] S. Paulotto, P. Baccarelli, F. Frezza, and D.R. Jackson, “Full-wave modal dispersion

analysis and broadside optimization for a class of microstrip CRLH leaky-wave

antennas,” IEEE Trans. Microw. Theory & Techn., vol. 56, no. 12, pp. 2816-2837,

December 2008.

[12] M.A. Antoniades, “Microwave Devices and Antennas Based on Negative-

Refractive-Index Transmission-Line Metamaterials,” Ph.D. dissertation, Dept. of

Electrical and Computer Engineering, University of Toronto, Toronto, Canada,

2009.

Chapter 4

A Printed Dual-band Coupled-line

Coupler with Generalized NRI-TLs

4.1 Introduction

Conventional microstrip coupled-line couplers are limited by their low achievable coupling

magnitude, which depends on the difference between the odd and even modes of the

device, and consequently, on the separation between the coupled lines; higher coupler

levels require smaller gaps which may not be technologically possible. The metamaterial

coupled-line coupler first reported in [1] solves this problem and achieves high coupling

(up to 0 dB) with feasible line dimensions by combining an unloaded microstrip (MS)

transmission line and a negative-refractive-index transmission line (NRI-TL). Building

on this latter device, this chapter presents a dual-band coupled-line coupler using a

generalized NRI-TL and a microstrip line [2].

In the analysis in [3], it was shown that backward coupling in the MS/NRI-TL coupler

occurs at the frequency where the dispersion curves of the isolated microstrip line and

of the left-handed propagation band of the NRI transmission line intersect. About this

point, a coupled-mode stopband is formed which features two eigenmodes with complex

conjugate propagation constants, thus leading to the oppositely directed power flows on

each line. The interesting property mentioned above (and variously reported in [1]-[5])

was the higher coupling levels possible in the MS/NRI TL coupler compared to traditional

microstrip edge couplers of similar dimensions. Also, in [6], it was observed that one of

the modes in the stopband exhibits negative group velocity despite the coupler being

formed from an ideally lossless circuit; the observed negative group delay allows the

coupler to offer inherent phase equalization attributes.

58

Chapter 4. A Printed Dual-band Coupler with G-NRI-TLs 59

The key contribution of this chapter is to create a fully printed dual-band coupled line

coupler using G-NRI-TLs, as illustrated in Figure 4.1. As already seen, the generalized

NRI-TL has two pairs of right- and left-handed propagation bands arising from the

inclusion of four resonators in the equivalent circuit as opposed to two in the standard

NRI-TL; the two left-handed regions are used to generate backward-wave coupling over

two frequency bands. Multiconductor transmission-line theory is used to analyze the

behaviour of the periodic coupler unit cell, and parametric studies examining the effects

of varying the cell dimensions and coupler length are included to explain key design

choices.

Microstrip TL

G-NRI-TL

Input

Coupled

Through

Isolated

Unit cell

Figure 4.1: Illustration of dual-band MS/G-NRI-TL coupler.

4.2 Previous Work

Single-band coupled-line couplers using metamaterial components have been reported in

[1], [7], and [8]. Prior to this work, dual-band couplers were based on quadrature or rat-

race topologies (e.g. [9]-[11]) and usually relied on NRI-TLs to synthesize 90° line lengths

at two different frequencies. As in [12], this concept could be expanded to include gener-

alized NRI-TLs, thereby yielding four operating bands; however, this approach may lead

to a larger board area than that required by a coupled-line coupler. An additional disad-

vantage of the quadrature topology is its potentially higher loss: a multi-band quadrature

coupler requires a least four G-NRI-TL cells whereas the edge coupler designed here uses

three. It is desirable to limit the number of G-NRI-TL cells since they typically com-

prise many fine features that increase the device’s overall conductor losses. Finally, a

dual-band 3 dB coupler using only right-handed transmission lines was reported in [10],


but it suffers from the drawback that the frequency ratio of its operating bands is depen-

dent on the coupling magnitude between pairs of coupled lines; this is not the case for a

metamterial coupled-line coupler.

4.3 G-NRI-TL Unit Cell Design

As in the previous chapter, the modified version of the π-derived unit cell is used here. An

illustration of the fully printed cell is given in Figure 4.2 with the corresponding circuit

elements and dimensions labelled. The capacitances CHS and CHP are synthesized by

parallel plates which yield a constant capacitance over a larger bandwidth than would

an interdigitated capacitor. As shown in the figure, these parallel plates overlap on one

side of the trace only; on the other side, they are directly connected to the main line

by vias through the substrate. Therefore, this unit cell comprises three metallization

layers (including the ground) and two substrate layers with the LV P vias run from the

top-most layer to the ground. As with the dual-band leaky-wave antenna, the dimensions

of the printed unit cell can be adjusted to match a desired frequency response computed

from the G-NRI-TL circuit model and design equations of Chapter 2; however, fine

tuning of the complete full-wave model will also be required to optimize the coupler’s

performance. The final dimensions of the printed cell are given in Table 1 along with the

circuit values extracted from HFSS. In the present case, equivalent circuit values were

initially selected based on what could be reasonably attained with printed components

(i.e., a 2 pF capacitance is roughly the upper limit from an interdigitated capacitor in

this frequency range), and what approximate operating bands were desired- initially,

somewhat arbitrarily designated as 2.4 GHz and 4.8 GHz.


Figure 4.2: Implementation of a generalized NRI-TL circuit as a fully printed unit cell

for an edge coupler. (a) Top view where dotted lines show areas of overlap for the parallel

plate capacitors and solid black areas denote underlying parallel plates. (b) Side profile

view showing CHS and LV P elements with dimensions exaggerated.


Table 4.1: Coupler’s printed dimensions and equivalent circuit values

Circuit Values Printed Cell Dimensions

CHS 0.68 pF CHS Overlap 0.8 mm

LHS 3.64 nH CHP Overlap 0.4 mm

CHP 0.93 pF LHP Gap 1.4 mm

LHP 2.23 nH LHP Trace Width 0.2 mm

CV S 0.45 pF CV S Width/Length 3/3.5 mm

LV S 4.64 nH LV S Width/Length 0.3/4.8 mm

CV P 0.72 pF LV S Trace Width 5.2 mm

LV P 2.27 nH LV P Width/Length 0.3/2.3 mm

Layer 1 Height 1.524 mm

Layer 2 Height 0.127 mm

Substrate εr 2.2

4.4 Multiconductor Transmission Line Analysis

A single unit cell of this coupled-line coupler may be analyzed using multiconductor

transmission-line (MTL) analysis [13]. Figure 4.3 shows the equivalent circuit for the

device where there are two lines representing the right-handed microstrip line and gener-

alized NRI-TL, respectively. The coupling mechanism is accounted for by mutual induc-

tances Lm on both signal lines and by a mutual capacitance Cm between the lines [7].


(a)

(b)

Figure 4.3: (a) MTL schematic with ports and voltage and current conventions labeled.

(b) Equivalent circuit for MTL coupler unit cell. For clarity, only half the unit cell is

shown as it is symmetric about the right-most vertical axis.

The propagation properties for the overall cell can be determined from its ABCD

matrix, which for the 4-port network illustrated in Figure 4.3, takes the formV11

V21

I11

I21

= TUnitCell

V12

V22

I12

I22

(4.1)

where TUnitCell is found by cascading the ABCD matrices of each of the individual ele-

ments in the unit cell. These component matrices are given below.


TSeries =

1 0 ZLR 0

0 1 0 ZHS

0 0 1 0

0 0 0 1

THP =

1 0 0 0

0 1 0 ZHP

0 0 1 0

0 0 0 1

TLm =

1 0 0 ZLm

0 1 ZLm 0

0 0 1 0

0 0 0 1

TY =

1 0 0 0

0 1 0 0

0 0 1 0

0 Y 0 1

TCm =

1 0 0 0

0 1 0 0

YCm −YCm 1 0

−YCm YCm 0 1

TCR =

1 0 0 0

0 1 0 0

YCR 0 1 0

0 0 0 1

(4.2)

where

ZLR = jωLR2

YCR = jωCR2

ZLm = jωLm2

YCm = jωCm2

ZHP =

(jω2CHP +

2

jωLHP

)−1ZHS =

jωLHS2

+1

jω2CHS

Y = jω2CV P +2

jωLV P+

(jω2LV S +

2

jωCV S

)−1(4.3)

The overall cell ABCD matrix is therefore

TCell = TSeriesTY TCRTHPTLmTCmTCmTLmTHPTCRTY TSeries

TCell =

[AF BF

CF DF

](4.4)

As described in [14], the dispersion equation for this lossless, reciprocal, and symmetric


unit cell is found from

det(AF − cosh(γd)I) = 0 (4.5)

where γ is the propagation constant through the unit cell of length d. The resulting

expression for the propagation constant takes the form

γd = α± jβ (4.6)

where the plus sign is associated with the so-called γC mode which carries power forward

on the microstrip line and backward on the G-NRI-TL; the reverse holds true for the

minus sign and the γπ mode.

Using equation (4.5), the dispersion diagram for the coupler was plotted and is shown

in Figure 4.4. The circuit values of the host microstrip transmission line, LR=2.72 nH

and CR=1.1 pF, were obtained from full-wave simulations. In Figure 4.4(a), there is

no coupling between the MS and G-NRI-TL lines in order to identify more easily the

dispersion curves of the isolated components; in Figure 4.4(b), coupling is accounted for

and the dispersion results calculated from HFSS’s eigenmode solver are superimposed

on the figure; these latter results are obtained from an eigenmode simulation on a single

unit cell of the MS/G-NRI-TL coupler, as shown in Figure 4.1 The circuit component

values are as specified in Table 4.1 while the mutual inductance and capacitance values

were determined to fit the curves, yielding values of Lm=1.5 nH and Cm=0.15 pF. It

is seen that good agreement between the two methods is obtained. The graph shows

the expected band splitting where the microstrip mode dispersion curve intersects the

left-handed bands of the generalized NRI-TL cell, and therefore, backward wave coupling

is anticipated at approximately 2.5 GHz and 4.4 GHz.


(a)

(b)

Figure 4.4: (a) Dispersion diagrams for (a) isolated microstrip TL and G-NRI-TL. (b)

Dispersion diagram for coupled MS/G-NRI-TL showing analytical solution (solid line)

and HFSS full-wave simulation (dots).

4.5 Coupler Design Considerations

In the design of this coupler, numerous parametric sweeps of the cell geometry were

carried out in HFSS and this section will explain the rationale behind certain key design

decisions. This coupler was designed to have approximately a -3 dB coupling level at

both frequencies, and so the first feature to be examined is the number of cells to employ.


With the port designations given in Figure 4.3(a), Figure 4.5 compares the coupling (S31)

magnitude for couplers with a varying number of cells. Three cells were chosen since this

layout best satisfied the sought-after design criterion at both bands.

1 2 3 4 5 6−30

−20

−10

−3

0

Frequency (GHz)

Mag

nitu

de (

dB)

2 Cells3 Cells4 Cells

Figure 4.5: (a) Simulated S31 coupling magnitude for coupler of varying cell number: two

cells ( ), three cells ( ), and four cells ( ).

Another important feature is the overall length of the individual unit cell. Figure 4.6

compares the coupling magnitude for a three-cell coupler for several different cell lengths.

A small cell is desirable to make the device more compact, but it has several drawbacks.

First, incorporating all the required elements places a restriction on the minimum possible

cell size, and coupling between closely spaced elements leads to discrepancies in the

response between the equivalent circuit and the printed device. Secondly, as shown in

the figure, a smaller cell results in the coupling bands being raised in frequency; this effect

may also be seen by reducing the values of CHS and LV P in the equivalent circuit (i.e.,

by modelling a smaller section of transmission line). The printed components such as

the meandered inductors and parallel plate capacitors have a limited bandwidth, beyond

which their intended circuit value is no longer constant. Therefore, it is difficult to

synthesize a particular response over a wide frequency range, and this fact must be taken

into account when selecting values for the equivalent circuit. A cell length of 14 mm was

used as a compromise between minimizing overall coupler length and ease of component

fabrication.


1 2 3 4 5 6−40

−30

−20

−10

0

Frequency (GHz)

Mag

nitu

de (

dB)

Cell Length=10 mmCell Length=12 mmCell Length=14 mmCell Length=16 mm

Figure 4.6: (a) Simulated S31 coupling magnitude for three-cell coupler for varying cell

lengths: 10 mm ( ), 12 mm ( ), 14 mm ( ), and 16 mm ( ).

4.6 Simulated Performance of Final Design

After the decision was made on coupler and cell lengths in the previous section, a large

number of parametric sweeps were conducted in HFSS to find the best possible matching

and isolation for the three-cell coupler across the two operating bands. To reduce the

computational load, perfect conductors were assumed, but substrate dielectric losses

(tanδ=0.0009) were included in the simulation. All ports were terminated with 50 Ω

loads. Figure 4.7 shows the final simulated S-parameters as well as the insertion loss

(IL) calculated from

IL = −10 log(|S11|2 + |S21|2 + |S31|2 + |S41|2) (4.7)

The coupling frequencies are well predicted by the analytical and eigenmode solution

methods. The peak coupling magnitude at the lower and upper bands is 3.5 dB and

2.2 dB, respectively, while the return loss (−20 log(|S11|)) and isolation (−20 log(|S41|))reach at least 15 dB. The insertion loss is less than 0.2 dB over the lower coupling band

and less than 0.5 dB over the upper band.


1 2 3 4 5 6−20

−15

−10

−5

0

5

Frequency (GHz)

Mag

nitu

de (

dB)

CoupledThroughInsertion Loss

(a)

1 2 3 4 5 6−30

−20

−10

0

Frequency (GHz)

Mag

nitu

de (

dB)

ReflectionIsolation

(b)

Figure 4.7: (a) Simulated S-parameters for three-cell edge coupler showing magnitude

for coupled (S31) and through (S21) signals, isolation (S41), and reflection (S11). The

calculated insertion loss is also shown.

The Poynting vectors on both the microstrip and G-NRI-TL lines at both lower

and upper bands are plotted in Figure 4.8. According to [3], for the input port on

the microstrip line, the coupler’s γC mode is excited; as stated earlier, this mode is

characterized by forward power flow on the MS line and backward power flow on the

G-NRI-TL line. The field plots, obtained from full-wave simulation in HFSS, confirm

that this is indeed the case where forward power flow in Figure 4.8 is from right to left.


(a)

(b)

Figure 4.8: (a) Field plots of Poynting vector on the coupler at (a) the lower band

(2.6 GHz) and at (b) the upper band (4.5 GHz). The ports are labelled following Fig. 4

and the input is at Port 1.

4.7 Measured Results

The fabricated coupler is shown in Figure 4.9. It is manufactured on a Rogers RT/Duroid

5880 substrate (εr=2.2, tan δ = 0.0009) with a 0.127 mm top layer and a 1.524 mm bottom

layer. Measured results are given in Figure 4.10 and the coupler shows good agreement

with the theoretical performance simulated in HFSS. Peak coupling levels of 3.5 dB and

4.4 dB are observed at 2.7 GHz and 4.7 GHz, respectively. The return loss is better

than 20 dB and the isolation over the two coupling bands is also better than 20 dB; both

these parameters either meet or exceed those obtained in [7] and [12], and a significant


improvement in the isolation is obtained over that reported in [8]. The directivity of this

coupler is found to be approximately 20 dB and 17 dB at the lower and upper bands and

is very similar to the results of [10].

1 Input

4Isolated3 Coupled

2Through

Figure 4.9: Photograph of fabricated edge coupler with port conventions labeled. The

G-NRI-TL line is 5.2 mm wide, the microstrip line is 4.8 mm wide, and the line spacing

is 0.4 mm. Including the feed lines, the overall size is 30 mm x 90 mm.


1 2 3 4 5 6−20

−15

−10

−5

0

5

Frequency (GHz)

Mag

nitu

de (

dB)

CoupledThroughInsertion Loss

(a)

1 2 3 4 5 6−30

−20

−10

0

Frequency (GHz)

Mag

nitu

de (

dB)

ReflectionIsolation

(b)

Figure 4.10: (a) Measured S-parameters for three-cell edge coupler showing magnitude

for coupled (S31) and through (S21) signals, isolation (S41), and reflection (S11). The

calculated insertion loss is also shown.

The insertion loss calculated from measurements for this coupler over the lower band

(somewhat arbitrarily defined as a ±2 dB amplitude bandwidth from 2.6 GHz - 2.8 GHz)

is usually below 1 dB although it reaches 1.4 dB at the band edge; over the upper band

from 4.65 GHz to 4.8 GHz, the maximum loss is 1.9 dB but is also typically around

1 dB. These results compare favorably with previous coupler designs: in [9], a dual-band

NRI-TL rat race coupler had similar losses of 0.9 dB, while in [12], a multi-band hybrid

coupler based on another version of generalized NRI-TLs suffered insertion losses ranging


from 1.6 dB to 4.7 dB; finally, with only right-handed transmission lines the dual-band

branch line coupler of [10] had a maximum insertion loss of 1.3 dB.

The upward shift in coupling band frequencies can be attributed to errors introduced

during the complex fabrication process: Air gaps between the top and bottom layers could

not be completely eliminated and were not accounted for in the simulation. Secondly,

with a thickness of only 0.127 mm, the superstrate layer is prone to warping, an effect

difficult to model in HFSS. Finally, the length of the shorted stubs was slightly increased

as the vias were soldered in place, thus contributing small errors to the final fabricated

version; similar difficulties afflicted the connecting vias that were part of the CHS and

CHP elements. A comparison of the measured and simulated results is given in Table 4.2.

Given both the fabrication complexity and the limits of printed components operating

over two widely-spaced frequency bands, the correspondence between theoretical and

measured results is good.

Table 4.2: Summary of measured and simulated results

Parameter Simulated Measured

Coupling bands (GHz) 2.4-2.7 4.4-4.7 2.6-2.8 4.65-4.8

Maximum Coupling (dB) -3.5 -2.2 -3.5 -4.4

Minimum Return Loss (dB) 25.17 19.6 21.9 30.6

Minimum Isolation (dB) -27.9 -24.3 -23.2 -21.6

Maximum Directivity( dB) 22.9 19.1 19.7 17.1

Typical Insertion Loss (dB) 0.2 0.5 1 1


4.8 Conclusion

A dual-band microstrip/G-NRI-TL coupled-line coupler using a fully-printed geometry

has been designed, fabricated, and tested. The modified-π generalized NRI-TL topology

has been used to minimize component count, very good performance has been obtained,

and deviations from the theoretical results have been discussed. Specifically, peak cou-

pling levels of 3.5 dB and 4.4 dB were measured at 2.7 GHz and 4.7 GHz while maintaining

the return loss and isolation to under 20 dB, and the insertion loss to approximately 1 dB

over the two bands. Although this latter figure is higher than for conventional MS/MS

couplers, greater coupling magnitude and dual-band performance are significant benefits

of the new design. The proposed approach is also compact in size, allows arbitrary cou-

pling magnitudes, and permits the coupling frequencies to be specified independently of

the desired coupling levels. The device therefore represents a significant advance over

the prior state of the art.


4.9 References

[1] R. Islam and G. V. Eleftheriades, “A planar metamaterial co-directional coupler

that couples power backwards,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadel-

phia, PA, June, 2003, pp. 321-324.

[2] C.G.M. Ryan and G.V. Eleftheriades, “A printed dual-band coupler using gen-

eralized negative-refractive-index transmission lines,” in Proc. IEEE MTT-S Int.

Micro. Symp., Baltimore, MD, June, 2011, pp. 1-4.

[3] R. Islam, F. Elek, and G. V. Eleftheriades, “Coupled line metamaterial coupler

having co-directional phase but contra-directional power flow,” IEE Electron. Lett.,

vol. 50, no. 5, pp. 315-317, March, 2004.

[4] C. Caloz and T. Itoh, “A novel mixed conventional microstrip and composite

right/left-hand backward-wave directional coupler with broadband and tight cou-

pling characteristics,” IEEE Microw. & Wireless Components Lett.,, vol. 14, no. 1,

pp. 31-33, February, 2004.

[5] E. Jarauta, M. A. G. Laso, T. Lopetegi, F. Falcone, M. Beruete, J. D. Baena, A.

Marcotegui, J. Bonache, J. Garca, R. Marquss, and F. Martin, “Novel microstrip

backward coupler with metamaterial cells for fully planar fabrication techniques,”

Microw. & Opt. Technol. Lett.,, vol. 48, no. 6, pp. 1205-1209, April, 2006.

[6] H. Mirzaei H and G. V. Eleftheriades, “Negative and zero group velocity in

microstrip/negative-refractive-index transmission line couplers,” in IEEE MTT-S

Int. Microw. Symp. Dig., May, 2010, pp. 37-40.

[7] C. Caloz, A. Sanada, and T. Itoh, “A novel composite right-/left handed coupled

line directional coupler with arbitrary coupling level and broad bandwidth,” IEEE

Trans. Microw. Theory & Techn., vol. 52, no. 3, pp. 980-992, March, 2004.

[8] S. H. Mao, and M. S. Wu, “A novel 3 dB directional coupler with broad bandwidth

and compact size using composite right/left-handed coplanar waveguides,” IEEE

Microw. & Wireless Component Lett., vol. 17, no. 5, pp. 331-333, April, 2007.

[9] I.-H. Lin, M. DeVincentis, C. Caloz, and T. Itoh, “Arbitrary dual-band components

using composite right/left handed transmission lines,” IEEE Trans. Microw. Theory

& Techn., vol. 52, no. 4, pp. 1141-1149, April, 2004.


[10] L. K. Yeung, “A compact dual band 90° coupler with coupled line sections,” IEEE

Trans. Microw. Theory & Techn., vol. 59, no. 9, pp. 2227-2232, September, 2011.

[11] J. Bonache, G. Siso, M. Gil, A. Iniesta, J. Garca-Rincon, and F. Martin, “Appli-

cation of composite right/left handed (CRLH) transmission lines based on com-

plementary split ring resonators (CSRRs) to the design of dual band microwave

components,” IEEE Microw. & Wireless Components Lett., vol. 18, no. 8, pp. 524-

526, August, 2008.

[12] M. Duran-Sindreu, G. Siso, J. Bonache, and F. Martin, “Planar multi-band mi-

crowave components based on the generalized composite right/left handed trans-

mission line concept,” IEEE Trans. Microw. Theory & Techn., vol. 58, no. 12,

pp. 3882-3891, December, 2010.

[13] J. A. Brandao-Faria, Multiconductor Transmission Line Structures, New York:

John Wiley & Sons, 1993.

[14] F. Elek and G.V. Eleftheriades, “Dispersion analysis of the shielded Sievenpiper

structure using multiconductor transmission-line theory,” IEEE Microw. & Wire-

less Components Lett., vol. 14, no. 9, pp. 434-436, August, 2004.

Chapter 5

A Single-Ended All-Pass Generalized

Negative-Refractive-Index

Transmission Line Using a

Bridged-T Circuit

5.1 Introduction

As has been seen, a periodic arrangement of the generalized NRI-TL cells used so far

has four passbands consisting of two pairs of left- and right-handed bands. Although the

stopband within each pair (that separating the right- and left-hand bands) can be closed

under certain conditions, the stopband between pairs is always present. The consequence

of this stopband is that large single-cell insertion phases are inherently associated with

decreasing transmission magnitudes – a phenomenon that is common to standard NRI-

TLs as well. This thesis has already given examples of the design difficulties faced which

arise from the stopband: for instance, both the dual-band leaky-wave antenna and the

dual-band coupled-line coupler operate at regions of their unit cell’s dispersion curve

which are relatively near to the band edge. Transmission lines that have a relatively

large electrical length of 90° are also common in filters and other types of couplers [1]-[2]

and so the application of NRI-TLs in these devices requires balancing the achievable

insertion phase with the resulting insertion loss.

One solution to this problem is simply to use more NRI-TL or G-NRI-TL unit cells,

each implementing smaller phase shifts where the transmission magnitude remains high;

the downside is that more components are required, thus increasing design and simulation

77

Chapter 5. An All-Pass G-NRI-TL Using a Bridged-T Circuit 78

time as well as the insertion loss of the fabricated structure. An interesting approach is the

lattice-network equivalent of the generalized NRI-TL, presented in [3], which eliminates

the troublesome stopband and thus has an all-pass magnitude response. It still preserves

the phase response of the four left- and right-hand bands and so this circuit could be

useful in creating the above-mentioned devices. Unfortunately, it too suffers its own

drawback: a lattice is a differential network and requires twice as many circuit elements

as does the single-ended G-NRI-TL used until this point. A printed lattice equivalent

of the standard NRI-TL was shown in [4], but developing a printed version of the G-

NRI-TL lattice circuit would be a daunting task, especially considering that the small

dimensions of the underlying differential transmission line (the gap between co-planar

strip or co-planar waveguide lines, in particular) would make it difficult to incorporate

all the shunt circuit components into the available space.

Fortunately, we can convert the differential quad-band lattice into a single-ended

microstrip circuit more amenable to printed design and fabrication. The transforma-

tion relies on Bartlett’s Bisection Theorem [5] and the result is a single-ended, all-pass,

bridged-T G-NRI-TL circuit [6].

5.2 Circuit Analysis

5.2.1 Lattice Network

Figure 5.1 shows both the single-ended G-NRI-TL and its lattice equivalent. The dashed

lines in Figure 5.1(b) indicate that the series and shunt branches are identical as the

diagram has been simplified for clarity. The circuit analysis for the lattice network begins

by transforming it into the bridge circuit of Figure 5.1(d); with the voltage and current

definitions as shown, four equations may be obtained from KVL and KCL analysis around


(a)

(b)

(c)

- V2+

+

V1

-

I1

I2

I3

I4

I2+I

3

I1-I3

(d)

Figure 5.1: Circuit diagram of (a) standard G-NRI-TL and (b) its lattice equivalent.(c) Block diagram of lattice. (d) Block diagram of bridge circuit.


the loop of the bridge circuit:

−I3Z1 − (I3 + I2)Z3 + V1 = 0

−Z4(I1 − I2 − I3)− Z3(−I3 − I2) + V2 = 0

I1(−Z2 − Z4) + I2(Z3 + Z4) + I3(Z1 + Z2 + Z3 + Z4) = 0

I1 + I4 = I2 + I3

(5.1)

Since we are interested in applying periodic analysis to the lattice unit cell, the ABCD

parameters can be found to be

A =Z1 + Z2

Z1 − Z2

B =(Z1+Z2

2)2

(Z1−Z2

2)

+Z2 − Z1

2

C =2

Z1 − Z2

D =Z1 + Z2

Z1 − Z2

.

(5.2)

Thus, as before, the dispersion equation of the lattice circuit is given by

cos(βd) =A+D

2

=1 + Z2

Z1

1− Z2

Z1

(5.3)

and the Bloch impedance is

ZBloch = ± BZ0√A2 − 1

= ±√Z1Z2

(5.4)


As with the standard G-NRI-TL, the stopbands may be closed and the conditions

for doing so can be derived from the Bloch impedance. For the circuit of Figure 5.1(b),

equation (5.4) becomes

ZBloch = ±

√((1− LHPCHPω2)(1− LHSCHSω2)− LHPCHSω2) /((jωCHS)(1− LHPCHPω2))

((1− LV PCV Pω2)(1− LV SCV Sω2)− LV PCV Sω2) /((jωLV P )(1− LV SCV Sω2)).

(5.5)

Closing the stopbands results in an all-pass magnitude response, which means that

ZBloch must equal a constant, K. For Z1 = num1/denom1 and Y2 = num2/denom2, we

have num1/num1 = Kdenom1/denom2. Denoting the denominators of Z1 and Y2 to be

aω2 + b and cω2 + d, and the numerators to be eω4 + fω2 + g and hω4 + kω2 + l, the

general form of the two divisions is

denom1/denom2 = a/c+b− ad/ccω2 + d

(5.6)

and

num1/num2 = e/h+ω2(f − ke/h) + g − le/h

hω4 + lω2 + l(5.7)

For these two to be equal (within a constant multiple), bc = ad which corresponds to

LHPCHP = LV SCV S. In that case,

num1

num2

= K(denom1

denom2

)= K(1). (5.8)

Then,((1− LHPCHPω2)(1− LHSCHSω2)− LHPCHSω2)

((1− LV PCV Pω2)(1− LV SCV Sω2)− LV PCV Sω2)= K. (5.9)

Equation (5.9) then becomes

(1− LHPCHPω2)(1− LHSCHSω2)− LHPCHSω2 =

K(1− LHPCHPω2)(1− LV PCV Pω2)−KLV PCV Sω2

or

(1− LHPCHPω2)(1−K + ω2(KLV PCV P − LHSCHS)) = ω2(LHPCHS −KLV PCV S)

and so

1−K − ω2(1−K)LHPCHP + ω2(KLV PCV P − LHSCHS)

−ω4LHPCHP (KLV PCV P − LHSCHS) = ω2(LHPCHS −KLV PCV S)

(5.10)

Therefore, for the last equality to hold, K = 1, which then requires LV PCV P = LHSCHS,


and in turn, LHPCHS = LV PCV S.

In summary, the closed stopband conditions are

CHSLHS = CV PLV P

CV SLV S = CHPLHP

CHSLHP = CV SLV P

(5.11)

As an added verification, all the poles and zeros of the Bloch impedance are next

shown to overlap when the above criteria are met. The zeros occur where

ω = 0

1− CV SLV Sω2 = 0

(1− CHSLHSω2)(1− CHPLHPω2)− ω2LHPCHS = 0.

(5.12)

The roots of the last expression can be found by completing the square which yields

ω =

(±

√−1

LHSCHSLHPCHP+

1

4

(LHSCHS + LHPCHP + CHSLHP

LHSCHSLHPCHP

)2

+LHSCHS + LHPCHP + CHSLHP

2LHSCHSLHPCHP

) 12

. (5.13)

The poles of the Bloch impedance occur where

ω = 0

1− CHPLHPω2 = 0

(1− CV PLV Pω2)(1− CV SLV Sω2)− ω2LV PCV S = 0.

(5.14)

Again, the last expression is solved for ω:

ω =

(±

√−1

LV SCV SLV PCV P+

1

4

(LV SCV S + LV PCV P + CV SLV P

LV SCV SLV PCV P

)2

+LV SCV S + LV PCV P + CV SLV P

2LV SCV SLV PCV P

) 12

. (5.15)

It may be seen that the poles and zeros do indeed overlap when equation (5.11) is met.

Finally, under these closed stop-band conditions, the Bloch impedance reduces to the


frequency-independent value

ZBloch = ±√LHSCV P

(5.16)

which corresponds to the characteristic impedance of the underlying transmission line.

Figure 5.2 shows the dispersion curve of the resulting lattice unit cell under closed-

stopband conditions and indicates the locations of the Bloch impedance’s poles and zeros.

These results are simulated based on all capacitors in the circuit being set to 0.6 pF and all

inductors being equal to 1.3 nH. All-pass behaviour is achieved and there is no stopband

in the lattice’s dispersion curve. Furthermore, the first left-handed band actually extends

to a frequency of 0 Hz. Such behaviour for a single-ended G-NRI-TL would be non-causal

since it represents a finite insertion phase shift (180°) with an electrical length of zero.

However, this phenomenon of the lattice network can be explained by considering its

equivalent circuit diagram of Figure 5.1(b): at zero frequency, the series branches are

open-circuited due to the infinite impedance of the series capacitor CHS, while the shunt

branches are short-circuited from the zero impedance of the inductor LV P . Therefore, at

zero frequency, the positive terminal of port 1 is connected to the negative terminal of

port 2 (and vice versa), thus resulting in a 180° phase shift.

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

10

12

βd (deg)

Fre

quen

cy (

GH

z)

Figure 5.2: Dispersion curve of lattice network with zeros (red circles) and poles (green

x’s) of Bloch impedance shown.


5.2.2 Bartlett’s Bisection Theorem

To convert the differential lattice circuit to a single-ended circuit suitable for a microstrip

layout, Bartlett’s Bisection Theorem is used. As illustrated, this theorem allows the

transformation from a T-circuit (Figure 5.3(a)) to a lattice circuit (Figure 5.3(b)). Short-

and open-circuits are applied along the plane of symmetry and the corresponding short-

and open-circuit equivalent impedances become the lattice’s series and shunt impedances,

respectively.

ZShortCircuit = Z1 ZOpenCircuit = Z1+Z2

Z1

Z1

Z2

Z2

(a)

Z1

Z1

ZOpenCircuit

ZShortCircuit

(b)

Figure 5.3: Bartlett’s Bisection Theorem: (a) block diagram of T-circuit and (b) block

diagram of lattice network.

For the T-circuit as shown,

ZShortCircuit = Z1 and ZOpenCircuit = Z1 + Z2. (5.17)

The same transform may be applied to a bridged-T circuit, as in Figure 5.4(a) and the

equivalent lattice is given in Figure 5.4(b). These two circuits have identical frequency

responses (i.e., all-pass magnitude and quad-band phase shifts). It should be noted that

while this transform always allows a lattice network to be realized from a T (or bridged-

T) network, the reverse transform is not always physically possible since negative circuit

values might be required.


ZShortCircuit= Z1||Z3/2 ZOpenCircuit= Z1+Z2

Z1

Z1

Z2

Z2

Z3/2 Z

3/2

(a)

Z1

Z3/2

Z3/2

Z1

(b)

Figure 5.4: Bartlett’s Bisection Theorem applied to a bridged-T circuit: (a) block dia-

gram of Bridged-T circuit and (b) block diagram of resulting lattice network.

5.2.3 Bridged-T Circuit

Bartlett’s Bisection Theorem provides a means of implementing a differential lattice

network as a single-ended T-circuit. However, while the lattice block diagram of Fig-

ure 5.4(b) resembles that of Figure 5.1(b) it is not identical; it represents, in fact, the

dual of the original lattice (i.e., that in which the series connection of the CHSLHS

and CHPLHP resonators are transformed to a parallel connection, and vice-vera for the

CV SLV S and CV PLV P resonators). Therefore, an intermediate stage is necessary before

the bisection theorem can be applied. Figure 5.5 summarizes the steps necessary to

complete the transformation between a quad-band lattice G-NRI-TL and a single-ended

all-pass bridged-T circuit. The process starts with the original quad-band lattice; the

dual version of it is obtained and its block diagram is shown in Step 3. The bisection

theorem is applied, resulting in the bridged-T schematic of Step 4. Finally we arrive at

Figure 5.6 which shows the complete circuit diagram of the bridged-T network. This

transformation is possible only with an additional constraint being placed upon the cir-

cuit elements: as indicated in Figure 5.5, the impedance ZC must appear in both the


series and shunt branches, and therefore,

jωLHS +1

jωCHS= jωLV S +

1

jωCV S

LHS = LV S and CHS = CV S

(5.18)

Taken together with the constraints of equation (5.11), three circuit elements can be

freely specified: LHS, CHS, and either CHP or LHP . The remainder are determined by

the equations already given. Despite these restrictions, there are still enough degrees of

freedom to produce useful devices, as will be seen in Section 5.5.

ZC

ZA/2

ZB

ZC

ZC

ZA

1 2

34

Figure 5.5: Steps in transforming a lattice to a bridged-T circuit: the G-NRI-TL lattice

is converted to its dual version prior to implementation in bridged-T form.


/2

2

2 /2

Figure 5.6: Quad-band bridged-T circuit.

The dispersion curves and magnitude responses of the single-ended G-NRI-TL, its

lattice equivalent, and the bridged-T G-NRI-TL are plotted in Figures 5.7(a)-5.7(b) and

Figure 5.8 plots the insertion phase of all three circuits. All the inductors’ values are set

equal to 1.3 nH and the capacitors’ values equal to 0.6 pF. For the magnitude response,

the curves of the latter two circuits exactly overlap. The other interesting feature to

note is that the dispersion curves of the original lattice and of the bridged-T circuit are

mirror images of each other which occurs because the bridged-T was derived based on

the dual lattice network. As a consequence, a right-handed band now extends to zero

frequency and so zero transmission phase results when the bridged-T circuit has zero

electrical length. The single-ended all-pass circuit is therefore causal.


0 30 60 90 120 150 1800

2

4

6

8

10

12

14

βd (degrees)

Fre

quen

cy (

GH

z)

G−NRI−TL T−circuitG−NRI−TL latticeBridged−T circuit

(a)

2 4 6 8 10 12 14−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Mag

nitu

de (

dB)

Frequency (GHz)

G−NRI−TL T−circuitG−NRI−TL latticeBridged−T circuit

(b)

Figure 5.7: (a) Dispersion curves and (b) S -parameter magnitudes for G-NRI-TL T-

circuit ( ), its lattice equivalent ( ), and for bridged-T circuit ( × ).


0 2 4 6 8 10 12 14

−150

−100

−50

0

50

100

150

Frequency (GHz)

Inse

rtio

n P

hase

(de

gree

s)

G−NRI−TL T−circuitG−NRI−TL latticeG−NRI−TL bridged−T

Figure 5.8: Insertion phase for G-NRI-TL T-circuit ( ), for its lattice equivalent

( ), and for the bridged-T circuit ( × ).

5.2.4 A Bridged-T NRI-TL

The same transformation can be equally applied to the dual NRI-TL lattice, as in Fig-

ure 5.9. Again the dual version of the lattice is the necessary starting point for the

transformation since the lattice’s shunt element must be a series combination of ele-

ments. Figure 5.10 shows the dispersion diagram for the standard single-ended NRI-TL,

its dual lattice, and the bridged-T transformation; the dispersion curves of the latter two

overlap since the circuits are functionally equivalent.

/2

2

2

/2

(a) (b)

Figure 5.9: Bridged-T representation of an all-pass NRI-TL circuit: (a)NRI-TL dual

lattice, and (b) corresponding bridged-T circuit.


0 20 40 60 80 100 120 140 160 1800

2

4

6

8

10

12

14

βd (degrees)

Fre

quen

cy (

GH

z)

NRI−TL T circitLattice network (dual)NRI−TL bridged−T circuit

Figure 5.10: Dispersion curves of NRI-TL circuit as single-ended T-network ( ), a

lattice network ( ), and as bridged-T network ( ).

5.3 Printed Circuit

Now that the all-pass circuit has been derived, the next step is to produce a fully-printed

version of it in a microstrip layout. Figure 5.11(a) shows an HFSS model of the printed

structure, which was designed on a Rogers R3003 substrate (thickness of 1.524 mm,

εr = 3, tanδ = 0.0013). To make fabrication possible, the bridge section is printed on a

thin layer (thickness of 0.127 mm) of the same substrate and suspended above the main

line by a foam layer. The circuit components LHS and CV P are synthesized by the host

transmission line as with the standard G-NRI-TL. The figure shows the correspondence

between the printed components and each of the remaining circuit elements. Each ele-

ment was simulated in isolation in HFSS to find the dimensions that best matched the

desired circuit response (that obtained with the capacitors set to 0.6 pF and the induc-

tors to 1.3 nH); the overall structure’s geometry was then tuned around those values to

optimize transmission magnitude. Figures 5.11(b)- 5.11(c) show the two layers of the

fabricated all-pass cell although the via which synthesizes the shunt inductor LV P is not

visible. The final dimensions of the printed cell are summarized in Table 5.1.


2LHP

CHS

CHP/2

LVP/2w

h

(a)

(b) (c)

Figure 5.11: (a) HFSS model of bridged-T circuit; for clarity, the substrate layers are not

shown and the height of the air gap (h) is exaggerated. Also, photographs of fabricated

device’s (b) top layer and (c) bottom layer.

Table 5.1: Dimensions of fabricated all-pass unit cell

Parameter Value (mm) Parameter Value (mm)

w 4 LV P radius 0.4

h 0.381 Cell length 14

CHS 2.25 Bottom layer 1.524

LHP 2.2 Top layer 0.127

CHP 1

5.4 Simulated and Measured Results

Figure 5.12 compares the measured S -parameters to those obtained from full-wave sim-

ulation in HFSS. To accommodate the coaxial feed connectors on either end of the mi-

crostrip line, the cell has been lengthened and so the bands are shifted lower in frequency

as compared to the dispersion curve from the circuit model. However, this extra cell

length has been accounted for in HFSS to provide a fair comparison between simulated

and measured data. There are two 180° points and one 0° point at approximately the


frequencies predicted by the circuit model. Although the measured return loss is higher

than expected, the cell still shows all-pass behaviour over a very wide frequency range

(1 GHz - 8 GHz) and the phase characteristics are in reasonably good agreement with

the full-wave simulations. The group delay for the fabricated all-pass cell and the stan-

dard G-NRI-TL are plotted in Figure 5.13. As is known from filter theory, group delay

increases near a band edge and this is indeed observed for the case of the standard G-

NRI-TL. However, because the bridged-T circuit has no stopbands, its phase variation

with respect to frequency is smaller and its group delay is lower; this is confirmed by the

simulated and measured data.

The response of the bridged-T circuit degrades at higher frequencies due to the limited

bandwidth of the printed components. There are other sources of error, too, which

include maintaining the integrity of the very thin (0.127 mm) superstrate layer and

creating a constant 0.38 mm air gap between the layers. Given the relatively crude

construction of this prototype unit cell, the results are good and it is expected that more

precise fabrication could improve these results. Alternatively, to simplify fabrication, the

bridged-T could be created on a single layer, instead of the vertical bridge approach used

here. Nevertheless, the current device and obtained data are presented as a “proof of

principle” to verify the behaviour of the proposed artificial transmission-line cell.


1 2 3 4 5 6 7 8−40

−30

−20

−10

0

Frequency (GHz)

Mag

nitu

de (

dB)

SimulatedMeasured

(a)

1 2 3 4 5 6 7 8−180

−90

0

90

180

Frequency (GHz)

Pha

se (

degr

ees)

SimulatedMeasured

(b)

Figure 5.12: (a) S11 and S21 magnitude and (b) S21 phase of bridged-T circuit. Dottedlines indicate measured results and solid lines indicate simulated data.


1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Gro

up D

elay

(ns

)

Frequency (GHz)

Simulated G−NRI−TLSimulated Bridged−TMeasured Bridged−T

Figure 5.13: (a) Measured group delay of bridged-T circuit ( ). (b) Simulated groupdelay of bridged-T circuit ( ). (c) Simulated group delay ofG-NRI-TL T-circuit ( ).

5.5 Potential Applications

As mentioned earlier, there are several uses for an all-pass cell in creating multi-band

microwave components and this section will briefly cover how it may be applied to a

quad-band impedance inverter, a Wilkinson divider, and a hybrid coupler. The results

for the latter two devices are from circuit simulations only; no attempt was made to

convert these to printed devices, although such a step is conceptually straightforward.

5.5.1 Impedance Inverter

Since small sections of the all-pass unit cell function as a standard transmission line with

a characteristic impedance given by Equation (5.16), it can be used as an impedance-

matching quarter-wave transformer. Figure 5.14(a) shows a schematic representation

of the circuit and Figure 5.14(b) plots the S11 magnitude for the inverter matching a

ZL = 100 Ω load to a Zin = 50 Ω input. In this case, the circuit elements LHS and CV P ,

which are associated with the microstrip’s characteristic impedance, are chosen to satisfy

Zin =

√Z0

ZL (5.19)


with Z0 defined as before. Thus, at each of the 90° frequencies of the unit cell, an

arbitrary load impedance may be matched to the system impedance.

ZL

Bridged-T1

(a)

2 4 6 8 10 12 14−40

−30

−20

−10

−3.8

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

(b)

Figure 5.14: (a) Impedance inverter diagram. (b) Simulated S11 of inverter usingbridged-T unit cell. All capacitors are 0.6 pF and all inductors are 1.3 nH.


The performance of the fabricated unit cell as an impedance inverter can be assessed

from Figure 5.15 where a 100 Ω load is transformed to a 25 Ω input:

1 2 3 4 5 6 7 8−35

−30

−25

−20

−15

−10

−5

0

S11

Mag

nitu

de (

dB)

Frequency (GHz)

HFSS sim.Measured

Figure 5.15: Measured and simulated response of the microstrip all-pass cell as an

impedance inverter.

Overall, the measured results show good agreement with the full-wave simulations

from HFSS, but, once again, the performance of the inverter begins to degrade at higher

frequencies.

5.5.2 Wilkinson Divider

The Wilkinson divider is another device which uses 90° delay lines. When a bridged-T cir-

cuit is used instead, as in Figure 5.16(a), four operating bands result with good matching

and ideal -3 dB coupling.


R

Bridged-T

Bridged-T

1

2

3

(a)

2 4 6 8 10 12 14−40

−30

−20

−10

−3

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

S21

S31

(b)

Figure 5.16: (a) Wilkinson divider diagram. (b) Simulated S -parameters of Wilkinson

divider using bridged-T unit cells. All capacitors are 0.6 pF, all inductors are 1.3 nH,

and the resistor is 65.8 Ω.

5.5.3 Hybrid Coupler

Four bridged-T circuits may be combined to form a quadrature hybrid coupler of Fig-

ure 5.17(a). Again, four operating bands are observed with high isolation, low reflection

magnitude, and -3 dB coupling.


4 3

Bridged-T

Bridged-T

Bridged-T

Brid

ged-T

1 2

(a)

2 4 6 8 10 12 14−20

−15

−10

−5

−3

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

S21

S31

S41

(b)

Figure 5.17: (a) Hybrid coupler diagram. (b) Simulated S -parameters of hybrid couplerusing bridged-T unit cells. The high-impedance transmissions lines use 0.6 pF capacitorsand 1.3 nH inductors, while the low-impedance lines use 0.84 pF capacitors and 0.91 nHinductors.

5.5.4 The Same Applications with Standard G-NRI-TLs

Each of the three applications discussed above has been repeated using the original

G-NRI-TL circuit, and with the same circuit values given previously, to illustrate the

advantages of the bridged-T alternative. For both the divider and the coupler, the results

in Figures 5.19-5.20 show that the changing magnitude response for large insertion phase

shifts negatively affects the devices’ performance: the S11 and coupling bandwidth of

the Wilkinson divider is reduced, the matching of the hybrid coupler is slightly worse,

and the hybrid coupler no longer yields an even -3 dB split, except exactly at the design

frequencies. Therefore, optimization of the G-NRI-TL’s circuit element values would be


required for these devices to function properly. Depending on the application however,

the G-NRI-TL inverter may actually be more desirable than its bridged-T counterpart

because of its higher out-band-rejection over the closed-stopband region of the G-NRI-TL

unit cell, leading to greater frequency selectivity.

2 4 6 8 10 12 14−40

−30

−20

−10

−3.8

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

Figure 5.18: Simulated S11 of impedance inverter using G-NRI-TL unit cells.

2 4 6 8 10 12 14−40

−30

−20

−10

−3

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

S21

S31

Figure 5.19: Simulated S -parameters of Wilkinson divider using G-NRI-TL unit cells.


2 4 6 8 10 12 14−20

−15

−10

−5

−3

0

Frequency (GHz)

Mag

nitu

de (

dB)

S11

S21

S31

S41

Figure 5.20: Simulated S -parameters of hybrid coupler using G-NRI-TL unit cells.

5.6 Conclusion

This chapter has presented a single-ended bridged-T circuit equivalent of the standard G-

NRI-TL circuit used so far in this thesis. This new approach yields an all-pass magnitude

response while preserving the quad-band phase characteristics of the original unit cell.

Theoretical results, from both circuit and full-wave simulations, show close agreement

with the measured performance of the fabricated prototype cell. Finally, several possible

applications for this new design have been explored; the advantages of the bridged-T

circuit in terms of impedance matching and bandwidth are clear.

Simpler to fabricate than a lattice network and suitable for use in microstrip tech-

nology, the bridged-T circuit can form the basis for multi-band passive devices such as

impedance inverters, couplers, and power dividers operating over a wide frequency range.


5.7 References

[1] Duran-Sindreu M., Siso G., Bonache J., Martin F, “Planar multi band microwave

components based on the generalised composite right/left handed transmission line

concept,” Electron. Lett., vol. 58, no. 12, pp. 3882-3891, December 2010.

[2] D. M. Pozar, Microwave Engineering, 3rd ed., Hoboken, NJ: John Wiley & Sons,

2005.

[3] L. Markley and G.V. Eleftheriades, “Quad-band negative-refractive-index

transmission-line unit cell with reduced group delay,” Electron. Lett., vol. 46, no. 17,

August 2010.

[4] F. Bongard J. R. Mosig, “A novel composite right/left handed unit cell and poten-

tial antennas applications,” in Proc. IEEE Int. Symp. Antennas & Propag., July,

2008, pp. 1-4.

[5] A. Williams and F. Taylor, Electronic Filter Design Handbook, 4th ed., New York:

McGraw-Hill, pp. 95-96, 2006.

[6] C.G.M. Ryan and G.V. Eleftheriades, “A single-ended all-pass generalized negative-

refractive-index transmission line using a bridged-T circuit,” in Proc. IEEE MTT-S

Int. Microw. Symp., Montreal, Canada, June, 2012, pp. 1-3.

Chapter 6

A Wideband Meander-Line Antenna

with Metamaterial Loading

6.1 Introduction

To reduce its size, the meander antenna’s monopole arm is folded back upon itself. Shown

in Figure 6.1, dual-band and multi-band versions are possible by adding extra meandered

lengths [1], [2], but the drawback of this type of antenna is that currents run in opposite

directions on the meandered sections, thus leading to a partial cancellation of the radiated

field, and consequently, to a lower radiation efficiency [3].

(a) (b)

Figure 6.1: Schematics of (a) standard meander-line antenna and (b) metamaterial-

loaded antenna. Transmission-line models of (c) standard meander-line antenna and

(d) metamaterial-loaded antenna.

102

Chapter 6. A Wideband Metamaterial Meander-Line Antenna 103

If, however, the direction of current on specific sections of the antenna could be

reversed, this cancellation would not occur and so the antenna’s performance should

improve: its radiation resistance would be greater leading to both higher radiation ef-

ficiency and greater bandwidth since more of the energy is being radiated instead of

stored. Since metamaterial-loaded transmission lines can display negative phase velocity

with respect to unloaded transmission lines [4], it was thought that combining both NRI-

and PRI-TLs in one antenna would lead to the desired outcome. Figure 6.2 illustrates

this concept: Figure 6.2(a) depicts a standard meander-line antenna, and in Figure 6.2(c)

the antenna’s two sections are unfolded into a simple transmission-line model with the

direction of the current as shown. In Figure 6.2(d) one antenna section is replaced by

an NRI-TL and the phase velocity is then reversed compared to that on the unloaded

section. It can be imagined that as this new antenna is folded back into its meandered

shape (Figure 6.2(b)), the currents on the two branches will be in-phase. As will be seen,

the intended goal of higher efficiency was not achieved, but the attempt led to other,

unexpected benefits and new areas which are the subject of this chapter [5].

(a) (b)

(c) (d)

Figure 6.2: Schematics of (a) standard meander-line antenna and (b) metamaterial-

loaded antenna. Transmission-line models of (c) standard meander-line antenna and

(d) metamaterial-loaded antenna.


6.2 Single Antenna Design

6.2.1 Antenna Layout with Metamaterial Unit Cell

The proposed antenna is shown in Figure 6.3(a) with the dimensions as indicated. Fed

from a microstrip line on a 10 mil (0.254 mm) Rogers RO3003 substrate (εr = 3,

tanδ = 0.0013), the antenna incorporates a single metamaterial unit cell on the lower

arm: the interdigitated capacitor synthesizes the series capacitance, while the shunt in-

ductor is implemented by the meandered ground plane extension that is connected to

the antenna by a via though the substrate. The antenna was simulated in HFSS, and

Figure 6.3(b) shows the simulated current flow on the structure at the onset of the op-

erating band at 3.5 GHz. It is observed that in-phase currents are established on both

arms. For comparison, a meander-line antenna without the metamaterial unit cell has

also been designed and simulated over the same frequency range. Figure 6.3(c) shows

the direction of the current flow on this right-handed antenna, where it is clear that no

reversal of the current direction occurs, and so the currents on each of the arms remain

out-of-phase.

Although this single-cell design does not qualify the antenna as a metamaterial one,

the principle could be applied to a meander-line antenna with many bends; this latter de-

vice in the conventional case would suffer from reduced radiation efficiency, but applying

metamaterial components to each arm would result in all the arms radiating in-phase,

with the expectation of increasing the efficiency, radiation resistance, and bandwidth.


Arm 1

Arm 3

Arm 2

6.15 mm

6 mm

2 mm

0.5 mm

2 mm3.5 mm

x

y

0.5 mm

1.5 mm

(a)

(b) (c)

Figure 6.3: (a) Geometry of metamaterial-inspired antenna with the ground plane (size:

15 mm × 60 mm) coloured light grey; (b)-(c) surface current direction on metamaterial-

inspired and conventional meander antennas, respectively.

6.2.2 Comparison of Conventional and Metamaterial Meander

Antennas

Another benefit of the new antenna is its wider bandwidth as compared to the conven-

tional meander as shown in Figure 6.4. The Smith chart of Figure 6.4(a) shows that

a second loop appears in the response of the new metamaterial-inspired antenna and

a significantly wider bandwidth is obtained. In Figure 6.4(b), the −10 dB bandwidth

extends from 3.5 GHz to 6.5 GHz (60% fractional bandwidth), whereas the conventional

meander antenna has a −10 dB S11 bandwidth from 3.6 GHz to 5 GHz. This extra

resonance arises since the ground trace now forms a second resonant length in addition

to that of the antenna itself. Figures 6.5(a) and 6.5(b) plot the magnitude of the surface

current as simulated in HFSS at 4 GHz and 5.6 GHz, respectively. It is seen that current


flows over the entire antenna at the lower frequency, but is confined to the first arm and

the ground extension at the upper band. Although not shown here, more resonances can

be introduced by adding arms with metamaterial loading, raising the possibility of an

extremely wideband and compact antenna.

0.2

0.5

1.0

2.0

5.0

+j0.2

−j0.2

+j0.5

−j0.5

+j1.0

−j1.0

+j2.0

−j2.0

+j5.0

−j5.0

0.0 ∞

(a)

3 3.5 4 4.5 5 5.5 6 6.5 7−40

−30

−20

−10

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

RH AntennaMM Meander SimulatedMM Meander Measured

(b)

Figure 6.4: (a) Smith chart representation of reflection coefficient magnitude for conven-

tional ( ) and metamaterial ( ) antenna. (b) Cartesian plot of S11 magnitude

for simulated conventional and metamaterial antenna and for measured metamaterial

antenna.


(a) (b)

Figure 6.5: Simulated current magnitude at (a) 4 GHz and (b) 5.6 GHz.

6.2.3 Measured Results

The measured return loss is also shown in Figure 6.4(b). The total measured −10 dB

return loss bandwidth is 2.5 GHz (corresponding to 52% fractional bandwidth) and rea-

sonably good agreement between the two sets of data is obtained. The discrepancy in

overall magnitude between measured and simulated results is due to the relatively large

radius of the coaxial feeding pin; simulations confirm a degradation of matching levels

when the inductance of the feed line is decreased as the line itself is widened. Simu-

lated 3D radiation patterns are shown in Figures 6.6(a)-6.6(b); Figures 6.6(c)-6.6(d) plot

simulated and measured radiation patterns across the operating band in the xy- and

xz-planes, respectively. The patterns themselves are fairly isotropic and, overall, good

agreement is obtained.


(a) (b)

−10.0667

−10.0667

−2.5333

−2.5333

5 dB

5 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(c)

−10.7333

−10.7333

−3.8667

−3.8667

3 dB

3 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(d)

Figure 6.6: Simulated 3-D radiation patterns at 3.7 GHz: (a) Gain-φ and (b) Gain-θ. A

comparison of measured (solid lines) and simulated (dotted lines) radiation patterns is

also shown: (c) Gain-φ in xy-plane and (d) Gain-θ in xz-plane at 3.6 GHz ( ), 4.3 GHz

( ), and 5.5 GHz ( ).

It is tempting to view this device as a “small antenna” with a large bandwidth. To

qualify as such, the relation ka ≤ 1 must hold where k = 2πλ

is the free-space wavenumber

and a is the radius of the smallest sphere enclosing the antenna [6]. Since the dimensions

of the meander antenna itself are 6.5 mm x 14 mm, ka = 0.73. The Chu limit on the


fractional bandwidth of such an antenna is

FBW =

(1

(ka)3+

1

ka

)−1

= 25.6%

(6.1)

With its simulated 60% fractional bandwidth, this antenna seemingly violates the

Chu bandwidth limit by a wide margin. However, the primary radiating structure is not

the meandered line itself, but the ground plane. This may be verified in the Figure 6.7,

which compares the simulated radiation pattern of a meander-line antenna with that

of an unfolded version at 4 GHz. Were the antenna itself the primary radiator, the

orientation of the patterns should change with the changing antenna geometry, but as

in Figure 6.7(c-d), the patterns are largely unaffected, indicating the role of the ground

plane in radiating power. With ground plane dimensions of 15 mm x 60 mm, this device

cannot be considered a small antenna and the limit calculated above does not apply.


(a) (b)

−10.4

−10.4

−3.2

−3.2

4 dB

4 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(c)

−12.0667

−12.0667

−6.5333

−6.5333

−1 dB

−1 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(d)

Figure 6.7: Layout of (a) meander-line antenna and (b) straight-line version for same

orientation as above. A comparison between radiated fields for meander antenna ( )

and straight antenna ( ): (c) Gain-φ in xy-plane and (d) Gain-θ in xz-plane at

onset of operating band at 4 GHz.

6.2.4 Comparison of Radiation Efficiency

The radiation efficiency reported in Table 6.1 was calculated using McKinzie’s Wheeler

cap method [7] and was above 87% across the band.


Table 6.1: Measured and simulated efficiency of metamaterial meander antenna

Frequency ηRad Simulated ηRad Measured

3.6 GHz 97% 96.1%

4.3 GHz 98% 87.4%

5.5 GHz 99% 91.1%

3 4 5 6 70.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Frequency (GHz)

η Rad

Figure 6.8: Simulated radiation efficiency of standard ( ) and metamaterial ( )

meander antennas.

Also, Figure 6.8 compares the simulated efficiencies of both the standard meander an-

tenna and the metamaterial version. Despite the out-of-phase versus in-phase currents,

both antennas achieve close to 100% efficiency across the operating band and conse-

quently, the radiation efficiency does not improve with metamaterial loading. There are

several reasons for this result. First, the loss associated with this antenna (RLoss) is ex-

pected to be negligible since we use a high-quality substrate and avoid narrow conductors

which would contribute to conductor loss. Since the radiation efficiency is given by

ηRad =RRad

RRad +RLoss (6.2)

for a small RLoss, the efficiency would be nearly constant even as the radiation resistance

RRad is changed. Second, as noted earlier, the primary radiator is the ground plane and

not the antenna itself and so changes to the current on the antenna’s arms have only


a minor impact on its radiation properties. Finally, the effect of out-of-phase currents

cancelling the radiated fields assumes these currents are of equal magnitude on both

antenna arms and consequently, for the metamaterial antenna to avoid this effect, its

sections would ideally have in-phase currents also of equal magnitudes. However, from

Figure 6.5, the magnitude is clearly not constant on both arms over the entire operating

band. The relative phase difference itself is also not constant at exactly 0° : it changes

with frequency, and above approximately 11.5 GHz (where an additional resonance ap-

pears as seen in Figure 6.9), the two currents become out-of-phase. These effects conspire

to render the initial purpose of this work infeasible with the current design. Neverthe-

less, this investigation has still resulted in a novel, high-efficiency, ultra-wideband antenna

whose bandwidth has been increased by 66% compare the unloaded printed meandered

monopole.

2 4 6 8 10 12 14−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

Figure 6.9: S11 of metamaterial meander antenna over extended frequency range.

6.3 Two-Antenna System with Low Mutual Coupling

6.3.1 Introduction

Given the excellent single antenna results, a two-antenna system with a small size was

sought in which low mutual coupling could be obtained while yet preserving the individual

wideband return-loss characteristics already described. Such a device would have several

advantages: first, due to the decoupling, multiple antennas could occupy a smaller space

with little impact on their individual performance, and second, these antennas could have


potential uses in MIMO (multiple-input, multiple-output) technology. In this latter role,

a low coupling, (described here using the S -parameters’ transmission gain S21) can be

related to the correlation coefficient between two antennas. Low coupling, and hence,

low correlation, implies the channels seen by the individual antennas are independent,

thus leading to higher overall data rates [8].

6.3.2 Exciting Two Characteristic Modes on a Ground Plane

The characteristic modes of a structure depend upon its size and shape, and are inde-

pendent of any kind of excitation [9]. They are derived from the eigenvalue equation

X( ~Jn) = λnR( ~Jn) (6.3)

where λn are the eigenvalues, Jn are the eigenvectors or eigencurrents, and X and R

form the impedance operator Z, relating the surface current density ( ~J) to the tangential

electric field on the surface of the conducting structure:

~Etan = Z ~J = (R + jX) ~J. (6.4)

The eigencurrents form the natural resonating modes of the structure and maximize the

radiated power; importantly for this application, they are, by definition, orthogonal and

the coupling between these modes is zero. Therefore, to obtain two decoupled antennas,

we seek to excite two characteristic modes on the same ground plane over the same

frequency band. The challenges, however are that different modes do not share the same

resonance frequency (the frequency at which the eigenvalue equals zero and the radiated

power is maximized), and that any given mode may not be excited for the antenna’s

chosen feed port locations.

With surface current density plots from HFSS, our approach is illustrated in Fig-

ure 6.10 using initially two different ground plane sizes at the same frequency. In Fig-

ure 6.10(a), the ground plane is electrically smaller to excite a half-wave mode and when

the ground becomes larger as in Figure 6.10(b), a full-wave resonance is supported. These

two current distributions qualitatively correspond to two characteristic modes of a rect-

angular ground plane [10]. Since it is not practical to dynamically change the size of the

ground plane, the novel approach used here is to combine both ground shapes into one,

as illustrated in Figure 6.11. The intent was to allow each antenna to excite different

modes on different areas of the ground, and various configurations (including tapering

the transition between the two ground regions) were investigated. The figure shows the


optimal geometry. This figure also shows that at a frequency of 4 GHz, either a half-wave

or full-wave mode is excited depending on which antenna is active. Consequently, low

coupling between the antennas can be achieved.

(a)

(b)

Figure 6.10: Ground plane surface current plots and schematics at 4 GHz for ground

plane widths of (a) 30 mm and (b) 50 mm.

(a) (b)

Figure 6.11: Simulated surface current distribution on modified ground plane showing

(a) Antenna 1 (on top) exciting the half- wave mode and (b) Antenna 2 (on bottom)

exciting the full-wave mode.


To verify that two orthogonal modes are indeed being excited, the FEKO simulation

tool was used to perform a characteristic mode analysis on the antenna of Figure 6.11.

Both half-wave and full-wave modes are obtained, as shown in Figure 6.12. These two

modes maintain their same current distribution between 3 GHz and 4.5 GHz. The eigen-

value of the two modes versus frequency is plotted in Figure 6.13(a), showing that the

resonance frequency of each mode is close.

(a)

(b)

Figure 6.12: (a) Current distributions simulated in FEKO for (a) half-wave characteristic

mode and (b) full-wave characteristic mode.


1.5 2 2.5 3 3.5 4 4.5 5 5.5−10

−7.5

−5

−2.5

0

2.5

5

Frequency (GHz)

Eig

enva

lue

Mag

nitu

de

Half−waveFull−wave

(a)

2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (GHz)

Nor

mal

ized

Exc

itatio

n C

oeffi

cien

t

Ant. 1 Active: Half−waveAnt. 1 Active: Full−waveAnt. 2 Active: Half−waveAnt. 2 Active: Full−wave

(b)

Figure 6.13: (a) Eigenvalues of full-wave and half-wave characteristic modes. (b) Nor-

malized excitation coefficients for both modes for individual antenna excitation.

Another important parameter is the modal excitation coefficient, which describes

how effectively the mode is excited for a particular feed location [11]. Figure 6.13(b)

shows that between 3 GHz and 4.5 GHz, when Antenna 2 excites the full-wave mode,

Antenna 1 excites the half-wave mode more effectively than it does the full-wave, thus

leading to reduced coupling between the antennas; however, it is observed that Antenna 2

also excites the half-wave up to 4 GHz, and so there is still some finite coupling. At

4.5 GHz and beyond, the current distribution of the modes changes, and so the pattern


of excitation between antennas 1 and 2 also changes. Nevertheless, these results are

consistent with the HFSS field plots above.

6.3.3 Simulated and Measured Results

The two-antenna system, shown in Figure 6.14, was fabricated on the same substrate

mentioned previously. To accommodate the feed cables, the antennas had to be moved

farther apart than in initial simulations and are separated by 10 mm which corresponds

to λ0/5 at the highest frequency.

(a)

(b) (c)

Figure 6.14: (a) Dimensions of two-antenna system and photographs of fabricated de-

vices’s (b) top layer and (c) bottom layer.

The simulated and measured S -parameters are shown in Figure 6.15. Overall, good

agreement is obtained between the two sets of data. A very wide measured return-loss

bandwidth from approximately 3.3 GHz to 6 GHz is achieved and the coupling between

the two antennas never exceeds −20 dB over that interval. Perhaps as a result of the non-

ideal coaxial feeds connectors being soldered onto the ground plane (and thereby affecting

the ground plane current distribution) the coupling performance is actually better than

that predicted by simulation. It is interesting to note that in simulation the coupling

levels remain approximately the same even as the antenna lateral spacing decreases from


the case shown in Figure 6.14 to that of Figure 6.11. Finally, beyond approximately

4.5 GHz the simulated S21 magnitude increases and nears −10 dB. Above this frequency,

the full-wave and half-wave modes are not excited independently by the two antennas;

indeed a half-wave distribution appears regardless of which antenna is active and this

accounts for the observed increase in coupling.

1 2 3 4 5 6 7 8−60

−50

−40

−30

−20

−10

0

Frequency (GHz)

Mag

nitu

de (

dB)

Figure 6.15: Measured (solid lines) and simulated (dotted lines) S-parameters for two

antenna system: S11 ( ); S22 ( ); S21 ( ).

The correlation between the two ports can be calculated using the S -parameters and

radiation efficiencies [12]:

ρ12 =

∣∣S∗11S12 + S∗21S22

∣∣∣∣(1− |S211| − |S2

21|)(1− |S222| − |S2

12|)ηRad1ηRad2∣∣ 12 (6.5)

Figure 6.16 plots the resulting correlation coefficient determined from the simulated

S -parameters where it is seen that over the operating band the correlation is less than

0.1; a value of 0.3 has been set as an acceptable limit for current wireless systems [13].


1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (GHz)

Cor

rela

tion

Coe

ffici

ent

Figure 6.16: Correlation coefficient calculated from simulated S -parameters.

Figure 6.17 compares the measured and simulated radiation patterns for each in-

dividual antenna where roughly omni-directional patterns are obtained. The greatest

discrepancy occurs in the backlobe of the E-plane of the antennas and is due to radiation

from both the feed cable and the 50 Ω load used to terminate the non-fed antenna which

was not completely suppressed. Overall, however, the behaviour of the fabricated device

shows very good agreement with its simulated counterpart. Finally, Table 6.2 gives the

radiation efficiencies for each antenna. Although lower than those predicted by simula-

tions (which use ideal feeding ports), the measured values range from 79% to 85% across

the band and demonstrate good performance. The discrepancy between simulated and

measured values may again be attributed to the two large coaxial connectors soldered

to the ground plane, which affect the radiating currents. Furthermore, the 0.254 mm

substrate used here is thin and very flexible and so the weight of both connectors warps

the board, bending both ground and antennas away from the simulated planar structure.


−10.4

−10.4

−3.2

−3.2

4 dB

4 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(a)

−10.4

−10.4

−3.2

−3.2

4 dB

4 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(b)

−10.0667

−10.0667

−2.5333

−2.5333

5 dB

5 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(c)

−10.7333

−10.7333

−3.8667

−3.8667

3 dB

3 dB

90o

60o

30o

0o

−30o

−60o

−90o

−120o

−150o

180o

150o

120o

(d)

Figure 6.17: Measured (solid lines) and simulated (dashed lines) radiation patterns at

3.5 GHz ( ), 4.5 GHz ( ), and 5.5 GHz ( ). (a)-(b) Gain-φ in xz-plane for antennas

1 and 2. (c)-(d) Gain-θ in xz-plane for antennas 1 and 2.


Table 6.2: Measured and simulated efficiency of two-antenna system

Frequency Antenna 1 ηRad Antenna 2 ηRad

Meas. Sim. Meas. Sim.

3.5 GHz 79% 94% 84% 95%

4.6 GHz 78% 98% 80.5% 98%

5.8 GHz 86% 99% 79% 99%

6.4 Conclusion

Metamaterial meander-line antennas have been used to create a two-antenna system

that has a very wide 2.7 GHz return loss bandwidth and low −20 dB coupling despite

having a maximum separation of only λ0/5. The metamaterial loading on each individual

antenna results in co-directed currents and introduces a second resonance which increases

bandwidth; the novel ground plane shape allows for two orthogonal modes to be excited

thus leading to excellent isolation and low correlation. Although the original goal of

improving radiation efficiency was not achieved, the combination of small size, good

matching, high decoupling, and high radiation efficiency makes this new design well-

suited for use in next-generation mobile handset radios.


6.5 References

[1] L. Jian-Ying, Y.Y. Kyi, and G.W. Beng, “Analysis of dual-band meander line

antenna,” in IEEE Int. Symp. Antennas & Propagation, Albuquerque, NM, 2006,

pp. 2033-2036.

[2] H.M. Hsiao J.-W. Wu, J.-H. Lu, Y.-D. Wang, “Multi-band dual-meander-line an-

tenna for mobile handsets,” in IEEE Int. Symp. Antennas & Propagation, Albu-

querque, NM, 2006, pp. 4705-4708.

[3] M.J. Ma and K. Deng, “The study and implementation of meander-line antennas

for an integrated transceiver design,” M.S. thesis, Dept. of Tech. & Built Environ.,

Univ. of Gavle, Gavle, Sweden, 2010.

[4] G. V. Eleftheriades and K. G. Balmain, “Negative-Refractive-Index Transmission-

Line Metamaterials” in Negative Refraction Metamaterials: Fundamental Princi-

ples and Applications, Hoboken, NJ: John Wiley & Sons, 2005, ch. 1, pp. 19-20.

[5] C.G.M. Ryan and G.V. Eleftheriades, “Two compact, wideband, and decoupled

meander-line antennas based on metamaterial concepts,” IEEE Antennas & Wire-

less Propag. Lett., vol. 11, pp. 1277-1280, November, 2012.

[6] R. W. Ziolkowski and A. Erentok, “At and below the Chu limit: passive and active

broad bandwidth metamaterial-based electrically small antennas,” IET Microw.,

Antennas & Propag., vol. 1, no. 1, pp. 116-128, February, 2007.

[7] W.E. McKinzie, III, “A modified Wheeler cap method for measuring antenna ef-

ficiency,” in IEEE Int. Symp. Antennas & Propagation, Montreal, Canada, July

1997, pp. 542-545.

[8] M. S. Sharawi, “Printed MIMO Antenna Systems: Performance Metrics, Implemen-

tations and Challenges,” Forum in Electromagnetic Research Methods and Appl.

Technol., vol. 1, February, 2014.

[9] M. Capek, P. Hazdra, P. Hamouz, and J. Eichler, “A method for tracking charc-

teristic numbers and vectors,” Progress in Electromagnetic Research B., vol. 33,

pp. 115-135, 2011.

[10] M. Cabedo-Fabres, E. Antonino-Daviu, A. Valero-Nogueria, and M. Bataller, “The

theory of characteristic modes revisited: a contribution to the design of antennas for


modern applications,” IEEE Antennas & Propag. Mag., vol. 49, no. 5, pp. 52-68,

October, 2007.

[11] M. Cabedo-Fabres, “Systematic design of antennas using the theory of character-

istic modes,” Ph.D. dissertation, Polytechnic Univ. of Valenica, Valencia, Spain,

2007.

[12] P. Hallbjrner, “The significance of radiation efficiencies when using S-parameters

to calculate the received signal correlation from two antennas,” IEEE Antennas &

Wireless Propag. Lett., vol. 4, pp. 97-99, June, 2005.

[13] M. S. Sharawi, “Printed multi-band MIMO antenna systems and their performance

metrics,” IEEE Antennas & Propag. Mag., vol. 55, no. 5, pp. 218-232, October 2013.

Chapter 7

Transparent Circularly-Polarized

Patch Antennas using Metamaterial

Loading

7.1 Introduction

In contrast to traditional satellite technology which is the preserve of large and well-

funded government agencies, miniature satellites are designed and controlled by small

teams of researchers around the world and so must be relatively inexpensive in order

to achieve widespread use. The small size of these satellites, however, means that their

usable surface area is at a premium as solar cells must cover the exterior to provide power

while still leaving enough space for the inclusion of antennas and other sensors. This

chapter addresses that conflict and presents an antenna that is easily manufacturable

and which sits directly on top of a satellite’s solar cell panel, balancing both power

generation requirements and RF performance.

7.2 Background

There are two main types of transparent antenna that would be suitable for our purpose:

those that use the wire-mesh approach [1] and those which use transparent conductive

oxides (TCO) (such as Indium-Tin-Oxide or Aluminum-Zinc-Oxide, for example). Al-

though near-total optical transparency can be achieved using these transparent metals,

their main drawbacks are their cost and high loss [2]. Wire-mesh antennas, on the other

hand, are inexpensive and simple: solid metal surfaces are divided into fine grids with

124

Chapter 7. Transparent Circularly-Polarized Antennas 125

small electrical spacing between elements. Thus, light can pass through the grid but at

microwave frequencies the antenna still electrically resembles a solid metal piece. De-

pending on the width of the grid lines, high antenna transparency can again be achieved,

but the supporting substrate must be equally transparent and consequently is often made

of quartz or plastic films which present separate fabrication challenges.

As a third option, we present transparent patch antennas that use the wire-mesh

approach and are built not on a glass wafer, but on standard ceramic substrates; we do

this by cutting the same grid pattern into both the antenna and substrate. Standard

microwave fabrication techniques can then be used, thus making the construction easier

and cheaper. Furthermore, our antennas are circularly-polarized (CP), as is usual for

satellite antennas: CP antennas are used to avoid polarization mismatch loss if the

satellite rotates with respect to its ground station or if the signal is distorted as it passes

through the atmosphere [3].

We achieve dual-band circular polarization by applying metamaterial concepts to one

patch antenna, instead of the more usual techniques of using stacked patches (where

individual CP patches are tuned to resonate at different frequencies) [4] or slot-loaded

patches (in which slots alter the electrical path length and relative phase difference of

the patch’s orthogonal modes) [5]. A metamaterial-based dual-band CP antenna was

reported in [6] but is not suitable for our purpose since its second metamaterial antenna

embedded within a conventional patch occupies a large area and would make increas-

ing antenna transparency difficult. Our own metamaterial-inspired mesh-grid approach

yields a potentially simpler and more intuitive design [7].

This chapter first describes the design of a single-band CP transparent patch an-

tenna and then shows how metamaterial concepts may be applied to yield dual-band

performance. Simulated and measured results for both antennas are presented.

7.3 Single-band Circularly-Polarized Transparent

Antenna

7.3.1 Antenna Design

To produce circular polarization, two orthogonal radiators must be excited with equal

amplitudes and a 90° relative phase difference. A simple method of achieving this is

the truncated square patch [8], shown in Figure 7.1. The two orthogonal modes are the

diagonal modes of the patch and the required phase shift is obtained from the truncated

corners and the offset feed point. As mentioned above, we employ the “wire-mesh”


approach in which a solid metal patch is divided into a grid. There are two important

effects of this meshed conductor. First, the resonant frequency of the meshed patch

antenna is lower than that of a solid metal patch since current flowing vertically, for

instance, will also flow on the horizontal conductor lines and so the overall electrical

path length is greater [9]. Second, the radiation efficiency of the patch antenna decreases

as the patch becomes more transparent. The current density on a solid patch is highest

at the patch edges, whereas for the meshed conductor, the density remains high over all

the conductor lines; this leads to greater conductor losses and lower efficiency as the lines

are made narrower.

Figure 7.1: Photograph of fabricated single-band antenna. The patch is a truncated

corner square of side length 35.75mm, built on a 60mil Rogers 4003 substrate.

These effects hold true for the present design, but because the grid pattern is also

applied to the substrate and not solely to the patch and ground metallization, the impact

of grid density on resonant frequency is reduced. Figure 7.2(a) plots the S11 for a solid

metal patch, a patch in which the grid is applied to the metallization layers only, and

a patch in which both substrate and metal have the grid pattern. Figure 7.2(b) shows

the effect of antenna transparency on the resonant frequency both for the “fully-gridded”

antenna and for the “partially-gridded” antenna (i.e. that with patch and ground grids

only). The result is that applying the grid to the metal lowers the resonant frequency,

but applying it to the substrate reduces the effective permittivity (since there are now

air gaps in the substrate) which raises the resonant frequency. As in Figure 7.2(b), these

two trends largely cancel out as antenna transparency is changed.


1 1.5 2 2.5 3−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

No gridPatch & GNDgridFull grid

(a)

1.5 1.75 2 2.25 2.5−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

Full Grid: 10% TransparentFull Grid: 30% TransparentFull Grid: 70% TransparentPartial Grid: 10% TransparentPartial Grid: 30% TransparentPartial Grid: 70% Transparent

(b)

Figure 7.2: (a) Effect of grid on S11 of CP patch antenna. (b) Effect of varying grid

density on S11 of CP patch antenna

For this design, the grid spacing was chosen to be less than λg/10 and the line width

selected primarily to maximize transparency. However, thin and delicate grid lines make

the antenna more difficult to fabricate as these lines are prone to warping and breaking.

Thus, the grid spacing (3 mm corresponding to 0.04λ at 2.3 GHz) was selected as a

compromise between antenna performance and what could be reasonably manufactured.

The antenna was fabricated on a 1.524 mm Rogers 4003 substrate, and with the

chosen grid pattern, 70% of the material has been removed from the patch area.



Figure 7.3(a) shows the measured S11 for the single-band CP antenna and compares it

to the frequency response simulated in HFSS. We obtain good matching at our design

frequency and close agreement between measured and simulated data; the broadside

axial ratio, shown in Figure 7.3(b), is below 3 dB over the operating band and verifies

that the antenna radiates a circularly-polarized wave. The peak gain of the antenna

at broadside is 4.1 dB and was calculated according to [12] using two linear x- and

y- polarization gain measurements and a correction factor determined from the axial

ratio; the result versus frequency is also given in Figure 7.3(b). Figures 7.3(c)-7.3(d)

show the simulated 3-D gain pattern and axial ratio. Finally, the radiation efficiency of

this antenna was estimated following [13]. Since the standard Wheeler Cap efficiency

measurement assumes a single mode present on the antenna, this new method involves

taking the average of two measurements at frequencies slightly above and below the CP

operating band where the antenna is more linearly polarized. This yields a measured

efficiency of 69%, which is reasonably close the value of 65% simulated in HFSS. This

somewhat low efficiency is the cost of increased transparency; nevertheless, this antenna

still shows good performance.


2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

SimuatedMeasured

(a)

2.2 2.205 2.21 2.215 2.22 2.225 2.23 2.235 2.240

1

2

3

Axi

al R

atio

(dB

)

Frequency (GHz)2.2 2.205 2.21 2.215 2.22 2.225 2.23 2.235 2.24

2

3

4

5

RH

C G

ain

(dB

)

(b)

(c) (d)

Figure 7.3: (a) Simulated ( ) and measured ( ) S11 of the single-band circularly-

polarized antenna. (b) Measured axial ratio and RHCP gain at broadside versus fre-

quency. Simulated (c) 3-D gain pattern and (d) 3-D axial ratio at 2.24 GHz.


7.4 Dual-band Transparent Circularly-Polarized

Antenna with Metamaterial Loading

7.4.1 Antenna Design

As is well known, NRI-TLs produce a single insertion phase at two different frequencies

[6] and by applying this metamaterial concept to a resonant structure, we seek to intro-

duce a 90° phase difference between the orthogonal modes of the patch at two frequencies.

To illustrate this concept, Figure 7.4 shows a possible equivalent circuit of the proposed

design. Based on the transmission-line model of a microstrip patch antenna, the four

radiating patch edges and fringing capacitances are represented by RRad and CF , respec-

tively, while the distance from each edge of the patch to the feed point is modelled by a

transmission line; the metamaterial loading in each orthogonal direction is denoted by se-

ries capacitors CMM,X/Y and shunt inductors LMM,X/Y . The input impedance seen at the

feed point depends on the parallel impedance combinations of CF and RRad transformed

along the lengths of transmission line. The horizontal and vertical branches resonate

when the input reactance is zero and it can be understood that, with the addition of the

metamaterial components, there will be two such resonant frequencies in each branch

corresponding to the NRI-TL’s left- and right-hand bands.

Figure 7.4: Circuit model of metamaterial-loaded circularly-polarized patch antenna.


This simple circuit model ignores several aspects of the antenna, including the cou-

pling between fields emanating from opposite radiating edges and the radiation from the

capacitive slots and meandered inductors; this latter factor in particular did have a sig-

nificant impact and thus required an examination of the radiated fields for every design

iteration. Therefore, it is not the intention of this section to capture all the nuances of

the antenna’s behaviour, but merely to illustrate the concept behind the metamaterial-

loaded patch.

Figure 7.5(a) shows an enlarged schematic of the proposed antenna with its key di-

mensions, and the fabricated version is shown in Figure 7.5(b). The metamaterial loading

comprises a series interdigitated capacitor and a shunt meandered inductor which is con-

nected to the ground plane by a via. Each capacitor/inductor combination is adjusted

individually to create the required 90° phase shift between the orthogonal resonant modes.

The feed port is at the upper left corner of the patch to accommodate the metamaterial

components. For this dual-band antenna, 60% of the patch area is transparent while the

substrate area itself was increased to allow space for mounting screws which can secure

the antenna to an underlying solar panel.


(a)

(b)

Figure 7.5: (a) Enlarged section of HFSS model of transparent dual-band CP antenna.

The patch is 35 mm × 35 mm , each grid hole is 4.8 mm × 4.8 mm, and the lengths

of each meander-line inductor and interdigitated capacitor are as shown. The feed point

is at the upper left corner. (b) Photograph of fabricated antenna, which was built on a

50 mm × 40 mm 3.05 mm thick Rogers 6002 substrate.

7.4.2 Wheeler Matching Network

It was found necessary to include a matching network in the dual-band design. Since

a match at two frequencies is required, we use the modified Wheeler matching network

of [11] in which a shunt LC circuit (the printed implementation of which is shown in

Figure 7.6) is tuned to resonate at a frequency between the antenna’s two intended de-

sign frequencies and therefore provides inductive loading at the low band and capacitive

loading at the high band. The use of the Wheeler circuit, however, requires the antenna’s

impedance (prior to the inclusion of the matching network) to resemble that of a series

RLC circuit. To satisfy this condition, a length of transmission line inserted between


the match circuit and antenna feed transforms the antenna’s impedance (shown in Fig-

ure 7.7(a)) and ensures it is capacitive at the low band and inductive at the high band

(Figure 7.7(b)). Figure 7.7(c) shows the simulated input impedance after the matching

circuit is included. A coaxial cable feeds one end of the transmission line while the other

end connects to the antenna by a via running through both substrates; the grid pattern is

cut through both the antenna and matching circuit layers, thus preserving transparency.

(a)

(b)

Figure 7.6: (a) HFSS model of dual-band matching network; the microstrip line is 3 mmwide and 21 mm long on a 0.762 mm Rogers 6002 substrate. (b) Profile view of matchingcircuit integrated with patch antenna. The grid perforations are not shown.


0.2

0.5

1.0

2.0

5.0

+j0.2

−j0.2

+j0.5

−j0.5

+j1.0

−j1.0

+j2.0

−j2.0

+j5.0

−j5.0

0.0 ∞

(a)

0.2

0.5

1.0

2.0

5.0

+j0.2

−j0.2

+j0.5

−j0.5

+j1.0

−j1.0

+j2.0

−j2.0

+j5.0

−j5.0

0.0 ∞

(b)0.

2

0.5

1.0

2.0

5.0

+j0.2

−j0.2

+j0.5

−j0.5

+j1.0

−j1.0

+j2.0

−j2.0

+j5.0

−j5.0

0.0 ∞

(c)

Figure 7.7: (a) S11 of antenna without matching circuit. (b) S11 of antenna with inter-

mediate transmission line. (c) S11 of antenna with matching circuit.


The S11 frequency response for the dual-band transparent CP antenna is given in Fig-

ure 7.8. Due to the inclusion of the Wheeler matching network which results in a multi-

layer structure, the fabrication of this antenna is more complicated: the main difficulties

are in obtaining a good electrical connection between the two ground planes and in main-

taining the rigid integrity of the two substrates; the matching network in particular is

fragile and can easily be bent and distorted. Several attempts were made to overcome

these challenges, including soldering the two ground planes together with solder paste

and bonding them with a conductive epoxy. Perhaps ironically, the best solution was


simply to use nylon screws to secure the layers together. In the end, although there

is a discrepancy between simulated and measured data, the fabricated antenna yields

two resonant frequencies very close to the intended operating bands and the matching

remains below -10 dB.

2.2 2.3 2.4 2.5 2.6 2.7 2.8−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

SimulatedMeasured

Figure 7.8: Simulated ( ) and measured ( ) S11 of the dual-band circularly-

polarized antenna.

As a verification that the metamaterial-loaded patch is indeed producing two orthog-

onal modes, a plot of the simulated electric field in the substrate, obtained from HFSS, is

shown in Figure 7.9. At frequencies slightly higher and lower than the CP resonance, the

antenna should display one of the excited orthogonal modes since the antenna is more

linearly polarized in these frequency regions. For the first CP band at approximately

2.35 GHz, the field plots are taken at 2.3 GHz and 2.4 GHz (Figures 7.9(a) and 7.9(b),

respectively). A half-wave variation is evident in the electric field in the x-direction at

the lower frequency, while the same variation occurs along the y-direction at the higher

frequency; thus, these fields correspond to the TM10 and TM01 modes. The second

CP band occurs at approximately 2.7 GHz and the fields plots are shown for 2.65 GHz

(Figure 7.9(c)) and 2.75 GHz (Figure 7.9(d)). Now, the TM01 mode occurs below the

CP resonance and the TM10 is above; this is the reverse of the situation at the lower

frequencies and indicates that the antenna radiates a circularly-polarized wave in both

the right-handed and left-handed senses. Furthermore, these field plots confirm that it is

the fundamental mode of the patch that is excited at both CP bands; we are not using

higher-order modes as the multi-band CP antennas cited earlier do.


(a) (b)

(c) (d)

Figure 7.9: Field plots of the electric field inside the substrate at (a) 2.3 GHz; (b) 2.4 GHz;

(c) 2.65 GHz; and (d) 2.75 GHz.


Figure 7.10 shows the measured axial ratio and measured CP gain data at broadside

across the two operating bands. For this antenna, right-handed and left-handed circular

polarization is obtained at the lower and higher frequency ranges, respectively. Since

they are very similar to those of the single-band antenna, the simulated 3-D gain and

axial ratio patterns are not repeated. Overall, the measured peak gains are 1.1 dB and

1.2 dB below the simulated values for each of the two bands which are reasonable results

considering the already-mentioned difficulties encountered in fabrication. The efficiencies

of the dual-band transparent antenna were determined to be 70% and 78% at the two

bands, respectively. The efficiency at the high band is actually greater than the simulated

value: as mentioned, [13] assumes a single mode of operation but the low axial ratio

values of Figure 7.10(a) indicate there are two modes present over a wide bandwidth,

thus leading to small errors in the efficiency. The results are still in reasonably close

agreement and are summarized in Table 7.1.

Table 7.1: Summary of results for dual-band antenna

Parameter Simulated Measured

Operating Frequency 2.35 GHz/2.71 GHz 2.35 GHz/2.73 GHz

Peak Gain 5.5 dB/6 dB 4.4 dB/4.8 dB

Radiation Efficiency 73%/74% 70%/78%


2.3 2.35 2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.75 2.80

5

10

15

Frequency (GHz)

Axi

al R

atio

(dB

)

(a)

2.3 2.32 2.34 2.36 2.38 2.4−2

−1

0

1

2

3

4

5

Frequency (GHz)

RH

CP

Gai

n (d

B)

(b)

2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.762

2.5

3

3.5

4

4.5

5

Frequency (GHz)

LHC

P G

ain

(dB

)

(c)

Figure 7.10: (a) Measured axial ratio at broadside versus frequency. (b)-(c) Measured

circularly-polarized gain at broadside for lower and upper bands, respectively.


7.5 Solar Panel Transparency Testing

The transparency figures cited so far have been based simply on the percentage of metal

removed from the antenna area. Both single- and dual-band antennas were also tested on

solar panel backings to determine what power levels could reasonably be achieved in each

case. The single-band antenna was redesigned since its original feed would have required

a hole for the coaxial cable to be drilled through the solar panel, and the new approach

uses an edge-mounted coaxial feed which does not interfere with the underlying panel.

Furthermore, the original antenna was designed in a free-space environment without

considering the solar panel backing and so redesigning the antenna offered the opportunity

to correct this oversight. Since the optimization of the dual-band antenna proved to be

difficult and time-consuming, no revised version of it was completed and the transparency

testing used the version described in Section 7.4.

(a) (b)

Figure 7.11: (a) Single-band CP antenna and (b) dual-band CP antenna on solar panel.

The updated single-band antenna and the dual-band antenna are shown in Fig-

ures 7.11(a) and 7.11(b) respectively with the solar panel included (each antenna was

simply placed on top of the panel with no extra adhesives or mounting hardware). To

test the transparency of each design, the output power of the solar cell with and without

the antenna layers was measured and compared. Testing was performed outside with the

sun as the source; during the testing period, the sky was cloudless, the sun’s elevation was

roughly constant (according to U.S Naval Observatory tables, the elevation was between

63.7°and 67.1°), and the temperature of the solar panel was monitored and stabilized as

needed. Furthermore, the solar panel and antenna assembly was placed in a lidless box


which sheltered the panel from any wind gusts. These precautions were taken to avoid

sudden temperature changes in the solar panel which can affect efficiency and to ensure

that a valid comparison could be made between each test case. Finally, because each test

could be completed in approximately one minute, the incident solar power for each case

was assumed to be constant. To confirm these results, each test was run a second time,

with nearly identical outcomes.

Figure 7.12 plots the measured Power-Voltage curves for the solar panel in isolation and

in combination with each of the two antennas under test. The single-band antenna has

approximately 70% of its surface area removed and the peak power generated was 70%

of that of the uncovered solar panel. The dual-band antenna has a total of 40% of its

surface area removed (this number is low due to the increased substrate size which allows

mounting screws to be included) and its peak power was approximately 50% compared

to the uncovered solar panel. An additional factor which lowered the dual-band trans-

parency was the increased thickness of its 3.05 mm substrate compared to the single-band

antenna on a 0.762 mm substrate. When the light source is not exactly at the antenna’s

broadside direction, the high grid walls cast shadows on the solar panel, thus reducing

the power generated; subsequent versions should therefore be produced on the thinnest

possible substrate. Furthermore, subsequent simulations have shown that the grid can

be extended beyond the patch metallization to cover the entire substrate; in this manner,

60% of the total surface area could be removed and so the transparency would naturally

increase.


0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Voltage (V)

Pow

er (

W)

Solar Panel AloneSolar Panel w/ Single−band Ant.Solar Panel w/ Dual−band Ant.

Figure 7.12: Measured power vs. voltage characteristics for solar panel alone ( ), for

single-band antenna on solar panel ( ) and for dual-band antenna

on solar panel ( ).

Finally, the S11 of the new single-band design was tested with the underlying solar

panel in place. The result is shown in Figure 7.13. Following [14], the solar panel was

modelled as a bulk silicon/gallium arsenide medium with a small conductivity (σ =

10 Siemens/m and εr = 12.5), backed by a conductive ground plane. As seen in the

figure, the patch’s measured resonant frequency is shifted but is still relatively close to the

intended operating point. As mentioned in [14], the conductivity of a solar panel can vary

with production process, but simulations varying σ from 0.1 to 100 show this parameter

has little effect on the antenna’s S11 response. Therefore, to resolve the discrepancy

between measured and simulated results, a solar panel medium with a higher permittivity

should be used instead in simulation.


2 2.2 2.4 2.6 2.8 3−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

SimulatedMeasured

Figure 7.13: Comparison of simulated ( ) and measured ( ) S11 of new single-band

CP antenna with solar panel backing.

7.6 Conclusion

Circularly polarized patch antennas have been demonstrated which use a simple grid of

perforations to improve optical transparency and as a result, neither transparent metals

nor transparent substrates are required and fabrication can follow a standard microwave

lithography process. Dual-band operation is achieved by incorporating metamaterial

components onto a patch, which controls the relative phase difference between the an-

tenna’s fundamental orthogonal modes. Overall, good measured results have been ob-

tained, although the fabrication challenges of the dual-band design led to a slight decrease

in performance compared to the simulated results. Finally, these antennas were tested

in conjunction with solar panels and up to 70% transparency was achieved.


7.7 References

[1] T. W. Turpin and R. Baktur, “Meshed patch antennas integrated on solar cells,”

IEEE Antennas & Wireless Propag. Lett., vol. 8, pp. 693-696, July, 2009.

[2] J. R. Saberin and C. Furse, “Challenges of optically transparent patch antennas,”

IEEE Antennas & Propag. Mag., vol. 54, no. 3, pp. 10-16, June, 2012.

[3] T.N. Thi, K.C. Hwang and H.B. Kim, “Dual-band circularly-polarised spidron frac-

tal microstrip patch antenna for Ku-band satellite communication applications,”

IET Electron. Lett., vol. 49, no. 7, March, 2013.

[4] A. Narbudowicz, X. L. Bao, and M. J. Ammann, “Dual-band omnidirectional cir-

cularly polarized antenna,” IEEE Trans. Antennas & Propag., vol. 61, no. 1, pp.

77-83, January, 2013.

[5] Nasimuddin, Z. N. Chen, and X. Qing, “Dual-band circularly polarized S-shaped

slotted patch antenna with a small frequency-ratio,” IEEE Trans. Antennas &


[6] S. T. Ko, B.-C. Park, and J.-H. Lee, “Dual-band circularly polarized hybrid meta-

material patch antenna,” in Proc. Asia-Pacific Microw. Conf., November, 2013,

pp. 342-344.

[7] C.G.M. Ryan and G.V. Eleftheriades, “Single- and dual-band transparent circularly

polarized patch antennas with metamaterial loading,” IEEE Antennas & Wireless

Propag. Lett., vol. 14, pp. 470-473, November, 2014.

[8] P. C. Sharma and K. C. Gupta, “Analysis and optimized design of single-feed

circularly-polarized microstrip antennas,” IEEE Trans. Antennas & Propag., vol.

31, no. 6, pp. 949-955, November, 1983.

[9] G. Clasen and R. Langley, “Meshed patch antennas,” IEEE Trans. Antennas &


[10] G. V. Eleftheriades and K. G. Balmain, “Negative-Refractive Index Transmission-

Line Metamaterials” in Negative-Refraction Metamaterials : Fundamental Proper-

ties and Applications, Hoboken, NJ.: J. Wiley & Sons, 2005, pp. 11-18.

[11] M. Selvanayagam and G. V. Eleftheriades, “A compact printed antenna with an

embedded double-tuned metamaterial matching network,” IEEE Trans. Antennas

& Propag., vol. 58, no. 7, pp. 2354-2361, July, 2010.


[12] T. A. Milligan, “Properties of antennas” in Modern Antenna Design, 2nd ed., Hobo-

ken, NJ.: Wiley-IEEE, 2005, pp. 26-27.

[13] D.C. Nascimento and J. C. da S. Lacava, “Circularly polarized microstrip antenna

efficiency simulation based on the wheeler cap method,” in Proc. IEEE Int. Symp.

Antennas & Propag., June, 2009, pp. 1-4.

[14] T. Turpin and R. Baktur, “Integrated Optically Transparent Solar Cell Antennas

Made from Meshed Conductors,” in 22nd AAIA Conference on Small Satellites,

Logan, UT, 2008.

Chapter 8

Conclusion

8.1 Summary of Work

This thesis has explored the generalized negative-refractive-index transmission line, and

has shown how it and the simpler NRI-TL may be applied to the design of multi-band mi-

crowave circuits and antennas. From the Foster network representation of the G-NRI-TL,

it was shown how even more passbands could be implemented through the addition of

extra resonant elements and, although not explored further, this concept could be applied

immediately using the printed microstrip structure already developed.

Many TL-metamaterial-based devices have been presented here for the first time. A

dual-band leaky-wave antenna achieved frequency scanning and two broadside radiation

frequencies using a periodic arrangement of G-NRI-TLs. Although the fabricated antenna

did not perform well at one band, some methods to overcome both the manufacturing

difficulties as well as spurious radiation from the G-NRI-TL elements were suggested, and

an alternative layout of the LWA that shows good simulated performance was developed.

A G-NRI-TL-based dual-band coupled-line coupler was also developed and it showed

good correspondence between the equivalent circuit, full-wave simulation model, and

physical device. Through the proper choice of metamaterial circuit elements, both the

coupling level and the two operating frequencies can be specified, and the coupler is less

lossy and better matched than other G-NRI-TL dual-band couplers previously reported.

Due to its unity transmission magnitude, the all-pass version of the G-NRI-TL could

prove to be a very useful innovation as it allows large single-cell phase shifts without

encountering any band edges. It can be applied to many multi-band applications requir-

ing fixed TL electrical lengths, but only a sample few were chosen to assess the all-pass

circuit’s performance. Measured results were also good, and it was only the bandwidth

of the printed components themselves which limited the overall operating frequency.

145

Chapter 8. Conclusion 146

Finally, the G-NRI-TL unit cell was turned into a resonant antenna. Matched at

four frequencies with omni-directional patterns, the radiation efficiency is high and the

antenna construction is simple and inexpensive.

NRI-TLs were also applied to two antennas in this thesis. First, metamaterial loading

was applied to one arm of a meander-line antenna with the goal of creating co-directional

currents to improve radiation efficiency. Such currents were indeed observed in simula-

tion, but had little impact on antenna efficiency. These extra elements, however, formed a

second resonance, unexpectedly resulting in a compact, wideband antenna. A wideband,

decoupled two-antenna system was then created by exciting two orthogonal character-

istic modes on a ground plane. With its small size and broad bandwidth, this antenna

is ideal for use in MIMO-enabled handsets. Second, a dual-band circularly polarized

patch antenna was achieved using NRI-TL loading; series capacitors and shunt inductors

applied to one corner of a patch resulted in the required 90° phase shifts for orthogonal

modes at two frequencies. The patch itself was made optically transparent so that it

could be integrated directly on top of a solar panel for use on a microsatellite. Overall,

the dual-band antenna allowed approximately 50% of the solar energy through, although

this efficiency can be increased by extending the transparent gridding technique, by ori-

enting the antenna directly at the sun, and by using thinner substrates which result in

less shadowing.

In general, then, despite the complexity of the unit cell, a diverse array of prototype

multi-band devices with good performance has been produced. Some new directions

where NRI-TLs and G-NRI-TLs can be applied will be described to conclude this chapter,

after noting the specific contributions made to the field in the next section.

8.2 Contributions

A number of publications, which are listed below, have resulted from this work.

Refereed Journal Papers

1. C.G.M. Ryan and G.V. Eleftheriades, “Single- and dual-band transparent circularly

polarized patch antennas with metamaterial loading,” IEEE Antennas & Wireless

Propag. Lett., vol. 14, pp. 470-473, November, 2014.

2. C.G.M. Ryan and G.V. Eleftheriades, “Two compact, wideband, and decoupled

meander-line antennas based on metamaterial concepts,” IEEE Antennas & Wire-

less Propag. Lett., vol. 11, pp. 1277-1280, November, 2012.


3. C.G.M. Ryan and G.V. Eleftheriades, “Multiband microwave passive devices using

generalized negative-refractive-index transmission lines (invited paper),” Int. J. RF

& Microw. Computer Aided Eng., vol. 22, no. 4, pp. 459-468, July, 2012.

4. C.G.M. Ryan and G.V. Eleftheriades, “Design of a printed dual-band coupled-

line coupler with generalised negative-refractive-index transmission lines,” IET Mi-

crow., Antennas, & Propag., vol. 6, no. 6, pp. 705-712, April, 2012.

Refereed Conference Proceedings

1. C.G.M. Ryan and G.V. Eleftheriades, “A single-ended all-pass generalized negative-

refractive-index transmission line using a bridged-T circuit,” in Proc. IEEE MTT-S

Int. Microw. Symp. Dig., Montreal, Canada, June 17-22, 2012, pp. 1-3.

2. C.G.M. Ryan and G.V. Eleftheriades, “A wideband metamaterial meander-line

antenna,” in Proc. Eur. Conf. Antennas & Propag., Prague, Czech Republic,

March 26-30, 2012, pp. 2329-2331.

3. C.G.M. Ryan and G.V. Eleftheriades, “A printed dual-band coupler using gen-

eralized negative-refractive-index transmission lines,” in Proc. IEEE MTT-S Int.

Microw. Symp. Dig., Baltimore, USA, June 5-10, 2011, pp. 1-4.

4. C.G.M. Ryan and G.V. Eleftheriades, “A dual-band leaky-wave antenna based

on generalized negative-refractive-index transmission lines,” in Proc. Int. Symp.

Antennas & Propag., Toronto, Canada, July 11-17, 2010, pp. 1-4.

8.3 Future Work

This thesis has presented a few ideas which were explored in simulation, but not pursued

further. The single-layer leaky-wave antenna of Chapter 3 currently shows reasonably

good performance, but could benefit from fine-tuning before a physical version is pro-

duced. The G-NRI-TL-based multi-band resonant antennas discussed in the Appendix

are also interesting devices: well-matched at four frequencies and displaying high radi-

ation efficiency and omni-directional radiation patterns, the “crossed-dipole” version in

particular is ideally suited for use in cell phones and should be fabricated and tested.

Chapter 2 suggested the quad-band G-NRI-TL concept could be extended to higher-

order versions and demonstrated a printed unit cell that had six right-handed and left-

handed bands. With mobile radios processing multiple data streams and operating on

different standards between countries, antennas and microwave circuits with flexibility to


accommodate multiple bands are highly desirable, so devices based on this “hex-band”

transmission-line unit cell (or even higher-order versions of it) could find great use. The

challenge is that the complicated layout of the microstrip unit cell makes its response

time-consuming to tune and potentially increases its insertion losses. Nevertheless, it

provides a simple, easy-to-design, and compact method of creating multi-band microwave

components

In addition, extending the G-NRI-TL concept to millimetre-wave (mm-wave) frequen-

cies could be a fertile area of exploration. Due to the high path loss at mm-wave bands,

high-gain antenna arrays are often used to compensate, but the designer must then bal-

ance the link budget with the larger size of an array which could become incompatible

with small system-on-chip or system-in-package solutions. Furthermore, with the very

broad spectrum available (for instance, an unlicensed 57-64 GHz band in the United

States), multi-band or broadband communication systems are needed to exploit this

bandwidth. Metamaterial mm-wave antennas have made an appearance [1]-[3], but since

the primary motivation for using metamaterial concepts has been size reduction and not

dual-band or multi-band performance, there is ample opportunity to explore the benefits

of multi-band G-NRI-TLs in this field. Printed NRI-TL bandpass filters and coupled-line

couplers have also been produced on high-resistivity silicon substrates in [4]; however,

even the single-cell filter of this work suffered insertion losses of nearly 6 dB, and so

overcoming the high-conductor loss at mm-wave bands could be a significant challenge

in implementing more complex G-NRI-TL devices. These advances at least demonstrate,

however, the possibility of creating metamaterial devices at millimetre-wave frequencies

using current fabrication technology.

Finally, a longer-term goal is to automate the design of metamaterial components

so they could be created immediately from user-input performance requirements; such

a digital toolbox would add significant functionality to existing EM and RF circuit de-

sign packages. This automation could be achieved by combining NRI-TL and G-NRI-TL

circuit theory, existing semi-analytical formulas for printed circuit components, and op-

timization algorithms which are already part of commercial simulators.

Together, then, these new fields and applications show the G-NRI-TL has great po-

tential not only for future research, but also for deployment in real-world scenarios where

its compact size, simple construction, and broadband or multi-band performance can be

put to good effect. The demand for greater data rates in mobile devices, the opening of

new frequencies in the RF spectrum, and the ubiquity of potential applications mean that

these G-NRI-TLs are ideally suited to become indispensable components in microwave

transceiver systems.


8.4 References

[1] A.-C. Bunea, F. Craciunoiu, M. Zamfirescu, R. Dabu, and G. Sajin, “Laser ablated

millimeter wave metamaterial antenna,” in Int. Semiconductor Conf., Sinaia, 2011,

pp. 185-188.

[2] H. Zhang, R.W. Ziolkowski, and H. Xin, “A compact metamaterial-inspired mmW

CPW-fed antenna,” in IEEE Int. Workshop on Antenna Technology, Santa Monica,

CA, 2009, pp. 1-4.

[3] G. Sajin, I.A. Mocanu, F. Craciunoiu, and M. Carp, “MM-wave left-handed trans-

mission line antenna on anisotropic substrate,” in European Microwave Conf.,

Nuremberg, 2013, pp. 668-671.

[4] A.-C. Bunea, S. Simion, F. Craciunoiu, A.A. Muller, A. Dinescu, G. Stavrinidis,

and G. Sajin, “Metamaterial millimeter wave devices on silicon substrate: band-

pass filter and directional coupler,” in Int. Conf. on Computers as a Tool, Lisbon,

2011, pp. 1-4.

Appendix A

Multi-band Resonant G-NRI-TL

Antennas

This appendix presents two other antennas based on the G-NRI-TL unit cell. Only sim-

ulated results are given since these devices were never fabricated, but these two antennas

show good performance and would each be an interesting candidate for future develop-

ment. Each antenna makes use of the multiple 0° and 180° insertion phases of a single

G-NRI-TL unit cell to create either monopoles or dipoles that have electrical lengths of

a half-wavelength (or multiples thereof); these antennas are therefore compact, but op-

erate at multiple frequency bands. Illustrating the concept, Figure A.1(a) shows the unit

cell’s dispersion diagram and highlights the expected resonant frequencies. Figure A.1(b)

plots the S11 and S21 magnitudes of the printed cell showing the two passbands of the

cell extending from approximately 2 GHz - 2.7 GHz and from 3.5 GHz - 5.5 GHz. If N

cells were cascaded to form a resonant antenna, we would expect even more resonances

where the electrical length of the single cell (βd) satisfied

βd =nπ

N, n = ...,−1, 0, 1, ... (A.1)

Although the antennas of this section use a closed-stopband unit cell, it is clear that

deliberately opening the stopbands would yield a greater number of βd = 0° resonant

frequencies; exciting those resonances, however, depends on the kind of cell termination

and the open circuit applied below excites only the shunt-mode and not the series-mode

resonances. Therefore, the actual number of operating bands may not increase in a

practical resonant antenna which uses an open-stopband unit cell.

150

Appendix A. Multi-band Resonant G-NRI-TL Antennas 151

0 20 40 60 80 100 120 140 160 1801

1.5

2

2.5

3

3.5

4

4.5

5

5.5

βd (degrees)

Fre

quen

cy (

GH

z)

(a)

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5−40

−35

−30

−25

−20

−15

−10

−5

0

Mag

nitu

de (

dB)

Frequency (GHz)

S11

S21

(b)

Figure A.1: (a) Dispersion diagram of G-NRI-TL unit cell showing expected resonant

frequencies and (b) S-parameters of unit cell.

There are two challenges, therefore: first, the antenna must excite multiple resonant

frequencies and be matched at those points, and second (and depending on the intended

application), the radiation pattern of the antenna should be consistent over the operating

bands. Unlike the conventional NRI-TL, the shunt mode of the G-NRI-TL is dependent

not on a single shunt inductor, but on a combination of parallel resonant circuits; this

added complexity means the radiation pattern can vary from one frequency to the next.


The following two antennas attempt to address these issues.

A.1 Dual-band G-NRI-TL Monopole Antenna

Depicted in Figure A.2(a), this antenna is a single microstrip G-NRI-TL unit cell. It is fed

from a microstrip line and is terminated in an open circuit. To match the antenna at two

frequencies, a modified Wheeler matching network was included at the input which uses

a parallel combination of a capacitor (represented by the short sections of open-circuited

TL stubs) and an inductor (the vias connecting the antenna to an underlying ground

plane). Figure A.2(b) shows the equivalent circuit model of the antenna with matching

network and gives the L−C component values which were chosen to match the antenna

at 2.6 GHz and 4.3 GHz. These frequencies were chosen, first, to yield component values

which could be readily synthesized in a microstrip equivalent, and second, to obtain the

best possible match at at least two frequencies.

(a)

(b)

Figure A.2: (a) Illustration of printed G-NRI-TL antenna with matching network. (b)

Equivalent circuit model with component values as labelled.


The S11 of the resulting antenna is shown in Figure A.3(a) and the simulated radi-

ation patterns at both bands are depicted in Figure A.3(b) and Figure A.3(c). Good

matching is obtained at both intended frequencies and the antenna shows other reso-

nances which roughly correspond to the βd = 0° or βd = 180° frequencies of the unit

cell in Figure A.1(a). The field patterns at the two bands are not the same however: at

2.6 GHz (corresponding to the first βd = 0° frequency), the pattern appears monopolar

and is likely due to the vertical vias, whereas the upper band’s pattern has two distinct

lobes. This discrepancy may result from matching the antenna at a frequency between

its “natural” resonances, occurring at 3.7 GHz and 5.5 GHz according to Figure A.1(a).

An additional drawback is the small efficiency at the low band (56%, compared to the

high-band efficiency of 95%), and so this design was abandoned in light of more promising

results from the quad-band crossed-dipole antenna, as described in the next section.


1 2 3 4 5 6−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

Mag

nitu

de (

dB)

Circuit ModelHFSS

(a)

(b) (c)

Figure A.3: Simulated results of G-NRI-TL monopole antenna: (a) S11, (b) radiation

pattern at 2.6 GHz, and at (c) 4.3 GHz.

A.2 Quad-band Crossed-Dipole Antenna

This antenna is shown in Figure A.4(a). The term “crossed-dipole” is loosely applied

here, since the structure is still a microstrip antenna, with the metallization as shown

above ground plane. The coaxial feed is at the middle of the cross and each of the

G-NRI-TL cells terminates in an open circuit.


(a)

1 2 3 4 5 6−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S11

(dB

)(b)

Figure A.4: (a) Illustration of crossed-dipole antenna. (b) Simulated S11.

The development of this antenna began with the observation that because the open

circuit termination excites the shunt mode antiresonances, the G-NRI-TL unit cell has a

large input impedance at its operating frequencies; this single cell is difficult to match,

but combining four such unit cells in parallel lowers the impedance and from the plot of

S11 shown in Figure A.4(b), the antenna is indeed matched at four frequencies (the dip

in S11 at 5.35 GHz is due to a capacitor’s self-resonance). The substrate electric field

profile is shown in Figure A.5(a) and Figure A.5(b) where it be seen that either a 0° or

180° resonance is obtained at approximately the frequencies predicted by the single unit

cell’s dispersion diagram.


(a) (b)

Figure A.5: Substrate electric field plots showing (a) 0° resonance at 2.45 GHz and

3.85 GHz and (b) 180° resonance at 2.8 GHz and 5.6 GHz.

Finally, the simulated patterns and radiation efficiencies are presented for this antenna

at each of the four operating bands. In Figure A.6, the patterns are all similar to those

of a monopole antenna, indicating once again the role of the vias (and the coaxial feed

pin) in radiating. The rotational symmetry about the axis also helps to cancel radiation

from the shunt meander line/capacitive patch combination and so maintains a uniform

pattern. The gain is approximately constant and the efficiencies are all relatively high.


2.8 GHz2.45 GHz

ηrad

=80% ηrad

=85%

3.85 GHz 5.6 GHz

ηrad

=92%ηrad

=90%

X

YZ

Figure A.6: Radiation patterns and efficiencies of G-NRI-TL crossed-dipole antenna.

A.3 Conclusions

This appendix has presented the design and simulated results from two G-NRI-TL-based

resonant antennas. The cross layout in particular shows promise as a compact multi-band

antenna, and its simple structure makes fabrication straightforward and inexpensive.

Documents

Multi-band Microwave Antennas and Devices based on … · 2016-07-19 · a device, achieving quad-band operation between 2.5 GHz and 5.6 GHz, with a minimum radiation e ciency of