Microwave Devices and Antennas Based on Negative-Refractive-Index Transmission-Line ...

283 Pages·2009·5.42 MB·English

Microwave Devices and Antennas Based on
Negative-Refractive-Index Transmission-Line Metamaterials
by
Marc A. Antoniades
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Electrical and Computer Engineering
University of Toronto
Copyright (cid:2)c 2009 by Marc A. Antoniades
Abstract
Microwave Devices and Antennas Based on Negative-Refractive-Index
Transmission-Line Metamaterials
Marc A. Antoniades
Doctor of Philosophy
Graduate Department of Electrical and Computer Engineering
University of Toronto
2009
Several microwave devices and antennas that are based on negative-refractive-index
transmission-line (NRI-TL) metamaterials are presented in this thesis, which exhibit
superior performance features compared to their conventional counterparts. These are a
Wilkinson balun, a 1:4 series power divider, a four-element printed dipole array, a leaky-
wave antenna, and an electrically small folded-monopole antenna. The Wilkinson balun
employs+90◦ and−90◦ NRI-TLmetamateriallinesattheoutputbranchesofaWilkinson
divider, toachieve asix-foldincreaseinthemeasured differentialoutputphasebandwidth
compared to that of an analogous balun employing transmission lines, while occupying
only 55% of the area. The 1:4 series power divider comprises four non-radiating 0◦ NRI-
TL metamaterial lines, each with a compact length of λ /8, to provide equal power split
0
to all four output ports. Compared to a conventional series power divider employing one-
wavelength long transmission lines, the metamaterial divider provides a 154% increase
in the measured through-power bandwidth, while occupying only 54% of the area. The
metamaterial series power dividing concept is also applied to a four-element fully-printed
dipole array that is designed to radiate at broadside, in order to demonstrate that the
array exhibits reduced beam squinting characteristics. It is shown that the metamaterial-
fed arrayhas a measured scan-angle bandwidth that is 173%greater than anarraythat is
fed using a conventional low-pass loaded line. The reduced-beam squinting property that
NRI-TL metamaterial lines offer is subsequently exploited to create aleaky-wave antenna
ii
that radiates a near-fixed beam in the forward +45◦ direction, with an average measured
beam squint of only 0.031◦/MHz. This is achieved by operating the antenna in the upper
right-handed band where the phase and group velocities are the closest to the speed of
light. Finally, anelectrically smallantenna comprising four 0◦ NRI-TLmetamaterial unit
cells is presented which supports a predominantly even-mode current, thus enabling it
to be modeled as a multi-arm folded monopole. This significantly increases its radiation
resistance, which allows it to be matched to 50 Ω, while maintaining a high measured
efficiency of 70%.
iii
Αρχή σοφίας φόβος Κυρίου,
και βουλή αγίων σύνεσις·
το γάρ γνώναι νόμον,
διανοίας εστίν αγαθής.

Παροιμίαι Σολωμώντος, ΙΧ. 10

The fear of the Lord is the beginning of wisdom,
and the counsel of the saints is understanding;
for to know the law
is the character of a sound mind.

Proverbs 9:10

iv
Acknowledgements
I would like to express my sincere appreciation to my supervisor Prof. George V.
Eleftheriades, who has skilfully mentored me throughout my graduate studies. I am
grateful for all of your guidance and support, and for teaching me discerning new ways
to approach engineering problems. Perhaps more importantly, however, you have taught
me the importance of taking personal responsibility and pride in one’s own work and to
do all things in life with ethical integrity. For this and for our close friendship I am very
grateful.
I would like to thank Prof. Keith G. Balmain, Prof. Costas D. Sarris, Prof. Sean V.
Hum, Prof. Mo Mojahedi and Prof. Sergei Dmitrevsky of the Electromagnetics group for
numerous motivating discussions which have shaped my understanding of many concepts
in Electromagnetics. I would also like to thank Prof. Sarris, Prof. Hum, Prof. Mojahedi
and Prof. Michal Okoniewski from the University of Calgary for being members of my
Ph.D.examination committee andfor providing me with valuablefeedback on thisthesis.
I would like to acknowledge our lab managers Gerald Dubois and Tse Chan for their
assistance with the many practical aspects of my work. Thanks are also due to all of my
fellow graduate students in the Electromagnetics group who have greatly enriched my
graduate experience at U of T through our lively technical discussions, our adventurous
outings, as well as our many coffee breaks. Many of you I consider friends for life.
I would also like to acknowledge the financial support that I have received from
the Ontario Graduate Scholarship, the Ontario Graduate Scholarship in Science and
Technology, the Edward S. Rogers Sr. Ontario Graduate Scholarship, and the University
of Toronto Department of Electrical and Computer Engineering Graduate Scholarship.
Last but not least, I am deeply grateful for the support, love and encouragement of
my parents, my sister Margarita, my brother-in-law Vincent, and my beloved girlfriend
Diana. The journey throughout my graduate studies has been long and rewarding, but
one which I could not have completed without your prayers and loving support.
v
Contents
List of Acronyms x
List of Symbols xi
List of Figures xiv
List of Tables xx
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Metamaterial Background . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.2 Negative-Refractive-Index Transmission-Line Metamaterials . . . 3
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Negative-Refractive-Index Transmission-Line Theory 8
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Positive Refractive Index (PRI) Media . . . . . . . . . . . . . . . . . . . 9
2.2.1 Incremental Circuit Analyzed Using Telegrapher’s Equations . . . 10
2.2.2 Lumped-Element Circuit Analyzed Using Periodic Analysis . . . . 14
2.3 Negative Refractive Index (NRI) Media . . . . . . . . . . . . . . . . . . . 17
2.3.1 Incremental Circuit Analyzed Using Telegrapher’s Equations . . . 18
2.3.2 Lumped-Element Circuit Analyzed Using Periodic Analysis . . . . 20
2.4 Negative-Refractive-Index Transmission-Line (NRI-TL)
Metamaterial Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 Proposed Phase Compensating Structure . . . . . . . . . . . . . . 23
2.4.2 Propagation Characteristics of the T Unit Cell . . . . . . . . . . . 26
vi
2.4.3 Propagation Characteristics of the π Unit Cell . . . . . . . . . . . 32
2.4.4 Effective Medium Propagation Characteristics . . . . . . . . . . . 35
2.4.5 Multi-Stage NRI-TL Metamaterial Phase-Shifting Lines . . . . . . 41
2.4.6 Loading-Element Values . . . . . . . . . . . . . . . . . . . . . . . 43
2.5 Non-radiating NRI-TL Metamaterial Phase Shifting Lines . . . . . . . . 45
2.6 Analysis of 0◦ MTM, NR-MTM and TL Phase-Shifting Lines . . . . . . . 49
2.6.1 Choice of the Number of Unit Cells . . . . . . . . . . . . . . . . . 49
2.6.2 Phase Variation Characteristics . . . . . . . . . . . . . . . . . . . 57
3 A NRI-TL Metamaterial Wilkinson Balun 65
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Practical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.5 Simulation and Experimental Results . . . . . . . . . . . . . . . . . . . . 77
4 A NRI-TL Metamaterial Series Power Divider 82
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Power Divider Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3 Design of the 0◦ NR-MTM lines . . . . . . . . . . . . . . . . . . . . . . . 86
4.4 Design of the NR-MTM and TL Power Dividers . . . . . . . . . . . . . . 88
4.5 Simulation Results Using Ideal, Lossless Components . . . . . . . . . . . 89
4.6 Non-Ideal Simulation and Experimental Results . . . . . . . . . . . . . . 94
5 A NRI-TL Metamaterial Series-Fed Antenna Array 101
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Uniform Linear Arrays Employing True-Time Delay Phase Shifters . . . 103
5.3 Tapered Amplitude Distribution in Linear Arrays . . . . . . . . . . . . . 105
5.4 Transmission-Line Fed Series Uniform Linear Arrays . . . . . . . . . . . 109
5.4.1 Low-Pass Loaded Transmission Line . . . . . . . . . . . . . . . . 114
5.5 Metamaterial-Fed Series Uniform Linear Arrays . . . . . . . . . . . . . . 115
5.6 Transmission Line and Metamaterial Series-Fed Printed Dipole Arrays . . 118
5.6.1 Four-Element Series-Fed Printed Dipole Array . . . . . . . . . . . 118
5.6.2 Grounded Four-Element Series-Fed Printed Dipole Array . . . . . 124
5.6.3 Physical Realizations of the Proposed Structures . . . . . . . . . . 129
vii
5.6.4 Simulation and Experimental Results . . . . . . . . . . . . . . . . 134
6 A NRI-TL Metamaterial Leaky-Wave Antenna 143
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.2 Proposed Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2.1 LWA Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2.2 Leaky Transmission Line Model . . . . . . . . . . . . . . . . . . . 147
6.2.3 Reduced Beam Squinting Principle of Operation . . . . . . . . . . 149
6.3 Design of the NRI-TL Metamaterial LWA . . . . . . . . . . . . . . . . . 157
6.3.1 General Design Considerations . . . . . . . . . . . . . . . . . . . . 157
6.3.2 Design Procedure for the NRI-TL Metamaterial Unit Cell . . . . 158
6.3.3 Physical Realization in CPS Technology . . . . . . . . . . . . . . 163
6.3.4 Determination of the Complex Propagation Constant . . . . . . . 166
6.3.5 Printed Balun Design . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.4 Simulation and Experimental Results . . . . . . . . . . . . . . . . . . . . 171
6.4.1 Return Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.4.2 Far-Field Radiation Patterns . . . . . . . . . . . . . . . . . . . . . 172
6.4.3 Beam Squinting and Gain Characteristics . . . . . . . . . . . . . . 175
7 An Electrically Small NRI-TL Metamaterial Antenna 178
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.2.1 Proposed Topology . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.2.2 Even-Odd Mode Analysis . . . . . . . . . . . . . . . . . . . . . . 181
7.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.3.1 Physical Implementation . . . . . . . . . . . . . . . . . . . . . . . 185
7.4 Simulation and Experimental Results . . . . . . . . . . . . . . . . . . . . 194
8 Conclusion 203
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A Equivalent Circuit for the NRI-TL MTM Medium 211
A.1 Incremental Circuit Analyzed Using Telegrapher’s Equations . . . . . . . 212
viii
A.2 Lumped-Element Circuit Analyzed Using Periodic Analysis . . . . . . . . 214
B Choice of Z in a Series Power Divider 217
0
C Beam Squinting Analysis 223
C.1 Derivation of the Beam Squinting Equation . . . . . . . . . . . . . . . . 223
C.2 Derivation of the Approximate Beam Squinting Equations . . . . . . . . 224
C.3 Group Velocity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
D Measured Efficiency Using the G/D Method 230
D.1 Directivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
D.1.1 Numerical Integration Technique . . . . . . . . . . . . . . . . . . 234
D.2 Gain and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
D.3 Measured Radiation Pattern Data . . . . . . . . . . . . . . . . . . . . . . 237
E Measured Efficiency Using the Wheeler-Cap Method 239
E.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
E.2 A Modified Wheeler Cap Method by McKinzie . . . . . . . . . . . . . . . 241
E.3 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
E.4 Measured Reflection Coefficient Data . . . . . . . . . . . . . . . . . . . . 246
References 250
ix
List of Acronyms
ADS Advanced Design System by Agilent Technologies
AF Array Factor
BW Backward-Wave
CPS Coplanar-Strip
HFSS High-Frequency Structure Simulator by Ansoft Corporation
LH Left-Handed
LHM Left-Handed Medium
LPL Low-Pass Loaded
LWA Leaky-Wave Antenna
MIMO Multiple-Input Multiple-Output
MTM Metamaterial
NRI Negative Refractive Index
NRI-TL Negative-Refractive-Index Transmission-Line
NR-MTM Non-Radiating Metamaterial
PRI Positive Refractive Index
RH Right-Handed
RHM Right-Handed Medium
SMA Sub-Miniature version A
SRF Self-Resonant Frequency
SRR Split-Ring Resonator
TEM Transverse Electro-Magnetic
TL Transmission Line
TLM Transmission-Line Matrix
TTD True-Time Delay
x