metamaterial-inspired cmos tunable microwave … · metamaterial-inspired cmos tunable microwave...

244
Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For Steerable Antenna Arrays by Mohamed A.Y. Abdalla 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 c Copyright by Mohamed Abdalla 2009

Upload: phamthu

Post on 03-Jul-2018

252 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Metamaterial-Inspired CMOS Tunable

Microwave Integrated Circuits For

Steerable Antenna Arrays

by

Mohamed A.Y. Abdalla

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

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

c© Copyright by Mohamed Abdalla 2009

Page 2: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Metamaterial-Inspired CMOS Tunable MicrowaveIntegrated Circuits For Steerable Antenna Arrays

Mohamed A.Y. Abdalla

Doctor of Philosophy, 2009

Graduate Department of Electrical and Computer Engineering

University of Toronto

Abstract

This thesis presents the design of radio-frequency (RF) tunable active inductors (TAIs)

with independent inductance (L) and quality factor (Q) tuning capability, and their

application in the design of RF tunable phase shifters and directional couplers for

wireless transceivers.

The independent L and Q tuning is achieved using a modified gyrator-C architecture

with an additional feedback element. A general framework is developed for this Q-

enhancement technique making it applicable to any gyrator-C based TAI. The design

of a 1.5V, grounded, 0.13µm CMOS TAI is presented. The proposed circuit achieves a

0.8nH-11.7nH tuning range at 2GHz, with a peak-Q in excess of 100.

Furthermore, printed and integrated versions of tunable positive/negative refractive

index (PRI /NRI) phase shifters, are presented in this thesis. The printed phase shifters

are comprised of a microstrip transmission-line (TL) loaded with varactors and TAIs,

which, when tuned together, extends the phase tuning range and produces a low return

loss. In contrast, the integrated phase shifters utilize lumped L-C sections in place of

ii

Page 3: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

the TLs, which allows for a single MMIC implementation. Detailed experimental results

are presented in the thesis. As an example, the printed design achieves a phase of -40o

to +34o at 2.5GHz.

As another application for the TAI, a reconfigurable CMOS directional coupler is pre-

sented in this thesis. The proposed coupler allows electronic control over the coupling

coefficient, and the operating frequency while insuring a low return loss and high iso-

lation. Moreover, it allows switching between forward and backward operation. These

features, combined together, would allow using the coupler as a duplexer to connect a

transmitter and a receiver to a single antenna.

Finally, a planar electronically steerable patch array is presented. The 4-element

array uses the tunable PRI/NRI phase shifters to center its radiation about the broad-

side direction. This also minimizes the main beam squinting across the operating

bandwidth. The feed network of the array uses impedance transformers, which allow

identical interstage phase shifters. The proposed antenna array is capable of continu-

ously steering its main beam from -27o to +22o off the broadside direction with a gain

of 8.4dBi at 2.4GHz.

iii

Page 4: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Acknowledgments

I would like to gratefully acknowledge the enthusiastic supervision of my advisors Pro-

fessor Khoman Phang, and Professor George Eleftheriades for their continuous guid-

ance, and inspiration. Throughout the course of my Ph.D. I have learned alot from

them, and I will always remain indebted to them. I would like to thank Professor

Khoman Phang for consistently being there for me, week after week to meet and dis-

cuss all the different aspects of this work. As for Professor George Eleftheriades, I

would like to deeply thank him for his invaluable advice and feedback, without which

this work would not have been accomplished.

I would also like to extend my thanks the former and current graduate students in my

research group as well as in the electro-magnetics group for their invaluable technical

assistance and friendship from which I have learned alot. From the electronics group,

I would like to thank Dr. Anas Hamoui, Dr. Ahmed Gharbiya, Dr. Mohammad Ha-

jirostam, Joseph Aziz, Pradip Thachile, Masum Hossain, Farsheed Mahmoudi, Stephen

Liu, Euhan Chong, Kentaro Yamamoto, Dr. Faisal Musa, Robert Wang, Dr. Afshin

Haftbaradaran, Imran Ahmed, Navid Yaghini, Oleksiy Tyshchenko, Kevin Banovic,

Tony Kao, David Allred, Akram Nafee, Trevor Caldwell, Samir Parikh, and Nasim

Nikkhoo.

From the Electro-magnetics group, I would like to thank Marco Antoniades for all

the long hours we spent in technical discussions, and also Rubaiyat Islam, Dr. Omar

iv

Page 5: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Acknowledgements

Siddiqui, Ashwin Iyer, Joshua Wong, and Peter Wang. Also, I would like to thank Tse

Chan and Gerald Dubois for their continuous technical support.

I would also like to extend my thanks the Canadian Microelectronics Corporation

(CMC) for providing the fabrication facilities, and for NORTEL Networks, and the

Natural Sciences and Engineering Research Council (NSERC) of Canada for financially

supporting this work.

Lastly, I would like to thank my beloved wife Aliaa, my parents, and my sister for

their continuous support, and encouragement throughout the course of my Ph.D., and

last but not least, I would like to thank my daughter Jana, whom without knowing has

been a motivation for my accomplishments. The least I can do is to dedicate this work

to them.

v

Page 6: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Related Publications

The material presented in this thesis has been presented in part in the following journal

and conference publications.

Journal Publications

1. M. Abdalla, K. Phang, and G. V. Eleftheriades, “A 0.13µm CMOS phase shifter

using tunable positive/negative refractive index transmission line,” IEEE Microw.

Wireless Components Lett., Vol. 16, no. 12, pp. 705-707, Dec. 2006.

2. M. Abdalla, K. Phang, and G. V. Eleftheriades, “Printed and integrated CMOS

positive/negative refractive-index phase shifters using tunable active inductors,”

IEEE Trans. Microw. Theory and Tech., Vol. 55, no. 8, pp. 1611-1623, August

2007.

3. M. Abdalla, K. Phang, and G. V. Eleftheriades, “A compact highly- reconfig-

urable CMOS MMIC directional coupler,” IEEE Trans. Microw. Theory and

Tech., Vol. 56, no. 2, pp. 305-3019, Feb. 2008.

4. M. Abdalla, K. Phang, and G. V. Eleftheriades, “A Planar Electronically Steer-

able Patch Array Using Tunable PRI/NRI Phase Shifters,” IEEE Trans. Microw.

Theory and Tech., accepted for publication Dec. 2008.

vi

Page 7: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Conference Publications

1. M. Abdalla, and K. Phang , “A 0.13µm CMOS active inductor based on a modi-

fied gyrator-C architecture,” Micronet Annual Workshop, Ottawa, Canada, May

2005.

2. M. Abdalla, G. V. Eleftheriades, and K. Phang, “A differential 0.13µm CMOS

active inductor for high frequency phase shifters,” Proc. IEEE Circuits and Sys-

tems ISCAS 06, Kos, Greece, pp. 3341-3344, May 2006.

3. M. A. Y. Abdalla, K. Phang, and G. V. Eleftheriades, “a tunable metamaterial

phase-shifter structure based on a 0.13µm CMOS active inductor,” Proc. 36th

European Microwave Conf., Manchester, Great Britain, pp. 325-328, Sept. 2006.

4. M. A. Y. Abdalla, K. Phang, and G. V. Eleftheriades, “A bi-directional elec-

tronically tunable CMOS phase shifter using the high-pass topology,” 2007 IEEE

MTT-S Int. Microwave Symp. Dig., Honolulu, Hawaii, pp. 2173-2176, June

2007.

5. M. A. Y. Abdalla, K. Phang, and G. V. Eleftheriades, “A steerable series-fed

phased array architecture using tunable PRI/NRI phase shifters,” Invited paper,

Int. Workshop on Antenna Tech. iWAT 08, Chiba, Japan, March 2008.

vii

Page 8: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Contents

List of Figures xii

List of Tables xviii

List of Acronyms xx

List of Symbols xxii

1 Introduction 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Phased Antenna Array Front-Ends . . . . . . . . . . . . . . . . . . . . 11.3 Thesis Scope and Outline . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Background 82.1 Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Metamaterial Applications . . . . . . . . . . . . . . . . . . . . . 10

2.2 Tunable Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 MEMS Tunable Inductors . . . . . . . . . . . . . . . . . . . . . 112.2.2 Varactor-Based Tunable Inductors . . . . . . . . . . . . . . . . . 122.2.3 Transmission-Line Tunable Inductors . . . . . . . . . . . . . . . 132.2.4 Gyrator-C Tunable Inductors . . . . . . . . . . . . . . . . . . . 13

2.3 Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.1 Switched-Line Phase Shifters . . . . . . . . . . . . . . . . . . . . 23

viii

Page 9: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Contents

2.3.2 Reflection-Type Phase Shifters . . . . . . . . . . . . . . . . . . . 242.3.3 Transmission-Type Phase Shifters . . . . . . . . . . . . . . . . . 252.3.4 Lumped-Element L-C Phase Shifters . . . . . . . . . . . . . . . 262.3.5 PRI/NRI Metamaterial Phase Shifters . . . . . . . . . . . . . . 30

2.4 Directional Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.1 Branch-Line Directional Couplers . . . . . . . . . . . . . . . . . 342.4.2 Coupled-Line Directional Couplers . . . . . . . . . . . . . . . . 352.4.3 Lumped-Element L-C Directional Couplers . . . . . . . . . . . . 362.4.4 PRI/NRI Metamaterial Directional Couplers . . . . . . . . . . . 38

2.5 Phased Antenna Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . 392.5.1 Antenna Arrays Basics . . . . . . . . . . . . . . . . . . . . . . . 392.5.2 Microstrip Patch Antenna . . . . . . . . . . . . . . . . . . . . . 432.5.3 Phased Array Feed Network Topologies . . . . . . . . . . . . . . 452.5.4 Metamaterial Phased Antenna Arrays . . . . . . . . . . . . . . . 51

3 CMOS Tunable Active Inductors 533.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2 Traditional Gyrator-C Architecture . . . . . . . . . . . . . . . . . . . . 54

3.2.1 Quality Factor Analysis . . . . . . . . . . . . . . . . . . . . . . 553.2.2 Q-Enhancement Technique For Gyrator-C TAIs . . . . . . . . . 57

3.3 The Modified Gyrator-C Architecture . . . . . . . . . . . . . . . . . . . 583.4 A Grounded 0.13µm CMOS TAI . . . . . . . . . . . . . . . . . . . . . 61

3.4.1 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.2 TAI Small-Signal Analysis . . . . . . . . . . . . . . . . . . . . . 643.4.3 TAI Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 663.4.4 Physical Realization and Experimental Characterization . . . . 68

4 Wide Tuning Range CMOS Phase Shifters 834.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.2 High-pass Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.2.2 Design and Physical Implementation . . . . . . . . . . . . . . . 904.2.3 Experimental Characterization . . . . . . . . . . . . . . . . . . . 91

4.3 TL PRI/NRI Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . 964.3.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.3.2 Design and Physical Implementation . . . . . . . . . . . . . . . 994.3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 100

4.4 MMIC PRI/NRI Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . 1034.4.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.4.2 Design and Physical Implementation . . . . . . . . . . . . . . . 108

ix

Page 10: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Contents

4.4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 110

4.5 Passive MMIC PRI/NRI Phase Shifter . . . . . . . . . . . . . . . . . . 115

4.5.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.5.2 Design and Physical Implementation . . . . . . . . . . . . . . . 120

4.5.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 121

4.6 Discussion and Comparison . . . . . . . . . . . . . . . . . . . . . . . . 124

4.6.1 Group Delay of PRI/NRI Phase Shifters . . . . . . . . . . . . . 128

5 A Highly-Reconfigurable Directional Coupler 1315.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.1.1 Tunable Coupling Coefficient Directional Couplers . . . . . . . . 133

5.1.2 Tunable Operating Frequency Directional Couplers . . . . . . . 133

5.2 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.2.1 Analysis of the MMIC Directional Coupler . . . . . . . . . . . . 134

5.2.2 MMIC Directional Coupler Modes of Operation . . . . . . . . . 138

5.3 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.3.1 MMIC Directional Coupler Design . . . . . . . . . . . . . . . . 144

5.4 Physical Implementation and Experimental Results . . . . . . . . . . . 146

5.4.1 Physical Implementation . . . . . . . . . . . . . . . . . . . . . . 146

5.4.2 Experimental Characterization of the MMIC Directional Coupler 148

5.5 Effect Of The TAI On The Coupler Noise Performance . . . . . . . . . 162

6 Electronically Steerable Series-Fed Patch Array 1666.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.2.1 Antenna Array Architecture . . . . . . . . . . . . . . . . . . . . 168

6.2.2 Feed Network Design . . . . . . . . . . . . . . . . . . . . . . . . 171

6.2.3 Interstage Phase Shifters . . . . . . . . . . . . . . . . . . . . . . 176

6.3 Antenna Array Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.4 Physical Implementation and Experimental Results . . . . . . . . . . . 182

6.4.1 Interstage Phase Shifter . . . . . . . . . . . . . . . . . . . . . . 182

6.4.2 Steerable Antenna Array . . . . . . . . . . . . . . . . . . . . . . 186

6.5 Antenna Array Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.6 Discussion and Comparison . . . . . . . . . . . . . . . . . . . . . . . . 197

7 Conclusion 2027.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

x

Page 11: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Contents

Appendix A: Beam Squinting Analysis 208

Appendix B: Simulation Procedure 210

References 212

xi

Page 12: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

1.1 Wireless network established between wireless device and access pointin the presence of interferers. . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 A transceiver front-end employing a phased antenna array. . . . . . . . 31.3 Prototype of a 2-D interface between a region with positive permittivity

and permeability (left-side) and a NRI region (right-side). . . . . . . . 41.4 Single-stage, two-stage, four-stage, and eight-stage metamaterial phase

shifters compared to a conventional TL phase shifter. . . . . . . . . . . 4

2.1 Photograph of the lefthanded metamaterial (LHM) sample, reproducedfrom [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Tunable TL inductor designed by terminating λ/4 TL with a tunablecapacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Circuit symbol of the gyrator, showing the polarities and directions ofthe port voltages and currents, respectively. . . . . . . . . . . . . . . . 14

2.4 (a) Block diagram implementation of the gyrator using transconductors.(b) Tunable active inductor designed by terminating the second port ofthe gyrator with a capacitor. . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 (a) CS-CD TAI using an NMOS-NMOS realization. (b) CS-CD TAIusing an NMOS-PMOS realization. . . . . . . . . . . . . . . . . . . . . 17

2.6 (a) CG-CS TAI using an NMOS-NMOS realization. (b) CG-CS TAIusing an NMOS-PMOS realization. . . . . . . . . . . . . . . . . . . . . 18

2.7 (a) CS-CD TAI using a cascoded CS stage. (b) CS-CD TAI using again-boosted cascoded CS stage. . . . . . . . . . . . . . . . . . . . . . . 19

2.8 Cascoded CS-CD TAI with a feedback resistance Rf . . . . . . . . . . . 212.9 A single stage of a switched-line phase shifter. . . . . . . . . . . . . . . 23

xii

Page 13: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

2.10 Reflection-type phase shifter utilizing a 3dB coupler loaded with varactors. 24

2.11 Single stage of a transmission-type phase shifter. . . . . . . . . . . . . . 25

2.12 Different high-pass and low-pass topologies for constant-impedance second-order L-C phase shifters. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.13 All-pass constant-impedance second-order L-C phase shifter. . . . . . . 29

2.14 PRI/NRI metamaterial phase shifter unit-cell. . . . . . . . . . . . . . . 30

2.15 Block diagram of a 4-port directional coupler. . . . . . . . . . . . . . . 32

2.16 Diagram of a microstrip branch-line directional coupler. . . . . . . . . . 33

2.17 Diagram of a microstrip coupled-line directional coupler. . . . . . . . . 35

2.18 lumped-element L-C low-pass and high-pass Π realizations of a branch-line coupler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.19 L-C lumped-element high-pass Tee realization of a branch-line coupler. 37

2.20 L-C lumped-element realization of a coupled-line coupler. . . . . . . . . 37

2.21 N-element uniform linear antenna array with equal amplitude excitationand a progressive phase constant φ. . . . . . . . . . . . . . . . . . . . . 40

2.22 Array factor of a 4-element antenna array fed in-phase and with dE = λ/2. 41

2.23 Array factor of a λo/2 4-element antenna array fed with a progressivephase shift of ±90o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.24 Rectangular microstrip patch antenna fed with a microstrip TL . . . . . 43

2.25 Inset-fed rectangular microstrip patch antenna. . . . . . . . . . . . . . 44

2.26 Elevation plane gain plot for a 2.4GHz rectangular microstrip patchantenna: (a) in the y-z plane, (b) in the x-z plane. . . . . . . . . . . . . 45

2.27 A 4-element parallel-fed antenna array. . . . . . . . . . . . . . . . . . . 47

2.28 A 4-element corporate-fed antenna array. . . . . . . . . . . . . . . . . . 47

2.29 A basic 4-element series-fed antenna array. . . . . . . . . . . . . . . . . 48

2.30 A 4-element series-fed traveling wave in-line antenna array using a ter-mination load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.31 A 4-element series-fed traveling wave out-of-line antenna array withouta termination load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.1 Gyrator-C architecture and its equivalent circuit. . . . . . . . . . . . . 54

3.2 Function f(RS) versus the negative series resistance RS. . . . . . . . . 57

3.3 Modified gyrator-C loop and its equivalent circuit. . . . . . . . . . . . . 58

3.4 The modified differential gyrator-C architecture. . . . . . . . . . . . . . 61

3.5 Proposed TAI circuit with the tunable feedback resistance. . . . . . . . 62

3.6 Digital/analog feedback resistance Rf . . . . . . . . . . . . . . . . . . . 64

3.7 Grounded active inductor equivalent circuit. . . . . . . . . . . . . . . . 65

3.8 Simplified TAI schematic with the main current and voltage noise sources,and equivalent lumped noise current model. . . . . . . . . . . . . . . . 67

3.9 Tunable active inductor die micrograph. . . . . . . . . . . . . . . . . . 68

xiii

Page 14: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

3.10 Measured TAI characteristics versus frequency when VC1=0V and VC2

changes from 0.3V to 0.6V: (a) Inductance, (b) Quality factor. . . . . . 703.11 Measured TAI characteristics versus frequency when VC1=0.1V and VC2

changes from 0.3V to 0.6V: (a) Inductance, (b) Quality factor. . . . . . 713.12 Measured TAI characteristics versus frequency when VC1=0.2V and VC2

changes from 0.3V to 0.4V: (a) Inductance, (b) Quality factor. . . . . . 713.13 Measured TAI characteristics versus frequency when VC1 changes from

0V to 0.4V and VC2=0.3V: (a) Inductance, (b) Quality factor. . . . . . 723.14 Theoretical and measured self-resonance frequency, fr, versus the induc-

tance, L, for the different bias conditions. . . . . . . . . . . . . . . . . . 733.15 Theoretical and measured peak quality factor frequency, fQ, versus the

self-resonance frequency, fr. . . . . . . . . . . . . . . . . . . . . . . . . 733.16 Measured Q versus frequency for different feedback voltages Vf . . . . . 753.17 Measured S11 of the TAI for different feedback voltages Vf . . . . . . . . 753.18 Measured and simulated results versus frequency when VC1=0V and VC2

is set to 0.6V and 0.4V: (a) inductance (b) series resistance. . . . . . . 773.19 Circuit setup used for the simulation of the TAI circuit. . . . . . . . . . 773.20 Experimental test setup used for characterizing the TAI circuit linearity. 783.21 Amplitude of the power reflected back by the TAI versus the input power

when applying a single RF signal source. . . . . . . . . . . . . . . . . 793.22 Amplitude of the power reflected back by the TAI at f1 and 2f1 − f2

versus the input power when combining two RF signal sources. . . . . . 80

4.1 Different series-fed phased array designs and their radiation patterns. . 844.2 High-pass phase shifter unit-cell. . . . . . . . . . . . . . . . . . . . . . . 874.3 Phase tuning range versus the capacitor tuning ratio rC . . . . . . . . . 894.4 Proposed high-pass phase shifter circuit implementation. . . . . . . . . 904.5 High-pass phase shifter die micrograph . . . . . . . . . . . . . . . . . . 914.6 Measured phase vs. freq., for different bias conditions . . . . . . . . . . 924.7 Measured S11 and S21 vs. freq., for different bias conditions . . . . . . . 934.8 Measured phase and S21 at 4GHz vs. VB . . . . . . . . . . . . . . . . . 934.9 Measured S21 at 4GHz versus the feedback voltage Vf . . . . . . . . . 944.10 Amplitude of the output power versus the input power when applying a

single 4GHz RF signal source . . . . . . . . . . . . . . . . . . . . . . . 954.11 Amplitude of the output power at f1 and 2f1−f2 versus the input power

when combining two RF signal sources . . . . . . . . . . . . . . . . . . 954.12 TL PRI/NRI metamaterial phase shifter unit-cell. . . . . . . . . . . . . 974.13 TL PRI/NRI metamaterial phase shifter unit-cell. . . . . . . . . . . . . 994.14 Photograph of the tunable PRI/NRI phase shifter unit-cell. . . . . . . . 1004.15 The measured and theoretical phase responses vs. freq. for different bias

conditions. The phase expression of Eq.(4.10) is used for the comparison. 101

xiv

Page 15: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

4.16 Measured S11 vs. freq. for different bias conditions. . . . . . . . . . . . 1024.17 Measured S21 vs. freq. for different bias conditions. . . . . . . . . . . . 1024.18 Proposed IC PRI/NRI metamaterial phase shifter unit-cell. . . . . . . . 1044.19 Dispersion diagram of the periodic structure composed of the proposed

MMIC PRI/NRI phase shifter unit-cells. . . . . . . . . . . . . . . . . . 1064.20 Proposed IC PRI/NRI metamaterial phase shifter unit-cell. . . . . . . . 1094.21 MMIC PRI/NRI metamaterial phase shifter die micrograph. . . . . . . 1104.22 The measured and theoretical phase responses vs. freq. for different bias

conditions. The phase expression of Eq.(4.19) is used for the comparison. 1114.23 Measured S11 vs. freq. for different bias conditions. . . . . . . . . . . . 1124.24 Measured S21 vs. freq. for different bias conditions. . . . . . . . . . . . 1124.25 Measured S21 and phase shift φ at 2.6GHz versus the TAI feedback

voltage Vf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.26 Unit cell of the proposed MMIC PRI/NRI tunable phase shifter. . . . . 1154.27 Dispersion diagram of the periodic structure composed of the proposed

passive PRI/NRI MMIC unit-cells. . . . . . . . . . . . . . . . . . . . . 1174.28 Proposed passive MMIC PRI/NRI phase shifter circuit implementation. 1194.29 Phase MMIC PRI/NRI shifter die micrograph . . . . . . . . . . . . . . 1214.30 Measured phase vs. freq., for different bias conditions . . . . . . . . . . 1224.31 Measured S11 and S21 vs. freq., for different bias conditions . . . . . . . 1224.32 Measured phase and S21 at 2.6GHz vs. the varactor reverse bias voltage

VB1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.33 The measured group delays of the metamaterial phase shifter and the

simulated group delay of two cascaded 2nd-order all-pass filters . . . . . 129

5.1 Block diagram of a 4-port directional coupler configured in: (a) theforward mode of operation, and (b) the backward mode of operation. . 132

5.2 The high-pass topology used by the proposed MMIC directional coupler. 1355.3 The equivalent circuit with even-mode excitation. . . . . . . . . . . . . 1355.4 The equivalent circuit with odd-mode excitation. . . . . . . . . . . . . 1365.5 Series capacitance C2 and the shunt inductance L required to satisfy the

conditions of Eq.(5.9) and Eq.(5.10) versus the series capacitance C1. . 1395.6 Coupling coefficients achieved by the MMIC coupler circuit . . . . . . . 1395.7 Operating frequency of the MMIC coupler and the series capacitance C1

versus the shunt inductance L. . . . . . . . . . . . . . . . . . . . . . . . 1425.8 Proposed lumped-element MMIC directional coupler circuit implemen-

tation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455.9 MMIC directional coupler die micrograph. . . . . . . . . . . . . . . . . 1475.10 Measured and theoretical coupling coefficients C vs. freq. for different

bias conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495.11 Measured isolation S41 vs. freq. for the same bias conditions as Fig. 5.10.149

xv

Page 16: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

5.12 Measured reflection coefficient S11 vs. freq. for the same bias conditionsas Fig. 5.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.13 Measured and theoretical S41 vs. freq., for different bias conditions . . 153

5.14 Measured S11 vs. freq., for different bias conditions . . . . . . . . . . . 154

5.15 Measured S21 and S31 to the left and S41 to the right vs. the coupleroperating frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.16 Measured MMIC coupler S-parameters vs. frequency. Case 1: forwardoperation, the input power is equally divided between ports 3 and 2while port 4 is isolated. . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.17 Measured MMIC coupler S-parameters vs. frequency. Case 2: backwardoperation, the input power is equally divided between ports 3 and 4 whileport 2 is isolated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.18 Differential phase response of the MMIC coupler vs. frequency for theforward and the backward modes of operation. . . . . . . . . . . . . . . 159

5.19 Duplexer operation (a) Receive mode is achieved by configuring the cou-pler in the forward mode. (b) Transmit mode is achieved by configuringthe coupler in the backward mode. . . . . . . . . . . . . . . . . . . . . 160

5.20 Measured S21 and S31 at 2.6GHz on the left and S41 at 2.6GHz on theright vs. the input power level. . . . . . . . . . . . . . . . . . . . . . . 161

5.21 Block diagram of a 3dB coupler with the noise current sources repre-senting the effect of the active circuits within the TAIs. . . . . . . . . . 163

6.1 Basic 4-element series-fed antenna array. . . . . . . . . . . . . . . . . . 169

6.2 4-element series-fed antenna array with λ/4 impedance transformers. . 169

6.3 Alternating patch array diagram indicating the required ideal powersplitting ratios and all the λ/4 transformer impedances. . . . . . . . . . 171

6.4 Power mismatch between the first and fourth antennas versus the inter-stage phase shifter insertion loss. . . . . . . . . . . . . . . . . . . . . . 175

6.5 Normalized array factors for a 4-element λo/2 antenna array. . . . . . . 175

6.6 Transmission-line tunable PRI/NRI metamaterial phase shifter unit-cell. 177

6.7 Photograph of the fabricated tunable TL PRI/NRI interstage phase shifter.183

6.8 The measured insertion phase φPS vs. freq. for different bias conditions. 184

6.9 Measured S21 and S11 at 2.4GHz versus the insertion phase of the inter-stage phase shifter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.10 Photograph of the fabricated electronically steerable series-fed patch ar-ray utilizing the tunable TL PRI/NRI interstage phase shifters. . . . . 186

6.11 Measured co- and cross-polarization and simulated co-polarization gainpatterns in the azimuth plane (x-z plane) for different bias conditions. . 189

6.12 Measured peak gain of the antenna array and the half-power beamwidthversus the scan angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

xvi

Page 17: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Figures

6.13 Measured co- and cross-polarization and simulated gain patterns in they-z plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

6.14 Input return loss, S11, of the antenna array versus frequency for all thedifferent bias conditions given by Fig. 6.11. . . . . . . . . . . . . . . . . 192

6.15 Beam squinting characteristics: antenna array main-lobe angle, θp, andthe peak gain, Gp, versus frequency. . . . . . . . . . . . . . . . . . . . . 193

6.16 Experimental setup used to characterize the linearity of the steerableantenna array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

6.17 Measured output power, Pout, of the horn antenna at 2.4GHz versus theantenna array input power Pin. . . . . . . . . . . . . . . . . . . . . . . 195

6.18 Measured horn output power at the fundamental frequency f1 and atthird-order intermodulation frequency 2f1−f2 versus the antenna arrayinput power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

B-1 Flow chart showing the procedure used to simulate the TL PRI/NRImetamaterial phase shifters. . . . . . . . . . . . . . . . . . . . . . . . . 211

B-2 Flow chart showing the procedure used to simulate the steerable antennaarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

xvii

Page 18: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Tables

2.1 Comparison Between Different Directional Coupler Topologies. . . . . . 39

2.2 Comparison Between Different Antenna Array Feed Network TopologiesAnd The Requirements On The Interstage Phase Shifters. . . . . . . . 51

3.1 Transistor Sizes of the TAI Circuit . . . . . . . . . . . . . . . . . . . . 63

3.2 Transistor Sizes of the Digital/Analog Tunable Feedback Resistance Rf 63

3.3 Measured Inductances for the TAI at 2GHz for Different Values of theBias Voltages VC1 and VC2. . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4 Comparison Between Different Tunable Active Inductor Implementations 81

4.1 Summary of The High-Pass Phase Shifter Performance. . . . . . . . . . 96

4.2 Summary of the TL PRI/NRI Phase Shifter Performance. . . . . . . . 103

4.3 Summary of the TAI-Based MMIC PRI/NRI Phase Shifter Performance. 114

4.4 Summary of the Passive MMIC PRI/NRI Phase Shifter Performance. . 124

4.5 Comparison Between Different Phase Shifter Designs Presented In ThisChapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.6 Comparison Between Different PRI/NRI Phase Shifter Implementations 127

5.1 Comparison Between the Proposed MMIC Directional Coupler and OtherVariable Coupling Coefficient Couplers . . . . . . . . . . . . . . . . . . 152

5.2 Comparison Between the Proposed MMIC Coupler and Other Couplerswith Variable Operating Frequency . . . . . . . . . . . . . . . . . . . . 156

5.3 Linearity Comparison Between Different TAI based Couplers . . . . . . 161

xviii

Page 19: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Tables

6.1 Series Feed Network Efficiency For Different Interstage Phase ShifterLoss Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.2 Comparison Between The Proposed Steerable Patch Array And OtherPublished Series-Fed Steerable Antenna Arrays. . . . . . . . . . . . . . 198

6.3 Comparison Between The Measured Beam Squinting Of The ProposedArray And Other Published Antenna Arrays. . . . . . . . . . . . . . . . 200

xix

Page 20: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Acronyms

1-D One-Dimensional

2-D Two-Dimensional

BiCMOS Bipolar Complementary Metal Oxide Semiconductor

BW Bandwidth

CD Common-Drain

CG Common-Gate

CMOS Complementary Metal Oxide Semiconductor

CPW Co-Planar Waveguide

CS Common-Source

DAC digital-to-analog converter

FOM Figure-of-merit

GaAs Gallium Arsenide

GSG Ground-Signal-Ground

GSGSG Ground-Signal-Ground-Signal-Ground

HPBW Half Power Beamwidth

xx

Page 21: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Acronyms

IC Integrated Circuit

ISM Industrial, Scientific and Medical

LHM Left-Handed Medium

LNA Low-Noise Amplifier

MEMS Micro-electromechanical systems

MESFET Metal-Semiconductor Field Effect Transistor

MIM Metal-Insulator-Metal

MMIC Monolithic Microwave Integrated Circuit

NF Noise Figure

NMOS N-channel Metal Oxide Semiconductor

NRI Negative Refractive Index

PCB Printed Circuit Board

PIFA Planar Inverted F Antenna

PMOS P-channel Metal Oxide Semiconductor

PRI Positive Refractive Index

QFN Quad Flat-Pack No Lead

TAI Tunable Active Inductor

TL Transmission-Line

TX Transmitter

RF Radio Frequency

RHM Right-Handed Medium

RX Receiver

SiGe Silicon Germanium

WSN Wireless Sensor Network

xxi

Page 22: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Symbols

AF Antenna array factorβ Propagation constantc Speed of lightC Directional coupler coupling coefficientC CapacitancedE Inter-element distancedPS Phase shifter lengthD Directional coupler directivityεr Relative dielectric constantεeff Effective relative dielectric constantE Electric fieldEF Antenna element factorf Frequencyft Transistor unity-gain frequencyφ Phase shiftgm TransconductanceG Interstage phase shifter absolute power gainγ Transistor noise coefficientΓe,o Reflection coefficient for even- and odd-mode circuitsh Substrate heightH Magnetic fieldi2nMx

mean-square value of the drain current thermal noise for transistor Mx

I Currentk Boltzmann constantL Inductance

xxii

Page 23: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

List of Symbols

λ Wavelengthnf Number of transistor fingersηfeed Feed network efficiencyN Number of antenna array elementsP powerQ Tunable active inductor quality factorQP Peak-QrC Capacitance tuning ratiorL Inductance tuning ratioro Transistor small-signal output resistanceR ResistanceRS Tunable active inductor series resistances Complex frequency variableS11 Input reflection coefficientSxy Transmission coefficient from port x to port yT TemperatureTe,o Transmission coefficient for even- and odd-mode circuitsTgd Phase shifter group delayθ Angle of antenna array main beamv2

nRxmean-square value of the thermal noise voltage for resistor Rx

V VoltageVDS,sat Transistor saturation drain-source voltageVEF Transistor overdrive voltageVGS Transistor gate-source voltageVTH Transistor threshold voltageW Patch antenna widthWf Transistor finger widthω Angular frequencyωo Zero phase frequencyωp Tunable active inductor peak-Q frequencyωr Tunable active inductor resonance frequencyX SusceptanceZ ImpedanceZA Antenna impedanceZo Characteristic impedanceZPS Phase shifter impedanceZT λ/4 transformer impedance

xxiii

Page 24: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 1

Introduction

1.1 Overview

W ireless communications is one of the major foundations of the current revolution

in information technology. Due to its unlicensed nature, the 2.4-2.5GHz indus-

trial, scientific and medical (ISM) band has become a popular choice for a variety of

wireless applications. Unfortunately, this popularity is causing congestion, resulting in

more interference and eventually degrading the performance of wireless links. Further-

more, the increasing level of interference from the neighboring wireless devices imposes

tough constraints on the transceiver design, starting with the specified level for the

transmitted power and ending with the specified receiver noise figure. To meet the

required performance from a wireless link, and at the same time relax the transceiver

design constraints, one can utilize the principle of phased antenna arrays.

1.2 Phased Antenna Array Front-Ends

Phased antenna arrays are capable of producing narrow, high-gain beams compared

to omni-directional antennas. In a phased array wireless link, the transmitted power

1

Page 25: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.2. PHASED ANTENNA ARRAY FRONT-ENDS 2

Interference

RX

TX

Wireless access

pointInterference

RX

TX

(a) (b)

Figure 1.1: Wireless network established between wireless device and access point inthe presence of interferers. (a) In this case, all devices use omni-directionalantennas, (b) In this case, the wireless device under consideration uses aphased antenna array, resulting in a narrow and steerable beam.

is focused towards the intended wireless device, and at the same time, the receiving

device is focused in the direction of the transmitting device. This is illustrated in

Fig. 1.1-a and Fig. 1.1-b, which show qualitatively how the effect of interference from

the neighboring devices and the effect of noise from the surrounding environment can

be reduced by deploying phased antenna arrays. This will result in higher signal to

noise ratios, leading to lower bit-error rates. It is also worth mentioning that, using

phased antenna arrays reduces the effects of issues such as multi-path fading.

A simplified block diagram of a transceiver front-end utilizing a phased antenna ar-

ray is shown in Fig. 1.2. The electronic beam steering network is required to feed the

different antennas with the appropriate signal amplitudes and phases by utilizing elec-

tronically tunable phase shifters. Currently, the use of phased arrays is largely limited

to high-precision military radar systems and satellite communications due to the lack

of compact, broadband, electronically tunable phase shifters that are cost-effective and

can easily be integrated onto the same printed circuit board (PCB) with printed anten-

nas. Furthermore, the large area occupied by the beam steering network of parallel-fed

arrays, which are, to date, the dominant choice for high data-rate applications, has also

been a deterring factor for deploying phased arrays in wireless consumer applications.

Page 26: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.2. PHASED ANTENNA ARRAY FRONT-ENDS 3

Duplexer

Power

Amplifier

Low Noise

Amplifier

TXRX

Transceiver

RSSI

Power monitoring

Electronic Beam Steering

Figure 1.2: A transceiver front-end employing a phased antenna array.

The beam steering network of series-fed arrays, on the other hand, is very compact, but

suffers from large beam squinting1 with frequency. However, with the recent develop-

ments in the field of metamaterials, there is the potential to design compact, broadband

phase shifters suitable for series-fed antenna arrays, allowing their deployment in high

data-rate wireless consumer applications.

Metamaterials are artificial dielectrics that display electromagnetic properties that

do not exist in naturally occurring materials: for example, simultaneous negative per-

mittivity and permeability. Consequently, they can possess a negative index of refrac-

tion (NRI). For radio frequency (RF) applications, the interest in metamaterials was

sparked by their compact planar implementation proposed in 2002 [3, 4], which allows

for its integration with various RF and microwave electronic systems. Fig. 1.3 shows a

photograph reproduced from [2] of a 2-D metamaterial. The unit-cell of this 2-D NRI

metamaterial is comprised of two microstrip TLs loaded with series capacitors and a

shunt inductor. Metamaterials concepts have been used to develop compact, broad-

band phase shifters with small and relatively flat group delays [5]. These phase shifters

are designed by cascading multiple 1-D unit-cells of a NRI metamaterial. The compact

implementation of these metamaterial phase shifters, which is illustrated in Fig. 1.4,

1Beam squinting is defined here as the variation in the angle of the main beam of the antenna arraywith frequency.

Page 27: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.2. PHASED ANTENNA ARRAY FRONT-ENDS 4

Figure 1.3: Prototype of a 2-D interface between a region with positive permittivity andpermeability (left-side) and a NRI region (right-side). Picture reproducedfrom [2]. The inset magnifies a single unit cell of the NRI region, consistingof a microstrip grid loaded with surface-mounted capacitors and an inductorembedded into the substrate at the central node.

Conventional 360o TL phase shifter

Metamaterial phase shifters

Figure 1.4: Single-stage, two-stage, four-stage, and eight-stage metamaterial phaseshifters compared to a conventional TL phase shifter. Picture reproducedfrom [5].

Page 28: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.3. THESIS SCOPE AND OUTLINE 5

is necessary for the beam steering networks of series-fed antenna arrays. Furthermore,

the low group delay of metamaterial phase shifters will result in smaller variations in

the direction of the array’s main beam across the operating bandwidth [6], which makes

them suitable for high date-rate applications. However, until now, metamaterial phase

shifters have utilized discrete, or printed capacitors and inductors having fixed values,

and as such, are not tunable. By utilizing the capabilities offered by CMOS monolithic

microwave integrated circuits (MMICs) to replace the fixed capacitors and inductors

with tunable ones, the phase response of these metamaterial phase shifters would po-

tentially be electronically tuned. Besides tunability, utilizing CMOS MMIC technology

would result in a more compact implementation compared to current, TL-based imple-

mentations. These compact, electronically tunable metamaterial phase shifters could

then be integrated within the feed network of series-fed antenna arrays. This would al-

low implementing the antenna array with the beam steering network on a single planar

PCB, making it more appealing for high data-rate wireless consumer applications.

The benefits of tunability could also extend to the duplexer. The duplexer in the

phased array front-end of Fig. 1.2 operates as a switch, and is a necessary component in

the transceiver front-end to allow sharing the same antenna array between the trans-

mitter and the receiver. However, duplexers are usually designed using discrete, or

printed components. Hence, duplexers are bulky and are not tunable. If the duplexers

could be made tunable, transceivers could be made to support multi-standard opera-

tion. This can also be achieved by using CMOS MMICs to design highly-reconfigurable

compact duplexers, which in the future will allow their integrating the duplexer with

the transceiver front-end on a single CMOS integrated circuit (IC). Moreover, the trans-

mitted and received power could be monitored by replacing the 3-port duplexer with

a 4-port highly-reconfigurable directional coupler. This would allow for precise control

over the level of the TX power and the gain of the low-noise amplifier.

1.3 Thesis Scope and Outline

This thesis investigates the design of RF tunable active inductors (TAIs), and their

application in the design of tunable phase shifters, directional couplers, and steerable

antenna arrays. An electronically tunable version of the compact, broadband, TL meta-

material phase shifter is presented. Furthermore, two novel fully-integrated, tunable,

Page 29: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.3. THESIS SCOPE AND OUTLINE 6

versions of the metamaterial phase shifter are presented in this thesis. Tunability is

achieved by combining the use of varactors and TAIs. The thesis also presents the

design of a compact, CMOS MMIC, highly-reconfigurable, directional coupler to re-

place the duplexer in wireless transceiver front-ends, and at the same time allow for

multi-standard operation as well as power monitoring. Similar to the tunable phase

shifters, the proposed MMIC directional coupler combines the use of varactors and

TAIs. Since the TAI plays a major role in the design of both the phase shifters and

the directional coupler, this thesis also presents a design methodology for TAIs that

allows independently tuning its inductance (L) and quality factor (Q). Tuning L and

Q independently is a key feature to overcome the degradation of the insertion loss and

return loss of the TAI-based circuits while electronically tuning their response. In addi-

tion, the tunable metamaterial phase shifters presented in this thesis are used to design

the beam steering network of a series-fed patch array, and electronic beam steering is

demonstrated using a prototype antenna array.

Chapter 2 of this thesis starts by briefly summarizing the recent developments in

the field of metamaterials and its applications. Following that, it gives the necessary

background information about TAIs, phase shifters, directional couplers, and phased

antenna arrays.

Chapter 3 presents a design methodology for RF TAIs that allows independent tuning

of their L and Q, by using a modified gyrator-C architecture with an additional feed-

back element. The proposed Q-enhancement technique is generalized for the gyrator-C

architecture, which makes it applicable to any gyrator-C based TAI. To verify the pro-

posed architecture, a novel grounded TAI design is presented along with the simulation

and experimental results.

In chapter 4, TL-based and fully-integrated versions of electronically tunable meta-

material phase shifters are presented. The TL-based phase shifters presented in this

thesis have evolved from the metamaterial phase shifter topology presented in [5] by

replacing the fixed, discrete components with IC, tunable, active elements (i.e. varac-

tors and the TAIs presented in chapter 3). Combining the use of varactors and TAIs

results in a wide phase tuning range, and allows the phase shifters to achieve a very

low return loss across their entire tuning range. To the author’s knowledge, the CMOS

MMIC designs presented in this chapter are considered the first attempts to design

fully-integrated, tunable, metamaterial phase shifters in a standard CMOS process.

Page 30: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

1.3. THESIS SCOPE AND OUTLINE 7

Following that, a novel CMOS MMIC, highly-reconfigurable directional coupler is

presented in chapter 5. The directional coupler uses varactors and the TAIs presented

in chapter 3 to allow extensive electronic control over the coupling coefficient. At

the same time, this allows the coupler to be re-configured for operation over a wide

range of frequencies. To the author’s knowledge, this is the first coupler that combines

those two features; i.e. simultaneously providing a tunable coupling coefficient and

a tunable operating frequency. Moreover, the symmetric configuration of the coupler

allows it to switch from forward to backward operation by simply exchanging the bias

voltages applied to the varactors. This makes the proposed directional coupler ideal to

replace the bulky passive duplexers in transceiver front-ends, enabling multi-standard

operation as well as power monitoring.

Chapter 6 presents a planar electronically steerable series-fed patch array for 2.4GHz

ISM band applications. The proposed steerable array uses the tunable TL metamate-

rial phase shifters, presented in chapter 4, to center its radiation about the broadside

direction and allow scanning in both directions off the broadside. Also, using the meta-

material phase shifters reduces the squinting of the main beam across the operating

bandwidth. The feed network of the proposed array uses λ/4 impedance transformers.

This allows using identical interstage phase shifters, which share the same control volt-

ages to tune all stages. Furthermore, using the impedance transformers in combination

with the CMOS-based, constant-impedance metamaterial phase shifters guarantees a

low return loss for the antenna array across its entire scan angle range. To the author’s

knowledge, the proposed antenna array is the first resonant antenna-element struc-

ture that demonstrates electronic beam steering utilizing tunable metamaterial phase

shifters.

Finally, Chapter 7 concludes the thesis and suggests directions for future research.

Page 31: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 2

Background

This chapter reviews the basic concepts in topics related to the work presented in this

thesis. This chapter does not present new material and readers can skip it and proceed

to chapter 3 for the main contributions of the thesis.

2.1 Metamaterials

A metamaterial is a broad word referring to any artificial material having properties

that are not found in nature. It stems from the Greek word meta meaning beyond.

Throughout this thesis, the term metamaterial will refer to mediums possessing a

negative permeability simultaneously with a negative permittivity.

2.1.1 History

In 1968, Veselago proposed that materials with simultaneously negative permeability

and permittivity will provide a negative index of refraction [7]. Furthermore, in such

a medium, the electric field, E, the magnetic field, H, and the propagation vector, k,

will form a left-handed triplet instead of a right-handed one, thus it can also be termed

8

Page 32: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.1. METAMATERIALS 9

Figure 2.1: Photograph of the lefthanded metamaterial (LHM) sample, reproducedfrom [1]. The LHM sample consists of square copper split ring resonatorsand copper wire strips on fiber glass circuit board material. The rings andwires are on opposite sides of the boards.

a left-handed medium. However, their realization was not possible before 1999 when

Pendry et al. showed how to realize a negative permeability from a split ring resonator

structure [8]. Following that, Smith et al. showed a composite 3-dimensional (3-D)

material that exhibits simultaneously negative permittivity and permeability [1, 9].

These structures use strip wires to realize the negative permittivity and use split ring

resonators to synthesize the negative permeability [8]. The dimensions of the split

ring resonators and strip wires determine their resonance frequencies and hence the

overlapping regions with negative permittivity and permeability [1,9]. Figure 2.1 shows

a photograph reproduced from [1] of a 3-D NRI medium based on an array of split

ring resonators and strip wires. The dependence on the resonance of the split ring

resonators to synthesize a negative permeability makes the NRI medium inherently

narrow-band, the design presented in [1] shows a negative index of refraction over a

range of frequencies from 10.2GHz to 10.8GHz. Furthermore, the implementation of

the 3-D NRI medium is quite bulky.

In his paper, Veselago pointed out many interesting phenomena related to wave

propagation in NRI metamaterials, such as: reversed refraction, or, in different terms,

inverted Snell’s law, and reversed Doppler effect. Hence, metamaterials moved from

a theoretical concept to a practically realizable medium, and their reverse refraction

characteristic made them suitable for focusing electromagnetic waves at a PRI1/NRI

boundary with sub-wavelength resolving properties. This idea was proposed in 2000

Page 33: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.1. METAMATERIALS 10

when a 3-D NRI metamaterial lens was presented in [10]. However, metamaterials still

remained bulky 3-D structures, which hindered their application within various RF

and microwave electronic systems.

In 2002, Eleftheriades et al. proposed a new approach to build a 2-dimensional

(2-D) NRI metamaterial by periodically loading TLs with series capacitors and shunt

inductors [11], thus replacing the bulky 3-D wire strips and split ring resonators by a 2-

D planar design. The same method was also proposed by another group at UCLA [12].

A photograph of a 2-D metamaterial designed using microstrip lines as the host TLs is

shown in chapter 1 in Fig. 1.3. The unit-cell of this NRI metamaterial is comprised of

microstrip TLs loaded with series capacitors and a shunt inductor. These developments

allowed the first experimental demonstration of focusing from a planar 2-D PRI/NRI

interface [3]. Following this, interest in NRI metamaterials was sparked in the RF and

microwave community.

2.1.2 Metamaterial Applications

Novel RF and microwave circuits were designed utilizing the additional degree of free-

dom offered by NRI media, such as building compact broadband TL PRI/NRI zero-

degree phase shifters with small and relatively flat group delays [5]. These phase shifters

are designed by cascading the 1-D version of the unit-cell shown in Fig. 1.3 to create

a 1-D metamaterial line. One application that would benefit from these PRI/NRI

phase shifters is series-fed antenna arrays, as will be described in more detail through-

out this thesis. Furthermore, broadband PRI/NRI series power dividers have been

proposed in [13] to feed loads in phase that are not electrically close to each other.

Directional couplers can also benefit from the advances in planar NRI metamaterials;

a dual-frequency branch-line coupler was presented in [14] and two high directivity

coupled-line couplers were presented in [15] and [16]. Moreover, it was demonstrated

in [17] that one of the dimensions of a coupler can be significantly reduced by coupling

the electromagnetic power between a NRI line and a PRI TL as opposed to a conven-

tional coupler design in which power is coupled between two PRI TLs. The compact

planar metamaterial implementation also enabled other applications, such as the leaky

1PRI stands for a positive-refractive-index media, which corresponds to having a positive permittivityand permeability.

Page 34: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 11

backward-wave antennas presented in [18]. Also, electrically-small, metamaterial-based

antennas have recently been presented in [19, 20]. Hence, the field of metamaterials

appears to have much potential for both RF and microwave applications.

Electronically tuning the characteristics of metamaterials, by replacing the fixed se-

ries capacitors and shunt inductors with electronically tunable capacitors and inductors,

can provide re-configurability to all the different metamaterial applications. Further-

more, this may open-up a whole new range of applications, such as designing planar

RF lenses which posses a tunable focal length. Since tunable capacitors can easily be

obtained by using varactors, the next section will focus instead on techniques used to

design tunable inductors.

2.2 Tunable Inductors

The most widely used method to design printed inductors on PCBs or integrated induc-

tors in current IC technologies is by means of planar spirals. However, the inductance

of spiral inductors is a function of their geometry. Hence, spiral inductors provide only

fixed inductances.

2.2.1 MEMS Tunable Inductors

Micro-electromechanical systems (MEMS) have demonstrated the capability of synthe-

sizing RF tunable inductors. For instance, a MEMS tunable RF inductor is presented

in [21], which consists of two loops self-assembled with a specific angle between them.

By controlling the ambient temperature of the inductor, this angle and hence the effec-

tive distance between the two loops can be varied, which in turn changes the mutual

inductance component. This, however, results in a limited inductance tuning range;

0.83-0.65nH at 4GHz for varying the temperature from 25oC to 200oC, respectively,

and a low Q of 6, where Q is a measure of the efficiency of an inductor, and is given

by Im(Zin)/Re(Zin).

In another more recently published paper [22], an electronically tunable MEMS in-

ductor was presented. This inductor is composed of an aluminum layer micro-machined

on top of an amorphus silicon layer. The tunability of the inductor is based on the

bimorph effect, which can be explained as follows. When a voltage is applied across

Page 35: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 12

the inductor, its structure deforms in a controllable manner, which occurs due to dif-

ference in the thermal expansion coefficients of the two layers. The inductor achieves

a 6.5-9.8nH tuning range at 3GHz, and achieves quality factors ranging from 5 to 15

respectively. However, the inductor dissipates 220mW to actuate the necessary de-

formation in its structure. This power is required to raise the temperature of the

structure.

Although MEMS tunable inductors, in general, can provide high self-resonance fre-

quencies and high-speed operation, most of them use thermal effects to tune the in-

ductance. This dramatically reduces the speed of switching, which is the time required

to change the inductance from one value to another. Furthermore, most of the MEMS

inductors rely on vertical movements to tune their inductance. Consequently, the re-

sulting 3-D moving structures make it challenging to package and to integrate MEMS

inductors with electronic circuits fabricated in a standard CMOS process.

2.2.2 Varactor-Based Tunable Inductors

Another common method to tune the inductance of IC spirals is to use varactors.

By connecting a varactor in series, or in shunt, with a fixed spiral inductor, one can

tune the effective inductance by varying the bias voltage applied across the varactor.

On such example is demonstrated in [23], where a series varactor is used to tune the

inductance of a 2-port, i.e. series, spiral inductor to design a tunable phase shifter.

However, this technique is only valid over a very narrow-band of frequencies (with

fractional bandwidths of 10%-20% as reported in [23]), since the effective inductance

can only be assumed constant over a narrow-band of frequencies. This is a result of the

direct relation between the effective inductance and the frequency, which for a shunt

connection is given by:

Leff = L− 1

ω2C, (2.1)

where L and C are the fixed spiral inductance and the tunable varactor capacitance re-

spectively. Furthermore, this technique results in low quality factors, since the effective

Q is limited by the low-Q of the IC spiral inductors.

Page 36: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 13

CL/4

in

Figure 2.2: Tunable TL inductor designed by terminating λ/4 TL with a tunable ca-pacitor.

2.2.3 Transmission-Line Tunable Inductors

Another very simple approach to build tunable inductors can be derived from the basic

TL model. Terminating a λ/4 TL with an arbitrary impedance ZL, where λ = c/f

is the wave-length, c is the speed of light, and f is the design frequency, results in an

input impedance of:

Zin =Z2

o

ZL

, (2.2)

where Zo is the characteristic impedance of the TL [24]. As Eq.(2.2) indicates, a λ/4

TL acts as an impedance inverter. Hence, loading this TL with a capacitor results in

an inductive input impedance, with an inductance of:

L = Z2oCL, (2.3)

where CL is the load capacitance. Furthermore, the inductance can be tuned by replac-

ing the fixed capacitor with a varactor as shown in Fig. 2.2. Although this technique

might seem unsuitable for IC designs due to the need for TLs, when operating at high

frequencies the TL size becomes practical for IC implementations. However, this tech-

nique results in very narrow band inductors; since Eq.(2.2) is only valid at the design

frequency f , which limits its applicability.

2.2.4 Gyrator-C Tunable Inductors

The most popular technique used to build tunable synthetic inductors is by terminating

a gyrator with a capacitive load. This technique has greatly benefited from the advances

in modern CMOS technologies, which are now capable of providing transistors with very

high unity-gain frequencies (ft), allowing the design of RF TAIs. The use of RF TAIs

have been demonstrated in numerous applications. For instance, they were used by

Page 37: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 14

V1

I1 +

-

V2

+

-

I2

(a)

V1

I1 +

-

V2

+

-

I2

(b)

CL

Figure 2.3: Circuit symbol of the gyrator, showing the polarities and directions of theport voltages and currents, respectively.

Mukhopadhyay et al. in [25] to design wide-tuning range voltage-controlled oscillators

(VCOs), they were also used by Wu et al. in [26] to design RF tunable filters, and

in [27] and [28] to design RF phase shifters and power dividers respectively.

History

The gyrator, of which circuit symbol is shown in Fig. 2.3-a was originally introduced

as a new circuit element in 1948 by Tellegen [29]. Using the standard 2-port network

representation, the impedance matrix of a gyrator can be defined as:

[V1

V2

]=

[0 −r1

r2 0

][I1

I2

], (2.4)

where V1,2 and I1,2 are the voltage and current at ports 1 and 2 of the gyrator, respec-

tively, as indicated in Fig. 2.3-a, and r1 and r2 are the gyration resistances. Terminat-

ing a gyrator with a load impedance ZL, as shown in Fig. 2.3-b, results in an input

impedance Zin, which is expressed as:

Zin =r1r2

ZL

. (2.5)

Hence, terminating the circuit with a capacitive load CL results in an inductive input

impedance with an inductance L expressed as:

L = r1r2CL. (2.6)

According to Eq.(2.6), the inductance of the circuit can simply be tuned by varying

either the load capacitance or the gyration resistances r1 or r2. Hence, the gyrator-C

Page 38: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 15

ZinCL

-gm2

gm1

-gm2

gm1

V1

I1

V2

I2

(a) (b)

io1=gm1vin1

io1vin1

io2=-gm2vin2

io2

vin2

Figure 2.4: (a) Block diagram implementation of the gyrator using transconductors.(b) Tunable active inductor designed by terminating the second port of thegyrator with a capacitor.

architecture is capable of synthesizing a tunable inductance. The gyrator-C inductors

are termed active, since gyrators are implemented using active devices (transistors).

Furthermore, unlike Eq.(2.1), Eq.(2.5) is valid for all frequencies as long as the gyrator

characteristics can still be described by the impedance matrix of Eq.(2.4).

To the author’s knowledge, the first circuit implementation of a gyrator was presented

by Morse et al. in 1964, and was based on operational amplifiers [30]. The proposed

circuit implementation used four operational amplifiers. Following that, other designs

were presented in the literature trying to minimize the number of operational ampli-

fiers required to implement the gyrators. For instance, the design in [31] was published

in 1971, and requires only two operational amplifiers. An alternative circuit imple-

mentation for a gyrator is to use two transconductors connected back-to-back (gm1

and gm2) as shown in Fig. 2.4-a. This approach was originally proposed by Sharpe

in 1957 [32], and the first circuit implementation of a such a circuit was presented

along with its experimental characterization in 1965 [33]. Using operational ampli-

fiers initially seemed more attractive to build gyrators, due to their standard designs.

However, most of the RF TAIs presented in the literature use transconductors, since

this approach is more suitable for high-speed applications [25, 26, 34–43]. Hence, our

focus here is directed towards this latter approach to build TAIs, and throughout this

Page 39: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 16

thesis, the term gyrator-C TAI will refer to the transconductor-based design. It is

worth mentioning that, the gyrator-C active inductor in Fig. 2.4-b is single-ended, or,

in other words, it represents a grounded inductor. Although the generalized gyrator-C

circuit in Fig. 2.3-b can produce 2-port, or floating, inductors, the difficulty of its im-

plementations prohibits the design of 2-port active inductors. This will be one of the

main factors in the selection of the appropriate architectures for the TAI-based phase

shifters and the TAI-based coupler in chapters 4 and 5, respectively.

First-Order Analysis of Gyrator-C TAIs

Assuming ideal transconductors, one can show that the impedance matrix of the circuit

in Fig. 2.4-a is given by:

[V1

V2

]=

0 − 1

gm11

gm2

0

[I1

I2

]. (2.7)

By comparing Eq.(2.7) with Eq.(2.4), it becomes evident that the circuit is equivalent

to a gyrator. Furthermore, terminating the circuit with a capacitive load CL, as shown

in Fig. 2.4-b, results in an inductive input impedance, and the inductance L can be

expressed as:

L =CL

gm1gm2

. (2.8)

According to Eq.(2.8), the inductance of the circuit can simply be tuned by varying

the load capacitance CL, gm1, or gm2. This analysis assumes ideal transconductors with

infinite input and output impedances as well as zero input and output capacitances.

This results in an ideal inductor with an infinite Q, which is defined as:

Q =Im(Zin)

Re(Zin), (2.9)

where Zin is the input impedance of the gyrator-C circuit. A more detailed analysis of

the gyrator-C architecture will be presented in chapter 3 which takes into account the

second-order effects.

Page 40: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 17

Vdd

M1

M2

Zin

M2

M1

Zin

I2

I1

Vdd

I1

Vdd I2

Vdd

(a) (b)

Figure 2.5: (a) CS-CD TAI using an NMOS-NMOS realization. (b) CS-CD TAI usingan NMOS-PMOS realization.

Overview of Transistor-Based Gyrator-C TAIs

The simplest implementation of a high-Q TAI can be obtained by replacing each

transconductor in Fig. 2.4 with a single-transistor transconductor2. Only two different

combinations of transistor topologies are possible to maintain the negative feedback;

a common-source, common-drain topology (CS-CD), and a common-gate, common-

source topology (CG-CS). Using different combinations of NMOS and PMOS transis-

tors results in eight different TAI circuit implementations. These eight different TAI

realizations are summarized in [34]. Figure 2.5-a shows the CS-CD topology using

an NMOS-NMOS realization, whereas Fig. 2.5-b shows the CS-CD topology using an

NMOS-PMOS realization. In either case, the capacitor CL, used to terminate the gyra-

tor in Fig. 2.4, is removed and the circuit relies on the input capacitance of the second

transconductor instead, i.e. the capacitance at the gate of M2. Eliminating CL and re-

lying on the parasitic capacitance makes the TAI circuit capable of operating at higher

speeds. The circuit in Fig. 2.5-a was originally proposed in [45], and requires a mini-

mum supply voltage of 2VGS +VDS,sat. The circuit in Fig. 2.5-b was originally proposed

in [46], and requires only VGS +2VDS,sat making it more appealing for low-voltage oper-

2Active inductors can also be designed using a single transistor. For example, in the presence of agate resistance the impedance looking into the source terminal of a common-drain amplifier, hasan inductive component [44]. However, this techniques are not suited for high-Q wide-tuning rangeactive inductors.

Page 41: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 18

M1

M2VB

Zin

M2VB

Zin

M1

Vdd

I1,2

Vdd

I2

Vdd

I1+I2

(a) (b)

Figure 2.6: (a) CG-CS TAI using an NMOS-NMOS realization. (b) CG-CS TAI usingan NMOS-PMOS realization.

ation. However, one can show that for both transistors to be ON and operating in the

saturation region the value of the overdrive voltage of transistor M2, which is given by

VEFF2 = VSG2−|VTHP |, has to satisfy the following equation: VEFF2 < VTHN −|VTHP |,where VTHN and VTHP are the threshold voltages of the NMOS and PMOS transis-

tors respectively. In modern CMOS processes, where the values of VTHN and VTHP

are close, this results in a small ft for transistor M2 making the circuit of Fig. 2.5-b

incapable of high-speed operation. The two other CS-CD TAI circuit realizations can

be derived from Fig. 2.5 by using a PMOS-PMOS and a PMOS-NMOS configuration

for M1 and M2 respectively.

Figure 2.6-a shows the CG-CS topology using an NMOS-NMOS realization. This

circuit was originally proposed in [47], and requires a minimum supply voltage of

VGS + VDS,sat. This makes it suitable for low-voltage applications. Furthermore, both

transistors use the same bias current making this TAI topology suitable for low-power

applications. The NMOS-PMOS realization of the CS-CG topology is shown in Fig. 2.6-

b. It requires a minimum supply voltage of VGS +2VDS,sat, which is slightly higher than

that of the NMOS-NMOS realization. Also, the ability to control the bias current of

both transistors results in a wider inductance tuning range at the expense of higher

power consumption.

Page 42: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 19

Vdd

M1

M2

ZinI2

I1

Vdd

M3

VB

Vdd

M1

M2

ZinI2

I1

Vdd

M3

VB+

-

(a) (b)

A

Figure 2.7: (a) CS-CD TAI using a cascoded CS stage. (b) CS-CD TAI using a gain-boosted cascoded CS stage.

Quality Factor Enhancement Techniques For Gyrator-C TAIs

Replacing each transistor with its small-signal equivalent model and neglecting all the

capacitances except for Cgs2, one can show that the input impedance of the CS-CD

TAI circuit of Fig. 2.5-a can be approximated as:

Zin ≈ 1

gm2 × (ro1gm1)+

sCgs2

gm1gm2

. (2.10)

Equation (2.10) indicates that the TAI can be modeled by an inductor in series with a

resistor. The series resistor represents the loss associated with the TAI circuit. To min-

imize the losses and achieve a high-Q, it is desired to minimize the value of this series

resistance. In other words, it is desired to move the zero of the input impedance transfer

function, i.e. the zero of the numerator of Eq.(2.10) ωz = 1/ro1Cgs2, to lower frequen-

cies. On the other hand, more elaborate analysis reveals that the input impedance

of the TAI circuit has a pole frequency at ωp = gm2/Cgs2, which is responsible for

degrading the inductor Q at high frequencies. Hence, it is desired to move the pole to

higher frequencies. It is worth mentioning that, adding an extra capacitor CL at the

gate of M2 to terminate the gyrator results in the following expression for the input

Page 43: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 20

impedance:

Zin ≈1

ro1

+ s(Cgs2 + CL)

(gm1 + sCL)(gm2 + sCgs2). (2.11)

Hence, besides affecting the value of the TAI inductance, the capacitor CL also adds a

pole frequency which further limits the operating frequency of the TAI circuit. There-

fore, in most high-speed TAIs the load capacitor CL is not used and the circuit relies on

the parasitic capacitances of the transistors. By investigating Eq.(2.10) closely, one can

show that the series resistance is equal to the resistance looking into the source of M2

divided by the CS stage gain, i.e. gm1ro1. To reduce the series resistance of the TAI, a

cascode device can be added to the circuit as shown in Fig. 2.7-a. Adding the cascode

device, increases the output impedance of the CS amplifier and consequently increases

its gain by a factor of gm3ro3, this decreases the series resistance by approximately the

same factor. This technique was proposed in [42], furthermore, the authors of [42]

proposed a gain-boosted cascode implementation, which is shown in Fig. 2.7-b. This

reduces the series resistance by a factor A×gm3ro3 compared to the circuit of Fig. 2.5-a,

where A is the gain of the feedback amplifier. This Q-enhancement technique can be

applied to any of the various CS-CD or CG-CS TAI topologies.

Another approach that is used to enhance the Q of TAIs is by using cross-coupled

differential pairs to generate a negative resistance to cancel the resistive losses. This

technique was used in [47] to enhance the Q of a differential CG-CS TAI, and in [43] to

enhance the Q of a differential-pair-based TAI. However, this technique is more suited

for two port inductors excited by differential signals. Using more elaborate transcon-

ductors, such as differential pairs in [43] and [40], to implement the TAIs enhances the

inductor characteristics by giving the designer more freedom in shaping its frequency

response, namely in the locations of the zeros and poles of the input impedance trans-

fer function. This comes at the expense of power dissipation. Whether a TAI circuit

uses a two-transistor topology or a differential-pair-based topology, the inductance is

electronically tuned by changing the bias currents of the two transconductors, or it

can also be tuned by changing the value of the load capacitor CL, when one is used to

terminate the gyrator.

Another Q enhancement technique that has recently been proposed for TAIs involves

adding a feedback resistance in the gyrator loop. This was first proposed in [41], where

Page 44: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.2. TUNABLE INDUCTORS 21

Vdd

M1

M2

ZinI2

I1

Vdd

M3

VB

Rf

Figure 2.8: Cascoded CS-CD TAI with a feedback resistance Rf .

a differential-pair-based TAI used a tunable MOS-based resistance inserted between

the output of the first differential-pair and the input of the second differential pair.

However, no analysis was presented that explained the effect of adding the feedback

resistance in the gyrator loop. Following that, another TAI circuit employing a feedback

resistance within a cascoded CS-CD topology was presented in [39]. This TAI circuit

is shown in Fig. 2.8, where the feedback resistance is inserted between the output of

the cascoded CS stage and the input of the CD transistor. In [39], the analysis of the

cascoded CS-CD TAI circuit with the additional feedback resistance was presented,

and experimental results were provided to validate the idea. The same circuit, i.e.

the CMOS cascoded CS-CD TAI, was also presented in [25] together with a BiCMOS

implementation using a common-emitter, common-collector topology. Both circuits

in [25] use the feedback resistance to enhance the Q. However, the analysis presented

in [39] and [25] is limited to the specific circuits presented by each paper. Consequently,

an intuitive understanding of the effect of adding this feedback resistance is missing.

This will be explained later on in chapter 3, as it is one of the contributions of this

thesis to generalize this Q-enhancement technique (i.e. adding a feedback resistance to

the gyrator-C architecture), and to explain its effect with the aid of very simple and

intuitive equations.

Page 45: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 22

TAIs with Tunable Inductance and Quality Factor

Most of the previously published TAI implementations suffer from one major drawback,

which is their inability to independently control both the TAI inductance and Q. Tun-

ing the inductance without affecting the Q is a key feature to overcome the degradation

of the insertion loss and return loss in any TAI-based application, due to the decrease

of the TAI’s Q when its inductance is being tuned. Moreover, it is important to have

control over the TAI’s Q without affecting its inductance, since this allows controlling

the level of the losses in a TAI-based application without significantly affecting the

desired response. Very few published TAI circuits have demonstrated independent L

and Q tuning capability [25,38,48]. The designs presented in [48] and [38] utilize GaAs

MESFETs. The first CMOS TAI with L and Q tuning capability was presented in [25].

The CMOS design in [25] employs a tunable feedback resistance in the gyrator loop.

Besides enhancing the Q of the TAI, the additional tunable feedback resistance allows

tuning both the L and the Q. Again, the methods used to achieve the independent

tuning in [25,38,48] are specific to each individual presented circuit. Hence, a general-

ized method that can be directly applied to the gyrator-C architecture is missing and

would prove to be very useful. This will be discussed in more detail in chapter 3, as it

is one of the contributions of this thesis to provide a general method applicable to any

gyrator-C TAI to achieve the independent L and Q tuning capability.

2.3 Phase Shifters

Electronically tunable phase shifters are essential building blocks for many RF and

microwave applications. In steerable antenna arrays, the direction of the antenna

array’s main beam is controlled by the inter-element phase shift. An excellent review for

the different classifications of phase shifters can be found in [49] and [24]. This section

will very briefly summarize the main types of electronically tunable phase shifters.

Electronically tunable phase shifters can be classified into many categories depending on

different criteria. For example, phase shifters can be analog in nature or digital, which

refers to having a continuous phase tuning range or discrete phase values respectively.

At the same time, phase shifters can be classified according to their design into five

main categories:

Page 46: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 23

L1

L2

Figure 2.9: A single stage of a switched-line phase shifter.

• Switched-line or switched-network phase shifters

• Reflection-type phase shifters

• Transmission-type or loaded-line phase shifters

• Lumped-element L-C phase shifters

• PRI/NRI metamaterial phase shifters

2.3.1 Switched-Line Phase Shifters

Switched-line phase shifters rely on using single pole, double throw switches to select

between one of two TLs having different lengths as shown in Fig. 2.9. The differential

phase shift, i.e. the phase difference between the two paths, is given by:

|∆φ| = β |L1 − L2| , (2.12)

where β is the propagation constant of the two TLs, and L1 and L2 are their lengths. To

obtain a large differential phase shift, the difference between the length of the TL should

be increased. Also, more than one stage can be cascaded to obtain larger phase shifts.

Usually, each stage of a cascaded switched-line phase shifter is designed to achieve

binary weighted phases. For example, a 3-bit phase shifter would employ 180o, 90o,

and 45o stages, which results in a maximum phase shift of 315o and a minimum phase

shift (resolution) of 45o. Hence, the resolution of the discrete phase shifter depends

on the number of digital control bits. For an n-bit phase shifter employing 180o,

90o, 45o, etc. stages, the resolution of the phase shifter becomes 360o/2n. The same

concept can be used to design a lumped-element phase shifter by switching between

different networks, for example, switching between a low-pass network and a high-pass

Page 47: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 24

(1)

(4)

(2)

Output port

Input port

(3)

CL

-90o

-90o

-180

o -180 o

CL

Figure 2.10: Reflection-type phase shifter utilizing a 3dB coupler loaded with varactors.

network [50].

The insertion loss of the switched-line phase shifters becomes an issue as more stages

are cascaded to increase its resolution. This is a result of the increasing number of

switches that the signal has to propagate through. This problem becomes more obvious

for IC implementations, which use transistor-based switches. To overcome the losses of

the switches, amplifiers can be employed. This, however, makes the phase shifters uni-

directional. Furthermore, switched-network phase shifters occupy a large area, since

they require at least two networks for each control bit.

2.3.2 Reflection-Type Phase Shifters

Reflection-type phase shifters, rely on terminating a 3dB coupler with a reactive load.

Either varactors or TAIs can been used to terminate a 3dB coupler, however varactors

are more commonly used. Fig. 2.10 shows a simplified diagram of a reflection-type

phase shifter terminated with varactors. Assuming that the coupler is ideal, i.e. the

coupler has no losses, equally divides the input power from port 1 among ports 2 and

3, and provides -90o and -180o phase shifts at the two ports respectively, one can show

that the power reflected back from ports 2 and 3 adds up in-phase at port 4 and out-of-

phase at port 1. Furthermore, the phase of the output signal at port 4 is proportional

to the phase of the reflection coefficient at ports 2 and 3, Γ, which is given by:

Γ =ZL − Zo

ZL + Zo

=1− jωCLZo

1 + jωCLZo, (2.13)

Page 48: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 25

CL

S21

S11

Figure 2.11: Single stage of a transmission-type phase shifter.

where ZL is the varactor impedance, CL is its capacitance. Using Eq.(2.13), one can

show that the output phase at port 4 can be expressed as:

φ = −2 tan−1 (ωCLZo) . (2.14)

If the varactor capacitance is varied from CLmax to CLmin, the phase tuning range is

given by:

|∆φ| = 2 tan−1 (ωCLmaxZo)− 2 tan−1 (ωCLminZo) . (2.15)

The return loss, i.e. S11, of reflection-type phase shifters remains very low as long as the

two varactors are perfectly matched. Reflection-type phase shifters tend to have a small

bandwidth on the order of 15% [49], with the main limiting factor being the bandwidth

of the 3dB coupler. Furthermore, reflection-type phase shifters tend to occupy a large

area, since their size is mainly governed by the size of the 3dB coupler. Hence, the

focus of research into reflection-type phase shifters has been directed towards designing

lumped-element couplers to reduce area [51,52].

2.3.3 Transmission-Type Phase Shifters

Transmission-type (or loaded-line) phase shifters are one of the popular methods to

implement phase shifters due to their simplicity. A transmission-type phase shifter

consists of a TL loaded with a shunt reactive impedance, which in most cases is a

varactor. A simplified diagram of such a phase shifter is shown in Fig. 2.11. One

can show that if a TL with a characteristic impedance Zo is loaded with a varactor

with a capacitance CL, the return loss and the transmission coefficient, as indicated on

Page 49: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 26

Fig. 2.11, are expressed as:

S11 =−jωCLZo

2 + jωCLZo

, and (2.16)

S21 =2

2 + jωCLZo

(2.17)

respectively. Hence, the excess phase shift due to loading the TL with the varactor is

given by:

φ = − tan−1

(ωCLZo

2

). (2.18)

If the varactor capacitance is varied from CLmax to CLmin, the phase tuning range is

expressed as:

|∆φ| = tan−1

(ωCLmaxZo

2

)− tan−1

(ωCLminZo

2

). (2.19)

By comparing Eq.(2.19) with Eq.(2.15), one can conclude that for the same capacitance

tuning range, transmission-type phase shifters result in a smaller phase tuning range

compared to reflection-type phase shifters. However, they do not require a 3dB coupler

which makes them more compact. Furthermore, transmission-type phase shifters are

more wide-band compared to reflection-type phase shifters.

Examining Eq.(2.16) reveals that, unlike reflection-type phase shifters, transmission-

type phase shifters always suffer from finite return losses. In other words, S11 does not

approach zero except for CL = 0, which limits the phase tuning range of such phase

shifters. To overcome this, the TL can be loaded with two identical varactors separated

by λ/4, where λ is the wavelength of the propagating signal. This causes the reflected

signals from the two varactors to cancel-out and reduces the return loss of the phase

shifter [24].

2.3.4 Lumped-Element L-C Phase Shifters

The first three phase shifter topologies presented in this chapter mainly rely on using

either TLs or coupled TLs. For IC applications operating in the low GHz frequency

range, the length of these TLs becomes excessively long, which makes these techniques

unsuitable for such applications. Hence, most IC designs operating in the low GHz fre-

Page 50: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 27

C C

L C C

L

L

C

L

L

C

L

(a) (b)

(c) (d)

Figure 2.12: Different high-pass and low-pass topologies for constant-impedancesecond-order L-C phase shifters [53].

quency range use standard lumped-element filters (low-pass, high-pass, etc.) to imple-

ment phase shifters. Although R-C filters have been extensively used by IC designers to

implement on-chip phase shifters (for example, for the generation of quadrature-phase

signals in RF transceivers), R-C filters are not suitable for beam steering applications.

This stems from the fact that they cannot provide matching to a real impedance (Zo).

Although matching is usually not an issue for on-chip applications, the focus of this

thesis is directed towards phase shifters for beam steering applications, and so matching

is one of the main criteria.

This leads us to L-C phase shifters, which can provide both the matching as well

as the required phase shift. Second-order bi-directional L-C phase shifters can take

one of the four implementations shown in Fig. 2.12 [53]. The high-pass T architecture

of Fig. 2.12-a and the low-pass Π (Pi) architecture of Fig. 2.12-b use the minimum

number of inductors and hence occupy a smaller area. This makes the high-pass T and

the low-pass Π architectures more suitable for compact IC implementations.

The phase shift, φHP , of the high-pass Tee phase shifter of Fig. 2.12-a can be ex-

pressed as3:

φHP ≈√

2

ω√

LC. (2.20)

Page 51: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 28

Equation (2.20) indicates that the phase can be tuned by changing the capacitance and

the inductance, which can be achieved by using varactors and TAIs. Simultaneously

changing the capacitance from Cmax to Cmin and the inductance from Lmax to Lmin

results in the following phase tuning range:

|∆φHP | =√

2

ω√

LminCmin

−√

2

ω√

LmaxCmax

. (2.21)

If the capacitance and inductance tuning ratios are defined as rC = Cmax/Cmin and

rL = Lmax/Lmin, Eq.(2.21) can be re-written as:

|∆φHP | = φHPmin

(1− 1√

rC × rL

). (2.22)

Similarly, the phase response of the low-pass phase shifter of Fig. 2.12-b can tuned

by changing the capacitance and the inductance. However, since the low-pass Π archi-

tecture uses a floating (or 2-port) inductor, it becomes difficult to replace the inductor

with a TAI. For this reason, the phase response of L-C low-pass phase shifters is usu-

ally tuned using varactors [54, 55], whereas for high-pass designs, both varactors and

TAIs can be employed to extend the tuning range. In spite of this, most high-pass L-

C phase shifter designs published in the literature use a single tuning element to tune

their phase response; varactors in [56,57], and TAIs in [27]. Although it is evident from

Eq.(2.22) that combining the use of varactors and TAIs will extend the phase tuning

range, to the author’s knowledge, until now, a phase shifter that combines the use of

varactors and TAIs has not been published. A detailed discussion about combining the

use of varactors and TAIs is presented later in chapter 4.

L-C phase shifters can also be designed using all-pass networks. For example,

Fig. 2.13 shows a second-order all-pass phase shifter, which has a constant resistive

input and output impedance Zo for all frequencies [53]. The transmission-coefficient of

3This phase expression is derived under the assumption that the phase shifter is matched, the detailedderivation of this expression is presented later on in chapter 4.

Page 52: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 29

L2

C2

C1C1

L1

Figure 2.13: All-pass constant-impedance second-order L-C phase shifter.

the all-pass phase shifter can be expressed as:

S21 =

s2 − ωr

Qp

s + ω2r

s2 +ωr

Qp

s + ω2r

, (2.23)

where ωr and Qp are the frequency and the quality factor of the complex conjugate

poles. Using Eq.(2.23), the phase shift can be expressed as:

φ = −2 tan−1

(ωωr/Qp

ω2r − ω2

). (2.24)

Equation (2.24) indicates that the phase can be tuned by varying the value of ωr.

However, since the values of the circuit components (the capacitors and inductors) are

related to the all-pass filter parameters by the following equations: L1 = 2Zo/ωrQp,

C1 = Qp/ωrZo, L2 = QpZo/2ωr, and C2 = 2Qp/ωr(Q2p−1)Zo, this necessitates changing

the values of all the circuit elements. Tuning four different elements simultaneously

complicates the tuning process. Furthermore, as discussed in section 2.2.4, the floating

inductor is difficult to synthesize using TAIs. However, this approach using all-pass

filters results in a relatively flat magnitude response compared to the low- and high-pass

approaches.

All-pass phase shifters have also been designed using active circuits. For example

a recently published design in [58] uses two transistors in feedback, where a series

resonator consisting of a fixed inductor and a varactor form the feedback path. The

Page 53: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 30

L

TL CTL

d/2 d/2

C

Figure 2.14: PRI/NRI metamaterial phase shifter unit-cell.

phase is tuned via a single varactor voltage, and the phase shifter achieves 100o tuning

range at 1GHz. Another active phase shifter that was published in [23], combines a

gain stage together with two different classes of phase shifters. The design in [23] uses

a switched-network phase shifter, but instead of cascading multiple stages to cover the

entire phase tuning range, only one stage is used to realize a coarse tuning of 180o,

while the rest of the phase tuning range is covered by varactor-tuned L-C low-pass

phase shifters. In spite of the numerous advantages offered by amplifier-based active

phase shifters, using amplifiers to design all-, low-, or high-pass phase shifters results in

uni-directional designs which makes them unsuitable for operating in both the transmit

and receive modes when incorporated within the beam steering network of a wireless

transceiver.

2.3.5 PRI/NRI Metamaterial Phase Shifters

The recent developments in the field of metamaterials have generated strong interest

in building phase shifters by cascading NRI metamaterial lines with PRI TLs [5].

Figure 2.14 shows the unit-cell of a TL PRI/NRI phase shifter [5]. It is composed of a

regular microstrip line (PRI section) loaded with two series capacitors, C, and a shunt

inductor, L (NRI section). Cascading the PRI TL, which has a low-pass response, with

the NRI section, which has a high-pass response, compensates the phase shift incurred

by the propagating signal. One can show that, the phase shift of the PRI/NRI phase

shifter in Fig. 2.14 can be approximated as:

φ ≈√

2

ω√

LC− 2θTL, (2.25)

Page 54: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.3. PHASE SHIFTERS 31

where θTL is the phase shift of a single microstrip TL. Equation (2.25) was originally

derived in [5]. According to Eq.(2.25), the PRI/NRI phase shifter can be designed

to produce a zero-degree phase at the design frequency. This is achieved through the

phase compensation process as opposed to accumulating a -360o or a +360o, which

would be necessary to achieve the zero-degree phase in a traditional low-pass or high-

pass topology respectively. Although, both approaches seem identical in terms of the

phase value at the design frequency, the latter approach (using low- or high-pass struc-

tures) results in a significantly larger group delay and consequently a much smaller

bandwidth. Hence, using the PRI/NRI approach allows building compact broadband

phase shifters with a linear frequency response, this was demonstrated in [5] and will

be also demonstrated in chapter 4 of this thesis. Centering the phase shift at 0o is de-

sirable, for example, for scanning about the broadside direction in series-fed steerable

antenna arrays. This will be explained in more detail in section 2.5.1, as well as in

chapter 6.

It is obvious from the phase expression of Eq.(2.25), that the phase of the PRI/NRI

phase shifter can be tuned using the capacitance C and the inductance L. Simultane-

ously changing the capacitance from Cmin to rC ×Cmin and the inductance from Lmin

to rL × Lmin results in the following phase tuning range:

|∆φ| =√

2

ω√

LminCmin

(1− 1√

rLrC

). (2.26)

Equation (2.26) reveals that, tuning both the capacitance and inductance results in in-

creasing the phase tuning range compared to only varying the capacitance. A tunable

composite PRI/NRI TL phase shifter was presented in [59] using two tunable loading

elements: series and shunt ferroelectric varactors. However, this implementation re-

quires high control voltages (15V ). Furthermore, the design in [59] uses a fixed shunt

inductor which makes it impossible to achieve a low return loss across the entire phase

tuning range. This will be explained in more detail in chapter 4. Also, the ferroelectric

varactors result in a modest phase tuning range of 12.5o/unit-stage.

The above discussion summarizes the different types of phase shifters and the state-

of- the-art in phase shifters’ design. This section also described the recent advances in

metamaterial-based phase shifters, and highlighted the main differences and similarities

between them and traditional phase shifters.

Page 55: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 32

(1)

(4)

(2)

(3)

Through port

Coupled portIsolated port

Input port

S31S41

Figure 2.15: Block diagram of a 4-port directional coupler.

2.4 Directional Couplers

Since chapter 5 of this thesis describes a novel MMIC directional coupler, it is instruc-

tive to present here a brief section describing directional couplers. Directional couplers

are one of the most commonly used building blocks in microwave and RF systems.

Some applications of directional couplers are: signal monitoring and automatic level

control, in-phase/quadrature-phase modulators, signal splitting, combining, and phase

shifting. The block diagram of a 4-port directional coupler is shown in Fig. 2.15. The

input signal is applied to port 1 and is divided among the through and coupled ports,

ports 2 and 3 respectively, according to the value of the coupling coefficient C. A direc-

tional coupler is characterized by the coupling coefficient C, and the isolation I, which

are defined as:

C = 10 log

(P1

P3

)= −20 log |S31|, and (2.27)

I = 10 log

(P1

P4

)= −20 log |S41|, (2.28)

where P1 is the input power at port 1, and P3 and P4 are the output powers from the

coupled and isolated ports respectively. If a directional coupler is designed to achieve

equal output powers at the coupled and through ports, P2 = P3 (in other words, a

3dB coupling coefficient), it is usually termed as a hybrid coupler. The isolation of a

coupler indicates how well the coupler prevents the input signal from leaking to port

4 (isolated port). Another popular parameter used in the literature to characterize

couplers is the directivity D, which is defined as:

D = 10 log

(P3

P4

)= 20 log

∣∣∣∣S31

S41

∣∣∣∣ . (2.29)

Page 56: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 33

/4

/4

(1)

(4)

(2)

(3)

Through port

Coupled portIsolated port

Input port

Figure 2.16: Diagram of a microstrip branch-line directional coupler.

However, the directivity can be inferred from the coupling coefficient and the isolation

using the following equation:

D = I − C (dB). (2.30)

Using printed microstrip TLs to design directional couplers is one of the most com-

mon methods to implement planar couplers suitable for low form factor RF and mi-

crowave systems. An instructive review of printed TL directional couplers is available

in [24]. Printed TL implementations of directional couplers impose limitations on the

area occupied by the couplers especially for systems operating in the low GHz frequency

range. This has hindered the integration of couplers into MMICs and has motivated the

development of various lumped-element coupler topologies [60]. Directional couplers

can be classified into four main categories according to their structure:

• Branch-line directional couplers

• Coupled-line directional couplers

• Lumped-element L-C directional couplers

• NRI/PRI metamaterial directional couplers

The following sections summarize the main topologies of printed and integrated direc-

tional couplers and highlights the recent advances in the design of directional couplers

using NRI metamaterials.

Page 57: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 34

2.4.1 Branch-Line Directional Couplers

A branch-line coupler consists of four λ/4 TLs with a characteristic impedance of

Z1 = Zo, and Z2 = Zo/√

2 connected as shown in Fig. 2.16, where λ is the wavelength.

Following the analysis outlined in [24], one can show that if the coupler is excited

at port 1 while the rest of the ports are terminated with Zo, then the input port is

perfectly matched at the design frequency, i.e. S11(ω = ωo) = 0. Furthermore, the

transmission coefficients of the through, coupled, and isolated ports can be expressed

as:

S21(ω = ωo) = − j√2, (2.31)

S31(ω = ωo) = − 1√2, and (2.32)

S41(ω = ωo) = 0 (2.33)

respectively. Equation (2.31) and Eq.(2.32) indicate that the input signal power is

equally divided among the through and coupled ports. Furthermore, the two signals

at the through and coupled ports have a 90o phase difference. On the other hand,

Eq.(2.33) indicates that port 4 is completely isolated from the input signal. However,

since the operation of the branch-line coupler relies on having λ/4 TLs, its bandwidth

is usually limited to about 15% [24]. Branch-line couplers can be designed for different

coupling coefficients, by changing the characteristic impedances of the microstrip TLs

Z1 and Z2. In fact, one can show that, in the general case [61], the amplitude of the

through and coupled signals can be expressed as:

S21(ω = ωo) = −jZ1

Zo

, and (2.34)

S31(ω = ωo) = −Z1

Z2

. (2.35)

Hence, the ratio Z1/Z2 can be used to determine the coupling coefficient of a branch-line

coupler. However, for a lossless design, power conservation dictates that the following

equation should be satisfied:

(Z1

Zo

)2

+

(Z1

Z2

)2

= 1. (2.36)

Page 58: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 35

/4(1)

(3)

(2)

(4)

Through port

Isolated portCoupled port

Input port

Figure 2.17: Diagram of a microstrip coupled-line directional coupler.

This can be obtained from the more intuitive expression |S21|2 + |S21|2 = 1, and using

Eq.(2.34) and Eq.(2.35) to substitute for S21 and S31, respectively.

2.4.2 Coupled-Line Directional Couplers

A printed coupled-line coupler consists of two closely spaced microstrip TLs, as shown

in Fig. 2.17. The amount of coupling, and hence the coupling coefficient, C, between

the two microstrip TLs is a function of their width and spacing, as well as the substrate

thickness and dielectric constant [24]. But, the amount of power coupled to port 3, is

not only a function of the coupling coefficient, C, but is also a function of the length

of the coupler. To maximize the coupled power an electrical length of π/2 is usually

picked for the design of coupled-line couplers, which corresponds to a λ/4 length.

Given a specific coupling coefficient C, and a characteristic impedance Zo, then the

required even- and odd-mode characteristic impedances of the coupled TLs should be

calculated using the following equations:

ZoE = Zo

√1 + C1− C , and ZoO = Zo

√1− C1 + C . (2.37)

The even- and odd-mode characteristics impedances, ZoE and ZoO, are used to charac-

terize any two coupled TLs when excited by a common-mode and a differential signal

respectively [24]. Based on the values of ZoE and ZoO, obtained from Eq.(2.37), one

can determine the coupled TLs parameters such as their width, separation, and the

required substrate height and dielectric constant using standard charts, such as the one

found on page 388 of [24]. In practice coupled-line couplers are usually used to achieve

small power coupling levels. In contrast, higher power coupling levels close to 3dB

Page 59: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 36

Figure 2.18: lumped-element L-C low-pass and high-pass Π realizations of a branch-linecoupler.

are only achievable using branch-line couplers. However, coupled-line couplers usually

have much larger bandwidths compared to branch-line couplers.

2.4.3 Lumped-Element L-C Directional Couplers

Printed branch- and coupled-line couplers occupy a large area, since they rely on λ/4

TLs, which tend to be a few centimeters for applications operating in the low GHz

frequency range. This prevents their integration with other RF and digital circuits

on the same chip for a fully-integrated system, and has motivated the development of

various lumped-element topologies for implementing integrated couplers [60].

Most of the lumped-element realizations of couplers are inspired from the TL branch-

line or the TL coupled-line topologies. For example, replacing each λ/4 TL of the

branch-line coupler in Fig. 2.16 with a -90o low-pass, Π, L-C phase shifter results in

the L-C coupler realization of Fig. 2.18-a. On the other hand, using +90o high-pass, Π,

L-C phase shifter results in the L-C coupler realization of Fig. 2.18-b. In both designs

of Fig. 2.18, the values of the inductors and capacitors are chosen to achieve the desired

±90o phase shift, and, at the same time, set the required line impedances. Both the

L-C couplers of Fig. 2.18 use four inductors, and four capacitors. It is interesting to

note that the high-pass, Π, L-C coupler topology of Fig. 2.18-b constitutes the core

of a 2-D unit-cell of a NRI metamaterial medium. This points out the strong relation

between the field of NRI metamaterials and directional couplers. In fact, couplers have

Page 60: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 37

C1

C1

C2C2

L

L

L

(1)

(4)

(2)

(3)

L

C2

C1

C1

C2

Figure 2.19: L-C lumped-element high-pass Tee realization of a branch-line coupler.

C1C1

L1

L1(1)

(4)

(2)

(3)

C1C1

C2 C2

Figure 2.20: L-C lumped-element realization of a coupled-line coupler.

benefited from the recent developments in the field of metamaterials [4,17,62–65], and

this point will be discussed in more detail in section 2.4.4.

Other L-C coupler realizations can be obtained by using -90o low-pass, Tee, L-C phase

shifters or by using +90o high-pass, Tee, L-C phase shifters. The former requires the

use of eight inductors, which makes the size of the coupler excessively large compared to

the architectures of Fig. 2.18. On the other hand, using +90o high-pass Tee L-C phase

shifters, as shown in Fig. 2.19, results in the same number of inductors, however it

requires eight capacitors. IC capacitors usually occupy a much smaller area compared

to IC inductors, so this does not result in a larger area. However, having two capacitors

in the signal path of each phase shifter will result in more losses especially for a tunable

coupler design where these capacitors are to be replaced with on-chip varactors.

Page 61: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.4. DIRECTIONAL COUPLERS 38

Lumped-element L-C couplers can also be designed based on TL coupled-line couplers

by replacing the two λ/4 TLs with two -90o, Π, L-C sections (L1 and C1), as shown

in Fig. 2.20, and adding two coupling capacitors, C2, to model the coupling occurring

between the two TLs. This implementation requires only two spiral inductors, which

makes it very attractive for designing compact on-chip couplers. Furthermore, for IC

implementations the two inductors can be replaced with two coupled spiral inductors.

This further reduces the area occupied by the L-C coupler [66]. Although lumped-

element couplers, in general, offer numerous advantages over their printed counterparts,

such as small area and ease of integration with RF and digital circuits, lumped-element

couplers have smaller bandwidths compared to printed couplers. One technique that

is used to extend the bandwidth of L-C couplers is to use a cascade of multiple L-C

sections [67].

2.4.4 PRI/NRI Metamaterial Directional Couplers

PRI/NRI metamaterial coupler designs [4, 17, 62–65] are relatively new and have all

emerged following the planar L-C realization of metamaterials. The interesting prop-

erties of NRI metamaterial lines have motivated designers to investigate the benefits

of using NRI lines to build branch-line and coupled-line couplers. In [17], it was shown

that combining the use of PRI and NRI lines to design printed branch-line couplers

results in a much more compact size without any bandwidth degradation. Two branch-

line couplers designs were presented in [17]. In the first design, the low impedance

lines (50/√

2Ω) were implemented using regular PRI microstrip TLs, whereas the high

impedance lines (50Ω) were implemented using NRI lines. This resulted in an area of

λ/4×λ/12 (i.e. length by width) for the coupler, which corresponds to an area savings

of 66% compared to a traditional branch-line coupler. The second design presented

in [17] uses NRI lines to implement the low impedance lines (50/√

2Ω), and regular

PRI microstrip TLs to implement the high impedance lines (50Ω). In this case, the area

of the coupler is λ/4 × λ/14, which corresponds to an area savings of 77% compared

to a traditional branch-line coupler.

Furthermore, NRI metamaterial lines have been used to design dual-band branch-

line couplers [4]. Dual-band operation is enabled by replacing the PRI microstrip TLs

of a branch-line coupler with NRI metamaterial TLs. As demonstrated in [4], NRI lines

Page 62: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 39

Table 2.1: Comparison Between Different Directional Coupler Topologies.Parameter Branch-line Coupled-line Lumped-element Printed PRI/NRIIntegration X X

√X

Coupling coeff. >3dB <3dB Arbitrary ArbitraryBandwidth Average Large Small AverageSize Large Medium Very small Medium

allow full control over the values of the two frequencies f1 and f2 at which the NRI lines

achieve a +90o and a +270o (which is equivalent to -90o) phase shift respectively. This

guarantees identical operation of the branch-line coupler at the two frequencies f1 and

f2, allowing for dual-band operation. On the other hand, in a traditional branch-line

coupler using only PRI TLs, the PRI TLs would achieve the -90o and a -270o (which is

equivalent to -90o) phase shifts only at fo and 3×fo respectively, where fo is the design

frequency. Hence, using traditional PRI TLs does not give control over the choice of

the two frequencies, since f2 has to be three times f1, which is usually not suitable for

most dual-band applications.

Coupled-line couplers have also benefited from the advances in metamaterials. NRI

/PRI metamaterial couplers have been designed by coupling a PRI TL with a NRI

metamaterial line in [4,62,64,65] and by coupling two NRI metamaterial lines together

in [63,65]. The main benefit from using NRI lines to design such couplers is the ability

to achieve high power coupling levels, as opposed to traditional coupled-line designs,

using only PRI TLs, which limit the coupling level to small values. By using NRI

metamaterial lines, coupling levels of -3dB were demonstrated in [62,63], and near 0dB

coupling levels were demonstrated in [4, 63].

Table 2.1 qualitatively compares between the achievable performance from the dif-

ferent directional coupler topologies presented in this section.

2.5 Phased Antenna Arrays

2.5.1 Antenna Arrays Basics

A phased antenna array, as defined by the glossary of telecommunication terms [68],

is a group of antennas in which the relative phases of the signals feeding the antennas

are set in such a way that the effective radiation pattern of the array is reinforced in

Page 63: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 40

Ae+j(N-1)

Ae+j2

Ae+j

A

dE dE

Figure 2.21: N-element uniform linear antenna array with equal amplitude excitationand a progressive phase constant φ.

a desired direction and suppressed in undesired directions. Generally, phased arrays

are either planar (2-D) or linear (1-D). This thesis focuses on linear arrays, as they are

considered the basic building block for planar arrays.

In general, the radiation pattern of an antenna array can be decomposed into the

product of two terms: an array factor AF (θ), which depends on the geometry of the

array, the number of elements, and the relative amplitudes and phases of the signals fed

to each antenna, and an element factor EF (θ), which represents the radiation pattern

of a single antenna [69]. Fig. 2.21 shows a uniform, linear antenna array, i.e. the

array has equally spaced elements which are excited with equal amplitudes A and a

progressive phase shift φ. The array factor of this array can be expressed as:

AF (θ) =1

N

sin

(N

2(kdE sin θ + φ)

)

sin

(1

2(kdE sin θ + φ)

) , (2.38)

In Eq.(2.38), dE is the inter-element spacing, θ is the angle measured from the normal

to the array axis, and k is the wave-number, which is related to the operating frequency

by k = ω/c, where c is the speed of light. The zeros of the array factor will result in

nulls in the antenna array’s radiation pattern. Also, if the individual antenna elements

are omni-directional, then the locations of the maxima in the array’s radiation pattern

are mainly determined by the maxima of the array factor. Using Eq.(2.38), one can

Page 64: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 41

30°

60°

90°−90°

−60°

−30°

−30−20

−100

Major lobe

Side lobesHPBW

Figure 2.22: Array factor of a 4-element antenna array fed in-phase and with dE = λ/2.

show that the maxima of the array factor occur at:

θm = sin−1

(λo

2πdE

(−φ± 2mπ)

), m = 0, 1, 2, . . . , (2.39)

where λo is the free-space wavelength, given by λo = c/f .

In many applications, it is desired to center the main beam of the array about the

broadside direction, i.e. at θ = 0o. The necessary condition for broadside radiation

can be obtained from Eq.(2.39) by setting θ0 = 0o to obtain the first maximum of the

radiation pattern at broadside. This results in the following condition for broadside

radiation:

φ = 0 (2.40)

indicating that a uniform array should be fed in-phase in order to center its main

beam at broadside. This is demonstrated in Fig. 2.22, which plots the theoretical

expression of the array factor, Eq.(2.38), of a 4-element array when the elements are

fed in-phase and the inter-element spacing, dE, is set to λo/2. The array factor plot of

Fig. 2.22 shows one major lobe and two side lobes. Side lobes represent radiation in

undesired directions, which should be minimized. According to Fig. 2.22, a 4-element

array with omni-directional antenna elements would achieve a side lobe level of -11dB.

Furthermore, its half-power beamwidth (HPBW) would be 26o as shown by Fig. 2.22.

Page 65: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 42

30°

60°

90°−90°

−60°

−30°

−30−20

−100

φ=+90o

φ=−90o

Figure 2.23: Array factor of a λo/2 4-element antenna array fed with a progressivephase shift of ±90o.

In general, when the antenna elements are fed with a progressive phase shift of φ,

the direction of the main beam (i.e. the scan angle) can be written as:

θ0 = − sin−1

(λo

2πdE

φ

). (2.41)

Equation (2.41) indicates that, using phase shifters capable of generating negative

progressive phase shifts results in positive scan angles θ0, and vice versa. Hence, to scan

the main beam about the broadside direction, the progressive inter-element phase shift

should acquire both positive and negative values. This conclusion plays an important

role in the selection of the topology of the inter-element phase shifters, especially in

series-fed arrays as will be described later. For a progressive inter-element phase shift

of ±90o the main beam of the array factor can be scanned all the way from −30o

to +30o about the broadside direction as illustrated in Fig. 2.23. Also, as the main

beam is scanned off the broadside direction another minor lobe appears in the radiation

pattern. However, its level remains below -11dB.

In most applications, it is also important to avoid the creation of grating lobes in

the radiation pattern (i.e. other global maxima for the array factor). Using Eq.(2.39),

it can be shown that, to avoid creating grating lobes in the radiation pattern while

Page 66: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 43

L

W

hr

Z

X

Y

Figure 2.24: Rectangular microstrip patch antenna fed with a microstrip TL .

operating the array at broadside, the following condition should be satisfied:

dE ≤ λo

2. (2.42)

Equation (2.42) is a fundamental equation, since it sets the maximum separation dis-

tance between two consecutive antenna elements. Hence, tight limitations are set on

the phase shifter dimensions to fit in-between the antenna elements of a series-fed

design, if it is desired to integrate the phase shifters with the antennas on a single

PCB. However, if the array uses a parallel feed network, such tight constraints are not

imposed on the phase shifter dimensions.

2.5.2 Microstrip Patch Antenna

Phased antenna arrays can use a variety of antenna elements. However, for wireless

consumer applications where size, weight, form factor, and cost are constrained, mi-

crostrip patch antennas become a popular choice. A patch antenna consists of either

a rectangular or circular shaped conductor on top of a ground plane. Figure (2.24)

shows a rectangular patch antenna fed with a microstrip TL. The geometry of a patch

antenna is a function of the desired resonance frequency, i.e. the frequency of opera-

tion, and the substrate properties [69]. Given the desired resonance frequency fr of a

rectangular patch and the substrate dielectric constant εr and height h, its width can

Page 67: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 44

L

W

yo

Figure 2.25: Inset-fed rectangular microstrip patch antenna.

be calculated using:

W =1

2fr√

µoεo

√2

1 + εr

. (2.43)

To a first order of approximation, the length of the patch is equal to the resonance

length, L ≈ λo/2√

εr, where λo is the free space wavelength. However, due to the

existence of fringing fields the patch antenna seems electrically longer than its physical

length. Hence, a more accurate estimate of the patch length can be obtained using the

following expression [69]:

L =λo

2√

εeff

− 2∆L, (2.44)

where

εeff =εr + 1

2+

εr − 1

2√

1 + 12h/W, and (2.45)

∆L = 0.4h(εeff + 0.3)(W/h + 0.27)

(εeff − 0.26)(W/h + 0.8). (2.46)

At resonance, the input impedance of a patch antenna is real and usually takes very

large values. For example, the patch resistance can take values close to 300Ω. This,

however, depends on the patch and substrate properties. To bring the patch resistance

down to reasonably low values (i.e. to values close to the characteristic impedance of

the microstrip feed line), the microstrip TL feeding the patch is recessed inwards as

shown in Fig. 2.25 [69]. The value of the inset feed point yo determines the value of

Page 68: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 45

30°

60°

90°−90°

−60°

−30°

−30−20

−100

10

30°

60°

90°−90°

−60°

−30°

−30−20

−100

10

(a) (b)

Figure 2.26: Elevation plane gain plot for a 2.4GHz rectangular microstrip patch an-tenna: (a) in the y-z plane, (b) in the x-z plane.

the patch resistance at resonance.

Figure 2.26-a and Fig. 2.26-b show the gain of a microstrip patch antenna in the

x-y plane (as shown in Fig. 2.24). The patch is designed to operate at 2.4GHz with

a dielectric constant, εr, of 4.5 and a substrate thickness h of 3.175mm (125mil). The

gain plot of Fig. 2.26-a is for the y-z plane, whereas that of Fig. 2.26-b is for the x-

z plane. Both plots show that the patch antenna has a large HPBW. Hence, when

patches are used it is necessary to employ arrays to produce more directive, high-gain

beams.

2.5.3 Phased Array Feed Network Topologies

The popular approach to building a phased array transceiver for low GHz applica-

tions is by using a single transceiver combined with a beam steering network to feed

the different antennas with the appropriate signal amplitudes and phases. As will

be described in this section, the beam steering network of this type of phased arrays

can either take a parallel or a series configuration. Aside from utilizing electronically

tunable phase shifters, in the RF domain, to generate the appropriate signal phases,

the beam steering network has to take care of the power splitting and combining.

The reason for the popularity of this approach for low GHz applications, is the large

size of the antennas and the large distance between them, which scale with the wave-

length. Consequently, the transmission-lines (TLs) connecting the printed antennas to

Page 69: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 46

the transceiver can readily be used for power splitting, combining, and phase shifting,

without significantly increasing the area occupied by the phased array. Furthermore,

the TLs provide an adequate means for designing low-loss power splitters and combin-

ers, which are very challenging to design and integrate on-chip at these frequencies. It

is also worth mentioning that, this type of phased array transceivers require only one

low-noise amplifier, mixer, and power amplifier.

On the other hand, for millimeter-wave applications, performing the phase shift-

ing in the RF domain becomes a challenge. This necessitates performing the phase

shifting at lower frequencies, which requires each antenna in the phased array to have

a separate transceiver. Consequently, the majority of millimeter-wave phased array

transceivers utilize a parallel architecture, which requires a separate transmit/receive

path for each antenna in the array [70, 71]. An N-element phased array transceiver of

this type would require roughly N times the area and the power consumption of a sin-

gle transceiver, which is why this approach is not attractive at the low GHz frequency

range. This approach has been used in many recent publications to design millimeter-

wave phased array transceivers, as it conveniently allows integrating the entire phased

array transceiver onto a single chip. Furthermore, at these high frequencies the an-

tenna dimensions shrink, allowing their integration with the transceivers on a single

chip. This, however, is still being investigated, as there are many challenges facing the

design of efficient on-chip antennas in silicon [72–74].

The objective of this thesis is to demonstrate beam steering for 2.4GHz ISM band ap-

plications. Consequently, the first approach, is adopted to design the steerable phased

array.

Feed networks for microstrip patch arrays can take a series or a parallel configuration.

A good review of the different feeding configuration of patch arrays can be found in [75].

Parallel-Fed Arrays

In parallel-fed arrays, the individual antennas are fed in parallel using a TL power

division network as illustrated in Fig. 2.27. Parallel-fed arrays are the popular choice

for electronic beam steering, since they easily allow inserting phase shifters to control

the phase excitation of each patch. However, the simplified parallel architecture of

Fig. 2.27 uses unequal TLs to feed the individual patches, which results in unequal

Page 70: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 47

dE<

Figure 2.27: A 4-element parallel-fed antenna array.

dE<

Figure 2.28: A 4-element corporate-fed antenna array.

Page 71: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 48

dE<

Figure 2.29: A basic 4-element series-fed antenna array.

phase variations across the signal bandwidth. Figure 2.28 shows another version of

the parallel-fed architecture, which uses equal length TLs to feed the patches, termed

the corporate-fed architecture. Using equal length TLs makes the phase excitations,

and hence the radiation pattern of the array, less sensitive to frequency variations,

i.e. results in less beam squinting. This makes corporate-fed arrays relatively wide-

band, making them a popular choice for beam steering in high data-rate applications.

This, however, comes at the expense of the large area occupied by the feed network.

Occupying a large area also increases the insertion losses associated with the feed

network lowering the array’s efficiency. Furthermore, another disadvantage of parallel-

and corporate-fed architectures is that they require phase shifters having a very wide

tuning range; an N-element parallel- or corporate-fed array requires a maximum phase

shift of (N − 1)φ to produce a progressive phase shift of φ.

Series-Fed Arrays

In a series-fed array, the individual patch antennas are excited in series as illustrated

in Fig. 2.29. Here, the power is delivered to the patch antennas one after the other.

The feed network of this type has the advantage of being less complex, and much more

compact in terms of area compared to the parallel or corporate types. Its compact

size also minimizes the insertion losses, and the undesired radiation caused by the feed

network. This makes series-feed arrays more efficient than their parallel- or corporate-

fed counterparts. Furthermore, an N-element series-fed array requires a maximum

phase shift of only φ to produce a progressive phase shift of φ, since in the series

configuration each phase shifter is reused by more than one patch.

Page 72: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 49

Zo

dE< LPS

Figure 2.30: A 4-element series-fed traveling wave in-line antenna array using a termi-nation load.

dE<

LPS

Figure 2.31: A 4-element series-fed traveling wave out-of-line antenna array without atermination load.

Page 73: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 50

Series-fed arrays can use in-line feeding or out-of-line feeding. In-line fed arrays

utilizes a single TL which directly feeds all the patch antennas as shown in Fig. 2.30.

On the other hand, out-of-line fed arrays utilize short TLs to connect the patches

to the main feed line as shown in Fig. 2.31. Series-fed arrays using the in-line feeding

technique occupy a very small area [76,77], and hence have the smallest insertion losses

associated with the feed network. However, the in-line feeding technique makes the

series-fed array very narrow band as it makes the inter-element phase shift a function

of the patch’s narrow-band impedance and the interconnecting TLs. On the other hand,

the out-of-line feeding technique alleviates the dependence of the inter-element phase

shift in series-fed arrays on the patch characteristics [78]. Furthermore, as illustrated

in Fig. 2.31, moving the patches off the centerline of the array gives more room for the

inclusion of the inter-element phase shifters required for beam steering.

Series-fed antenna arrays can also be classified into resonant [76–78] or traveling

wave arrays [77]. Resonant series-fed arrays can be designed using the in-line or the

out-of-line architectures. In either case, the array is terminated with either a short

circuit or an open circuit. Hence, the reflected wave creates a standing wave. Placing

the microstrip patches m× λ apart, where m could take any integer value, excites all

the patches with the same amplitude and with the same phase, i.e. φ = 0o. This makes

resonant series-fed arrays a very popular technique to build broadside arrays. However,

resonant arrays are not usually used for electronic beam steering. Furthermore, they

are very narrow-band, as any frequency variation changes the way the incident and

reflected waves add up at the patches, resulting in mismatches at the array input.

On the other hand, the feed-line of a traveling wave array is designed to be well

matched, and ideally free of any reflections. Similar to series-fed resonant arrays,

traveling wave arrays can be designed using the in-line or the out-of-line architectures.

However, the spacing between the elements does not have to be multiple integers of

the λ, which allows series-fed traveling wave arrays to produce off-broadside beams,

as well as broadside beams, if their spacing is a multiple of λ. For electronic beam

steering, this is achieved using electronically tunable inter-element phase shifters. The

signal amplitude on the main feed-line of a traveling wave array tapers due to the

power radiated by the patches and due to the insertion loss of the phase shifters. This

results in an imbalance in the signal power feeding each patch antenna. However, by

using proper design techniques, this amplitude imbalance can be eliminated. This will

Page 74: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 51

Table 2.2: Comparison Between Different Antenna Array Feed Network Topologies AndThe Requirements On The Interstage Phase Shifters.

Parameter Parallel-Fed Series-FedCorporate In-line Out-of-line

Feed network size Large Very small SmallScan angle rangea Small Large LargeBandwidth Large Small SmallBeam Squinting Low High HighReq. phase tuning range (N-1)φ φ φReq. phase shifter losses Relaxed Small SmallReq. phase shifter size Relaxed Very small Small

aScan angle range is estimated for the same phase tuning range.

be described later on in chapter 6. At the end of a series-fed traveling wave array, the

remaining power is usually absorbed by a termination impedance, usually a 50Ω load, as

illustrated in Fig. 2.30 for an in-line architecture. This implies that a small percentage

of the input power in the TX mode (or the received power in the RX mode) is dissipated

in the termination, which reduces the overall efficiency of the array. To increase the

efficiency of a traveling wave series-fed array, the conductance of the individual antennas

can be increased to couple into them more power from the main feed-line. However,

this loads the main feed-line resulting in higher mismatches. Alternatively, higher array

efficiencies are achieved by increasing the number of elements [79]. Another approach

used is to design the array in such a way that the last patch absorbs this remaining

power, as illustrated in Fig. 2.31 for the out-of-line architecture.

Table 2.2 qualitatively compares the achievable performance from the different feed

network topologies presented in this section as well as the requirements set on the

interstage phase shifters.

2.5.4 Metamaterial Phased Antenna Arrays

With the recent advances in metamaterial phase shifters, it is natural that antenna

arrays would also benefit from these advances. As described in section 2.3.5, metama-

terial phase shifters are capable of achieving zero-degree phase shifts using the concept

of phase compensation, and it was demonstrated in [5] that these metamaterial-based

phase shifters achieve much lower group delays as opposed to a traditional -360o TL

Page 75: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

2.5. PHASED ANTENNA ARRAYS 52

segment. A low group delay is necessary to minimize the beam squinting with fre-

quency variations in series-fed antenna arrays. In order to demonstrate this, one can

obtain the derivative of the main beam angle θo using Eq.(2.41). This results in the

following expression:dθo

dω≈ λo

2πdE

ω+ Tgd

), (2.47)

where Tgd = −dφ/dω is the group delay of the inter-element phase shifters. Equation

(2.47) clearly indicates that a low group delay would result in less beam squinting

with frequency variations. This was verified experimentally in [6] where a series-fed

dipole array using PRI/NRI metamaterial phase shifters was presented. In [6], the

performance of a zero-degree metamaterial-based dipole array was compared to two of

the traditional approaches which achieve a -360o phase at the design frequency; the

first uses long meandered TLs, and the second uses a capacitively loaded TL. It was

demonstrated that the metamaterial-based dipole array results in less beam squinting

and occupies a more compact area compared to the traditional designs.

It is the aim of chapter 6 of this thesis to demonstrate the use of the electronically

tunable PRI/NRI metamaterial phase shifters, presented in chapter 4, towards the

design of series-fed antenna arrays in order to achieve electronic beam steering as well

as low beam squinting.

Page 76: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 3

CMOS Tunable Active Inductors

3.1 Introduction

T he most popular technique used to build tunable active inductors (TAIs) is by

using gyrators. This technique has greatly benefited from the advances in modern

CMOS technologies, which are now capable of providing transistors with very high

unity-gain frequencies (fts), thereby allowing the design of RF TAIs. However, most

of the published TAI designs suffer from one major drawback, which is their inabil-

ity to independently control both the TAI inductance and quality factor. Moreover,

the few published TAI designs which demonstrated the independent L and Q tuning

capability [25,38,48] use techniques which are specific to each individual circuit imple-

mentation. Hence, a generalized technique that can be directly applied to the gyrator-C

architecture is missing and would prove to be very useful.

In this chapter, the addition of a feedback element to enhance the Q of TAIs is

generalized to the block diagram level of the gyrator-C architecture, thus making this

Q-enhancement technique applicable to any TAI based on the gyrator-C architecture

as opposed to previously published work [25, 38, 48], which do not provide this gen-

eral framework. The effect of adding the feedback resistance is analyzed and design

53

Page 77: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.2. TRADITIONAL GYRATOR-C ARCHITECTURE 54

gm1

-gm2

Cin1+Co2

Co1

Cin2

Zin

Cin1+Co2ro2

L

RsZin

ro2

ro1

Figure 3.1: Gyrator-C architecture and its equivalent circuit.

equations are presented. It will be shown that the modified gyrator-C architecture

allows independent control over L and Q. The proposed architecture is used to design

a 0.13µm CMOS grounded TAI operating from a 1.5V supply. Experimental results

from a test chip are used to verify some of the design equations, and to demonstrate

that the L and Q can be independently tuned.

The principles of enhancing the Q of the traditional gyrator-C architecture are de-

scribed in section 3.2. Following that, the modified gyrator-C architecture is presented

in section 3.3. Finally, the design of the grounded TAI is presented in section 3.4.

3.2 Traditional Gyrator-C Architecture

The gyrator-C architecture consists of two transconductors (gm1 and gm2) connected

back-to-back, as shown in Fig. 3.1. If the output resistance and capacitance of the

transconductor gmi (where i = 1, 2) are modeled by roi and Coi, respectively, and its

input capacitance is modeled by Cini, then the input impedance, Zin, of the gyrator-C

circuit is expressed as:

Zin =

1

ro1

+ s(Co1 + Cin2)

s2 (Co1 + Cin2) (Cin1 + Co2) + s

(Co1 + Cin2

ro2

+Cin1 + Co2

ro1

)+

1

ro1ro2

+ gm1gm2

.

(3.1)

This can be represented by the equivalent circuit shown in Fig. 3.1, where the series

and parallel resistors (RS and ro2) model the losses, and the capacitor is incorporated

Page 78: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.2. TRADITIONAL GYRATOR-C ARCHITECTURE 55

to model the self-resonance of the TAI circuit. Furthermore, the inductance, L, and

the series resistance, RS, of the equivalent circuit are given by:

L =Co1 + Cin2

gm1gm2

, and (3.2)

RS =1

gm1gm2ro1

. (3.3)

According to Eq.(3.2), the inductance of the TAI circuit can simply be tuned by varying

the transconductances gm1 and gm2. This is usually done by varying the bias currents of

the two transconductors. However, this will also affect the value of the series resistance

RS.

3.2.1 Quality Factor Analysis

To understand the effect of tuning the inductance, L, on the TAI’s Q, one has to derive

the expression for Q using its basic definition Q = Im(Zin)/Re(Zin), which results in

the following expression:

Q = ω × Lro2 (1− ω2 (Cin1 + Co2) L)− ro2(Cin1 + Co2)R2S

R2S + ro2RS + ω2L2

. (3.4)

It is instructive to obtain the expression of the circuit’s self-resonance frequency, ωr,

since it helps in pointing out the dominant terms in Eq.(3.4). The self-resonance fre-

quency is defined as the frequency at which the imaginary part of the input impedance

becomes zero, which for a gyrator-C TAI is expressed as:

ωr =

√L− (Cin1 + Co2)R2

S

(Cin1 + Co2)L2. (3.5)

Equation (3.5) indicates that for a high-Q TAI to have a high self-resonance frequency,

which is necessary for high-speed operation, L should be much greater than (Cin1 +

Co2)R2S, resulting in the following simplification for the self-resonance frequency:

ωr ≈√

1

(Cin1 + Co2)L. (3.6)

Page 79: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.2. TRADITIONAL GYRATOR-C ARCHITECTURE 56

Furthermore, the quality factor expression of Eq.(3.4) can be simplified to:

Q ≈ ω × Lro2(1− ω2(Cin1 + Co2)L)

f(RS), (3.7)

where the function

f(RS) = R2S + ro2RS + ω2L2. (3.8)

As Eq.(3.7) indicates, Q is a function of frequency, starting at a low value and increases

with frequency until it peaks, then it starts to drop again due to the resonance with

the parasitic capacitance. The frequency at which Q reaches its peak value, ωp, can be

found by differentiating Eq.(3.7) and equating the derivative to zero. This results in

the following expression for ωp:

ωp =2RS + ω2

rL2

4L2×

(1 +

√1− 8RSω2

rL2(ro2 + RS)

(2RS + ω2rL

2)2

), (3.9)

which can be approximated as:

ωp ≈ ωr ×√

1

2− RSro2

ω2rL

2≈ ωr√

2. (3.10)

It is interesting to note that, the ratio between peak-Q frequency, ωp, of a gyrator-C

TAI and its self-resonance frequency, ωr, is approximately fixed and equal to 1/√

2.

To arrive at the result of Eq.(3.10), the frequency dependence of the equivalent series

resistance RS was neglected. This simplification results in a very small error between

the values of ωp predicted by Eq.(3.10) and the values obtained from the experiential

characterization of a gyrator-C based TAI, which will be demonstrated later in section

3.4.4. Substituting with ωp in Eq.(3.7) results in a peak-Q, Qp, of:

Qp ≈ ro2

2f(RS)×

√L

2(Cin1 + Co2). (3.11)

In order for the gyrator-C TAI to have a high peak-Q, the value of the function f(RS)

should be minimized. According to Eq.(3.3), which only allows positive values for RS,

this implies that RS should be very small in order to minimize f(RS). Consequently,

Page 80: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.2. TRADITIONAL GYRATOR-C ARCHITECTURE 57

0

Negative RS

Figure 3.2: Function f(RS) versus the negative series resistance RS.

one can neglect the first two terms of Eq.(3.8). Combining this with Eq.(3.10) and

Eq.(3.6), one can simplify Eq.(3.11) to:

Qp ≈ ro2 ×√

(Cin1 + Co2)

2L. (3.12)

Equation (3.12) shows the direct relationship between the inductance and the peak-Q

for a gyrator-C TAI, indicating that as L is tuned, via gm1 and gm2, the peak-Q also

changes, which is not desirable in most applications. Instead, having independent con-

trol over L and Q is necessary to provide the capability of optimizing the performance.

3.2.2 Q-Enhancement Technique For Gyrator-C TAIs

To overcome this interdependence between the L and Q of a gyrator-C TAI, we further

exploit the dependence of the peak-Q on f(RS), and hence RS. Figure 3.2 shows a

sketch for the quadratic function f(RS) versus RS, the function f(RS) has two negative

real roots given by:

RS1,2 = −ro2

2± 1

2

√r2o2 − 4ω2

pL2. (3.13)

Values of RS between the two roots (RS1 and RS2) will produce a negative Q possibly

resulting in an unstable TAI, therefore this region is avoided in general. Otherwise, if

Page 81: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.3. THE MODIFIED GYRATOR-C ARCHITECTURE 58

gm1

-gm2

Cin1+Co2

Co1

Rf

Cin2

Zin

ro2

ro1

Cin1+Co2ro2

L

RsZin

Z

Figure 3.3: Modified gyrator-C loop and its equivalent circuit.

RS < RS2 or RS > RS1, the Q is positive and the circuit is stable. To obtain a high

value for the peak-Q, RS should be picked close to either of the two roots but outside

the unstable region. Consequently, the TAI circuit has two possible operating points

on Fig. 3.2; P1 and P2 in regions 1 and 2 respectively. From Eq.(3.5), operating at P1

with a smaller |RS|, will result in a higher self-resonance frequency than operating at

P2, but will make the Q more sensitive to any parasitic resistance that might add to

RS. Also, the effect of RS on the Q differs according to the operating point chosen;

increasing RS while operating at P1 lowers the Q. On the other hand, increasing RS

while operating at P2 increases the Q. In the next section, a modified structure for

the gyrator-C architecture, which uses an additional feedback resistance, is proposed.

Adding a feedback resistance allows the series resistance RS to achieve negative values.

Furthermore, it allows RS to be tuned without affecting the inductance. Consequently,

this modified gyrator-C architecture will achieve independent L and Q tuning.

3.3 The Modified Gyrator-C Architecture

This section analyzes the effect of adding a feedback resistance to the traditional

gyrator-C architecture. It will be shown that adding a feedback resistance to the

gyrator-C architecture generates the negative resistance RS necessary to enhance the

TAI’s Q. The modified gyrator-C block diagram and its equivalent circuit are shown in

Fig. 3.3, where the resistance Rf is the additional feedback resistance. One can show

Page 82: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.3. THE MODIFIED GYRATOR-C ARCHITECTURE 59

that the expression for the input impedance of the modified gyrator-C architecture is:

Zin =

1

ro1

+ s

(Co1 + Cin2

(1 +

Rf

ro1

))+ s2Co1Cin2Rf

D(s), (3.14)

where

D(s) = s3RfCin2Co1(Co2 + Cin1)

+ s2

(Co1Cin2

Rf

ro2

+ (Cin1Cin2 + Co1Co2)

(1 +

Rf

ro1

)+ Cin1Co1 + Co2Co1

)

+ s

(Cin1 + Co2

ro1

+Co1

ro2

+Cin2

ro2

(1 +

Rf

ro1

))

+1

ro1ro2

+1

gm1gm2

. (3.15)

Although Eq.(3.14) appears to be very cumbersome, comparing it to Eq.(3.1) shows

that adding the feedback resistance Rf to the gyrator-C loop adds a zero and a pole to

the input impedance transfer function, which allows more control over the frequency

response of the TAI. To be specific, the additional zero in the input impedance transfer

function generates a negative, frequency dependent term that can be used to enhance

the TAI Q.

To understand more how the Q-enhancement takes place, the same approach of

section 3.2 is followed here and the circuit is modeled by the L-C circuit shown in

Fig. 3.3. It can be shown that the impedance of the inductive branch (Z), given by

the series combination of the equivalent inductance L and equivalent series resistance

RS, is expressed as:

Z =1

gm1gm2

×(

s2RfCo1Cin2 + s

(Cin2

(1 +

Rf

ro1

)+ Co1

)+

1

ro1

). (3.16)

Hence, the equivalent inductance L and the equivalent series resistance are expressed

as:

L =1

gm1gm2

×(

Cin2

(1 +

Rf

ro1

)+ Co1

), and (3.17)

RS =1

gm1gm2

×(

1

ro1

− ω2Cin2Co1Rf

). (3.18)

Page 83: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.3. THE MODIFIED GYRATOR-C ARCHITECTURE 60

Equation (3.17) indicates that the inductance is independent of the feedback resistance

Rf as long as the feedback resistance is much smaller than the output resistance ro1

of the first transconductor. On the other hand, Eq.(3.18) indicates that, RS can take

negative values, and its value can be controlled via the feedback resistance Rf . By

comparing the L-C models of Fig. 3.1 and Fig. 3.3, one can conclude that the addition

of the feedback resistance to the gyrator-C loop generates the negative tunable resis-

tance RS necessary for the Q-enhancement technique described in section 3.2. Thus, a

variable feedback resistance will allow us to control the TAI operating point on Fig. 3.2,

which will guarantee stable operation with a tunable high-Q. Furthermore, controlling

RS via Rf does not affect L (assuming ro1 >> Rf ), which consequently allows us to

independently tune L and Q. An intuitive way to explain how adding Rf enhances the

gyrator-C Q, is to consider the phase shift the output of the first transconductor gm1

undergoes before it feeds the second transconductor gm2. Tuning Rf allows us to set

this phase shift in order to push the loop towards positive feedback.

As previously explained in section 3.2.2, the circuit has two possible operating points

for high-Q operation, which are represented by points P1 and P2 in Fig. 3.2. If the

TAI operates at point P1, a smaller feedback resistance Rf is required. This will make

Q very sensitive to any interconnect resistance in the feedback path. Furthermore, if

the feedback resistance is slightly nonlinear, this will cause Q to be sensitive to the

signal level in the feedback path, which may lead to distortion and instability. This

nonlinearity might arise due to the implementation of the variable feedback resistance,

Rf , since, in most cases, Rf will vary with the signal level as will become evident in

section 3.4. On the other hand, the TAI will have a lower self-resonance frequency at

point P2. However, operating at point P2 requires a larger feedback resistance, which

alleviates the sensitivity, distortion, and instability issues.

It is worth mentioning that this Q-enhancement technique is applicable to any TAI

based on the gyrator-C architecture. Consequently, the previous analysis provides a

general framework for the design of TAIs with independent L and Q, unlike previously

published work [25, 39, 48]. Moreover, the 1-port, modified gyrator-C architecture of

Fig. 3.3 can be easily extended to build differential or 2-port TAIs simply by replac-

ing the single-ended transconductors gm1 and gm2 with differential transconductors as

shown in Fig. 3.4. Following the same theoretical procedure of the grounded architec-

ture presented in section 3.3, one can show that adding two tunable feedback resistors

Page 84: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 61

ro2

ro2

Zin,diff

L

Rs

L

Rs

gm1

-gm2

Cin2

Co1

Rf

+

-

Cin2

Rf

Co1

+

-

+

-

Cin1+Co2 Cin1+Co2

+

-

Zin,diff ro1 ro1

ro2 ro2

Cin1+Co2

Cin1+Co2

Figure 3.4: The modified differential gyrator-C architecture.

to the differential gyrator-C architecture produces a differential inductor with indepen-

dently tunable L and Q. This differential topology was presented in more detail by

the author in [80]. However, an in-depth analysis of this differential topology was not

included as part of this thesis since all the circuits presented in chapters 4, 5, and 6

rely on the single-ended, 1-port, architecture.

3.4 A Grounded 0.13µm CMOS TAI

This section presents the design of a grounded 0.13µm CMOS TAI circuit capable

of independently tuning the L and Q by using the modified gyrator-C architecture

presented in section 3.3.

3.4.1 Circuit Design

Figure 3.5 shows the proposed TAI circuit, the first transconductor gm1 of the modi-

fied gyrator-C architecture is replaced by a differential pair (M1−M2), and the second

transconductor gm2 is replaced by a common-source amplifier (M4). A tunable feedback

resistance Rf is inserted between the output of the first transconductor gm1 and the

input of the second transconductor gm2. Although the transconductors were replaced in

this design with a differential pair and common-source stages, as previously mentioned,

this Q-enhancement technique is applicable to any gyrator-C TAI. As another exam-

Page 85: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 62

IC

Vdd Vdd

Vdd

VddVdd

Vc1

Vc2

IB

Rf

M4

M1 M2

Zin

M3

M5M6

M7

M8

M9

M10

M11M12

-gm2

gm1

VCM

Figure 3.5: Proposed TAI circuit with the tunable feedback resistance.

ple, a differential, 2-port TAI circuit was presented by the author in [80], where two

differential-pair transconductors were used with the tunable feedback resistors. This

differential TAI, however, is not presented as part of this thesis, since it is not relevant

to the subsequent circuits presented in chapters 4, 5, and 6.

In the grounded TAI circuit of Fig. 3.5, transistors M3 and M5 mirror a ratio of the

reference current in (M7 − M8) and M6, respectively, to bias the circuit. Moreover,

M12 mirrors half of the current in M11 to generate the necessary current to bias M2.

To ensure that M3 and M9 mirror the desired current from the reference transistor

M7, a low-voltage cascode current mirror is used. Sizing cascode transistors M8 and

M10 appropriately will guarantee that the drains of M3, M7, and M9 have the same

potential, this is achieved by setting:

W8

L8

=W10

L10

= 2W2

L2

× W7/L7

W3/L3

. (3.19)

The transistor sizes of the proposed grounded TAI circuit are given in Table 3.1, where

Page 86: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 63

Table 3.1: Transistor Sizes of the TAI CircuitTransistor Size nf ×Wf × L Transistor Size nf ×Wf × LM1, M2 40× 2.85µm× 0.12µm M8,M10 4× 2.85µm× 0.12µmM3 60× 3.3µm× 0.2µm M7,M9 3× 3.3µm× 0.2µmM5 36× 4µm× 0.2µm M6 3× 4µm× 0.2µmM11 2× 4µm× 0.2µm M12 20× 4µm× 0.2µmM4 40× 4.5µm× 0.12µm

Table 3.2: Transistor Sizes of the Digital/Analog Tunable Feedback Resistance Rf

Transistor Size nf ×Wf × L Transistor Size nf ×Wf × LMf1 1× 0.5µm× 2µm Mf2 1× 0.5µm× 1µmMf3 1× 1µm× 1µm Mf4 1× 2µm× 1µmMf5 1× 4µm× 1µm Rf0 500ΩMN 4× 5µm× 0.12µm MP 12× 5µm× 0.12µm

nf is the number of fingers used to implement each transistor and Wf is the finger width.

The choice of the transistor sizes, especially M1, M2, and M4 dictates the achievable

range of inductances by the TAI circuit. In general, to achieve large inductances,

smaller sizes should be picked. However, using small sizes for the transistors makes

the TAI circuit incapable of supporting a large signal swing at its input port with an

acceptable level of distortion. On the other hand, to achieve smaller inductances, either

the sizes of the transistors should be large, which will add more parasitic capacitance

to the TAI circuit, or their bias current should be increased, which increases the power

dissipation. Hence, there exists many trade-offs between the desired inductance range,

power dissipation, speed, signal swing, and area. Consequently, careful simulations

were required to determine the appropriate transistor sizes.

Tunable Feedback Resistance

To implement the tunable feedback resistance Rf , binary weighted NMOS transistors

operating in the triode region are connected in parallel as shown in Fig. 3.6. The NMOS

transistors are also connected in parallel to a fixed resistance, Rf0, to improve linearity

by making the overall feedback resistance and hence Q less sensitive to the variations

in the overdrive voltage of the transistors. This will make Q less sensitive to the input

signal swing and will improve the circuit stability. The NMOS transistors are switched

Page 87: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 64

Rf0

Mf1

Mf5

Rf

Vf

D1

D5

Dig

ital

wo

rd

Vf

Figure 3.6: Digital/analog feedback resistance Rf .

ON and OFF using a 5-bit digital word, this allows coarse tuning of the Q. To enable

fine tuning, the digital word is applied to the gates of the NMOS transistors through

five CMOS inverters having a variable supply voltage, Vf , as shown in Fig. 3.6. The

voltage Vf is used to set the level of the gate voltage for the ON NMOS transistors [81].

Combining digital and analog control to tune the resistor value allows a wider tuning

range for the feedback resistance, and hence for the Q. This also makes the circuit more

robust to process and temperature variations. To reduce the number of pads required

by the TAI circuit and hence reduce the circuit area, the 5-bit digital word is serially

shifted into an on-chip shift-register. The sizes of the transistors used to implement

the digital/analog tunable feedback resistance Rf are given in Table 3.2.

3.4.2 TAI Small-Signal Analysis

An approximate expression for the TAI equivalent L and RS can be directly obtained

from Eq.(3.17) and Eq.(3.18) by replacing gm1 and gm2 with gm1,2/2 and gm4, respec-

tively. This results in the following expressions for the inductance and series resistance

Page 88: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 65

L

RsZinro4||ro5

Cgs1/2+Cgd1+

Cdb4+Cgd5+Cdb5

Z

Figure 3.7: Grounded active inductor equivalent circuit.

of the equivalent L-C circuit of Fig. 3.3:

L ≈ 2

gm1,2gm4

×(

Cgs4

(1 +

Rf

ro

)+ Co

), and (3.20)

RS ≈ 2

gm1,2gm4

×(

1

ro

− ω2CoCgs4Rf

), (3.21)

where ro and Co are the output resistance and capacitance of the differential pair

transconductor. Equation (3.20) shows that, provided that Rf is much smaller than

ro, L is independent of the feedback resistance and hence is independent of Q.

Also, by closely investigating Eq.(3.20), one will realize that the value of the in-

ductance has some dependence on process, supply, and temperature variations. Since

the focus of this work has been on the initial development and validation of the TAI,

a detailed sensitivity analysis of the performance of the TAI to process, supply and

temperature variations lies outside the scope of this thesis. However, when using this

circuit in a practical application, one can ensure that it achieves a process, supply, and

temperature independent inductance by using a constant-gm bias circuit [82] to bias

transistors M1,M2, and M4. Alternatively, since the circuit provides a tunable induc-

tance, one can simply ensure that the circuit’s tuning range is wide enough to calibrate

for process, supply, and temperature variations. Similarly, since Q is a function of the

feedback resistance which is implemented using MOS transistors it exhibits process,

supply, and temperature dependence. However, a high Q can be achieved by means of

the independent L and Q tuning capability of the circuit.

More elaborate circuit analysis replaces each transistor by its small-signal equivalent

model (gm, ro, Cgs, Cgd), but results in a fairly complicated expression for the input

impedance. To obtain a simplified expression, which is necessary to gain insight in

the circuit operation, the effect of the output resistance of the NMOS transistors is

Page 89: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 66

neglected. The input impedance Zin obtained from the analysis can be represented by

the equivalent circuit shown in Fig. 3.7. The impedance of the inductive branch, Z,

which consists of the series combination of L and RS, can be expressed as:

Z ≈ 2×s2RfCoCgs4 + s

(Co + Cgs4

(1 +

Rf

ro

))+

1

ro

gm1,2gm4

. (3.22)

This results in the same inductance and series resistance expressions given by Eq.(3.20)

and Eq.(3.21), respectively, which is consistent with our generalized gyrator-C block

diagram analysis presented in section 3.3.

3.4.3 TAI Noise Analysis

This section analyzes the noise generated by the TAI circuit due to the various tran-

sistors as well as the feedback resistor Rf . Our goal is to find an equivalent noise

current source (inL), which can be connected in parallel to the TAI circuit to model

the effect of the various noise sources. The results of this analysis will be used later on

in chapter 5 to quantify the noise performance of the TAI-based directional coupler.

In this analysis, the effect of the flicker noise generated by the transistors is neglected,

since for RF applications the design frequency is well above the 1/f corner frequency.

Therefore, only the thermal noise components are considered.

A simplified schematic of the TAI circuit with the different noise sources is shown

in Fig. 3.8, where i2nMxis the mean-square value of the drain current thermal noise

generated by transistor Mx, and v2nRf

is the mean-square value of the thermal noise

voltage generated by the feedback resistance Rf . For simplicity, the gate noise is

neglected throughout this analysis as well as the output resistances ro1,2, and the gate-

source capacitances Cgs1,2 of transistors M1 and M2. Assuming all the various noise

sources are uncorrelated, one can use superposition to show that, the mean-square

value of the input referred noise current (inL) at the inductor input port is expressed

Page 90: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 67

Vdd

Vdd

Vdd

Rf

M4

M1 M2

M3

M5

M12

vnRf

in1

in2

in12

in3in4

in5

+ -

LInductor

input port

inLInductor

input port

Figure 3.8: Simplified TAI schematic with the main current and voltage noise sources,and equivalent lumped noise current model.

as:

i2nL(ω) = i2n4+i2n5+g2m4×

i2n1 + i2n2 + i2n3

4+ i2n12 +

v2nRf

(1 + ω2C2or

2o)

r2o(

1

ro

− ω2RfCoCgs4

)2

+ ω2

(Co + Cgs4

(1 +

Rf

ro

))2 , (3.23)

where ro and Co are the output resistance and capacitance of the differential pair

respectively. If the TAI circuit is configured for high-Q operation, one should set the

feedback resistance Rf to cancel the resistive part of the circuit’s input impedance.

According to the approximate expression of Eq.(3.21), this results in the following

value for the feedback resistance:

Rf ≈ 1

ω2oroCoCgs4

, (3.24)

where ωo is the design frequency. Hence, for high-Q operation, the mean-square value

Page 91: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 68

Active

inductor

circuit

Digital

control

circuit

Open

ct. pad

Short

ct. pad

S GGG

GG S

S

1mm

0.5mm

Digital

circuitry

inputs

DC/bias

inputs

Figure 3.9: Tunable active inductor die micrograph.

of the input referred noise current becomes:

i2nL(ωo) ≈ i2n4 + i2n5 + g2m4 ×

i2n1 + i2n2 + i2n3

4+ i2n12 +

v2nRf

(1 + ω2oC

2or

2o)

r2o

ω2o

(Co + Cgs4

(1 +

Rf

ro

))2 . (3.25)

The transistor drain thermal noise current i2nMxis given by 4kTγgmx, whereas the

resistor thermal noise voltage v2nRf

is given by 4kTRf , where k = 1.38×10−23 J/K is the

Boltzmann constant, and T is the absolute temperature in degrees Kelvin. The value

of the coefficient γ typically ranges from 2 to 3 for short-channel transistors [44, 83].

This results in the following expression for the TAI equivalent noise current:

i2nL(ωo) = 4kTγ

gm4 + gm5 + g2

m4 ×2gm1,2 + gm3

4+ gm12 +

Rf (1 + ω2oC

2or

2o)

γr2o

ω2o

(Co + Cgs4

(1 +

Rf

ro

))2

.

(3.26)

3.4.4 Physical Realization and Experimental Characterization

Figure 3.9 shows the die micrograph of the fabricated grounded TAI circuit, the chip

was fabricated in a 1.5V , 0.13µm CMOS process. The TAI circuit occupies 150µm ×

Page 92: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 69

170µm. A 150µm-pitch GSG (ground-signal-ground) probe was used to probe the TAI,

while two 80µm-pitch multi-contact wedges with DC needles were used to provide the

bias and control voltages. A CS-5 calibration substrate was used to perform a 1-port

calibration to de-embed the frequency response of the RF probe, connectors, and cable.

The TAI was characterized by measuring the reflection coefficient, S11, that was in turn

used to extract the L and Q. As indicated by Fig. 3.9, open- and short-circuited pads

were included on the fabricated chip to estimate the input’s pad parasitic capacitance

and inductance. The pad capacitance and series inductance were obtained from the

measured input reflection coefficients of the open- and short-circuited pads respectively.

For a 65µm×65µm square pad, the measurements show that, the capacitance is 30fF,

and the inductance is 70pH. Consequently, they will not have a large effect on the TAI

performance, and all the measurements presented herein will include the effects of the

pad parasitics, i.e. the pad parasitics were not de-embedded. The tuning characteristics

of the TAI circuit are demonstrated through tuning modes I and II described below.

Tuning Mode I: Variable L and Fixed Peak-Q

In this mode, the inductance is tuned while maintaining a fixed peak-Q. The TAI L

is tuned via gm1,2 and gm4 according to Eq.(3.20), where the two transconductances

are set by the two bias voltages VC2 and VC1, respectively (see Fig. 3.5). However,

this will also change the value of the peak-Q according to Eq.(3.11). To compensate

for this change, the feedback resistance Rf is tuned to bring the peak-Q back to its

desired value. According to Eq.(3.20), changing Rf does not have a significant effect

on L. As indicated by Eq.(3.6), changing the bias point to tune L will also affect the

TAI self-resonance frequency, fr, since the change in L necessitates a change in the

frequency at which L resonates with the TAI parasitic capacitance.

To fully characterize the TAI circuit performance, the two bias voltages VC1 and VC2

are swept using two DC voltage sources and the measured L and Q are reported herein.

The measured L and Q are plotted in Fig. 3.10 when VC1 is fixed at 0V and VC2 is swept

from 0.3V to 0.6V. As indicated by Fig. 3.10-a, increasing VC2 results in a larger value

for the bias current IB, and consequently gm1,2 increases. This causes L to decrease.

Across this inductance tuning range, the peak-Q is maintained in excess of 100 as

shown by Fig. 3.10-b. This high Q is achieved by adjusting the value of the feedback

Page 93: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 70

1 2 3 4 5

0

1

2

3

4

Frequency (GHz)

Mea

sure

d T

AI i

nduc

tanc

e (n

H) * V

C2=0.3V, + V

C2=0.35V

∆ VC2

=0.4V, x VC2

=0.5VO V

C2=0.6V

1 2 3 40

50

100

150

200

250 * VC2

=0.3V, + VC2

=0.35V ∆ V

C2=0.4V, x V

C2=0.5V

O VC2

=0.6V

Frequency (GHz)

Mea

sure

d T

AI q

ualit

y fa

ctor

(a) (b)

Figure 3.10: Measured TAI characteristics versus frequency when VC1=0V and VC2

changes from 0.3V to 0.6V: (a) Inductance, (b) Quality factor.

Table 3.3: Measured Inductances for the TAI at 2GHz for Different Values of the BiasVoltages VC1 and VC2.

Voltage VC2

0.3V 0.35V 0.4V 0.5V 0.6V0V 4.4nH 2.1nH 1.3nH 0.9nH 0.8nH0.1V 5nH 1.9nH 1.5nH 1.1nH 0.9nH

VC1 0.2V 6.5nH 2.4nH 1.8nH0.35V 9.5nH0.4V 11.7nH

voltage Vf , which controls the value of the series resistance, RS. However, increasing

the inductance shifts the self-resonance frequency of the TAI to lower frequencies. This,

in turn, moves the the location of the peak-Q to lower frequencies as expected from

Eq.(3.10).

Figures (3.11) and (3.12) show the measured L and Q when VC1 is fixed at 0.1V and

0.2V, respectively, and VC2 is swept. In Fig. 3.11, VC2 is swept from 0.3V to 0.6V,

while in Fig. 3.12, VC2 is swept from 0.3V to 0.4V. On the other hand, Fig. 3.13 shows

the measured L and Q of the TAI circuit when VC1 is swept from 0.4V to 0V and VC2

is fixed at 0.3V. Decreasing VC1 results in a larger transconductance gm4, resulting in

a lower inductance.

Page 94: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 71

1 2 3 4 5

−1

0

1

2

3

4

5

Frequency (GHz)

Mea

sure

d T

AI i

nduc

tanc

e (n

H)

* VC2

=0.3V, + VC2

=0.35V ∆ V

C2=0.4V, x V

C2=0.5V

O VC2

=0.6V

1 1.5 2 2.5 3 3.5 40

50

100

150

Frequency (GHz)M

easu

red

TA

I qua

lity

fact

or

* VC2

=0.3V, + VC2

=0.35V ∆ V

C2=0.4V, x V

C2=0.5V

O VC2

=0.6V

(a) (b)

Figure 3.11: Measured TAI characteristics versus frequency when VC1=0.1V and VC2

changes from 0.3V to 0.6V: (a) Inductance, (b) Quality factor.

1 2 3 4

−1

0

1

2

3

4

5

6

Frequency (GHz)

Mea

sure

d T

AI i

nduc

tanc

e (n

H) ∆ V

C2=0.3V, O V

C2=0.36V

x VC2

=0.4V

1 1.5 2 2.5 30

50

100

150

200

250

Frequency (GHz)

Mea

sure

d T

AI q

ualit

y fa

ctor

∆ VC2

=0.3V, O VC2

=0.36V x V

C2=0.4V

(a) (b)

Figure 3.12: Measured TAI characteristics versus frequency when VC1=0.2V and VC2

changes from 0.3V to 0.4V: (a) Inductance, (b) Quality factor.

Page 95: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 72

0.5 1 1.5 2 2.5 3

0

5

10

Frequency (GHz)

Mea

sure

d T

AI i

nduc

tanc

e (n

H) O V

C1=0.4V, x V

C1=0.35V

∆ VC1

=0.15V, + VC1

=0V

0.4 0.6 0.8 1 1.2 1.4 1.60

50

100

150

200

250

300

Frequency (GHz)

Mea

sure

d T

AI q

ualit

y fa

ctor

O VC1

=0.4V, x VC1

=0.35V ∆ V

C1=0.15V, + V

C1=0V

(a) (b)

Figure 3.13: Measured TAI characteristics versus frequency when VC1 changes from 0Vto 0.4V and VC2=0.3V: (a) Inductance, (b) Quality factor.

In summary, the results show that the proposed TAI circuit has a very wide induc-

tance tuning range; the inductance can be tuned from 0.93nH to 2.7nH at the 2.4GHz

ISM band, while maintaining a peak-Q greater that 100 across the entire inductance

tuning range. However, the Q at 2.4GHz ranges from a maximum of 180, at the middle

of the inductance tuning range, to a minimum of 15 at the extremes of the tuning range.

The largest inductance tuning range is achieved by the circuit at 2GHz, where the cir-

cuit can provide inductances as low as 0.8nH and as high as 11.7nH while maintaining

a peak-Q in excess of 100. Table 3.3 summarizes the measured inductance values at

2GHz for the different values of the bias voltages VC1 and VC2.

As illustrated by the various inductance plots, when the inductance increases the

TAI’s self-resonance frequency, fr, decreases. As previously explained, this behavior

is expected from analyzing Eq.(3.6). The measured TAI self-resonance frequencies,

fr, are plotted versus the measured TAI inductance, L, in Fig. 3.14 together with

the theoretical values predicted from Eq.(3.6). The plot shows very good agreement

between the theoretical prediction and the measured values although the expression of

Eq.(3.6) is derived based on the gyrator-C block diagram and it neglects the second

term of Eq.(3.5). This also shows that the simple passive L-C model of Fig. 3.1 yields

accurate results.

Page 96: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 73

1 2 3 4 5 61.5

2

2.5

3

3.5

4

4.5

5

5.5

Measured TAI inductance, L (nH)

Res

onan

ce fr

eque

ncy,

f r (G

Hz)

MeasurementsTheory

Figure 3.14: Theoretical and measured self-resonance frequency, fr, versus the induc-tance, L, for the different bias conditions.

2 3 4 5 61

1.5

2

2.5

3

3.5

4

Resonance frequency, fr (GHz)

Pea

k−Q

freq

uenc

y, f p (

GH

z)

Measured TAITheoryCMOS TAI [25]CMOS TAI [39]GaAs TAI [48]

Figure 3.15: Theoretical and measured peak quality factor frequency, fQ, versus theself-resonance frequency, fr. The measured data presented is from theproposed circuit and from [25], [39], and [48], while the theoretical expres-sion used for the comparison is fQ = fr√

2, which is given by Eq.(3.10).

Page 97: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 74

As previously mentioned, increasing L causes the peak-Q frequency, fp, to shift to

lower values. This is a result of using the gyrator-C architecture to implement the

TAI, which results in a direct relationship between both its peak-Q and resonance fre-

quencies as given by Eq.(3.10). The measured peak-Q frequencies of the proposed TAI

circuit and the theoretical values predicted by Eq.(3.10) are plotted in Fig. 3.15 versus

the self-resonance frequency, fr. The figure shows good agreement between the mea-

surements and the theoretical expression of Eq.(3.10), although it was derived using the

generalized gyrator-C block diagram. To further demonstrate this, Fig. 3.15 also plots

fp versus fr for other gyrator-C based TAI circuits presented in the literature [25,39,48].

Despite being fabricated in different technologies; GaAs, 0.18µm CMOS, and 0.13µm

CMOS, in most of the cases, their peak-Q frequencies can be accurately estimated

from the theoretical expression of Eq.(3.10). This is true even though the derivation

of Eq.(3.10) neglects the frequency dependence of the equivalent series resistance RS.

The difference between the measured fp and the theoretical predication in Fig. 3.15 can

be attributed to the negative term of Eq.(3.10) which was neglected. Also, Fig. 3.15

shows that the proposed TAI circuit has a very wide tuning range as it can operate

with a peak-Q in excess of 100 over a very wide frequency range; 1.3-3.3GHz. The

circuit inductance, for each of these cases, can be obtained by combining the results of

Fig. 3.14 and Fig. 3.15.

Tuning Mode II: Variable Q and Fixed L

In this mode, L is fixed and the peak-Q is tuned by changing the feedback resistance Rf .

Increasing Rf will decrease the series resistance RS according to Eq.(3.21). Assuming

the TAI is operating at point P2 on Fig. 3.2, f(RS) will increase causing the peak-Q to

decrease. On the other hand, decreasing Rf will result in a higher peak-Q. Tuning the

peak-Q via the feedback resistance Rf does not affect the TAI bias point. Consequently,

the transconductances gm1,2 and gm4 are unaffected. Moreover, during the design phase

the feedback resistance Rf was chosen much smaller than the output resistance of

the differential pair transconductor, ro. According to Eq.(3.20), this ensures that the

inductance will remain unchanged while the Q is set to its desired value, thus allowing

us to achieve independent tuning.

The measured Q of the TAI is plotted versus frequency in Fig. 3.16 for different

Page 98: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 75

1 1.5 2 2.5 3 3.50

50

100

150

200

250

Frequency (GHz)

Mea

sure

d T

AI q

ualit

y fa

ctor

Vf increasing &

Rf decreasing

Vf=800mV

Vf=900mV

Vf=920mV

Vf=950mV

Figure 3.16: Measured Q versus frequency for different feedback voltages Vf .

6.7% variation in L at the peak Q frequency, f

Qp=2.4GHz

TAI resonates at f

r=3.1GHz

Vf=0.8V® 0.95V

Figure 3.17: Measured S11 of the TAI for different feedback voltages Vf .

Page 99: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 76

values of the feedback voltage Vf . These measurements were obtained with the TAI

configured for a nominal inductance of 1.7nH. The plot shows that the peak-Q can be

tuned from 10 to 200 by sweeping Vf from 800mV to 950mV. Across this tuning range,

the measured inductance variation at 2.4GHz is less than 6.7% of its nominal value.

As indicated by the measured Q plots, the peak-Q frequency, fp, remains relatively

fixed at 2.4GHz, which is a direct result of the independent L and Q tuning capability,

since the relatively unchanged L results in the same self-resonance as well as peak-Q

frequencies as indicated by Eq.(3.6) and Eq.(3.10) respectively. The measured reflection

coefficient of the TAI is plotted in Fig. 3.17 for the different values of the feedback

voltage. The TAI circuit resonates at 3.1GHz regardless of the value of its peak-Q.

It is also worth mentioning that, tuning Q using the feedback resistance Rf does not

require any additional power dissipation, as opposed to using traditional methods such

as cross-coupling a differential pair to generate a negative resistance [43].

Although all the measured results that were presented in the previous sections were

obtained from a single die, other dice were also tested to verify the consistency of the

results. Furthermore, the consistency of the die-to-die performance will be practically

demonstrated in chapter 6, through the use of multiple chips to design the steerable

antenna array, which uses 6 packaged TAI chips within its beam steering network.

Measurements Versus Simulations

The proposed TAI circuit does not use a capacitor to terminate the the output of the

differential-pair transconductor, instead it relies on the gate capacitance of transistor

M4. As previously explained in chapter 2, this makes the TAI circuit suitable for

high-speed operation. However, it makes the TAI circuit very sensitive to any parasitic

capacitance, requiring special care during the design, simulation, and layout phases in

order to obtain the desired response.

Figure 3.18 shows the simulated L and series resistance for a subset of the bias con-

ditions; (VC1=0V, VC2=0.6V) and (VC1=0V, VC2=0.6V), and compares the simulated

results with the measurements. Good agreement is achieved between the measured and

simulated inductances with a mismatch of approximately 15% at 2.4GHz. To achieve

this fairly good agreement between the measured and simulated inductance, a fixed

100pH inductor is added in series with the TAI, as shown in Fig. 3.19, to model the

Page 100: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 77

1 2 3 4 5−1

0

1

2

3

4

5

Frequency (GHz)

Indu

ctan

ce (

nH)

MeasurementsSimulations

Vc2=0.6V

Vc2=0.4V

1 1.5 2 2.5 3 3.5 4−5

0

5

10

15

20

Frequency (GHz)

Ser

ies

Res

ista

nce

(Ω)

MeasurementsSimulations

Vc2=0.4V

Vc2=0.6V

(a) (b)

Figure 3.18: Measured and simulated results versus frequency when VC1=0V and VC2

is set to 0.6V and 0.4V: (a) inductance (b) series resistance.

Vdd

M3

M1 M2VCM

Zin

VC2VC1

Cp

Lpad

Vf

TAI

circuit

100pH

100fF

Figure 3.19: Circuit setup used for the simulation of the TAI circuit.

Page 101: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 78

f1 Circulator

f2

RF signal

sources

+1-port

DUT

Spectrum

Analyzer

Grounded tunable

active inductor chip

RF signal

combiner

probe

Figure 3.20: Experimental test setup used for characterizing the TAI circuit linearity.

pad and input port interconnect inductance. Also, a fixed 100fF capacitor was added

at the gate of M4 to model the parasitic capacitance associated with this critical node.

The measured and simulated series resistance values, shown in Fig. 3.18-b, fairly match

with each other. However, they are off by approximately 4Ω at 2.4GHz.

To this end, the TAI was extensively characterized, and its measured S-parameters

were used to design all the subsequent circuits presented in this thesis (the phase

shifters, the directional coupler, and the antenna array). This approach will enable us

to accurately predict the response of the different TAI-based circuits, and achieve good

matching between the measured and the desired response.

Linearity Measurements

Numerous measures are incorporated in the design of the TAI to achieve good linearity.

The TAI circuit is designed to allow a large signal swing at its input port by setting the

common-mode voltage, Vcm, to VDD/2. Also, the bias current of transistor M4, IC , is

selected large enough to allow the TAI to supply and drain the input current without

considerably affecting the bias point of M4.

Despite being a 1-port device, the linearity of the grounded TAI circuit can be exper-

imentally characterized by using an RF signal source to excite it through a circulator

as shown in Fig. 3.20. The circulator directs the reflected wave from the TAI circuit

to its third port and the various inter-modulation components are analyzed using a

Page 102: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 79

−30 −25 −20 −15 −10 −5 0 5 10−45

−40

−35

−30

−25

−20

−15

−10

−5

Input power (dBm)

Out

put p

ower

(dB

m)

Figure 3.21: Amplitude of the power reflected back by the TAI versus the input powerwhen applying a single RF signal source.

spectrum analyzer. This experimental setup was presented in [84] to characterize the

linearity of a grounded GaAs TAI. The 1-dB compression point of the TAI circuit is

characterized by using only one RF signal source, and measuring the amplitude of the

power reflected by the TAI. Figure 3.21 shows the amplitude of the reflected power at

the same frequency of the RF signal source, f1, which was selected as 4GHz. The mea-

sured results show that the TAI achieves a +2.16dBm input compression point, which

corresponds to approximately an 800mVpp voltage swing at the TAI input port while

operating from a 1.5V supply. This is considered a very high 1-dB compression point

for an active inductor. However, this comes at the expense of the power consumption,

which is reported in the Table 3.4. The IIP3 (third-order input intercept point) of the

TAI is characterized by combining two input frequencies f1 and f2 and extrapolating

the measured output powers at f1 and 2f1 − f2 until they intersect. The measured

output power at f1 and 2f1 − f2 are plotted in Fig. 3.22, where f1 is chosen as 4GHz

and the frequency separation between the two input signals was chosen as 10MHz. As

indicated by Fig. 3.22, the TAI achieves an IIP3 of 12.5dBm.

Page 103: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 80

−30 −20 −10 0 10−140

−120

−100

−80

−60

−40

−20

0

Out

put p

ower

(dB

m)

Input power (dBm)

Ouput power at f1

Ouput power at 2f1−f

2

Figure 3.22: Amplitude of the power reflected back by the TAI at f1 and 2f1−f2 versusthe input power when combining two RF signal sources.

Page 104: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 81C

om

pari

son

ofTA

IPerf

orm

ance

Tab

le3.

4:C

ompar

ison

Bet

wee

nD

iffer

ent

Tunab

leA

ctiv

eIn

duct

orIm

ple

men

tati

ons

Spec

ifica

tion

[48]

[37]

[38]

[25]

[25]

[25]

[39]

This

wor

k

Min

.fe

atur

esi

ze1µ

m1µ

m1µ

m0.

18µm

0.18

µm

0.18

µm

0.18

µm

0.13

µm

Tec

hnol

ogy

GaA

sG

aAs

GaA

sB

iCM

OS

CM

OS

CM

OS

CM

OS

CM

OS

Ltu

ning

rang

e(n

H)

9.6⇒

5665⇒

9065⇒

110

1⇒8

2.1⇒

5.6

1⇒8.

55.

7,8

0.83⇒

11.7

mea

sure

dat

@1.

7GH

z–

–@

5GH

z@

2.1G

Hz

@2G

Hz

–@

2GH

z

Pea

kQ

Qp

3400

––

>50

–>

5070

,51

>10

0

Pea

kQ

freq

.f Q

(GH

z)1.

7–

–7⇒

21.

653⇒

0.5

1.55

,2.2

3.5⇒

0.75

Res

.fr

eq.

f r(G

Hz)

2.2

1.1

1>

9.5

–4.

1⇒2.

52.

5,2.

85.

35⇒

2.4

Qor

RS

tuni

ngra

ngea

RS:-20⇒

44R

S:-10⇒

15R

S:-5.

6⇒20

.8–

––

–Q

:10⇒

200

Lva

riat

ion

2%@

1.7G

Hz

4%–

––

––

6.7%

@2.

4GH

z

Supp

lyvo

ltag

eV

DD

9V–

6V1.

8V1.

8V1.

8V2V

1.5V

Pow

erdi

ss.

(mW

@V

DD

)36

9–

240⇒

901.

87.

27.

28

52.5⇒

22.5

TA

Isi

ze(µ

m×µ

m)

900×

700b

1200×1

700b

900×

700b

40×5

010

0×50

100×

5088×9

015

0×17

0

1dB

com

p.po

int

–-0

.9dB

mc

–-7

dBm

d–

––

+2.

16dB

m

IIP

3–

––

––

––

+12

.5dB

m

aTun

ing

mod

eII

can

bech

arac

teri

zed

bym

easu

ring

the

tuni

ngra

nge

for

eith

erR

Sor

Q.

bSi

zein

clud

esbi

asan

don

-waf

erm

easu

rem

ent

pads

cIn

put

pow

erat

whi

chst

rong

depe

nden

cew

asob

serv

edbe

twee

nbo

thL

and

RS

and

the

inpu

tpo

wer

leve

l.dSi

mul

ated

inpu

tpo

wer

atw

hich

the

2nd-o

rder

harm

onic

inth

ein

duct

orcu

rren

tbe

com

eseq

ualto

the

fund

amen

talco

mpo

nent

.

Page 105: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

3.4. A GROUNDED 0.13µm CMOS TAI 82

Table 3.4 presents a detailed comparison between the proposed TAI and different

TAIs presented in the literature [25, 37–39,48]. Among these recently published TAIs,

this work provides the largest inductance tuning range and the highest resonance fre-

quencies (with the exception of the BiCMOS design) in spite of the low-voltage CMOS

process. Furthermore, the proposed design provides a mechanism to control the Q with

very small variations in the inductance. Compared to the other CMOS and BiCMOS

implementations, the proposed TAI dissipates more DC power in order to achieve better

linearity. Unfortunately, linearity was not reported in most of the previous publications

to allow for an adequate comparison.

Page 106: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 4

Wide Tuning Range CMOS Phase Shifters

P hase shifters are essential building blocks for many RF and microwave applications.

One of the most important applications of phase shifters is electronically steerable

antenna arrays. The direction of the antenna array’s main beam can be controlled by

appropriately setting the relative phases of the signals feeding each antenna element in

the array. To achieve a wide scan-angle range, it is necessary to design phase shifters

with a wide tuning range. Furthermore, to avoid power losses due to reflections at

the input and output ports of a phase shifter, it is required to have a constant input

and output impedance across its entire tuning range. These two constraints (i.e., wide

tuning range, and matching) limit our choice of the phase shifter’s architecture.

4.1 Introduction

As described in chapter 2, to achieve a wide tuning range from an L-C phase shifter,

two tunable elements are necessary. This requires the use of both varactors and TAIs

to extend the phase tuning range. To facilitate using TAIs to design phase shifters, one

should use L-C phase shifter architectures requiring grounded inductors as opposed

to floating or 2-port inductors. Among the different L-C architectures in Fig. 2.12,

83

Page 107: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.1. INTRODUCTION 84

-ve

Electronic Beam Steering Network

C C

TAI

Electronic Beam Steering Network

(a) MMIC High-pass TAI-based PS

(b) Printed TAI-based PRI/NRI PS

-ve +ve

(c) MMIC Lumped-Element TAI-based PRI/NRI PS

(d) MMIC Lumped-Element Passive PRI/NRI PS

CLo

CoCo

CLo

CoCo

C

L

Lo

CoCo

CLo

CoCo

TAI

Cv

CC

TAI

Figure 4.1: Different series-fed phased array designs and their radiation patterns: (a)shows the high-pass phase shifters used by the top design, (b) to (d) showthe PRI/NRI phase shifters used by the lower design.

Page 108: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.1. INTRODUCTION 85

this limits us to the high-pass Tee architecture redrawn here in Fig. 4.1-a, since it

uses the minimum number of inductors as opposed to the high-pass Π architecture.

Consequently, the first wide tuning range phase shifter presented in this chapter uses

the high-pass Tee architecture. Although this is a standard phase shifter architecture,

the design presented here combines the use of varactors and TAIs to insure the matching

of the phase shifter across its entire phase tuning range besides extending its tuning

range.

The high-pass phase shifter is only capable of providing positive phase shifts, which

according to Eq.(2.41) will only result in negative scan angles if used in the feed network

of a series-fed phased array1. Figure 4.1 shows two series-fed phased arrays, the top one

uses tunable high-pass phase shifters, which makes the array only capable of achieving

negative scan angles. Whereas, the lower one uses phase shifters which enable the

antenna array to center its main beam around the broadside direction. To achieve this,

the phase shifters are required to generate both positive and negative phase shifts1. In

other words, their phase response should be centered around 0o. As described in chapter

2, PRI/NRI metamaterial phase shifters are capable of achieving 0o phase shifts with

much lower group delays compared to traditional −2π TL phase shifters. This makes

them more suitable for broadband applications, in which it is required to minimize the

beam squinting with frequency variations. To this end, this chapter presents three novel

electronically tunable PRI/NRI metamaterial phase shifter designs, which are capable

of achieving both positive and negative phase shifts. To the author’s knowledge, this

represents the first published attempt to design tunable PRI/NRI metamaterial phase

shifters that have a phase response centered around the 0o, and at the same time have a

low return loss across their entire phase tuning range. The proposed PRI/NRI tunable

phase shifters shown in Figs.(4.1-b), (4.1-c), and (4.1-d), can be used in series-fed

phased arrays to steer the main beam about the broadside direction.

The TL PRI/NRI tunable phase shifter of Fig. 4.1-b is presented in section 4.2. It

uses the same architecture of the TL PRI/NRI phase shifter presented in [5]. However,

electronic tunability and matching are simultaneously achieved by replacing the fixed

1This conclusion is reached assuming that the progressive inter-element phase shift is only generatedby the phase shifters, which neglects the phase contribution of the feed network. The effect of thefeed network phase response is discussed in more detail later in chapter 6 since it depends on thearray architecture.

Page 109: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.1. INTRODUCTION 86

series capacitors with varactors and the fixed shunt inductors with the grounded TAIs

presented in chapter 3. Following this, a fully-integrated version of the PRI/NRI

tunable phase shifter, shown in Fig. 4.1-c, is presented in section 4.3. This design

replaces the TL sections with lumped L-C sections, which enables integrating the entire

phase shifter on a single MMIC resulting in a much more compact implementation.

The CMOS grounded TAI of chapter 3 is used to design the first three tunable phase

shifters; the high-pass design of Fig. 4.1-a, the TL PRI/NRI design of Fig. 4.1-b, and

the MMIC PRI/NRI design of Fig. 4.1-c. The capability to tune its inductance and

quality factor independently is a key feature to overcome the degradation of the phase

shifter’s insertion loss and return loss due to the variation of the TAI’s Q when the TAI

inductance is tuned. Furthermore, having control over the TAI’s Q without affecting

its inductance, allows controlling the phase shifter’s insertion loss. Moreover, the TAI

is capable of generating a negative series resistance, which can be used to partially

compensate the varactor losses while maintaining the bi-directionality of the phase

shifters as opposed to using amplifiers.

Another MMIC PRI/NRI tunable phase shifter design is presented in section 4.5.

However, this design is passive and does not use TAIs to tune the shunt inductance.

Alternatively, it uses a variable capacitor connected in parallel with a shunt spiral

inductor as shown in Fig. 4.1-d. Compared to the TAI-based design of Fig. 4.1-c, this

design does not consume any DC power and at the same time it eliminates the noise

and non-linearity contributions of the TAI circuit.

In summary, this chapter presents four different electronically tunable phase shifter

designs:

• The high-pass TAI-based phase shifter of Fig. 4.1-a [Section 4.2]

• The TL PRI/NRI TAI-based phase shifter of Fig. 4.1-b [Section 4.3]

• The MMIC PRI/NRI TAI-based phase shifter of Fig. 4.1-c [Section 4.4]

• The MMIC PRI/NRI passive phase shifter of Fig. 4.1-d [Section 4.5]

Throughout this chapter, we follow the same procedure for each phase shifter design, by

presenting its design equations, implementation, and its experimental characterization.

Following that, the advantages and disadvantages of the different phase shifter designs

are discussed and they are compared to previous designs published in the literature.

Page 110: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 87

L

C C

Figure 4.2: High-pass phase shifter unit-cell.

4.2 High-pass Phase Shifter

This section presents the design of the tunable high-pass phase shifter. The phase

shifter achieves a wide phase tuning range and at the same time a low return loss

across its entire tuning range by combining the use of two tunable elements; varactors

and TAIs. Also, this section presents the experimental characterization of critical

performance limits of the TAI-based phase shifter, such as linearity, which is rarely

reported in other publications.

4.2.1 Analysis

Phase Response

If the high-pass phase shifter of Fig. 4.2 is terminated with a source and load impedance

of Zo, one can show that the forward transmission coefficient, S21, can be expressed as:

S21 =s3

(s +

1

CZo

)(s2 + s

Zo

2L+

1

2CL

) . (4.1)

Eq.(4.1) shows the high-pass nature of the phase shifter, and at the same time it reveals

that the phase shifter has one real pole at ωp1 = 1/CZo and a pair of complex poles

at ωp2,3 = 1/√

2CL. The operating frequency of the phase shifter should be chosen

greater than the pole frequencies in order to avoid attenuating the input signal. Using

Eq.(4.1), one can show that the insertion phase, φ, is expressed as:

φ =3π

2− tan−1

(2ωCZo(1− ω2LC)

1− ω2C(2L + CZ2o )

). (4.2)

Page 111: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 88

At the same time, to match the impedance of the phase shifter to the source and load

impedances, Zo, one equates the input reflection coefficient, S11, to zero:

S11 =1 + s2(2CL− Z2

oC2)(

s +1

CZo

)(s2 + s

Zo

2L+

1

2CL

) = 0. (4.3)

This results in the following matching condition:

L =1 + ω2C2Z2

o

2ω2C. (4.4)

Since the phase shifter should be designed to operate at frequencies higher than its

pole frequency, 1/CZo, the matching condition of Eq.(4.4) can be approximated as:

L ≈ CZ2o

2⇒ Zo =

√2L

C. (4.5)

Using the result of Eq.(4.4), the phase shift expression can be simplified to:

φ ≈√

2

ω√

LC. (4.6)

Equation (4.6) indicates that the phase shifter provides a phase advance, i.e. a positive

phase shift. Furthermore, the insertion phase, φ, can be tuned by varying the values

of both the series capacitors, C, and the shunt inductor, L. If L and C are varied from

their nominal value to rL×L and rC×C, the phase tuning range can be expressed as:

|∆φ| =(

1− 1√rLrC

√2

ω√

LC. (4.7)

Figure 4.3 plots the phase tuning range given by Eq.(4.7). To generate this plot, a

nominal value of 3nH is chosen for L, also the operating frequency is arbitrarily chosen

as 2.4GHz, and the value of C is calculated using the matching condition of Eq.(4.5).

The figure plots the tuning range for two cases; the first one assumes we use fixed

inductors and variable capacitors, i.e. rL=1, and the second one assumes we use both

variable capacitors and inductors with rL = rC . As indicted by Fig. 4.3, tuning both

elements results in increasing the tuning range by 53%. Furthermore, tuning both

Page 112: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 89

1 1.5 2 2.5 3 3.5 40

10

20

30

40

50

Capacitor tuning ratio rc

Pha

se tu

ning

ran

ge (

deg)

53% increase in tuning range

Tuning L and C → rL=r

c

Tuning only C → rL=1

Figure 4.3: Phase tuning range versus the capacitor tuning ratio rC .

elements allows one to maintain the matching condition of Eq.(4.5) across the entire

phase tuning range, by setting rL = rC . In contrast, designs using only one tunable

element are not capable of satisfying the matching condition across the entire tuning

range.

Loss Compensation

To investigate the effect of the series resistance, RS, associated with the shunt TAI,

on the phase shifter loss, one can derive the expression for the forward transmission

coefficient, S21 taking into account the effect of RS. Under the matching condition of

Eq.(4.5), S21 can be expressed as:

S21 =

s2

(s +

RS

L

)

(s +

1

CZo

)(s2 +

Zo + 2RS

CZ2o

s +1

C2Z2o

) . (4.8)

As previously mentioned the phase shifter has a pair of complex conjugate poles. How-

ever, Eq.(4.8) indicates that the quality factor associated with the complex conjugate

Page 113: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 90

Gyrator-C

active inductor

C C

gm1

-gm2

Zin

C

Rf

TAI

Figure 4.4: Proposed high-pass phase shifter circuit implementation.

poles, ωp2,3, is a function of RS, and is given by:

Qp2,3 =Zo

Zo + 2RS

. (4.9)

Hence, the value of RS determines the poles’ quality factor, i.e. it determines the

damping factor associated with the two poles. By generating a negative resistance, RS,

through the TAI circuit, higher values of Qp2,3 can be achieved. This will increase the

peaking that occurs in the frequency response of S21, which can be used to partially

compensate for the series capacitors’ losses. This will, in turn, minimize the phase

shifter insertion loss.

4.2.2 Design and Physical Implementation

The circuit diagram of the proposed high-pass phase shifter is shown in Fig. 4.4. It is

designed in the 1.5V, 0.13µm CMOS process. The variable capacitors are implemented

using 10×0.8µm×10µm on-chip hyper-abrupt junction varactors2, whereas the tunable

inductor is implemented using the same grounded TAI circuit described in chapter 3.

The reverse bias voltage across the varactors sets their capacitance. The cathode

voltages, VB, is set through the input and output ports of the phase shifter via two

external bias-Tees. On the other hand, their anode voltages have a fixed value which is

set from within the TAI circuit and is approximately equal to VCM of the TAI circuit.

The varactors’ capacitance can be tuned from 0.8pF to 0.3pF by changing the reverse

2Hyper-abrupt junction varactors have P-N junctions which are doped to optimize the range ofcapacitance versus the reverse bias voltage.

Page 114: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 91

500 m

550

mG G

G G

S S

DC/Bias inputs

Phase

shifter

25

0m

250 m

Figure 4.5: High-pass phase shifter die micrograph

bias voltage across them from 0V to 3V. Although the supply voltage for this process

is 1.5V, it offers varactors which can have reverse bias voltages up to 3V.

4.2.3 Experimental Characterization

Figure 4.5 shows the die micrograph of the fabricated phase shifter. The circuit occupies

250µm×250µm, out of which the TAI occupies 150µm×170µm. Two 150µm-pitch GSG

(ground-signal-ground) probes were used to characterize the phase shifter, while two

80µm-pitch multi-contact wedges with DC needles were used to provide the bias and

control voltages.

S-parameter Measurements

Figure 4.6 shows the measured insertion phase, φ, for different bias conditions. To tune

the phase shift φ, the series capacitance and the shunt inductance are varied using the

input and output port DC voltage, VB, and the TAI bias point (Vc1, Vc2, Vf ). VB is swept

from 0V to 3.6V, and for each bias voltage the appropriate inductance is generated by

the TAI circuit using Vc1 and Vc2 in order to satisfy the matching condition of Eq.(4.5).

Page 115: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 92

3 3.5 4 4.5 5−20

0

20

40

60

80

100

120

140

160

180

Frequency (GHz)

Inse

rtio

n ph

ase

φ (

deg)

φ tuning range at 4GHz = 14o to 110.5o

VB = 0V → 3.6V

Figure 4.6: Measured phase vs. freq., for different bias conditions

This will double the phase tuning range compared to tuning only the capacitance and

at the same time will ensure a low return loss across the entire tuning range. The phase

shift can be tuned from 14o to 110.5o at the design frequency, which for this design is

4GHz.

Figure 4.7 shows the measured input reflection coefficient, S11, and the insertion

loss, S21, for the same bias conditions used to generate the phase responses in Fig. 4.6.

Across the entire tuning range, the worst S11 at 4GHz is -18dB, and the phase shifter has

a bandwidth of 250MHz over which S11 <-10dB. Although the frequency independent

nature of the matching condition of Eq.(4.5) implies that the phase shifter will have

a wide bandwidth, the measurements indicate that the phase shifter has a relatively

narrow bandwidth. This is due to the self-resonance of the TAI, which according to

the measurements presented in chapter 3 resonates in the vicinity of the phase shifter

design frequency. For each of the bias points, used to generate the phase responses

of Fig. 4.6, the feedback voltage, Vf , of the TAI is selected to achieve an appropriate

negative resistance that partially compensates the varactor losses. As demonstrated

by Fig. 4.7, across the entire phase tuning range S21 varies from -1.3dB to -2.7dB at

4GHz. The tuning characteristics are presented in Fig. 4.8, which shows φ and S21 at

4GHz versus the varactor voltage, VB.

To demonstrate the effect of the negative resistance generated by the TAI on the

Page 116: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 93

3.5 3.75 4 4.25 4.5−30

−20

−10

0R

etur

n lo

ss S

11 (

dB)

Frequency (GHz)

← →

BW = 250MHz

Worst case S11

at 4GHz = −18dB

S21

at 4GHz varies from −1.3dB→ −2.7dB

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

Inse

rtio

n lo

ss S

21 (

dB)

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

3.5 3.75 4 4.25 4.5

−40

−30

−20

−10

0

Figure 4.7: Measured S11 and S21 vs. freq., for different bias conditions

0 0.5 1 1.5 2 2.5 3 3.5

20

40

60

80

100

Inse

rtio

n ph

ase

at 4

GH

z φ (

deg)

Varactor reverse bias voltage VB (V)

0 0.5 1 1.5 2 2.5 3 3.5−3

−2.5

−2

−1.5

−1

−0.5

0

Inse

rtio

n lo

ss a

t 4G

Hz

S21

(dB

)

Figure 4.8: Measured phase and S21 at 4GHz vs. VB

Page 117: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 94

Vf V

S21

dB

o

o

Figure 4.9: Measured S21 at 4GHz versus the feedback voltage Vf

phase shifter loss, RS is varied by sweeping the feedback voltage, Vf , of the TAI, and

the measured S21 is plotted in Fig. 4.9. This shows that the insertion loss can be

enhanced by 2dB with less than 23o phase variation. This variation is due to the slight

dependence between the TAI L and RS, as well as the additional terms that appear in

Eq.(4.8) due to RS. The effect of Vf on S21 can be explained by the variation in the TAI

series resistance, i.e. Re(Zin,TAI). Using the results of chapter 3, one can show that

the TAI series resistance Re(Zin,TAI) = ωL/Q is directly proportional to the function

f(RS), which was plotted in Fig. 3.2. Hence, as Vf increases, the feedback resistance

Rf decreases, resulting in an increase in the series resistance of the TAI equivalent

circuit, RS. This will lead to a decrease in Re(Zin), until f(RS) reaches its minimum

value. After that, Re(Zin) will start to increase. This is the reason behind the decrease

of S21 in Fig. 4.9 after it reaches the maximum loss compensation point.

Linearity Measurements

To characterize the linearity of the high-pass phase shifter, the 1-dB compression point

for an input signal at 4GHz is measured. As shown by Fig(4.10), the high-pass phase

shifter achieves a 1-dB input compression point of -2.2dBm, which corresponds to an

input signal swing of 0.55Vpp, while operating from a 1.5V supply. The inter-modulation

Page 118: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.2. HIGH-PASS PHASE SHIFTER 95

−40 −30 −20 −10 0 10 20−40

−30

−20

−10

0

10

20

Input power at 4GHz (dBm)

Out

put p

ower

at 4

GH

z (d

Bm

)

Figure 4.10: Amplitude of the output power versus the input power when applying asingle 4GHz RF signal source

−40 −30 −20 −10 0 10 20−150

−100

−50

0

50

Input power (dBm)

Out

put p

ower

(dB

m)

Output power at f1

Output power at 2f1−f

2

Figure 4.11: Amplitude of the output power at f1 and 2f1− f2 versus the input powerwhen combining two RF signal sources

Page 119: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 96

Table 4.1: Summary of The High-Pass Phase Shifter Performance.Parameter ValueDesign frequency 4GHzTechnology 0.13µm CMOSPhase shift 14o ⇒110.5o=96.5o

Insertion loss 1.3dB to 2.7dBFOMa 48.2o/dBSize 0.25mm×0.25mmNo. of unit-cells 1S11 -18dBBandwidthb 0.25GHzFractional BW 6.25%Max. bias volt. 3.6V1-dB comp. -2.2dBmIIP3 +7.4dBn

aFigure of merit [85]: FOM = | ∆φmin|S21|dB

|.bBandwidth measurement criterion: S11 < −10dB.

distortion components are also evaluated to fully characterize the linearity of the phase

shifter. Two signals the first at f1=4GHz and the second at f2 = f1-10MHz are

obtained from two RF signal generators and combined together using an RF signal

combiner. This frequency spacing is chosen to guarantee that the two input signals are

treated as in-band signals. The combined signal is then applied to the phase shifter, and

the inter-modulation products are measured at the output using a spectrum analyzer.

Figure 4.11 shows the output power at f1 and 2f1 − f2 versus the input power. The

phase shifter achieves an input third-order intercept point (IIP3) of +7.4dBm.

To summarize, the measured performance of the TAI-based high-pass shifter is pre-

sented in Table 4.1. The high-pass design achieves a figure of merit, FOM, of 48.2o/dB,

which is defined as the phase tuning range per dB of insertion loss [85].

4.3 TL PRI/NRI Phase Shifter

This section presents an electronically tunable TL PRI/NRI metamaterial phase shifter,

which is capable of achieving both positive and negative phase shifts. To the author’s

knowledge, this is considered the first published attempt to design an electronically

tunable TL PRI/NRI metamaterial phase shifter that has a phase response centered

Page 120: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 97

L

TL CTL

d/2 d/2

C

Figure 4.12: TL PRI/NRI metamaterial phase shifter unit-cell.

around the 0o, and at the same time has a low return loss across its entire phase tuning

range. The proposed phase shifter uses the same architecture of the TL PRI/NRI phase

shifter presented in [5]. However, electronic tunability and matching are simultaneously

achieved by replacing the fixed series capacitors with varactors and the fixed shunt

inductor with a TAI.

4.3.1 Analysis

Figure 4.12 shows the unit-cell of the TL PRI/NRI phase shifter [5]. It is composed of a

regular microstrip TL, with a characteristic impedance Zo =√

Lo/Co, where Lo and Co

are the TL inductance and capacitance per unit-length, respectively. The microstrip TL

is loaded with two series capacitors, C, and a shunt inductor, L. Cascading the PRI TL

with the NRI section compensates the phase shift incurred by the propagating signal.

The phase shifter unit-cell is analyzed herein using periodic analysis for terminated

periodic structures. This technique can be applied to a finite number of unit-cells

when terminated with the corresponding Bloch impedance [24]. Using this technique

simplifies the analysis and offers good design insight. One can show that the insertion

phase, φ, of the unit-cell is given by [3, 5]:

cos φ = cos 2θTL

(1− 1

2ω2CL

)+ sin 2θTL

(1

ωCZo

+Zo

2ωL

)− 1

2ω2CL, (4.10)

where θTL is the phase lag due to one section of the PRI microstrip TL, given by

θTL = βTLd/2 = ω√

LoCod/2. By equating the phase shift, φ, to zero, one can find the

zero-phase frequencies of the periodic structure. The full analysis of the TL PRI/NRI

unit-cell can be found in [3, 5], therefore only the important results are pointed-out

here. In summary, this analysis reveals that the underlying periodic structure exhibits

Page 121: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 98

a stop-band centered around the zero-phase frequency, ωo = 1/√

LCod, over which the

input signal is attenuated. In order to close this stop-band, the following condition has

to be satisfied:

Zo =

√Lo

Co

=

√2L

C. (4.11)

Interestingly, satisfying the stop-band closure condition of Eq.(4.11) insures that

the TL phase shifter is perfectly matched at the zero-phase frequency, ω = ωo. This

becomes evident by deriving the expression of the phase shifter reflection coefficient,

S11. If a unit-cell of the TL phase shifter is terminated with an impedance Zo, one can

show that, at the zero-phase frequency, the reflection coefficient is expressed as:

S11(ω = ωo) =

2L

C− Lo

Co

2L

C− Lo

Co

+ 2j

√LLo

Co

√d

. (4.12)

When the condition of Eq.(4.11) is satisfied, the two terms in the numerator of S11

cancel-out, which results in perfect matching at the zero-phase frequency. However,

when the component values (L and C) are varied to tune the phase shift, the location

of the zero-phase frequency, ωo = 1/√

LCod, changes. Hence the frequency at which

the phase shifter is matched changes. Nevertheless, the TL phase shifter still achieves

a low return loss across a wide range of frequencies as long as the stop-band closure

condition of Eq.(4.11) is satisfied. This is mainly due to the nature of the PRI TL

sections, which determines the characteristic impedance of the loaded TLs.

Under the stop-band closure condition, the phase shift can be approximated as:

φ ≈√

2

ω√

LC− 2θTL. (4.13)

Equation (4.13), which was originally derived in [5], indicates that positive and negative

phase shifts can be realized by a single unit-cell without having to go through a complete

phase rotation as in a traditional high-pass or low-pass architecture. Furthermore, the

phase can be tuned by simultaneously changing the values of both loading elements;

L and C. If L and C are varied from their nominal value to rL × L and rC × C, the

Page 122: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 99

CVAR CVARTL TL

d/2 d/2

Packaged

TAI chip

TAI

Gyrator-C

active inductor

gm1

-gm2

Zin

C

Rf

Figure 4.13: TL PRI/NRI metamaterial phase shifter unit-cell.

phase tuning range can be expressed as:

|∆φ| =(

1− 1√rLrC

√2

ω√

LC. (4.14)

Similar to the high-pass phase shifter, varying both L and C results in increasing the

phase tuning range compared to varying C only. Furthermore, setting rL = rC will

maintain the matching condition of Eq.(4.11) and will result in a low return loss across

the entire phase tuning range.

4.3.2 Design and Physical Implementation

The TAI circuit described in chapter 3 is packaged using a 4mm×4mm high-speed QFN

(Quad Flat-Package No Lead) package to minimize the parasitics associated with the

package, and the packaged chip is used to implement the TL PRI/NRI phase shifter.

Figure 4.13 shows the unit-cell of the proposed tunable TL phase shifter. The se-

ries capacitors, C, are replaced by discrete varactors, where the reverse voltage across

the varactors controls their capacitance. The PRI TL sections are implemented us-

ing printed microstrip lines on a low-loss 10mil Rogers RT/duroid 5880 substrate. To

design the TL PRI/NRI metamaterial phase shifter both circuit and electromagnetic

simulations had to be carried out. This was necessary to choose the appropriate varac-

tor capacitance tuning range and the properties of the printed TL structure. A detailed

explanation of the method used to simulate and consequently design the TL PRI/NRI

Page 123: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 100

RFin

DC bias/control lines Active inductor

chip

Varactors

10.8mm

10.4mm

RFout

Figure 4.14: Photograph of the tunable PRI/NRI phase shifter unit-cell.

metamaterial phase shifter is presented in Fig. B-1 in Appendix B.

A picture of the TL phase shifter is given in Fig. 4.14, the bias and control lines

going to the TAI chip are supplied from the lower side of the board, whereas the right

and left connectors are the input and output ports of the phase shifter, which also

supply the bias voltages to the series varactors. A low substrate permittivity, εr, of 2.2

was chosen to reduce the phase shift incurred by the signal, hence making the phase

shifter more wide-band. The varactors used are 1.7mm×0.9mm plastic packaged silicon

hyper-abrupt junction varactor diodes from Skyworks, Irvine, CA (SMV1232). The

TL phase shifter unit-cell size is 10.8mm×10.4mm; the TL and series varactors occupy

10.8mm×1mm, while the chip and the bias lines roughly occupy 10.8mm×9.4mm.

The unit-cell width is mainly set by the MMIC inductor package, which can be easily

reduced by more than 22% by using a smaller package size (3mm×3mm). The smaller

package was not used here, since the chip contained other test circuits that needed to

be packaged.

4.3.3 Experimental Results

Figure 4.15 shows the measured and theoretical phase responses when both the TAI

inductance and varactor capacitance are varied. The theoretical response is predicted

using the exact phase expression of Eq.(4.10). The figure shows good agreement be-

tween the measurements and theory. Using the approximate expression of Eq.(4.13)

Page 124: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 101

1.5 2 2.5 3 3.5−100

−50

0

50

100

Frequency (GHz)

Inse

rtio

n ph

ase

φ (

deg)

φ tuning range at 2.5GHz = −40o to +34o

Vvar

= 0V → 4.2V

MeasurementsTheory

Figure 4.15: The measured and theoretical phase responses vs. freq. for different biasconditions. The phase expression of Eq.(4.10) is used for the comparison.

results in an error of less than 6.5o, hence Eq.(4.13) can still serve as a good starting

point for initial hand calculations, and at the same time, it gives good design insight.

The good agreement between the theoretical and experimental results is achieved by

extracting the values of the different circuit components using accurate simulations

(electromagnetic/circuit simulations). The component values obtained are then used

to predict the phase response based on the theoretical equations.

At the design frequency of 2.5GHz, the phase can be varied from -40o to +34o passing

through the zero-phase point. The phase shifter unit-cell is capable of achieving both

positive and negative phase shifts at the design frequency without going through an

entire 360o rotation, which requires an 88mm microstrip TL. This corresponds to a 73%

area saving compared to meandering the microstrip TL. Furthermore, over the entire

phase tuning range the matching condition is satisfied, and S11 is maintained below

-19dB at the design frequency, as shown in Fig. 4.16. As the varactors’ reverse bias

voltage, Vvar, increases, their capacitance decreases, and the TAI’s L has to decrease to

satisfy Eq.(4.11). When Vvar approaches 4.2V, the matching condition is increasingly

difficult to satisfy, since the package adds a fixed inductance to the TAI inductance,

thereby setting a minimum achievable L. Nevertheless, the phase shifter achieves a

bandwidth of 2.6GHz over which S11 is less than -10dB (see Fig. 4.16). The measured

S21 is presented in Fig. 4.17, the insertion loss is set by the varactor losses and the

Page 125: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.3. TL PRI/NRI PHASE SHIFTER 102

1.5 2 2.5 3 3.5 4 4.5 5−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Inpu

t ref

lect

ion

coef

ficie

nt S

11 (

dB)

Worst case S11

at 2.5GHz = −19dB V

var = 3.9V & 4.2V

S11

< −10dB over a bandwidth of 2.6GHz

← →

Figure 4.16: Measured S11 vs. freq. for different bias conditions.

1 2 3 4 5 6−30

−25

−20

−15

−10

−5

0

5

Frequency (GHz)

Inse

rtio

n lo

ss S

21 (

dB)

S21

at 2.5GHz varies from −0.55dB → −1.1dB

Figure 4.17: Measured S21 vs. freq. for different bias conditions.

Page 126: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 103

Table 4.2: Summary of the TL PRI/NRI Phase Shifter Performance.Parameter ValueDesign frequency 2.5GHzTechnology 0.13µm CMOS/microstripPhase shift -40o ⇒+34o=64o

Insertion loss 0.5dB to 1.1dBFOM 128o/dBSize 10.8mm×10.4mmNo. of unit-cells 1S11 -19dBBandwidth 2.6GHzFractional BW > 100%Max. bias volt. 4.2VAv. power diss. [email protected]. Sim. NF 7.6dB

TAI Q. The insertion loss at 2.5GHz varies from 0.55dB to 1.1dB over the entire

phase tuning range. Across the entire 2.6GHz bandwidth, the insertion loss varies

from 0.25dB to 4.6dB.

The TL phase shifter dissipates an average DC current of approximately 32.9mA from

a 1.5V supply which corresponds to 49.4mW across the entire phase tuning range. This

power is required to bias the TAI circuit in order to generate the required inductance.

The average noise figure of the TL phase shifter is predicted from simulations to change

from 6.1dB to 9.3dB at 2.5GHz across the phase tuning range with an average value of

7.6dB. From simulations, the main noise contributor to the phase shifter’s noise figure

is the TAI circuit. The performance of the TL PRI/NRI phase shifter is summarized

in Table 4.2.

4.4 MMIC PRI/NRI Phase Shifter

To reduce the size of the TL PRI/NRI phase shifter unit-cell, it is desirable to get rid

of the TL sections. The TL sections are important to compensate the phase incurred

by the signal due to the NRI loading elements. By replacing each TL with a lumped-

element L-C section and carefully selecting the values of the series inductance and

shunt capacitance, a similar phase response can be achieved while occupying a much

smaller area. This implementation will eliminate the need for bulky microstrip TLs

and will allow integrating the entire PRI/NRI phase shifter onto a single MMIC. To

Page 127: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 104

C

L

Lo

Co Co CoCo

CLo

Figure 4.18: Proposed IC PRI/NRI metamaterial phase shifter unit-cell.

the author’s knowledge, this work is considered the first published attempt to design a

fully-integrated tunable PRI/NRI phase shifter.

The proposed MMIC PRI/NRI phase shifter unit-cell is shown in Fig. 4.18. The

microstrip TL sections are replaced with a low-pass Π section Lo-Co. The resulting

lumped-element phase shifter can admittedly be thought of as a band-pass filter, created

by cascading low-pass and high-pass sections. However, here we are mainly interested in

its phase response, as opposed to conventional band-pass filters which are mainly used

for their magnitude response. Moreover, the corresponding structure should be thought

of as being a periodic one and having the unit-cell of Fig. 4.18. This is also unlike band-

pass filters which typically are non-periodic. The architecture of the proposed lumped-

element PRI/NRI phase shifter is similar to that presented in [3] to model a TL, which

was loaded with discrete series capacitors and shunt inductors for the sake of analyzing

it. However, a complete Π section with two shunt capacitors and a series inductor

is used here to synthesize the TL sections. This creates two zeros in the reflection

coefficient transfer function, S11, resulting in two frequencies at which the phase shifter

is perfectly matched. This extends the MMIC phase shifter bandwidth as opposed to

a lumped-element phase shifter based on the unit-cell presented in [3]. Furthermore,

this topology makes the phase shifter more suitable for implementation in IC form,

since the discrete components are replaced with on-chip components fabricated on a

silicon substrate. More specifically, the explanation lies with the implementation of the

series capacitors C, which will be replaced with MOS capacitors, as will be described

later in section 4.4.2. The series MOS capacitors are associated with large parasitic

gate and drain/source diffusion capacitance to the substrate. Therefore, these parasitic

capacitors can be naturally lumped with the shunt capacitor Co, and accounted for as

a contributor to the phase of the PRI section. Similarly, the effect of the parasitic

Page 128: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 105

capacitance associated with the series inductors can also be lumped within the shunt

capacitors Co. This makes the proposed unit-cell in Fig. 4.18 well suited for the MMIC

phase shifter implementation.

4.4.1 Analysis

Using periodic analysis one can show that the phase shift of the MMIC PRI/NRI phase

shifter unit-cell is expressed as:

cos φ = 2ω4L2oC

2o

(1 +

Co

C

)− ω2LoCo

(4 +

6Co

C+

Lo

L+

LoCo

LC

)

+

(1 +

4Co

C+

Lo

L+

2LoCo

LC

)− 1

ω2LC. (4.15)

A simpler and more intuitive expression for the phase shift can be obtained by assuming

that the signal incurs a small phase shift φ, hence cos φ ≈ 1 − φ2/2. This is used to

simplify Eq.(4.15) resulting in the following expression:

φ ≈√

2

ω√

LC

√(1− ω2Lo(C + Co))×

√(1− ω2Co(Lo + 4L) + 2ω4C2

oLLo). (4.16)

By equating the phase shift φ to zero, one can find the zero-phase frequencies:

ωo1 =

√1

Lo(C + Co), and

ωo2,3 =

√Lo + 4L±√

L2o + 16L2

4CoLLo

. (4.17)

Furthermore, Eq.(4.16) reveals that there is a range of frequencies over which the

phase is imaginary. This indicates that the underlying periodic structure exhibits a

stop-band, over which the input signal is attenuated. Figure 4.19 shows the dispersion

diagram of the periodic structure, where the component values are picked in such a way

to show the stop-band. In order to close the stop-band centered around the 0o mark,

the two zero-phase frequencies, ωo1 and the lower frequency of ωo2,3 should coincide,

i.e. ωo1 = ωo2. This is similar to the method adopted in [3] for the TL-based structure.

Page 129: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 106

−150 −100 −50 0 50 100 1501

1.5

2

2.5

3

3.5

4

4.5

5

Fre

quen

cy (G

Hz)

Phase (deg)

periodic structure stop−band

ωo1

ωo2

L=3nH C=2.4pF L

o=1.7nH

Co=0.18pF pass−band

pass−band

Figure 4.19: Dispersion diagram of the periodic structure composed of the proposedMMIC PRI/NRI phase shifter unit-cells.

This results in the following stop-band closure condition:

2L

C=

Lo(C + Co)

Co(Co + 2C)⇒ 2L

C≈ Lo

2Co

. (4.18)

This approximation is based on the assumption that the shunt capacitor Co is smaller

than the series loading capacitor C, which will ensure that the cut-off frequency of the

low-pass section is higher than the cut-off frequency of the high-pass section. This stop-

band closure condition is similar to the condition obtained for the TL implementation

(Eq.(4.11)), since a TL section with a characteristic impedance Zo can be modeled by

two shunt capacitors, Co, and a series inductor, Lo, given that Zo =√

Lo/2Co.

If the stop-band closure condition of Eq.(4.18) is satisfied, then the phase shift per

unit-cell can be re-written as:

φ ≈√

2

ω√

LC× (1− ω2Lo(C + Co)) (4.19)

≈√

2

ω√

LC− 2

√2ω

√LoCo. (4.20)

Page 130: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 107

Similar to Eq.(4.13), the phase expression of Eq.(4.20) has two terms. The first term

results in a phase lead and is caused by the NRI section (high-pass), whereas the

second term results in a phase lag and is caused by the PRI section (low-pass). Hence,

similar to the TL phase shifter, a zero-degree phase shift can be realized by a single

unit-cell without having to go through a complete 360o phase rotation. Furthermore,

positive and negative phase shifts can be realized depending on which of the two terms

dominate. To center the phase shift around the zero-degree mark, the lumped-element

values should be chosen such that the phase contributions of the PRI and NRI sections

cancel out.

It is also important to investigate the return loss of the phase shifter unit-cell. When

a unit-cell of the MMIC phase shifter is terminated with an impedance Zo, one can

show that the reflection coefficient, S11, at the zero-phase frequency is expressed as:

S11(ω = ωo1) =

2L

C− Lo(C + Co)

Co(Co + 2C)

Lo(C + Co)

Co(Co + 2C)− 2L

C+ j

2L(C + Co)2

C2Co(Co + 2C)ωo1Zo

. (4.21)

Similar to Eq.(4.12), this indicates that by satisfying the stop-band closure condition

of Eq.(4.18), the MMIC phase shifter becomes perfectly matched at the zero-phase

frequency, ω = ωo1. However, when the component values are varied to tune the

phase response, the location of the zero-phase frequency changes according to Eq.(4.17).

Hence the frequency at which the phase shifter is matched changes. Since it is desired

to achieve a wide bandwidth, it is important to investigate the phase shifter matching

at frequencies different from the zero-phase frequency. One can derive the matching

condition by equating S11 to zero at frequencies different from the zero-phase frequency

(ω 6= ωo1). This results in the following matching condition:

Zo ≈√

(C(2L + Lo) + Co(4L + Lo))ω2 − 1

ω2C2. (4.22)

Equation (4.22) indicates that the proposed IC phase shifter has a second frequency

at which it is perfectly matched. This is a result of an additional zero in the reflection

coefficient transfer function. Using Eq.(4.22), one can show that this second frequency

Page 131: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 108

where S11 dips is expressed as:

ωm =1√

Lo(Co + 2C). (4.23)

Having two frequencies at which S11 dips, ωo1 and ωm, helps extend the bandwidth

of the MMIC phase shifter compared to a lumped element phase shifter based on the

unit-cell of [3], where S11 dips only at the zero-phase frequency. Also, as indicated by

Eq.(4.20), the MMIC implementation allows varying the phase contribution of both

the PRI and NRI sections, as opposed to the TL implementation which only allows

varying the phase of the NRI section. In the MMIC implementation, the phase of the

NRI section is tuned via L and C, while that of the PRI section is tuned via Co. To

demonstrate this, L, C, and Co are varied from their nominal values to become rL×L,

rC × C, and rCo × Co respectively. This results in the following phase tuning range:

|∆φ| =√

2

ω√

LC×

(1− 1√

rLrC

)+ 2

√2ω

√LoCo × (

√rCo − 1), (4.24)

where the tuning ratios rL, rC , and rCo should be chosen in order to satisfy the stop-

band closure condition of Eq.(4.18) as well as the matching condition of Eq.(4.22). By

comparing Eq.(4.14) and Eq.(4.24), one can see that the MMIC phase shifter has an ex-

tra term which further extends its phase tuning range compared to the TL phase shifter

while still satisfying the matching condition. Furthermore, integrating the phase shifter

on a single MMIC eliminates the parasitics associated with the individual component

packages, which in turn extends the tuning range even more.

4.4.2 Design and Physical Implementation

The schematic diagram of the MMIC PRI/NRI tunable phase shifter is shown in

Fig. 4.20. A 0.13µm CMOS process was chosen to fabricate the phase shifter since

the TAI has already been characterized in that process. The same TAI circuit de-

scribed in chapter 3 is used to implement the phase shifter’s shunt inductor. The series

capacitors, C, are implemented using on-chip MOS varactors; each MOS varactor con-

sists of an array of 16 by 15 small MOS varactors with an aspect ratio of 1µm/0.5µm,

and can be tuned from 0.38pF to 1.4pF via the gate to drain/source voltage. The gate

Page 132: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 109

Figure 4.20: Proposed IC PRI/NRI metamaterial phase shifter unit-cell.

voltage of the MOS varactors is set by the DC voltage applied at the input and output

ports of the phase shifter, VDC . On the other hand, the drain/source voltage is gener-

ated by the TAI, and is approximately equal to VCM ≈ 0.6V. The Q of the series MOS

varactors has a strong impact on the phase shifter insertion loss, given that its effect

can be modeled as a series resistance in the signal path. To achieve the large capaci-

tance value required to make the design frequency 2.6GHz, a larger series capacitance

is required. To this end, a fixed 0.67pF on-chip high-Q MIM (Metal-Insulator-Metal)

capacitor, CMIM , is connected in parallel with the MOS varactor to achieve the re-

quired capacitance without reducing S21. The shunt capacitors of the PRI sections,

Co, are implemented using on-chip hyper-abrupt junction varactors, which provide a

wide tuning range. The varactors’ capacitance can be tuned from 90fF to 270fF by

changing the varactor cathode voltage, VB, from 3.8V to -0.1V. The varactor anodes

are biased by the voltage generated by the TAI. The series inductors of the PRI sec-

tions, Lo, are implemented using on-chip 1.7nH spiral inductors with 2.5 turns and an

outer diameter of 200µm. The spiral inductors have a low-Q at the design frequency,

which will contribute to the insertion loss of the phase shifter.

The die micrograph of the MMIC phase shifter is shown in Fig. 4.21, it occupies

an area of 550µm×1300µm, from which the core circuit without the pads occupies

380µm×960µm. To the author’s knowledge, this is the smallest tunable PRI/NRI

metamaterial phase shifter reported in the literature, that operates in this frequency

band. The TAI occupies 150µm×170µm from the overall area, and is located in the

Page 133: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 110

960 m

1300 m

380

m

550

m

G

G

S

G

G

S

Series spiral

inductors (Lo)

TAI

DC/bias inputs

G

Series MIM

capacitors

(CMIM)

Figure 4.21: MMIC PRI/NRI metamaterial phase shifter die micrograph.

middle section of the layout. The spiral inductors to the left and right of the TAI are

the series inductors of the PRI sections, Lo. They occupy a larger area than the TAI,

and are surrounded by ground shields to minimize the coupling between them. The

series MIM capacitors, CMIM , occupy a very small area, and can be seen in the die

micrograph. On the other hand, the series MOS varactors and the shunt varactors are

not visible in the die micrograph because they are covered by the metal fill introduced

by the foundry to achieve certain layer densities. The bias and control voltages are

provided to the circuit from the bottom pads. Large on-chip de-coupling capacitors

are used to stabilize the bias and control voltages by providing a low-impedance path

to ground. The right and left pads correspond to the input and output ports of the

phase shifter, which also provide the bias voltage to the series MOS varactors.

4.4.3 Experimental Results

The MMIC phase shifter is characterized by probing the dies and measuring the S-

parameters. Two GSG probes are used for the RF ports while a multi-contact wedge

with 8 DC needles is used to probe the DC pads. Figure 4.22 shows the measured and

theoretical phase responses for different bias conditions. The theoretical response is

predicted here using the approximate phase expression of Eq.(4.19), which results in

Page 134: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 111

1.5 2 2.5 3 3.5

−50

0

50

100

150

Frequency (GHz)

Inse

rtio

n ph

ase

φ (

deg)

φ tuning range at 2.6GHz = −35o to +59o

VDC

& VB are swept

from −0.3V→2.05V & 3.8V→0V, resp.

MeasurementsTheory

Figure 4.22: The measured and theoretical phase responses vs. freq. for different biasconditions. The phase expression of Eq.(4.19) is used for the comparison.

good matching between the measurements and theory. Unlike the TL phase shifter, the

exact phase expression of Eq.(4.15) and the approximate phase expression of Eq.(4.19)

yield very accurate results. On the other hand, comparing the measured phase with

the approximate phase expression of Eq.(4.20) results in a 12.2o phase error; this is

mainly due to the approximations made in the derivation of Eq.(4.20) which utilizes

the approximate matching condition of Eq.(4.18). Still Eq.(4.20) can serve as a good

starting point for initial hand calculations, and at the same time, it gives good design

insight.

To tune the phase shift φ, the series loading capacitance, CMOS, the shunt inductance,

as well as the shunt capacitance, CV AR are varied using VDC , the TAI bias point (Vc1,

Vc2, Vf ), and VB, respectively. The voltage VDC is swept from -0.3V to 2.05V and for

each value the appropriate inductance is generated using Vc1 and Vc2 to satisfy the

matching condition given by Eq.(4.18). In addition to that, VB is swept from 0.1V to

3.8V to extend the phase tuning range. The phase shift at 2.6GHz can be tuned from

-35o to +59o passing through the zero-phase mark, without the need for an entire 360o

rotation. This represents a 50% increase in the phase tuning range compared to the

TL phase shifter presented in the previous section. As explained in section 4.4.1, this

is due to the ability to control the shunt capacitance, CV AR. Furthermore, the MMIC

phase shifter eliminates the parasitics associated with the TAI package, which limited

Page 135: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 112

1.5 2 2.5 3 3.5 4 4.5−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Inpu

t ref

lect

ion

coef

ficie

nt S

11 (

dB)

← →

S11

< −10dB over a bandwidth of 1.9GHz

Worst case S11

at 2.6GHz = −19dB

Figure 4.23: Measured S11 vs. freq. for different bias conditions.

1 1.5 2 2.5 3 3.5 4 4.5−15

−10

−5

0

Frequency (GHz)

Inse

rtio

n lo

ss S

21 (

dB)

S21

at 2.6GHz varies from −2.8dB→−3.8dB

S21

(2.6GHz)=−3.8dB for the case V

B=0V

& VDC

=2.05V

Figure 4.24: Measured S21 vs. freq. for different bias conditions.

Page 136: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.4. MMIC PRI/NRI PHASE SHIFTER 113

1 1.1 1.2 1.3 1.4 1.5−4

−3.9

−3.8

−3.7

−3.6

−3.5

−3.4

−3.3

−3.2

Inse

rtio

n lo

ss S

21 a

t 2.6

GH

z (

dB)

Feedback voltage Vf (V)

Maximum loss compensation |∆φ|≈7.4o

|∆φ|≈5.1o

1 1.1 1.2 1.3 1.4 1.50

2

4

6

8

10

12

14

Pha

se s

hift

φ a

t 2.6

GH

z (d

eg)

Figure 4.25: Measured S21 and phase shift φ at 2.6GHz versus the TAI feedback voltageVf .

the inductance tuning range in the TL phase shifter. Figure 4.23 shows the measured

input reflection coefficient S11, for the same bias conditions used to sweep the phase.

The worst case S11 at the design frequency is -19dB. The phase shifter has a bandwidth

of 1.9GHz across which S11 is less than -10dB. The MMIC phase shifter has a smaller

bandwidth compared to the TL phase shifter, which is expected, and is mainly due to

the frequency dependent nature of the matching condition of Eq.(4.22).

Figure 4.24 shows the measured insertion loss S21 for the same bias points. As

indicated by the figure, S21 varies from -2.8dB to -3.8dB at the design frequency.

Across the entire phase shifter bandwidth, i.e. the 1.9GHz, the insertion loss varies

from 2.8dB to a worst case of 7.2dB. The phase shifter insertion loss is mainly due

to the losses associated with the spiral inductors and the series MOS varactors. It is

also important to note that, as the shunt capacitance increases, the cut-off frequency

of the PRI section decreases, which increases the phase shifter insertion loss. Hence,

as indicated by Fig. 4.24, the worst case S21 results when VDC and VB are set to 2.05V

and 0V respectively.

To demonstrate the effect of the negative resistance generated by the TAI circuit

on the phase shifter performance, the amount of negative resistance RS is varied by

Page 137: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 114

Table 4.3: Summary of the TAI-Based MMIC PRI/NRI Phase Shifter Performance.Parameter ValueDesign frequency 2.6GHzTechnology 0.13µm CMOSPhase shift -35o ⇒+59o=96o

Insertion loss 2.8dB to 3.8dBFOM 34o/dBSize 0.38mm×0.96mmNo. of unit-cells 1S11 -19dBBandwidth 1.9GHzFractional BW 73%Max. bias volt. 3.3VAv. power diss. [email protected]. Sim. NF 10.3dB

sweeping the feedback voltage, Vf , of the TAI, and the measured S21 is plotted in

Fig. 4.25. The plot shows that, at 2.6GHz, the phase shifter insertion loss can be

enhanced by 0.8dB with less than 7.4o phase variation, which corresponds to a change

of 7.8% of the phase tuning range.

The MMIC phase shifter dissipates an average DC current of 21mA from a 1.5V

supply which corresponds to 31.5mW across the entire phase tuning range. This power

is required to bias the TAI circuit in order to generate the required inductance. The

MMIC PRI/NRI phase shifter has a lower average DC power consumption compared to

the TL-based design, which consumes 49.4mW. The higher average power consumption

of the TL-based design is mainly due to the parasitic package inductance, which adds

a fixed series inductance to the TAI. Hence, in order to satisfy the matching condition,

lower inductance values are required by the TAI in the TL-based design, which in turn

requires higher bias currents for the TAI circuit. The noise figure of the MMIC phase

shifter is predicted from simulations to change from 8.4dB to 12.8dB at 2.6GHz across

the phase tuning range, with an average value of 10.3dB. Similar to the TL phase

shifter, the main noise contributor is the TAI circuit. The performance of the MMIC

PRI/NRI phase shifter is summarized in Table 4.3.

Page 138: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 115

C

L

Lo

Co Co Co

CLo

CoCv

Figure 4.26: Unit cell of the proposed MMIC PRI/NRI tunable phase shifter.

4.5 Passive MMIC PRI/NRI Phase Shifter

This section presents another compact tunable MMIC PRI/NRI phase shifter. The

phase shifter is based on a similar L-C topology to that of the TAI-based MMIC

PRI/NRI phase shifter presented in the previous section. However, this design is

passive and does not use TAIs to tune the shunt inductance. Alternatively, it uses

a variable capacitor connected in parallel with a shunt spiral inductor as shown in

Fig. 4.26. The resulting topology still exhibits phase compensation properties which

allows it to center its phase response around the zero-degree mark while having a small

group delay. The series and shunt varactors are used to tune the phase and at the same

time maintain the matching, which allows the phase shifter to achieve a low return loss

across its entire phase tuning range. Compared to the TAI-based designs presented by

the previous sections, this design does not consume any DC power and at the same

time it eliminates the noise and non-linearity contributions of the TAI circuit.

4.5.1 Analysis

The passive MMIC PRI/NRI phase shifter consists of two lumped-element PRI sections

that replace the TLs in order to generate the low-pass response, which is required

to achieve the phase compensation. On the other hand, the high-pass response is

achieved via the series loading capacitors, C, and the shunt loading inductor, L. To

eliminate the active circuits used in the previous designs in order to tune the shunt

inductance L, a variable capacitor, Cv, is added in parallel with a shunt spiral inductor

to tune its effective inductance. The effect of adding this shunt capacitor on the phase

response, the tuning range, and the matching are explained in this section. Similar to

the previous designs, the passive MMIC PRI/NRI phase shifter unit-cell of Fig. 4.26

Page 139: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 116

is analyzed using the periodic analysis [24]. One can show that the phase shift per

unit-cell is expressed as:

cos φ = 2ω4L2oC

2o

(1 +

Co

C+

Cv

2C+

Cv

2Co

)

− ω2LoCo

(4 +

6Co

C+

Lo

L+

LoCo

LC+

Cv

Co

+2Cv

Co

)

+

(1 +

4Co

C+

Lo

L+

2LoCo

LC+

Cv

C

)− 1

ω2LC. (4.25)

A simpler and more intuitive expression for the phase shift can be obtained, by assuming

that the signal incurs a small phase shift, φ, hence cos φ ≈ 1 − φ2/2. This is used to

substitute in Eq.(4.25), resulting in the following expression:

φ ≈√

2

ω√

LC

√1− ω2Lo(C + Co) (4.26)

×√

1− ω2(Co(Lo + 4L) + CvL) + 2ω4CoLLo

(Co +

Cv

2

).

By equating the phase shift, φ, to zero, one can find the zero-phase frequencies:

ωo1 =1√

Lo(C + Co), and (4.27)

ωo2,3 =

√LCv + 4LCo + LoCo ±

√(LCv − LoCo)2 + 8L2Co(Cv + 2Co)√

2LLoCo(2Co + Cv). (4.28)

Furthermore, Eq.(4.26) reveals that there is a range of frequencies over which the

phase is imaginary. This indicates that the underlying periodic structure exhibits a

stop-band, over which the input signal is attenuated. Figure 4.27 shows the dispersion

diagram of the periodic structure, where the component values are picked in such a way

to show the stop-band. In order to close the stop-band centered around the 0o mark,

the two zero-phase frequencies, ωo1 and the lower frequency of ωo2,3 should coincide,

Page 140: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 117

−150 −100 −50 0 50 100 1501

1.5

2

2.5

3

3.5

4

4.5

5

Fre

quen

cy (G

Hz)

Phase (deg)

periodic structure stop−band

ωo1

ωo2

L=2.7nH C=1.5pF L

o=1.5nH

Co=0.17pF

Cv=1.3pF pass−band

pass−band

Figure 4.27: Dispersion diagram of the periodic structure composed of the proposedpassive PRI/NRI MMIC unit-cells.

i.e. ωo1 = ωo2. This results in the following stop-band closure condition:

2L

C=

Lo(C + Co)

Co(Co + 2C) + CvC/2⇒ 2L

C≈ Lo

2Co + Cv/2. (4.29)

This approximation is based on the assumption that the shunt capacitor Co is smaller

than the series loading capacitor C, which will guarantee that the cut-off frequency of

the PRI (low-pass) section is higher than the cut-off frequency of the NRI (high-pass)

section. Based on the stop-band closure condition of Eq.(4.29), the phase shift per

unit-cell can be re-written as:

φ ≈√

2

ω√

LC−√

2ω√

Lo(4Co + Cv). (4.30)

The phase expression of Eq.(4.30) has two terms. The first term results in a phase lead

and is caused by the NRI section, while the second term results in a phase lag and is

caused by the PRI section, and the additional shunt capacitor, Cv. Hence similar to the

previous two designs, a 0o phase shift can be realized by a single unit-cell without having

to go through a complete 360o phase rotation. Furthermore, positive and negative phase

Page 141: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 118

shifts can be realized depending on which of the two terms dominate. Hence to center

the phase shift around the 0o mark, the lumped component values should be chosen

such that the two terms in Eq.(4.30) cancel out.

It is also important to investigate the return loss of the phase shifter unit-cell. When

a unit-cell of the proposed passive MMIC PRI/NRI phase shifter is terminated with

an impedance Zo, one can show that the reflection coefficient, S11, at the zero-phase

frequency, ωo1, is expressed as:

S11(ω = ωo1) =

2L

C− Lo(C + Co)

Co(Co + 2C) + CCv/2

Lo(C + Co)

Co(Co + 2C) + CCv/2− 2L

C+ j

4L(C + Co)2

C2(2Co(Co + 2C) + CCv)ωo1Zo

.

(4.31)

This indicates that, by satisfying the stop-band closure condition of Eq.(4.29) the

MMIC phase shifter becomes perfectly matched at the zero-phase frequency. But

when the component values are varied to tune the phase shift, the location of the

zero-phase frequency changes. Since it is desired to achieve a wide bandwidth, it is

important to investigate the phase shifter matching at frequencies different from the

zero-phase frequency. One can derive the matching condition by equating S11 to zero

at frequencies different from the zero-phase frequency (ω 6= ωo1). This results in the

following matching condition:

Zo ≈√

(C(2L + Lo) + Co(4L + Lo) + LCv)ω2 − 1

ω2C2. (4.32)

Similar to the TAI-based design, Eq.(4.32) indicates that the passive MMIC phase

shifter has a second frequency at which it is perfectly matched. This is a result of an

additional zero in the reflection coefficient transfer function. Using Eq.(4.32), one can

show that the second frequency where S11 dips is expressed as:

ωm =1√

Lo(Co + 2C). (4.33)

Re-analyzing the PRI/NRI phase shifter unit-cell without the shunt capacitor, Co, in-

dicates that Co is the reason behind the additional zero that appears in the S11 transfer

Page 142: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 119

Lo

Co

L

VB1

CMIM

CMOS

Co

Lo

Co

CMIM

CMOS

Co

VB2

Cv

Figure 4.28: Proposed passive MMIC PRI/NRI phase shifter circuit implementation.

function. Having two frequencies at which S11 dips, ωo1 and ωm, helps extending the

bandwidth of the MMIC phase shifter compared to a lumped-element phase shifter

based on the unit-cell of [3], where S11 dips only at the zero-phase frequency.

Similar to the TAI-based design, this phase shifter allows varying both terms of the

phase expression of Eq.(4.30). If C, Co, and Cv are varied from their nominal values

to become rC × C, rCo × Co, and rCv × Cv, respectively, this results in the following

phase tuning range:

|∆φ| =√

2

ω√

LC×

(1− 1√

rC

)+ 2

√2ω

√Lo ×

(√4CorCo + CvrCv −

√4Co + Cv

),

(4.34)

where the varactor tuning ratios rC , rCo, and rCv should be chosen in order to satisfy

the stop-band closure condition of Eq.(4.29), and the matching condition of Eq.(4.32).

The effect of varying Cv can be seen from the second term of Eq.(4.34), which helps

extend the phase tuning range of the phase shifter although it does not use any active

circuits to tune the shunt inductance. Furthermore, integrating the entire phase shifter

on a single MMIC eliminates the parasitics associated with the individual component

packages, which in turn increases its tuning range even more as opposed to TL-based

design.

Page 143: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 120

4.5.2 Design and Physical Implementation

The schematic diagram of the passive fully-integrated PRI/NRI tunable phase shifter

is shown in Fig. 4.28. Since there is no need for any printed or off-chip components,

the phase shifter was implemented using a single MMIC. The series capacitors, C, are

implemented using on-chip MOS varactors, each MOS varactor consists of an array of

10 by 10 small MOS varactors with an aspect ratio of 2.3µm/0.5µm, and can be tuned

from 0.32pF to 1.26pF. The MOS capacitance, CMOS, is set via the gate voltage. The

gate voltage of the MOS capacitors is set by the DC voltage applied at the input and

output ports of the phase shifter, VDC . The Q of the MOS varactors has a strong

impact on the phase shifter insertion loss, given that its effect can be modeled as a

series resistance in the signal path. To achieve the large capacitance value required

to make the design frequency, fo, 2.6GHz, a larger series capacitor is required. To

this end, a fixed 0.96pF on-chip high-Q MIM capacitor, CMIM , is connected in parallel

to achieve the required capacitance without reducing S21. The shunt capacitors of

the PRI sections, Co, are implemented using on-chip hyper-abrupt junction varactors,

which provide a wide tuning range. The varactor capacitance can be tuned from 250fF

to 80fF by changing the varactor cathode voltage, VB1, from 0V to 3.3V. The series

inductors of the PRI sections, Lo, are implemented using on-chip 1.6nH spiral inductors

with 3.25 turns and an outer diameter of 200µm. However, the spiral inductors have

a low-Q at the design frequency, which will have a direct effect on the phase shifter

insertion loss. The shunt inductor, L, is implemented using a 1.1nH spiral inductor with

2.5 turns and an outer diameter of 240µm, while the shunt varactor, Cv, is implemented

using a hyper-abrupt junction varactor. The varactor capacitance Cv is controlled via

its cathode voltage, VB2, and can be tuned from 0.54pF to 1.6pF.

The passive MMIC PRI/NRI phase shifter was fabricated in a standard 0.13µm

CMOS process, and the die micrograph is shown in Fig. 4.29. The phase shifter oc-

cupies an area of 700µm× 1300µm. This is a very small area for a tunable PRI/NRI

metamaterial phase shifter operating in this frequency band. The spiral inductor lo-

cated in the middle section of the layout in Fig. 4.29 is the shunt inductor, L. Whereas,

the two spiral inductors to the left and right are the series inductors, Lo, of the PRI

sections. Each inductor is surrounded by a ground shield to minimize the coupling. The

bias and control voltages are provided to the circuit from the bottom pads. Whereas,

Page 144: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 121

1100 m

1300 m

380

m

700

m

G

G

S

G

G

S

Series spiral

inductors (Lo)

Shunt spiral

inductor (L)

DC/bias inputs

GSeries MIM

capacitors

(CMIM)

Figure 4.29: Phase MMIC PRI/NRI shifter die micrograph

the right and left pads correspond to the input and output ports of the phase shifter,

which also provide the bias voltage to the series MOS varactors.

4.5.3 Experimental Results

The passive MMIC PRI/NRI phase shifter was characterized by probing the dies and

measuring the S-parameters. Figure 4.30 shows the measured insertion phase, φ, for

different bias conditions. To tune φ, the series capacitor C, the shunt capacitors Co,

and Cv are varied using the input/output port DC voltage, VDC , and the bias voltages

VB1 and VB2, respectively. VB1 and VB2 are swept from 0V to 3.3V, and for each bias

condition the necessary series capacitance, CMOS is set through the bias voltage VDC in

order to satisfy the matching condition of Eq.(4.32). This will guarantee a low return

loss across the entire phase tuning range. The phase passes through the 0o mark at the

design frequency, 2.6GHz, and is tunable from -25.5o to +27o, which corresponds to a

51.5o per stage. Figure 4.31 shows both the measured input reflection coefficient S11

and the measured insertion loss, S21, for the same bias conditions used to sweep the

Page 145: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 122

1.5 2 2.5 3 3.5−100

−80

−60

−40

−20

0

20

40

60

80

100

120

Frequency (GHz)

Inse

rtio

n ph

ase

φ (

deg)

φ tuning range at 2.6GHz = −25.5o to 27o

VDC

& VB1,2

are swept from −0.6V→1.5V and 3.3V→0V

Figure 4.30: Measured phase vs. freq., for different bias conditions

1 1.5 2 2.5 3 3.5 4 4.5 5−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Inse

rtio

n &

Ref

lect

ion

loss

(dB

)

← →BW=2GHz

Worst case S11

at 2.6GHz = −21dB

S21

at 2.6GHz varies from −4.9dB→ −5.1dB

Figure 4.31: Measured S11 and S21 vs. freq., for different bias conditions

Page 146: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.5. PASSIVE MMIC PRI/NRI PHASE SHIFTER 123

0 0.5 1 1.5 2 2.5 3−30

−20

−10

0

10

20

30

Inse

rtio

n ph

ase

at 2

.6G

Hz

φ (

deg)

Varactor reverse bias voltage VB1

(V)

0 0.5 1 1.5 2 2.5 3

−5.4

−5.2

−5

−4.8

−4.6

Inse

rtio

n lo

ss a

t 2.6

GH

z S

21 (

dB)

Figure 4.32: Measured phase and S21 at 2.6GHz vs. the varactor reverse bias voltageVB1

phase. The worst case S11 at the design frequency is -21dB, and the phase shifter has

a very wide bandwidth of 2GHz, across which S11 is less than -10dB. This corresponds

to a fractional bandwidth of more than 76%. The wide bandwidth achieved is due to

the additional zero in the S11 transfer function, described in section 4.5.1. In practice,

the losses associated with the structure combines the two S11 dips into one wider dip,

resulting in a wide bandwidth. The insertion loss, S21, varies from -4.9dB to -5.1dB at

the design frequency. The relatively large insertion loss is mainly due to the series MOS

varactors’ low-Q, as well as the losses associated with the spiral inductors. It is worth

mentioning that, using this topology to design phase shifters at higher frequencies will

require smaller capacitors and inductors, which can be realized on-chip with higher Q

values, hence resulting in lower insertion loss.

The tuning characteristics of the phase shifter are presented in Fig. 4.32, where the

measured phase and insertion loss at 2.6GHz are plotted versus the shunt varactor

reverse bias voltage, VB1. The phase shifter has a very small insertion loss variation

of 0.2dB across the entire tuning range. Table 4.4 summarizes the performance of the

passive MMIC PRI/NRI phase shifter.

Page 147: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 124

Table 4.4: Summary of the Passive MMIC PRI/NRI Phase Shifter Performance.Parameter ValueDesign frequency 2.6GHzTechnology 0.13µm CMOSPhase shift -25.5o ⇒+27o=51.5o

Insertion loss 4.9dB to 5.1dBFOM 10.5o/dBSize 0.7mm×1.3mmNo. of unit-cells 1S11 -21dBBandwidth 2GHzFractional BW 76%Max. bias volt. 3.3VAv. power diss. 0Av. NFa 4.9dB to 5.1dB

aThe noise figure is roughly estimated from the phase shifter insertion loss.

4.6 Discussion and Comparison

Using the PRI/NRI phase shifter topology of [5] to build electronically tunable phase

shifters (i.e. the TL and the MMIC PRI/NRI phase shifters) has allowed building

compact, low group delay phase shifters with phase responses centered around the

zero-degree mark. As explained in section 2.5.1, compactness is an important feature

for beam steering networks, especially for series-fed arrays, in order to avoid capturing

grating lobes in the radiation pattern as the beam is scanned. Moreover, centering the

phase response around the zero-degree mark is desirable for series-fed antenna arrays in

order to allow scanning the main beam around the broadside direction. In addition, the

proposed phase shifter design approach maintains their bi-directionality, thus allowing

the same antenna array to operate as a transmitter and as a receiver. The low group

delay property of PRI/NRI phase shifters is described in detail in section 4.6.1, and its

importance for the design of series-fed antenna arrays will be demonstrated in chapter

6.

Using TAIs to design the TL and the MMIC PRI/NRI phase shifters resulted in a

wide phase tuning range and at the same time maintained the matching of the phase

shifters as opposed to other implementations published in the literature which use

a single tuning element [27, 56, 57], or use two tunable elements but in the form of

Page 148: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 125

Table 4.5: Comparison Between Different Phase Shifter Designs Presented In ThisChapter.

Parameter High-pass TL PRI/NRI MMIC PRI/NRI Passive PRI/NRITechnology Integrated Printed Integrated IntegratedPhase shift + ± ± ±Broadside rad. X

√ √ √Insertion loss Average Low Average HighSize Very small Large Small SmallBandwidth Small Large Large LargeAv. power diss. Average High Average 0IIP3 Average Average Average HighNoise figure High Average High Low

series and shunt varactors only [59]. On the other hand, as mentioned in chapter 3,

the TAI achieves a +2.16dBm 1-dB input compression point, which corresponds to

approximately a 0.8Vpp voltage swing while operating from a 1.5V supply voltage, and

a +12.5dBm IIP3. Consequently, using TAIs imposes limitations on the phase shifter’s

linearity, especially since it operates from a low-voltage supply of 1.5V. This will be

critical when an antenna array using these phase shifters operates in the transmit

mode. As an example, the TAI-based high-pass phase shifter presented in section 4.2

achieves a -2.2dBm 1-dB input compression point, and a +7.4dBm IIP3. Although

the proposed TAI-based phase shifters achieve a significantly higher 1-dB compression

point compared to other TAI-based phase shifters in the literature [86], their limited

power handling capability precludes their use in base stations. However, they can find

applications in short-range wireless applications requiring low transmit power levels

such as wireless sensor networks (WSN) and RF applications using ZigBee. Also,

designing the PRI/NRI phase shifters utilizing TAIs results in higher noise figures

compared to passive designs: 7.6dB and 10.3dB for the TL and MMIC phase shifters,

respectively. Nevertheless, in a practical application, the noise figure of the phase

shifter can be enhanced by preceding the phase shifter with a low noise amplifier when

operating within a receiver [23].

The passive PRI/NRI phase shifter tries to address some of the drawbacks of the

active designs by eliminating the TAI and using instead a shunt varactor. The result-

ing topology still exhibits phase compensation properties, which allows us to center its

phase response around the zero-degree mark while having a small group delay. Fur-

thermore, it is also capable of maintaining the phase shifter matching. The passive

Page 149: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 126

PRI/NRI design does not consume any DC power and at the same time it eliminates

the noise and non-linearity contributions of the TAI, which will potentially result in

a lower noise figure and a higher IIP3, respectively. This, however, comes at the ex-

pense of a slightly lower phase tuning range, and a higher insertion loss. Table 4.5

qualitatively compares between the different phase shifter designs presented in this

chapter.

The phase shifters presented here are prototypes fabricated to prove the concept and

to experimentally characterize them. When using these phase shifters within a practical

system, a look-up table together with multiple DACs (Digital-to-Analog Converters)

can be implemented to set the different bias voltages according to a single control

input. All of the biasing circuitry can be easily integrated on the same die with the

TAI for the case of the TL phase shifter or on the same die with the MMIC phase

shifters. This is one of the main advantages of using a standard CMOS technology to

implement the phase shifters as opposed to using other high ft technologies such as

GaAs. Furthermore, this should not result in a significant increase in the die sizes, since

removing the DC/bias pads would result in some area saving. Moreover, generating

the bias voltages on-chip will reduce the number of pins required from the TAI IC

package for the case of the TL phase shifter and from the IC package of the MMIC

phase shifter, making it possible to move to a smaller package size for both designs.

This will allow us to further shrink the dimensions of both designs.

Page 150: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 127

Tab

le4.

6:C

ompar

ison

Bet

wee

nD

iffer

ent

PR

I/N

RI

Phas

eShifte

rIm

ple

men

tati

ons

Spec

ifica

tion

TL

phas

esh

ifte

rIC

phas

esh

ifte

r[5

9][8

5][8

7]

Des

ign

freq

uenc

y2.

5GH

z2.

6GH

z17

GH

z6.

5GH

z10

GH

z

Tec

hnol

ogy

0.13

µm

CM

OS

0.13

µm

CM

OS

Ferr

oele

ctri

cva

ract

ors

Var

acto

rsFe

rroe

lect

ric

vara

ctor

s

&m

icro

stri

pFu

lly-int

egra

ted

&C

PW

&m

icro

stri

p&

CP

W

Pha

sesh

ift1

-40o⇒

+34

o=

64o

-35o⇒

+59

o=

96o

12.5

o32

o28

o

Inse

rtio

nlo

ss1

0.5d

Bto

1.1d

B2.

8dB

to3.

8dB

1dB

to1.

3dB

0.25

dBto

0.5d

B0.

8dB

to1d

B

FO

M2

128o

/dB

34o/d

B13

o/d

B60

o/d

B30

o/d

B

Size

110

.8m

m×1

0.4m

m0.

38m

m×0

.96m

m1.

8mm×0

.96m

m20

mm×5

mm

2.6m

m×0

.5m

m

No.

ofun

it-c

ells

11

46.

59

S11

-19d

B-1

9dB

-12d

B-9

dB-1

2dB

Ban

dwid

th3

2.6G

Hz

1.9G

Hz

>5G

Hz

1.9G

Hz

2.2G

Hz

Frac

tion

alB

W>

100%

73%

30%

30%

22%

Max

.bi

asvo

lt.

4.2V

3.3V

15V

26V

20V

Av.

pow

erdi

ss.

49.4

mW

@1.

5V31

.5m

W@

1.5V

00

0

Sim

ulat

edN

F6.

1dB⇒

9.3d

B8.

4dB⇒

12.8

dB–

––

1P

hase

shift

,in

sert

ion

loss

,an

dsi

zear

ere

port

edpe

run

it-c

ell.

Page 151: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 128

Table 4.6 presents a detailed comparison between the TAI-based TL and MMIC

PRI/NRI phase shifters along with related PRI/NRI phase shifters reported in the

literature. Note that, although the phase shifters presented in [59, 85, 87] utilize the

PRI/NRI structure, they do not achieve a phase centered around the zero-degree mark

at their design frequencies. Tuning the inductance in both the proposed TL and MMIC

phase shifters results in a very wide phase tuning range compared to the other imple-

mentations. To this end, the TL phase shifter achieves the highest figure of merit

(FOM=128o/dB). In contrast, the MMIC phase shifter has the largest phase tuning

range, but it achieves a figure of merit of only 34o/dB. This is attributed to the higher

losses of the MMIC phase shifter due to the low Q of the on-chip series spiral inductors

and MOS varactors. In spite of this, the MMIC phase shifter implementation occupies

a very small area compared to the other implementations, and has the potential of in-

tegration with RF and digital circuitry in a standard low-voltage and low-cost CMOS

process. Furthermore, the fractional bandwidth of both the TL and MMIC phase

shifters is much wider than those of other implementations reported in the literature.

This is mainly due to the ability to tune the shunt inductance, which allows one to

maintain the matching condition across the entire phase tuning range. Moreover, the

designs in [59, 85, 87] require very high control voltages; 15V up to 26V, which makes

them less suitable for hand-held applications.

4.6.1 Group Delay of PRI/NRI Phase Shifters

As previously described in chapter 2, a low group delay is necessary to minimize the

beam squinting with frequency variations in series-fed antenna arrays. In [5], it was

demonstrated that printed PRI/NRI phase shifters using fixed discrete components

achieve low group delays compared to traditional -360o TLs. In this section, we demon-

strate the same, but for the electronically tunable PRI/NRI phase shifters. As an exam-

ple, this is demonstrated here for the passive MMIC PRI/NRI phase shifter presented

in section 4.5.

The group delay of the passive MMIC PRI/NRI phase shifter, Tgd, can be obtained

using Eq.(4.30), which results in the following expression:

Tgd = −dφ

dω=

√2

ω2√

LC+√

2√

Lo(4Co + Cv). (4.35)

Page 152: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 129

1.5 2 2.5 3 3.5 4

0.15

0.2

0.25

0.3

0.35

Pha

se s

hifte

r gr

oup

dela

y (n

sec)

Frequency (GHz)

1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

All−

pass

filte

r gr

oup

dela

y (n

sec)

1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Figure 4.33: The measured group delays of the metamaterial phase shifter and thesimulated group delay of two cascaded 2nd-order all-pass filters achievinga -360o at 2.6GHz

Note that, the individual phase contributions of the PRI and NRI sections in Eq.(4.30)

do not need to be large to achieve the phase compensation. In fact, they can be small

in magnitude, and to achieve the phase compensation they only need to be equal.

Consequently, looking closely at Eq.(4.35), where the same two terms add up, one can

see that this architecture results in smaller group delays compared to using other types

of phase shifters which require a complete -360o or +360o phase rotation.

Since, all-pass filters are well suited to design phase shifters, we will use the group

delay of an all-pass filter as the reference for the comparison. Using the all-pass phase

shifter described in chapter 2 to achieve a -360o phase shift requires us to cascade two

of the 2nd-order constant-resistance stages. The resonance frequency of the all-pass

filter, ωr, is chosen as 2.6GHz, and the filter quality factor, Q, is chosen as 2 to result

in equal inductances. This results in the following group delay expression:

Tgd =2Qωr(ω

2 + ω2r)

Q2(ω2 − ω2r)

2 + ω2ω2r

. (4.36)

The group delay of the all-pass filter obtained from Eq.(4.36) is plotted in Fig. 4.33

with the measured group delays of the passive MMIC PRI/NRI phase shifter for all

the different bias conditions. As indicated by Fig. 4.33, the PRI/NRI phase shifter is

Page 153: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

4.6. DISCUSSION AND COMPARISON 130

capable of achieving the 0o phase with a 76% reduction in the group delay compared to

the reference all-pass phase shifter design. Furthermore, the PRI/NRI phase shifter’s

group delay varies by 63% over the entire 2GHz bandwidth compared to a variation

of 85% for the all-pass phase shifter design. It is also worth mentioning that, the

group delays of the passive MMIC PRI/NRI phase shifter plotted in Fig. 4.33 remain

relatively constant for the different bias conditions. This takes place because the phase

is tuned by varying the contribution of the NRI and PRI sections of Eq.(4.30) in an

opposite manner, which results in a very small variation in the group delay given by

Eq.(4.35). These results are not only specific to the passive MMIC PRI/NRI phase

shifter. In fact, it can be shown that the active TL and MMIC PRI/NRI phase shifters

also achieve low and relatively fixed group delays. As explained in section 2.5.4, the

low group delay property of PRI/NRI phase shifters is important to minimize the beam

squinting in series-fed antenna arrays. This will be described in more detail in chapter

6.

Page 154: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 5

A Highly-Reconfigurable Directional

Coupler

D uplexers are necessary building blocks for transceiver front-ends, since they allow

sharing the same antenna between the transmitter and the receiver, as shown

in Fig. 1.2. Duplexers are usually designed using printed or discrete components.

Consequently, they are bulky and do not provide any tunability. Also, for a transceiver

to support multi-standard operation, it is necessary to employ an electronically tunable

duplexer, capable of operating at different frequencies. In this chapter, the design of

a highly-reconfigurable CMOS MMIC directional coupler is presented. The proposed

directional coupler has the capability to operate with a tunable coupling coefficient, and

at the same time to operate at a tunable center frequency. Also, the proposed coupler

has the capability to switch the input power among its different ports. This makes it

suitable for replacing the bulky passive duplexers in transceiver front-ends. Also, as

explained in chapter 1, replacing the 3-port duplexer with 4-port highly-reconfigurable

directional coupler enables one to monitor the transmitted and received power. Thus,

allowing for precise control over the level of the TX power and the gain of the low-noise

amplifier.

131

Page 155: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.1. INTRODUCTION 132

(1)

(4)

(2)

(3)

Through port

Coupled portIsolated port

(1)

(4)

(2)

(3)

Isolated port

Coupled portThrough port

(a) Forward (b) Backward

Figure 5.1: Block diagram of a 4-port directional coupler configured in: (a) the forwardmode of operation, and (b) the backward mode of operation.

5.1 Introduction

The most popular method used to design directional couplers is using printed TL

structures. However, the TL implementations impose limitations on the area occupied

by the couplers, especially for systems operating within the low GHz frequency range.

This has hindered the integration of the couplers to produce single MMIC solutions

for such systems. Hence, various methods have been presented in the literature to

design lumped-element directional couplers [60]. Furthermore, the recent demand for

reconfigurable circuits capable of operating within multi-standard systems has created

a need for couplers capable of operating within different frequency bands [86, 88–92],

as well as capable of providing configurable coupling levels [93–95].

As a 4-port device, the directional coupler has the potential to simultaneously realize

multiple functions:

1. Tuning the coupling coefficient

2. Tuning the operating frequency

3. Switching from forward to backward operation, as illustrated by the block dia-

gram of Fig. 5.1, where the coupler is capable of switching the power between the

through port (P2) and the isolated port (P4) while perfectly isolating the other.

To date, existing reconfigurable couplers individually realize only one of the above

features [86,88–95]. Furthermore, to the author’s knowledge, none of the MMIC direc-

tional couplers reported in the literature has demonstrated the capability of electron-

ically switching between backward and forward operation. This feature could prove

to be very useful for diversity systems, in which it is desired to electronically switch

between different sub-systems (for example: antenna diversity systems). Also, it can be

Page 156: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.1. INTRODUCTION 133

used within transceivers to connect the TX and RX ports to the antenna (duplexing).

This will be explored in more detail later on in this chapter.

5.1.1 Tunable Coupling Coefficient Directional Couplers

Directional couplers with electronically tunable coupling coefficients are presented in

[93–95]. In [93] and [94], varactors are used to control the coupling between two printed

TLs. The design in [93] achieves a large tuning range of 4.1dB to 19dB for the coupling

coefficient, from the input port to the coupled port, over a wide bandwidth. Also,

the design in [94] achieves a 6dB to 10dB coupling coefficient tuning range. However,

in both designs the discrete varactors require a large reverse bias voltage; 25V for the

former and 10V for the latter. The design in [95] proposes to use switches to control the

coupling coefficient between two coupled TLs, resulting in coupling coefficients of 8dB

to 16dB. Nevertheless, the switches are not actually implemented and they are replaced

by hardwired connections (ideal short/open). Furthermore, both designs utilize printed

TL structures, hence they occupy a large area compared to a lumped-element approach.

To the author’s knowledge, lumped-element couplers with tunable coupling coefficients

have never been published yet in the literature.

5.1.2 Tunable Operating Frequency Directional Couplers

Directional couplers with electronically tunable operating frequencies have also been

presented in the literature [86,88–92]. In one of the most recently published papers [88],

varactors are used to terminate the open-circuited TL stubs of a dual-band TL coupler,

which was originally presented in [96]. Hence, the reverse bias voltage across the

varactors controls the operating frequency, within a limited range, around each of the

coupler bands by changing the effective electrical length of the stubs. Although the

reverse bias voltage across the discrete varactors goes up to 30V, this technique results

in a limited frequency tuning range of 0.62GHz to 0.9GHz and 1.63GHz to 1.8GHz for

the lower and upper frequency bands respectively. Furthermore, the coupler isolation

level is limited to 20dB and the design occupies a large area of approximately 6cm×6cm.

Other printed TL coupler designs have also been published in the literature [89–91]

that utilize varactors in different ways to tune the coupler operating frequency. But

all of them occupy a large area compared to lumped-element couplers and they require

Page 157: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 134

large reverse bias voltages for the discrete varactors. Furthermore, they do not achieve

a wide frequency tuning range: 1.3GHz to 1.7GHz and 1.7GHz to 2.17GHz for the

designs in [89,90] and [91] respectively.

Very few electronically tunable lumped-element directional coupler designs have been

published. The coupler published in [92] utilizes discrete varactors with chip inductors

to reduce the footprint of the coupler by 80% compared to the printed coupler of [91].

Nevertheless, using only tunable capacitors results in a limited frequency tuning range

(1.7GHz to 2.17GHz). To the author’s knowledge, the coupler published in [86] is the

first fully-integrated MMIC coupler achieving a tunable center frequency. The MMIC

coupler in [86] is based on the high-pass Tee L-C coupler topology of Fig. 2.19, and uses

TAIs with fixed on-chip Metal-Insulator-Metal (MIM) capacitors to achieve a tunable

operating frequency. However, it can only operate with a fixed coupling coefficient and

still does not offer the switching capability described in Fig. 5.1.

In this chapter, a highly-reconfigurable compact CMOS MMIC directional coupler

is presented. The MMIC directional coupler utilizes lumped-element varactors and

TAIs to allow electronic tuning of both the coupling coefficient as well as the coupler’s

operating frequency. To the author’s knowledge, this is the first coupler that combines

both functions. Furthermore, combining the use of varactors and TAIs results in a very

wide frequency tuning range while maintaining good isolation. Moreover, the MMIC

directional coupler can be electronically reconfigured to operate as a forward or as a

backward coupler, i.e. it is capable of switching the power from the through port to the

isolated port, see Fig. 5.1. The design equations of the MMIC directional coupler are

presented in section 5.2. Section 5.3 describes the MMIC directional coupler circuit

implementation. The experimental results are presented in section 5.4. Finally, the

noise performance of the MMIC coupler is evaluated in section 5.5.

5.2 Theoretical Analysis

5.2.1 Analysis of the MMIC Directional Coupler

The proposed MMIC lumped-element directional coupler uses the high-pass architec-

ture shown in Fig. 5.2. Each branch of the coupler consists of a lumped element L-C

section that provides the necessary 90o phase shift at the design frequency. The high-

Page 158: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 135

C1

C1

C2C2

L

L

L

L

(1)

(4)

(2)

(3)

Figure 5.2: The high-pass topology used by the proposed MMIC directional coupler.

C1

C1

L

L

L

L+1/2

Zo

Zo

+1/2

e

Te

e

Te

Figure 5.3: The equivalent circuit with even-mode excitation.

pass L-C topology requires grounded inductors as opposed to a traditional low-pass

topology which requires floating inductors [92]. This allows the use of the TAIs in

place of the spiral inductors. Furthermore, the high-pass Π topology is chosen to min-

imize the number of inductors, and hence the area occupied by the MMIC coupler. At

the same time, this topology reduces the number of series capacitors in the signal path,

which in turn, reduces the MMIC coupler insertion loss.

To analyze the operation of the proposed MMIC directional coupler, the lumped-

element L-C high-pass coupler is analyzed using the even-odd mode technique, origi-

nally presented in [97]. The effect of an input signal applied at any of the ports (port

1 in this case) while terminating the rest of the ports with an impedance Zo, is eval-

Page 159: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 136

C1

C1

2C22C2

L

L

L

L

2C22C2

+1/2

Zo

Zo

-1/2

o

To

V1 V2

I1 I2

2-port

Network

Odd mode circuit

To

o

Figure 5.4: The equivalent circuit with odd-mode excitation.

uated by decomposing the original coupler of Fig. 5.2 into two circuits: an even-mode

circuit shown in Fig. 5.3, and an odd-mode circuit shown in Fig. 5.4, where Te,o and

Γe,o are the transmission and reflection coefficients of the even- and odd-mode circuits,

respectively. The transmission coefficients S21, S31, S41 and the reflection coefficient S11

of the MMIC coupler can be obtained by properly superimposing the responses of the

even- and odd-mode circuits [97].

In standard 2-port network theory, the ABCD matrix is defined as:

[V1

I1

]=

[A B

C D

][V2

I2

], (5.1)

where V1,2 and I1,2 are the voltage and current, respectively, at ports 1 and 2 of the

odd-mode circuit shown in Fig. 5.4. Performing circuit analysis, one can show that the

ABCD matrix of the odd-mode circuit is expressed as:

1 +2β2 − 1

XL

β1

1

jβ1

2j

(2β2 − 1

XL

)−

(2β2 − 1

XL

)2

jβ1

1 +2β2 − 1

XL

β1

, (5.2)

Page 160: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 137

where β1, β2, and XL are the susceptances of the series capacitors C1, C2 and the reac-

tance of the shunt inductors L respectively. Using the standard relationship between

the scattering parameters and the ABCD matrix of a 2-port network [24], one can

evaluate the transmission and reflection coefficients of the odd-mode circuit, To and

Γo, which are expressed as:

To =2

2 +2

β1

(2β2 − 1

XL

)+

1

jβ1Zo

+ jZo

4β2 − 2

XL

(2β2 − 1

XL

)2

β1

, (5.3)

and

Γo =

1

jβ1Zo

− jZo

4β2 − 2

XL

(2β2 − 1

XL

)2

β1

2 +2

β1

(2β2 − 1

XL

)+

1

jβ1Zo

+ jZo

4β2 − 2

XL

(2β2 − 1

XL

)2

β1

. (5.4)

Similarly by analyzing the even-mode circuit, one can show that the transmission and

reflection coefficients of the even-mode circuit, Te and Γe, are expressed as:

Te =2

2

(1− 1

XLβ1

)− j

β1Zo

− jZo

(2

XL

− 1

β1X2L

) , (5.5)

and

Γe =

− j

β1Zo

+ jZo

(2

XL

− 1

β1X2L

)

2

(1− 1

XLβ1

)− j

β1Zo

− jZo

(2

XL

− 1

β1X2L

) . (5.6)

To fully characterize the lumped-element directional coupler, the S-parameters are

evaluated by superimposing Te,o and Γe,o, in Eq.(5.3) through Eq.(5.6), according to

Page 161: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 138

[24]. To guarantee a low reflection coefficient, S11, the following equation has to be

satisfied:

S11 =Γo

2+

Γe

2= 0. (5.7)

Furthermore, to guarantee high isolation, the following equation has to be satisfied:

S41 =Γe

2− Γo

2= 0. (5.8)

Solving Eq.(5.7) and Eq.(5.8) results in the following two conditions:

β21 =

1

Z2o

+ β22 ⇒ ω2

oC21 =

1

Z2o

+ ω2oC

22 , and (5.9)

XL =1

β1 + β2

⇒ ωoL =1

ωoC1 + ωoC2

, (5.10)

where ωo is the design frequency. Moreover, at the design frequency the transmission

coefficients of the through and coupled ports, S21 and S31 respectively, are given by:

S21(ω = ωo) = j

√1− β2

2

β21

= j

√1− C2

2

C21

, and (5.11)

S31(ω = ωo) =−β2

β1

=−C2

C1

. (5.12)

Hence, the output signals at the coupled and the through ports, P3 and P2 respectively,

have a 90o phase difference at the design frequency. At the same time, the magnitude

of the signals delivered to both ports is determined by the ratio of the series capacitors

C1 and C2.

5.2.2 MMIC Directional Coupler Modes of Operation

Tunable Coupling Coefficient

As indicated by Eq.(5.12), the coupling coefficient C of the MMIC directional coupler

can be tuned, and at the design frequency, is expressed as:

C(ω = ωo) = −20 log |S31| = −20 logC2

C1

. (5.13)

Page 162: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 139

1.3 1.5 1.7 1.9 2.1 2.3

0.6

0.8

1

1.2

1.4

1.6

1.8

Cap

acita

nce

C2 (

pF)

Capacitance C1 (pF)

1.3 1.5 1.7 1.9 2.1 2.3

1

1.2

1.4

1.6

1.8

2

Indu

ctan

ce L

(nH

)

Figure 5.5: Series capacitance C2 and the shunt inductance L required to satisfy theconditions of Eq.(5.9) and Eq.(5.10) versus the series capacitance C1.

1.4 1.6 1.8 2 2.21

2

3

4

5

6

7

8

9

Capacitance C1 (pF)

Cou

plin

g co

effic

ient

C (

dB)

Figure 5.6: Coupling coefficients achieved by the MMIC coupler circuit when thelumped-element components are chosen to satisfy both the matching andthe isolation conditions.

Page 163: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 140

For example, in order to implement a 3dB coupler, the capacitance C1 has to be chosen

equal to√

2× C2. Furthermore, if the series capacitors are replaced by varactors, the

coupling coefficient can be electronically tuned by changing the bias voltages applied

across the varactors. In order to achieve a low return loss and a very high isolation while

tuning the coupling coefficient, both conditions expressed by Eq.(5.9) and Eq.(5.10)

must be satisfied across the entire coupling coefficient tuning range. Equation (5.9)

reveals that, if C1 is increased to tune the coupling coefficient, the value of C2 must

also increase for the MMIC directional coupler to operate at the same frequency. At

the same time, the value of the shunt inductor L has to decrease according to the

condition of Eq.(5.10). Figure 5.5 shows the values of C2 and L resulting from the

theoretical expressions of Eq.(5.9) and Eq.(5.10) respectively when C1 is swept to tune

the coupling coefficient. This plot is generated assuming a nominal design frequency

of 2.6GHz and a 50Ω termination impedance (Zo). Although the coupling coefficient

depends on the ratio of the two series capacitances, the nonlinear relationship between

C1 and C2 in Eq.(5.9) is enough to result in an 8.5dB tuning range for the coupling

coefficient. This is demonstrated by Fig. 5.6 which plots the theoretical expression of

the coupling coefficient given by Eq.(5.13) versus the value of C1. For each point the

value of C2, calculated from Eq.(5.9), is used to calculate the coupling coefficient.

We have so far shown that, the coupling coefficient of the MMIC directional coupler

can be electronically controlled while maintaining a low return loss and a very high

isolation across the entire tuning range. However, to achieve full electronic tunability

for the coupling coefficient, electronically tunable inductors are required. Thus, the

lumped-element approach used to implement the coupler proves to be a valid choice,

since this enables the integration of the coupler with the active circuits necessary to

synthesize the TAIs on the same chip.

Further circuit analysis can be performed on the lumped-element coupler to show

that the power delivered to the coupled port (P3), and hence the coupling coefficient

are, in general, a function of frequency. Moreover, the power delivered to the coupled

Page 164: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 141

port is expressed as:

S31(ω) =

4C1C2Z2oL

3ω5

(Zo

(ω2

ω2o

− 1

)− jωL

)

(ωL− jZo)

(Zo

(2ω2

ω2o

− 1

)− jωL

)

× 1

(Zo (2C1Lω2 − 1)− jωL) (Zo (2C2Lω2 − 1)− jωL)(5.14)

Equation (5.14) indicates the high-pass nature of the lumped element coupler. Fur-

thermore, evaluating S31 at the design frequency ωo results in the simple expression of

Eq.(5.13) as long as the two conditions of Eq.(5.9) and Eq.(5.10) are satisfied.

Tunable Frequency of Operation

The frequency of operation of the lumped-element coupler is defined as the frequency

at which high isolation and low return loss are achieved, while realizing the desired

coupling coefficient. This can simply be obtained by re-writing Eq.(5.10), which results

in the following expression for the coupler operating frequency:

ωo =1√

L(C1 + C2). (5.15)

The coupler operating frequency, ωo, given by Eq.(5.15) is a function of the shunt

inductance L and the series capacitances C1 and C2. However, to achieve low return

loss and high isolation the condition of Eq.(5.9) must also be satisfied, which can re-

written as:

C1 =L

Z2o

+ C2. (5.16)

As confirmation, further circuit analysis showed the frequency dependent nature of

Page 165: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 142

0.8 1.2 1.6 2 2.4

1.6

2

2.4

2.8

3.2

3.6

Ope

ratin

g fr

eque

ncy

f o (G

Hz)

Inductance L (nH)

0.8 1.2 1.6 2 2.4

1.4

1.8

2.2

2.6

3

Cap

acita

nce

C1 (

pF)

Figure 5.7: Operating frequency of the MMIC coupler and the series capacitance C1

versus the shunt inductance L. The series capacitance C1 is chosen tosatisfy both the matching and the isolation conditions, while C2 is chosento achieve an arbitrary coupling coefficient of 3dB.

the isolation of the lumped element coupler, which could be expressed as:

S41(ω) =

jLZoω3 (ω2 − ω2

o) (ω2oL

2 − Z2o )

(ω2ω2oL

2 + Z2o (ω2 − ω2

o)− jω2oZoLω) (ωω2

oL + jZo (2ω2 − ω2o))

× (ωωoL + jZo (ω − ωo)) (ωωoL− jZo (ω + ωo))

(ω2ω2oL

2 − Z2o (ω2 − ω2

o) + jω2oZoLω) (ωL− jZo)

(5.17)

This result is derived under the assumption that the conditions of Eq.(5.9) and Eq.(5.10)

are satisfied. Equation (5.17) confirms the existence of a zero in the transfer function

of S41 at ω = ωo, which results in perfect isolation at the operating frequency.

To tune the operating frequency ωo of the coupler, the shunt inductance L is varied

and for each inductance value, the series capacitance C1 is calculated from Eq.(5.16).

This is necessary in order to guarantee a low return loss as well as high isolation across

the entire frequency tuning range. The resulting operating frequencies based on the

theoretical expression of Eq.(5.15) are plotted in Fig. 5.7 together with the values of

Page 166: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.2. THEORETICAL ANALYSIS 143

the shunt capacitance C1 versus the value of the shunt inductance L. To generate this

plot the value of the shunt capacitance C2 is chosen according to Eq.(5.13) in order

to achieve an arbitrary coupling coefficient of 3dB. Also, the termination impedance is

set to 50Ω. Figure 5.7 indicates that changing the operating frequency from 3.6GHz to

1.6GHz (a 77% tuning range) requires tuning the inductance by a factor of 2.2, and at

the same time it requires tuning the capacitance C1, and consequently C2, by a factor

of 2.2.

It is also possible to achieve a tunable frequency of operation for this MMIC coupler

by using a fixed shunt inductance and varying both series capacitances C1 and C2.

This will eliminate the need for TAIs if the coupler is only intended to have a tunable

operating frequency and not a tunable coupling coefficient as described earlier. How-

ever, this will drastically reduce the frequency tuning range. To demonstrate this, one

can show that the frequency tuning range achieved by tuning the shunt inductance L

as well as the series capacitance C1 while fixing C2 is expressed as:

∣∣∣∣∆ωo

ωo

∣∣∣∣ =2C1

C1 + C2

×∣∣∣∣∆L

L

∣∣∣∣ . (5.18)

On the other hand, if the shunt inductance is fixed and both series capacitors C1 and C2

are varied to tune the operating frequency, and at the same time, satisfy the condition

of Eq.(5.16), the frequency tuning range decreases to:

∣∣∣∣∆ωo

ωo

∣∣∣∣ =C1

C1 + C2

×∣∣∣∣∆C1

C1

∣∣∣∣ . (5.19)

Hence, for the same component tuning range, combining the use of varactors and TAIs

extends the frequency tuning range by 50% compared to a design that uses series

varactors and fixed shunt inductors. The wider tuning range makes the proposed

lumped-element directional coupler utilizing varactors and TAIs attractive for multi-

standard applications where the coupler would be required to operate over a wide range

of frequencies.

Page 167: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.3. CIRCUIT IMPLEMENTATION 144

Power switching

Another interesting feature of this lumped-element MMIC coupler is its ability to be

electronically reconfigured to operate as either a forward or a backward coupler, as

described in the introduction. One can argue by symmetry that interchanging the two

series capacitors C1 and C2 would result in interchanging the isolated and through

ports of the MMIC directional coupler. Thus, implementing the series capacitors C1

and C2 using varactors allows switching from forward to backward operation by simply

switching the bias voltage applied across the varactors.

This section has summarized the three different modes of operation of the proposed

MMIC directional coupler. The next sections describe the design details of the MMIC

directional coupler circuit as well as its experimental characterization.

5.3 Circuit Implementation

5.3.1 MMIC Directional Coupler Design

The schematic diagram of the proposed highly-reconfigurable CMOS directional cou-

pler is shown in Fig. 5.8. Since there is no need for any printed or off-chip components,

the entire directional coupler has been implemented on a single MMIC. The series ca-

pacitors C1 and C2 are implemented using on-chip MOS varactors, each MOS varactor

consists of an array of 5 by 18 small MOS varactors with an aspect ratio of 2µm/0.5µm,

and can be tuned from 0.25pF to 1pF. The Q of the varactors has a strong impact on

the coupler’s insertion loss, given that its effect can be modeled as a series resistance

in the signal path. To achieve the large capacitance value required to make the de-

sign frequency, fo, 2.6GHz, a larger series capacitance is required. To this end, a

fixed 0.95pF on-chip high-Q MIM capacitor, CMIM2, is connected in parallel. This

will slightly reduce the series capacitance tuning range, but it is necessary in order to

achieve a low insertion loss for the coupler. The series MOS capacitance, CMOS, is set

via the gate to drain/source voltage. The gate voltage of the series MOS capacitors in

the top and bottom branches of the coupler are set by the DC voltage Vr1 through a

10kΩ bias resistor R as shown in Fig. 5.8. Furthermore, the capacitance of the right

and left branches is set through the bias voltage Vr2. The drain/source voltage of all

the series MOS capacitors is set by the TAI circuit. To isolate the gate voltage of the

Page 168: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.3. CIRCUIT IMPLEMENTATION 145

(1)

(4)

(2)

(3)

R RVr2

R

Vr1

R

Vr1

Tunable Active

Inductor -gm2

gm1

Zin

C

CMIM2

CMOS

CMIM1

CMIM2CMOS

CMIM1

CMIM2

CMOS

CMIM1

CMIM2 CMOS

CMIM1

TAI

TAITAI

TAI

Figure 5.8: Proposed lumped-element MMIC directional coupler circuit implementa-tion.

Page 169: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 146

series MOS capacitors from the DC voltage generated by the TAI circuit, an additional

DC-blocking MIM capacitor CMIM1 is added in series. Since CMIM1 has a fixed value

and is connected in series with the effective tunable capacitor (the parallel combination

of CMOS and CMIM2), it reduces the tuning range of the overall series branch capac-

itance. To avoid the reduction in the tuning range, CMIM1 should be significantly

larger than CMOS + CMIM2. However, CMIM1 can not take an arbitrarily large value

since its parasitic capacitance to the substrate increases as well. This decreases its self-

resonance frequency and losses, which potentially increases the coupler losses. Since

CMOS + CMIM2 can vary from 1.2pF to 1.95pF, 10pF was found to be a good design

choice for CMIM1, which was also verified using simulations.

5.4 Physical Implementation and Experimental Results

5.4.1 Physical Implementation

The MMIC directional coupler was fabricated in a standard 0.13µm CMOS process.

The die micrograph is shown in Fig. 5.9, the dimensions of the fabricated chip are

1540µm×900µm, which includes the MMIC coupler as well as some test structures

and the biasing/RF pads. The MMIC directional coupler occupies 730µm×600µm

without the bias/RF pads. Arguably this is a very small area for a highly-reconfigurable

directional coupler operating in this frequency band.

Some test structures are fabricated beside the MMIC coupler circuit to help in char-

acterizing the TAI as well as the varactors. It is worth mentioning that, adding these

test structures together with their RF probing pads has resulted in some asymmetry in

the MMIC directional coupler layout, making the interconnecting wires from the RF

pads to two ports of the MMIC coupler (P3 and P4) longer than those of the two other

ports (P1 and P2) as shown in Fig. 5.9. The effect of this asymmetry on the MMIC

coupler performance will be discussed in the following section.

As indicated by Fig. 5.9, the majority of the area of the MMIC coupler is occupied by

the TAI circuits, which occupy 150µm×170µm, followed by the series MIM capacitors

CMIM1. On the other hand, the series varactors CMOS and the MIM capacitors CMIM2

occupy a very small area. The MOS varactors are not visible in the layout because

of the metal fill required by the foundry to maintain certain layer densities. The bias

Page 170: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 147

1540 m

730 m

900

m

DC/bias inputs

600

m

G

G

S

G

S

G

G

S

G

S

G

G

DC/bias inputsTest TAI

Test varactor

Directional coupler circuit

P4

P3

P1

P2

Shunt

TAI

P4

P3

P1

P2

Series MIM capacitor CMIM1

VDD

VDD

Series

capacitors

CMIM2 &

CMOS

Figure 5.9: MMIC directional coupler die micrograph. The top figure shows the en-tire fabricated chip and the bottom figure shows a close-up on the MMICdirectional coupler circuit.

Page 171: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 148

and control voltages are provided to the circuit from the top and bottom pads. The

rightmost and leftmost pads correspond to the four ports of the MMIC directional

coupler as indicated by Fig. 5.9. To distribute the bias and control voltages to the

different TAI circuits (VDD, Vcm, Vc1, Vc2) as well as the varactors reverse bias voltages

(Vr1, Vr2), the directional coupler circuit is surrounded by several bias distribution rings.

Each bias voltage is tapped off its ring whenever a connection is required to one of the

circuit components. This helps reduce the voltage drop across the bias lines, which

reduces mismatches between the responses of the different TAI circuits. Furthermore,

this facilitates the layout and routing process.

5.4.2 Experimental Characterization of the MMIC

Directional Coupler

The MMIC directional coupler was characterized by probing the dies and measuring the

corresponding 4-port S-parameters using a 4-port network analyzer. A pair of 150µm-

pitch differential GSGSG probes were used to probe the 4-ports of the MMIC coupler.

Two multi-contact wedges, each with 8 probe needles at 150µm-pitch, were used to

supply the bias and control voltages to the circuits. A CS-2 differential calibration

substrate from GGB Inc. is used to perform a 4-port calibration to de-embed the

frequency response of the RF probes, connectors, and cables. The different operating

modes of the MMIC directional coupler, which were described in section 5.2.2, have

been experimentally characterized and are summarized here.

Tunable coupling coefficient

The MMIC directional coupler was configured to operate at the nominal design fre-

quency of 2.6GHz, and the value of the series MOS capacitor C1 was varied using the

bias voltage Vr1 to tune the coupling coefficient of the MMIC coupler. To keep the

return losses low and the isolation of the coupler very high, the second series MOS

capacitor C2 is tuned via Vr2 and the shunt inductance is tuned via Vc1 and Vc2 accord-

ing to the conditions of Eq.(5.9) and Eq.(5.10) respectively. The resulting coupling

coefficient C and the isolation of the MMIC coupler for different biasing conditions are

plotted versus frequency in Fig. 5.10 and Fig. 5.11 respectively. Figure 5.10 also com-

Page 172: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 149

2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

2

4

6

8

10

Frequency (GHz)

Cou

plin

g co

effic

ient

C (

dB)

C tunable from 1.42dB to 7.14dB at 2.6GHz

C2/C

1 decreasing

MeasuredTheory

Figure 5.10: Measured and theoretical coupling coefficients C vs. freq. for different biasconditions.

2.2 2.4 2.6 2.8 3−50

−40

−30

−20

−10

0

← →

−10dB bandwidth = 0.45GHz

Worst case isolation at 2.6GHz is 41dB

Frequency (GHz)

Isol

atio

nS

41 (

dB)

Figure 5.11: Measured isolation S41 vs. freq. for the same bias conditions as Fig. 5.10.

Page 173: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 150

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Ret

urn

loss

S11

(dB

)

Figure 5.12: Measured reflection coefficient S11 vs. freq. for the same bias conditionsas Fig. 5.10.

pares the measured and theoretical coupling coefficients, which are predicted using the

expression of Eq.(5.14). The figure shows good agreement between the measurements

and theory. Using the exact expression of Eq.(5.14) is necessary for the comparison

in order to predict the frequency response of the coupling coefficient since the simple

expression of Eq.(5.13) is only valid at the design frequency.

The measurements in Fig. 5.10 and Fig. 5.11 show that the coupling coefficient of

the MMIC coupler can be electronically tuned from 1.4dB to 7.1dB at 2.6GHz, while

maintaining the isolation of the MMIC coupler higher than 41dB across the entire

coupling coefficient tuning range. This coupling coefficient tuning range corresponds to

directing 72% to 19% of the input power at port 1 to the coupled port (P3), respectively.

Furthermore, across this tuning range, the return loss is maintained below -16.5dB, as

indicated by Fig. 5.12. There is an exception to this, which takes place when the MMIC

coupler is configured to operate with a coupling coefficient of -1.42dB which results in

a S11 of -12.6dB.

The MMIC directional coupler draws an average DC current of approximately 139mA

from a 1.5V supply which corresponds to dissipating 208mW across the entire coupling

coefficient tuning range. This power is required to bias the TAI circuits in order to

Page 174: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 151

generate the required inductance. A more detailed discussion about power consumption

is presented towards the end of section 5.4.2.

Page 175: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 152

Tab

le5.

1:C

ompar

ison

Bet

wee

nth

eP

ropos

edM

MIC

Dir

ecti

onal

Cou

ple

ran

dO

ther

Var

iable

Cou

pling

Coeffi

cien

tC

ouple

rs

Spec

ifica

tion

[93]

[94]

[95]

This

work

Tec

hnol

ogy

Pri

nte

d/V

arac

tors

Pri

nte

d/V

arac

tors

Pri

nte

d/S

wit

ches

a0.

13µm

CM

OS

Cen

ter

freq

uen

cyFix

edFix

edFix

edTunab

le

at4.

5GH

zat

2GH

zat

5.2G

Hz

2.1⇒

3.1G

Hz

Cou

pling

coeff

.(C

)4.

1⇒19

dB

6⇒10

dB

8⇒16

dB

b1.

4⇒7.

1dB

Tunin

gC

onti

nuou

sC

onti

nuou

sD

iscr

ete

Con

tinuou

s

Ret

urn

loss

(S11)

-14⇒

-19d

B-1

7dB

-15d

B-1

2.6⇒

-32d

B

Isol

atio

n(S

41)

-22⇒

-45d

B-1

6⇒-3

5.4d

B-1

5dB

-41⇒

-51d

B

Max

bia

svo

ltag

e25

V10

V–

2V

Pow

erdis

sipat

ion

00

–20

8mW

@1.

5V

Siz

e12

mm×1

2mm

c14

.8m

m×2

.2m

m45

mm×5

0mm

730µ

m×6

00µm

aSw

itch

esar

eno

tim

plem

ente

d,th

eyar

ere

plac

edby

fixed

shor

t/op

enco

nnec

tion

s.bD

iffer

ent

coup

ling

coeffi

cien

tsar

eob

tain

edfr

omdi

ffere

ntpr

otot

ypes

.cSi

zees

tim

atio

nis

base

don

λ/4×

λ/4

for

anε r

of2.

2.

Page 176: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 153

2 2.2 2.4 2.6 2.8 3 3.2−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Isol

atio

n S

41 (

dB)

MeasuredTheory

Figure 5.13: Measured and theoretical S41 vs. freq., for different bias conditions

Table 5.1 summarizes the performance of the proposed MMIC directional coupler

with other tunable coupling coefficient couplers presented in the literature [93–95].

The proposed coupler provides a smaller coupling coefficient tuning range compared

to [93]. Also, using the lumped-element approach to design the proposed coupler results

in a smaller bandwidth compared to the printed designs in [93] and [94]. Nevertheless,

using the lumped-element approach to design the coupler results in a very compact

implementation. This enables fabricating the coupler in a standard CMOS process

allowing its integration with other RF/digital circuits on the same chip. Furthermore,

the integrated MOS varactors used in this design, require a much lower bias voltage

compared to the discrete varactors used in [93] and [94]. Moreover, the proposed MMIC

coupler achieves very high isolation levels compared to other designs.

Tunable Frequency of Operation

As explained in section 5.2.2, the proposed directional coupler is capable of operating

at different center frequencies. This is achieved by changing the value of the shunt

inductance via Vc1 and Vc2 and simultaneously changing the series MOS capacitance

C1 via Vr1 in order to satisfy the condition of Eq.(5.16). This will guarantee a low

Page 177: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 154

1.5 2 2.5 3 3.5−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Ret

urn

loss

S11

(dB

)

Figure 5.14: Measured S11 vs. freq., for different bias conditions

return loss and a very high isolation for the MMIC coupler across its entire frequency

tuning range. Figure 5.13 shows the measured coupler isolation for the different biasing

conditions, and compares it with the theoretical isolation, which is predicted using the

expression of Eq.(5.17). The figure shows good agreement between the measurements

and theory. As indicated by Fig. 5.13, the MMIC coupler can be electronically tuned to

operate over a very wide band of frequencies; namely 2.15GHz to 3.1GHz. Across this

wide frequency range, the isolation level between the input port (P1) and the isolated

port (P4) remains higher than 40dB. An exception to this happens when the coupler

is configured to operate at 3.1GHz, where the isolation drops to 34dB. At the same

time, the return loss of the MMIC coupler at each operating frequency is maintained

below -18.6dB over the entire frequency range, except for the case when the coupler is

configured to operate at 2.15GHz where the return loss goes slightly up to -15dB as

shown by Fig. 5.14.

As previously explained in section 5.2.2, varying L and C1 in order to tune the

operating frequency while fixing the value of C2 will affect the value of the coupling

coefficient. During measurements, in order to ensure that the coupler satisfies the

matching and isolation conditions, and achieves equal power splitting between the

through and coupled ports (S21 = S31), the value of C2 is linearly scaled with C1 using

Page 178: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 155

2 2.2 2.4 2.6 2.8 3 3.2−7

−6

−5

−4

−3

S21

& S

31 a

t fo (

dB)

Coupler center frequency fo (GHz)

2 2.2 2.4 2.6 2.8 3 3.2−60

−50

−40

−30

−20

−10

0

Isol

atio

nS

41 a

t fo (

dB)

Figure 5.15: Measured S21 and S31 to the left and S41 to the right vs. the coupleroperating frequency. Electronically tuning the capacitances C1 and C2

provides precisely equal power splitting between the through and isolatedports, i.e. S21 = S31.

Vr2. The measured MMIC coupler power levels at the coupled (P3) and through ports

(P2), as well as the coupler isolation levels are plotted versus the coupler operating

frequency in Fig. 5.15. The measured results show that across this entire range of

operating frequencies, S21 and S31 are equal and both of them vary from -3.35dB to

-4.44dB. This corresponds to a best case insertion loss of 0.35dB and a worst case of

1.44dB.

In this mode of operation, the MMIC directional coupler draws an average DC current

of approximately 132mA from a 1.5V supply, which corresponds to dissipating 197mW

across the entire frequency tuning range. According to Fig. 5.7, higher operating

frequencies require smaller inductance values, which require larger bias currents, and

vice versa. Hence, configuring the coupler to operate at 3.1GHz results in dissipating

the maximum power which is 216mW. On the other hand, configuring the coupler to

operate at the 2.15GHz results in dissipating the minimum power which is 132mW.

A more detailed discussion about power consumption is presented towards the end of

section 5.4.2.

Page 179: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 156

Tab

le5.

2:C

ompar

ison

Bet

wee

nth

eP

ropos

edM

MIC

Cou

ple

ran

dO

ther

Cou

ple

rsw

ith

Var

iable

Oper

atin

gFre

-quen

cy

Spec

ifica

tion

[4]

[89]

,[9

0][9

1][9

2][8

6]T

his

wor

k

Tec

hnol

ogy

Pri

nted

/Var

ac.

Pri

nted

/Var

ac.

Pri

nted

/Var

ac.

Lum

ped/

Var

ac.

0.18

µm

CM

OS

0.13

µm

CM

OS

Freq

.tu

ning

rang

e0.

62⇒

0.9G

Hz,

1.5⇒

1.93

GH

z,1.

7⇒2.

17G

Hz

1.7⇒

2.17

GH

z3.

2⇒4.

7GH

z2.

1⇒3.

1GH

z

1.63⇒

1.8G

Hz

1.3⇒

1.9G

Hz

Frac

.fr

eq.

rang

ea33

%,10

%25

%,35

%24

%24

%26

%36

%

Cou

plin

gco

eff.

(C)

Fix

edFix

edFix

edFix

edFix

edTun

able

3dB

20dB

3dB

3dB

3dB

1.4⇒

7.1d

B

Ret

urn

loss

(S11)

-24⇒

-10d

B,

-36⇒

-32d

B,

-27.

4⇒-2

1.1d

B-2

5⇒-1

4dB

-28⇒

-21d

B-4

3⇒-1

5.8d

B

-40⇒

-27d

B–

Isol

atio

n(S

41)

-25⇒

-20d

B,

<-4

3dB

,–

–-1

8⇒-1

4dB

-50⇒

-34d

B

-20d

B<

50dB

Inse

rtio

nlo

ss0.

5dB

–,0.

15dB

0.3⇒

0.8d

B1.

3⇒1.

4dB

0.2⇒

0.4d

B0.

3⇒1.

4dB

Max

bias

volt

age

30V

16V

,11

.2V

8V8V

1.8V

2V

Pow

erdi

ss.

(mW

)0

00

017

.6⇒

24.6

@1.

8V13

2⇒21

[email protected]

5V

Size

60m

m×6

0mm

–18

mm×1

8mm

8mm×8

mm

400µ

m×2

00µm

730µ

m×6

00µm

aFr

acti

onal

freq

.ra

nge

=∆

f/f

o.

Page 180: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 157

Table 5.2 summarizes the performance of the proposed MMIC coupler with other

couplers presented in the literature [86, 88–92]. The proposed MMIC coupler has the

widest frequency tuning range (∆f/fo), and at the same time, offers very high isolation

levels compared to the other designs. The design in [90] offers both a comparable

frequency tuning range and high isolation levels, but requires a high bias voltage of

11.2V for the discrete varactors. Besides, its printed implementation would require

a large area. Moreover, the compact CMOS implementation of the proposed MMIC

coupler allows integrating it with other RF/digital circuits, as opposed to the printed

designs of [88–91].

Similar to our proposed design, the coupler published in [86] also utilizes TAIs in a

high-pass topology. However, it does not employ varactors together with the TAIs. As

such, the coupler presented in [86] can only operate with a fixed coupling coefficient and

can not switch between forward and backward operation, as in the proposed design.

Furthermore, using TAIs only to tune the operating frequency does not allow satisfying

both the matching condition and the isolation condition simultaneously (see Eq.(5.15)

and Eq.(5.16)). This results in modest isolation and a lower relative frequency tuning

range, ∆f/fo. The design in [86] operates at slightly higher frequencies and consumes

less power, but this comes at the expense of the linearity of the coupler, and hence its

power handling capability, as will be discussed later.

Power switching

As described in section 5.2.2, one can electronically configure the MMIC coupler to

operate as either a forward coupler or as a backward coupler, i.e. switching the power

between the through port (P2) and the isolated port (P4). This is simply achieved

by interchanging the values of the bias voltages Vr1 and Vr2 applied at the gates of

the series MOS varactors C1 and C2 respectively. Figure 5.16 shows the measured

S-parameters of the MMIC coupler when it is configured to operate in the forward

mode at the nominal design frequency of 2.6GHz. By interchanging the values of the

bias voltages applied at the gates of the series MOS varactors, Vr1 and Vr2, the MMIC

coupler switches to the backward mode of operation as indicated by Fig. 5.17. For

both modes of operation, the MMIC coupler has an isolation level higher than 42dB

and a return loss that is less than -20dB. Furthermore, in both modes of operation

Page 181: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 158

1.5 2 2.5 3−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S−

para

met

ers

(dB

)

S21

S31

S41

Figure 5.16: Measured MMIC coupler S-parameters vs. frequency. Case 1: forwardoperation, the input power is equally divided between ports 3 and 2 whileport 4 is isolated.

1.5 2 2.5 3−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

S−

para

met

ers

(dB

)

S21

S31

S41

Figure 5.17: Measured MMIC coupler S-parameters vs. frequency. Case 2: backwardoperation, the input power is equally divided between ports 3 and 4 whileport 2 is isolated.

Page 182: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 159

2 2.2 2.4 2.6 2.8 3 3.260

70

80

90

100

110

120

130

140

Frequency (GHz)

Diff

eren

tial p

hase

(de

g)

94±2o over a bandwidth of 0.3GHz

← →

ForwardBackward

Figure 5.18: Differential phase response of the MMIC coupler vs. frequency for theforward and the backward modes of operation.

the output power is divided equally between the two output ports; P3 and P2 in the

forward case, and P3 and P4 in the backward case.

In the backward mode of operation, the MMIC coupler achieves a differential phase

(between P3 and P4) of 94±2o across a 0.3GHz bandwidth centered around the design

frequency. However, when the MMIC coupler is configured to operate in the forward

mode of operation, the asymmetry in the layout of the MMIC coupler, described in

section 5.4.1, results in some offset in the differential phase between the output ports

(P3 and P4), which becomes 98.6o. This is shown in Fig. 5.18, which plots the dif-

ferential output phase for both cases. This differential phase offset can be eliminated

by positioning the MMIC coupler circuit in the center of the fabricated chip to make

the interconnecting lines from the MMIC coupler circuit to the RF pads symmetrical.

However, in this fabricated prototype the test structures were positioned in between

the MMIC coupler circuit and the left-side RF pads due to area constraints.

One potential application for this mode of operation is to connect the TX and RX

ports of a transceiver to its antenna (duplexing) while providing very high isolation.

This is shown in Fig. 5.19, where in Fig. 5.19-a, the coupler is configured to operate

Page 183: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 160

(1)

(4)

(2)

(3)

RX

Monitoring

device

(1)

(4)

(2)

(3)

RX: IsolatedTX

(a) (b)

Antenna

TX: Isolated

Antenna

Forward operation: Receive mode,

Monitoring

device

Figure 5.19: Duplexer operation (a) Receive mode is achieved by configuring the cou-pler in the forward mode. (b) Transmit mode is achieved by configuringthe coupler in the backward mode.

in the forward mode. Hence, if the coupling coefficient, C, is configured to a very low

value (1.4dB), then most of the received power is directed to the receiver and only

a small portion goes to the through port, which could be connected to a monitoring

device to control the gain of the programmable LNAs in the receiver. Furthermore, the

TX port is isolated from the received signal. On the other hand, when transmitting,

the reconfigurable coupler is switched to the backward mode of operation. As shown in

Fig. 5.19-b, the input port of the coupler becomes port 4, which is connected to the TX

port. However, since the coupler is operating in the backward mode, the transmitted

signal is now isolated from the RX port and is divided among the antenna and the

monitoring device. In this case, the coupling coefficient can be configured to have a

very high value (7.1dB). Hence, most of the transmitted signal power is directed towards

the antenna. Finally, with measured operating frequencies ranging from 2.15GHz to

3.1GHz, the proposed design would be a suitable duplexer for multi-band applications.

The power dissipation of the proposed coupler, as it stands, is too high to be used

in portable transceivers, which tend to have low-power requirements. One possible

method to reduce the power consumption is to switch between more than one TAI

circuit in order to cover the required inductance tuning range. Hence, instead of in-

creasing the bias currents of transistors M1, M2, and M4 in Fig. 3.5, the TAI circuit

responsible for small inductances can use a larger gate width for transistors M1 and

M2 and a smaller width for M4. This follows from Eq.(3.20), which can be re-written

Page 184: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 161

−25 −20 −15 −10 −5 0−10

−9

−8

−7

−6

−5

−4

−3

S21

& S

31 a

t 2.6

GH

z (d

B)

Input power level (dBm)

−25 −20 −15 −10 −5 0−60

−50

−40

−30

−20

−10

0

Isol

atio

nS

41 a

t 2.6

GH

z (d

B)

Figure 5.20: Measured S21 and S31 at 2.6GHz on the left and S41 at 2.6GHz on theright vs. the input power level.

Table 5.3: Linearity Comparison Between Different TAI based Couplers

Specification [86] This work1dB compression point (P1dB) -16dBm -4.16dBmIsolation (S41) at P1dB – -28.3dB

as:

L ∝ Cgs4

gm1,2gm4

∝√

W4

IM1,2W1,2 × IM4

, (5.20)

where Wi and IMi are the width and bias current, respectively, of transistor Mi in

Fig. 3.5. Another method is to use a single TAI circuit, but replace each of the transis-

tors M1, M2, and M4 with more than one parallel-connected transistors. Hence, instead

of increasing the bias current, the TAI inductance can be decreased by appropriately

switching in and out transistors.

Linearity measurements

To characterize the linearity of the MMIC directional coupler, the circuit is biased to

operate at the nominal frequency of 2.6GHz. The input power of a 2.6GHz signal is

Page 185: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.5. EFFECT OF THE TAI ON THE COUPLER NOISE PERFORMANCE 162

swept from -20dBm to 0dBm and the resulting S-parameters are plotted in Fig. 5.20.

The MMIC coupler achieves a 1-dB compression point of -4.16dBm, which corresponds

to a peak-to-peak voltage swing of 391mV at the MMIC coupler input port while oper-

ating from a 1.5V supply. Also, as indicated by Fig. 5.20, as the input power increases

the isolation of the MMIC coupler drops and reaches a value of 28.3dB at the 1-dB

compression point. For input powers below -17dBm the isolation appears to remain

unchanged at approximately 55dB, which is due to the limited dynamic range of the

measurement setup. Table 5.3 summarizes the linearity performance of the proposed

MMIC coupler and compares it with the TAI-based coupler presented in [86]. Although

the proposed coupler achieves a significantly higher 1-dB compression point compared

to the TAI-based coupler in [86], its limited power handling capability precludes its use

in base stations. However, it can find applications in short-range wireless applications

requiring low transmit power levels such as wireless sensor networks (WSN) and RF

applications using ZigBee.

5.5 Effect Of The TAI On The Coupler Noise Performance

Combining the use of varactors and TAIs to implement this MMIC directional coupler

have made it a versatile highly-reconfigurable coupler capable of operating with differ-

ent coupling coefficients as well as operating at different frequencies while ensuring both

a low return loss and very high isolation. Furthermore, the coupler can electronically

switch between forward and backward operation. However, using active circuits and

varactors to synthesize the tunable inductors and capacitors, respectively, affects the

noise performance of the MMIC coupler, with the main noise contributors being the

TAI circuits. Hence, this section will demonstrate the effect of the noise contribution

of the TAI circuits on the MMIC coupler noise performance.

Figure 5.21 shows the block diagram of the MMIC coupler when it is configured to

operate in the forward mode as a 3dB coupler, which is used here to derive an expression

for the output referred noise of the MMIC coupler at its through and coupled ports.

The results will then be generalized for any arbitrary coupling level.

The noise contribution of each of the grounded (1-port) TAI circuits is modeled

by a shunt noise current source inLx where x is the port number. The relationship

between these noise current sources and the noise contribution of the various TAI

Page 186: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.5. EFFECT OF THE TAI ON THE COUPLER NOISE PERFORMANCE 163

inL1

(2)

inL2

(4)inL4

(3)inL3

Noiseless 3dB

coupler

Through port

Coupled portIsolated port

Zo

(1)

Zo

Zo

Input port

Figure 5.21: Block diagram of a 3dB coupler with the noise current sources representingthe effect of the active circuits within the TAIs.

circuit elements (the transistors and the feedback resistor Rf ) was presented in section

3.4.3. It is interesting to note that each of the noise sources of Fig. 5.21 sees the

same impedance, which is the parallel combination of the source impedance (Zs = Zo)

and the input impedance of the coupler Zin. This fact facilitates the calculation of

the output referred noise voltages of the MMIC coupler. Assuming that the noise

generated by the TAI circuits is uncorrelated, one can use superposition to show that,

the mean-square value of the output referred noise voltage at the through port P2 is

expressed as:

v2n2(ω) =

(Zo||Zin(ω))2

(i2nL1

(ω) + 2i2nL2(ω) + i2nL4

(ω))

. (5.21)

If the average noise power generated by the four TAI circuits is the same (i2nL1= i2nL2

=

i2nL3= i2nL4

), this results in the following:

v2n2(ω) = 2 (Zo||Zin(ω))2 × i2nL(ω). (5.22)

At the design frequency, the coupler input impedance is equal to Zo in order to achieve

good power matching. Hence the output referred noise voltage can be re-written as:

v2n2(ωo) =

Z2o

2× i2nL(ωo). (5.23)

Page 187: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.5. EFFECT OF THE TAI ON THE COUPLER NOISE PERFORMANCE 164

To obtain an expression for the total output noise, the noise contribution of the

source/termination impedances should be accounted for. Assuming that the noise

sources associated with each port are uncorrelated, the expression of the output re-

ferred noise voltage becomes:

v2n2(ωo) =

Z2o

2× i2nL(ωo) +

Z2o

(i2ns1

+ i2ns4

), (5.24)

where i2nsx= 4kT/Zo is the thermal noise current generated by the source/termination

impedance at port x. Since the noise power generated by all the source/termination

impedances are equal, the total output referred noise voltage at the through port P2

can be re-written as:

v2n2(ωo) =

Z2o

2× i2nL(ωo) +

Z2o

4× i2ns. (5.25)

From the symmetry of the coupler circuit, one can show that the output referred noise

voltage at the coupled port P3 is identical to that of the through port P2 given by

Eq.(5.25). Equation (5.25) also indicates that minimizing the noise current of the TAI

circuits is essential for optimizing the MMIC noise performance.

If the coupler is re-configured to operate with any arbitrary coupling level C, the

output referred noise voltage at the through port P2 becomes:

v2n2(ωo) =

i2nL1(ωo)Z

2o

4× (

1− A2)

+i2nL2

(ωo)Z2o

4+ (5.26)

i2nL4(ωo)Z

2o

4× A2 +

Z2o i

2ns1

4× (

1− A2)

+Z2

o i2ns4

4× A2,

where the factor A is given by A = 10−C/20. Again, assuming that the average noise

power generated by the four TAI circuits is the same, one obtains the same expression

of Eq.(5.25) for the output referred noise voltage at the through port. Hence, the noise

at the through and coupled ports remains the same for any arbitrary coupling level Cachieved by the MMIC coupler.

Substituting with the expression of the TAI’s noise current, given by Eq.(3.26), which

Page 188: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

5.5. EFFECT OF THE TAI ON THE COUPLER NOISE PERFORMANCE 165

was derived in chapter 3, the output referred noise voltage becomes:

v2n(ωo) ≈ kTZo + 2kTZ2

oγ (gm4 + gm5)

+2kTZ2oγg2

m4 ×2gm1,2 + gm3

4+ gm12 +

Rf (1 + ω2oC

2oR

2o)

γR2o

ω2o

(Co + Cgs4

(1 +

Rf

Ro

))2 , (5.27)

where k = 1.38× 10−23 J/K is the Boltzmann constant, and T is the absolute temper-

ature in degrees Kelvin. The value of the coefficient γ typically ranges from 2 to 3 for

short-channel transistors [83].

To verify the expression of Eq.(5.27), noise simulations were carried out for the

MMIC coupler while configured to operate as a 3dB coupler. The simulated MMIC

coupler output noise voltage, vn, and the TAI noise current, inL, were 5.25nV/√

Hz

and 0.17pA/√

Hz respectively at the design frequency. On the other hand, the cor-

responding noise voltage and current obtained from using the theoretical expression

of Eq.(5.27) and Eq.(3.26) are 6.2nV/√

Hz and 0.2pA/√

Hz respectively. This shows

that Eq.(5.27) provides a fairly accurate representation of the MMIC directional coupler

noise.

To minimize the noise of the MMIC coupler, one should design the TAI circuit using

small values for the transistor transconductances, as well as design the differential pair

to achieve a large output resistance Ro. On the other hand, large transconductances

are required to achieve the low inductance values which are necessary for configur-

ing the coupler to operate at high frequencies. Hence, a tradeoff exists between the

maximum frequency of operation and the noise generated by the MMIC coupler. In a

telecommunication system, the effect of the noise generated by the MMIC coupler on

the overall noise figure can be reduced by preceding it with a low noise amplifier [23].

Page 189: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 6

Electronically Steerable Series-Fed Patch

Array

6.1 Introduction

T he majority of consumer wireless applications use omni-directional antennas, and,

in some cases, antenna arrays are employed, producing narrow beams and pro-

viding better wireless coverage for specific, fixed areas. However, the lack of compact

electronically tunable phase shifters that can easily be integrated with printed antennas

has hindered the use of electronically steerable phased arrays in most wireless consumer

applications, and limited the use of electronic beam steering to high-precision, military

radar systems and satellite communications.

As explained in chapter 2, the compact feed network of a series-fed array is one of the

main advantages which make it more attractive as opposed to its parallel- or corporate-

fed counterparts. Besides compactness, the small size of series-fed arrays results in less

insertion loss and less radiation by the feed network. Also, the cumulative nature of the

phase shift in series arrays relaxes the design constraints on the phase tuning range of

the interstage phase shifters. For example, an N-element series-fed design can achieve

166

Page 190: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.1. INTRODUCTION 167

the same scan angle range as a parallel-fed design with (N-1) times less phase tuning

range. However, this cumulative nature also results in increased beam squintinga with

frequency variations, which is one of the main limitations in series-fed designs. Another

design challenge for series-fed designs is the tight limitations set on the size occupied by

the interstage phase shifters, as well as on the variation in its input impedance across

its phase tuning range. Furthermore, in most applications it is desired to center the

main beam about the broadside direction, which is achieved by feeding the individual

antennas, of a uniform array, in-phase. This implies that an inter-element phase shift

of zero-degrees is required. Moreover, to scan the angle of the main beam about the

broadside direction, the interstage phase shifters have to be capable of generating both

positive and negative phase shifts.

Traditionally, phase shifters have employed either a low-pass or a high-pass topology.

Hence, the in-phase feeding of the antennas was achieved by feeding them with an inter-

element phase shift of -360o or +360o, respectively. This, however, requires cascading

multiple stages, or using meandered delay lines to achieve such large phase shifts,

potentially increasing the size and insertion loss of the phase shifters. This also increases

the group delay of the phase shifters, which in turn results in more beam squinting.

With the recent developments in the field of metamaterials [3, 4], it is now possible

to design compact PRI/NRI phase shifters having phase shifts centered around the

zero-degree mark and at the same time having small group delays [5]. The work

in [5] was combined with CMOS microelectronic circuit techniques in chapter 4 of this

thesis to build printed as well as fully-integrated compact tunable PRI/NRI phase

shifters by using both varactors and TAIs. These tunable PRI/NRI phase shifters

also feature constant input impedance and are capable of producing both positive and

negative phase shifts. The compact size of these PRI/NRI phase shifters allows them

to be integrated with series-fed antenna arrays onto a single PCB. The resulting planar

structure is more appealing for low-cost wireless consumer applications, as opposed to

traditional designs in which the phase shifters and the antennas are implemented on

separate PCBs [98]. Furthermore, using the PRI/NRI phase shifters allows centering

the main beam of the array at the broadside direction and electronically scanning it in

both directions. In contrast, in the majority of the previously published designs this

aBeam squinting is defined here as the variation in the angle of the main beam of the antenna arraywith frequency.

Page 191: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 168

is achieved by physically terminating the input port and exciting the array from the

opposite port [98–100]. PRI/NRI phase shifters have been employed in [101] to design

a high-gain leaky-wave antenna array. This array is capable of electronically scanning

its main beam about the broadside direction, achieving both positive and negative

scan angles. However, using only varactors as the tunable elements results in a poor

return loss for the antenna array across its entire scan angle range, with a best case

of -12.5dB and a worst case of -6dB. Furthermore, the leaky-wave design results in a

very large gain degradation of 55% when the beam is merely scanned beyond ±6o off

the broadside direction.

In this chapter, an electronically steerable, series-fed patch array for 2.4GHz ISM

band applications is presented. The entire antenna array (i.e. the antennas, phase

shifters, and the feed network) is integrated onto a single PCB. The proposed steerable

array uses zero-degree tunable PRI/NRI phase shifters to center its radiation about

the broadside direction and allow scanning in both directions off the broadside. Also,

using these PRI/NRI phase shifters minimizes the squinting of the main beam across

the operating bandwidth. Furthermore, the feed network of the proposed array utilizes

λ/4 impedance transformers, which allows using identical interstage phase shifters,

and the sharing of the same control voltages to tune all stages. To the author’s knowl-

edge, the proposed antenna array is the first resonant antenna-element structure that

demonstrates electronic beam steering utilizing tunable PRI/NRI phase shifters. The

proposed steerable array uses the TAI-based, TL zero-degree PRI/NRI phase shifters

presented in chapter 4 in order to extend the scan angle range and at the same time

maintain a low return loss. Furthermore, the proposed array is capable of steering its

beam with small variations in its gain and its HPBW.

6.2 Theory

6.2.1 Antenna Array Architecture

The electronically steerable antenna array presented in this chapter consists of four

series-fed antennas and three interstage phase shifters as depicted by the basic archi-

tecture in Fig. 6.1. The array has a travelling-wave nature, however, it is not terminated

with a 50Ω load impedance as in traditional travelling-wave designs. Instead, the real

Page 192: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 169

dE<

PS PS PS

T

ZPS1 ZPS2 ZPS3

Figure 6.1: Basic 4-element series-fed antenna array.

PS PS PS

ZPS ZPS ZPS

dE< T

Figure 6.2: 4-element series-fed antenna array with λ/4 impedance transformers.

part of the antenna impedances are used as the termination for the array. Eliminat-

ing the load impedance improves the overall efficiency of the array, since it suppresses

the power dissipated in the termination, which could be on the order of 12.5% of the

input power as in the 5-element series-fed patch array in [99, 100]. For such an array

configuration, the standard and simplest design approach used in previously published

work (for example [98]) to feed the antennas is to progressively change the characteris-

tic impedance of the main feed line in order to maintain good matching for the array.

This, however, requires all the interstage phase shifters to have different impedance lev-

els, which complicates the array design by requiring different interstage phase shifter

designs. Furthermore, it complicates the process of electronic scanning by requiring a

separate set of control voltages to be applied to each interstage phase shifter.

An alternative approach is proposed in this chapter to allow using identical interstage

phase shifters, and to permit using a single set of control voltages to tune all the

stages. In this architecture, two λ/4 transformers are inserted before and after each

interstage phase shifter, which helps set the impedance level of the feed line to the value

required by the phase shifters (ZPS). Hence, the impedance of the λ/4 transformers is

Page 193: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 170

adjusted to achieve the desired matching, while keeping all the interstage phase shifters

identical. This allows using a single set of control voltages for tuning all the stages

simultaneously, thereby simplifying the steering of the antenna beam. Furthermore, if

constant input impedance phase shifters are utilized, the return loss of the series-fed

array can be minimized across the entire phase tuning range, or in other words, across

the entire scan-angle range. Moreover, these λ/4 transformers allow one to control the

power splitting ratios at each junction in Fig. 6.2, which helps ensure equal amplitude

excitation for the individual antennas. This will be described in more detail later in

section 6.2.2.

In the array architecture of Fig. 6.2, each λ/4 transformer contributes a -90o phase

shift. Hence, the total cumulative phase shift from one antenna to the next, φT , is

given by:

φT = −2× π

2+ φPS. (6.1)

To achieve the desired broadside radiation, the antennas need to be fed in-phase, i.e.

φT = 0, which according to Eq.(6.1) requires the phase response of the interstage

phase shifters φPS to be centered around +180o. But as described above, such large

phase shifts result in large group delays, which, in turn, will result in increased beam

squinting.

To address this problem, the array architecture in Fig. 6.2 is modified by alternating

the antennas with respect to the feed line as shown in Fig. 6.3. Alternating the antennas

is a known technique for the design of series-fed arrays. However, this is the first

time it has been used with tunable metamaterial PRI/NRI phase shifters to realize an

electronically steerable phased array. To achieve broadside radiation using the proposed

alternating architecture, the total cumulative phase shift φT should be set to 180o,

which is already realized by the intrinsic phase shift of the two λ/4 transformers. Hence,

according to Eq.(6.1) the interstage phase shift φPS should be centered around the zero-

degree mark. This means that the alternating series-fed array architecture of Fig. 6.3

can take advantage of the recent developments in small group delay metamaterial

PRI/NRI phase shifters to scan the main beam about the broadside direction, and at

the same time, minimize beam squinting.

Page 194: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 171

Zin1

ZT7

ZPS

ZT5ZT6ZT2ZT3 ZT1

PS

ZT4

ZPS

PS

ZPS

PS

(1:3)

(1:1)

(1:2)

PA

¼ PA

¾ PA

PB

PB

PB

PC

½ PC

½ PC

A B C

dE<

Figure 6.3: Alternating patch array diagram indicating the required ideal power split-ting ratios and all the λ/4 transformer impedances.

6.2.2 Feed Network Design

As described in section 6.2.1, the feed network of the antenna array uses λ/4 impedance

transformers, which allows us to use identical interstage phase shifters (i.e. the phase

shifters have the same phase shift φPS and the same impedance ZPS). Also, to simplify

the design, we use 4 identical antennas which have the same real input impedance, ZA,

at the design frequency. Starting the design of the feed network from the right-side of

Fig. 6.3, the characteristic impedance of the first λ/4 transformer, ZT1, should be set

to:

ZT1 =√

ZAZPS (6.2)

in order to guarantee that this interstage phase shifter is properly terminated and

consequently eliminate any reflections at its input and output ports. On the other

hand, the second λ/4 transformer, ZT2, gives us an additional degree of freedom to

adjust the impedance level which is loading the main feed line at junction C. One

should design this impedance level for a 1:1 power splitting ratio at junction C to

achieve equal amplitude excitations for the last 2 antennas. This, however, is only

valid under the assumption that the interstage phase shifters are lossless. Later on we

will demonstrate how the phase shifter loss can be incorporated in the design to still

Page 195: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 172

maintain the equal amplitude excitation. For the lossless case, the loading impedance

to the left side of junction C, Zin1 in Fig. 6.3, should be set to ZA. This is satisfied if

the second transformer has an impedance of:

ZT2 =√

Zin1ZPS =√

ZAZPS. (6.3)

Following the same procedure, one can derive the values of the characteristic impedances

of all the λ/4 transformers, which are given by the following equations:

ZT3 = ZT4 =

√ZAZPS

2, (6.4)

and

ZT5 = ZT6 =

√ZAZPS

3. (6.5)

The power splitting ratios are shown in Fig. 6.3. Note how the power splitting ratio

changes for each junction; at junction B, 1/3 of the power should be delivered to the

antenna whereas 2/3 of it should be directed to the subsequent stages, i.e. the power

splitting ratio should be 1:2. Similarly, at junction A, 1/4 of the input power should be

delivered to the antenna whereas 3/4 of it should be directed to the subsequent stages,

i.e. the power splitting ratio should be 1:3. Constraints represented by Eq.(6.2)-(6.5)

ensure the same amount of power is delivered to all the antennas regardless of the

power division happening at each junction. An additional λ/4 transformer is added

at the input port of the series-fed array in order to match its input impedance to the

source impedance, Zo. Hence, the characteristic impedance of the input transformer is

expressed as:

ZT7 =

√ZAZo

4. (6.6)

The feed network presented in [98] uses a similar approach to achieve equal power

splitting. However, the power splitting ratios at each junction are adjusted by varying

the impedance level of the interstage phase shifters. In contrast, in our proposed design,

this is achieved by varying the impedance of the interconnecting microstrip TLs while

using identical interstage phase shifters, which allows using only one set of control

voltages for beam steering.

Also, as previously mentioned, the λ/4 transformers inserted before and after each

Page 196: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 173

interstage phase shifter ensure matching the phase shifter’s input and output impedance

ZPS to its source and load impedances, respectively. Hence, when the electrical length

(or the phase shift φPS) of the interstage phase shifters is varied to scan the angle of

the main beam, the input impedance of the entire series-fed array remains unchanged.

This ensures a low return loss, S11, for the array for all scan angles. However, this is

only valid as long as the interstage phase shifters can provide a fixed impedance ZPS

across their entire phase tuning range, which imposes an important constraint on the

interstage phase shifter’s design. This will be explored in more detail in section 6.2.3.

If the interstage phase shifters have a finite insertion loss which can be represented by

their forward transmission coefficient S21, one can show that the power splitting ratios

at junctions A, B, and C should be modified to 1 : (1 + G + G2)/G3, 1 : (1 + G)/G2,

and 1 : 1/G, respectively, where the factor G represents the absolute power gain of

the interstage phase shifters given by G = 10S21/10, where S21 is in dB. Consequently,

the characteristic impedance of the different λ/4 transformers need to be adjusted

according to the following equations:

ZT1 =√

ZAZPS, and ZT2 =√

ZAZPSG, (6.7)

ZT3 =

√ZAZPSG

1 + G, and ZT4 =

√ZAZPSG2

1 + G, (6.8)

ZT5 =

√ZAZPSG2

1 + G + G2, and ZT6 =

√ZAZPSG3

1 + G + G2, (6.9)

ZT7 =

√ZoZAG3

1 + G + G2 + G3. (6.10)

Equation(6.7)-(6.10) ensure delivering the same amount of power to all the antennas

regardless of the interstage phase shifter losses, and regardless of the power division

taking place at each junction. Furthermore, one can extend this analysis to obtain an

expression for the efficiency of the proposed feeding network, which can be expressed

as follows:

ηfeed =

∑4i=1 Pantenna,i

Pin

=4G3

1 + G + G2 + G3(6.11)

Table 6.1 lists the achievable efficiency by the proposed feed network for different

Page 197: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 174

Table 6.1: Series Feed Network Efficiency For Different Interstage Phase Shifter LossValues

S21 G ηfeed

0dB 1 100%

-0.5dB 0.89 83%

-1dB 0.79 68%

-1.5dB 0.71 56%

-2dB 0.63 44%

values of the interstage phase shifter loss. It is clear from the table that using this

series architecture puts tight constraints on the interstage phase shifter losses.

To demonstrate how much the antenna power mismatch can be reduced by using the

proposed approach, Fig. 6.4 plots the maximum power mismatch, calculated between

the first and the fourth antennas versus the interstage phase shifter losses, |S21|. The

maximum power mismatch shown in Fig. 6.4 is computed for two different designs.

The first design employs only power splitting ratio compensation. Hence, the phase

shifters are assumed lossless in the design phase and Eq.(6.2)-(6.5) are used to size the

transformers. As the figure indicates, the power mismatch is only zero when the phase

shifter losses |S21|=0dB, and increases for higher values of |S21|. On the other hand, the

second design employs both phase shifter loss and power splitting ratio compensation.

A phase shifter loss of 1.5dB is assumed in the design phase and Eq.(6.7)-(6.10) are

used. Here we see that the location of the zero power mismatch has moved to the point

where |S21|=1.5dB. Consequently, when the phase shifters have a loss of 1.5dB, this

approach reduces the worst case power mismatch between the antennas by 64%.

Mismatches in the signal power feeding the antennas will affect the radiation pattern

of the array, which is a function of both the amplitude and the phase of the array exci-

tation. Figure 6.5 shows the normalized array factor for the previous two designs (i.e.

the design employing only power splitting ratio compensation and the one employing

both phase shifter loss and power splitting ratio compensation), and compares them

with the array factor of a standard array which does not employ any type of compen-

sation and assumes that the signals split equally at each junction. All three designs

assume a 4-element, λo/2 array, and a phase shifter loss |S21| of 1.5dB. As indicated

Page 198: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 175

0 0.5 1 1.5 2 2.5 3−60

−40

−20

0

20

40

60

80

Interstage phase shifter loss |S21

| (dB)

Pow

er m

ism

atch

(%) ↑

64% reductionin power mismatch

w power splitting comp.w PS loss and power splitting comp.

Figure 6.4: Power mismatch between the first and fourth antennas versus the interstagephase shifter insertion loss for two different cases: (a) array designed withpower splitting ratio compensation, (b) array designed with both phaseshifter loss and power splitting ratio compensation.

0° 15°30°

45°

60°

75°

90°−90°

−75°

−60°

−45°

−30°−15°

−40 −30 −20 −10 0

w/o comp.

w power splitting comp.

w PS loss and power splitting comp.

Figure 6.5: Normalized array factors for a 4-element λo/2 antenna array designed forthree different cases: (a) the standard design without compensation andassuming the signals split equally at each junction, (b) designed with powersplitting ratio compensation, (c) designed with both phase shifter loss andpower splitting ratio compensation.

Page 199: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 176

by the figure, reducing the power mismatch by employing compensation enhances the

quality of the radiation patterns by increasing the antenna rejection at the pattern

nulls. This is achieved at the cost of a 0.6dB drop in the gain of the antenna array.

6.2.3 Interstage Phase Shifters

As previously described in section 6.2.1, in order to center the radiation pattern of the

proposed antenna array at the broadside direction, tunable zero-degree phase shifters

should be used to implement the interstage phase shifters. As demonstrated in chapter

4, PRI/NRI phase shifters are capable of centering their phase response around the

zero-degree mark, and are capable of generating both positive and negative phase

shifts. This makes tunable PRI/NRI phase shifters a suitable choice to implement the

interstage phase shifters. Furthermore, the tunable PRI/NRI phase shifters presented

in chapter 4 are capable of maintaining a constant impedance, ZPS, across their entire

phase tuning range. This was achieved by employing both varactors and TAIs. Having

a constant impedance is important to provide the array with a low return loss across

its entire scan-angle range. It also helps to minimize the mismatch in the power level

feeding the different antennas, since the power splitting ratios are determined by the

impedance levels. Furthermore, these PRI/NRI phase shifters possess small group

delays, which is important to achieve low beam squinting. In order to quantify this,

Eq.(A-3) in Appendix A gives the relationship between the variation in the azimuthal

angle, θ, of the main beam of the proposed antenna array and the group delay, Tgd, of

the interstage phase shifters. The key result is that one should try to minimize Tgd in

order to reduce the effect of frequency on the direction of the main beam. This makes

the tunable PRI/NRI phase shifters of chapter 4 suitable for the implementation of the

interstage phase shifters.

Among the different tunable PRI/NRI phase shifters presented in chapter 4, the

TL-based design seemed a natural choice, due to several reasons. First of all, it can

be easily integrated onto the same PCB with the feed network, and the printed an-

tennas. Secondly, it provides the lowest insertion loss, and the highest FOM, i.e. the

highest phase tuning range per dB of loss. Also, the TAI package parasitics were al-

ready accounted for during the design phase of the TL PRI/NRI phase shifter, and no

additional packaging was required. This made the tunable TL PRI/NRI phase shifter

Page 200: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.2. THEORY 177

Figure 6.6: Transmission-line tunable PRI/NRI metamaterial phase shifter unit-cell.

more attractive for the design of the proposed printed antenna array.

The design of the TL PRI/NRI phase shifter was described in detail in chapter 4.

However, for completeness, some of the relevant design equations are briefly highlighted

in this section. Figure 6.6 shows the unit-cell of the TL tunable PRI/NRI phase shifter,

which is composed of a regular microstrip line, with a characteristic impedance Zo. The

microstrip line is loaded with two series varactors, with capacitance C, and a shunt

TAI, L. Cascading the PRI TL with the NRI section (i.e. the series capacitors and

shunt inductor in Fig. 6.6) compensates the phase shift incurred by the propagating

signal. The phase shift of the PRI/NRI phase shifter unit-cell can be approximated as:

φ ≈√

2

ω√

LC− 2θTL (6.12)

where θTL is the phase lag due to one section of the PRI microstrip TLs, given by

θTL = βTLdPS/2. Equation (6.12) indicates that positive and negative phase shifts

can be realized by a single unit-cell without having to go through a complete 360o

phase rotation as in traditional high-pass or low-pass architectures. This inherently

guarantees a small group delay for these phase shifters, which is expressed as:

Tgd = −dφ

dω≈ 1

ω

( √2

ω√

LC+ 2θTL

). (6.13)

Page 201: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.3. ANTENNA ARRAY DESIGN 178

One can intuitively understand this small group delay nature by investigating Eq.(6.12)

and Eq.(6.13) simultaneously; Eq.(6.12) indicates that one achieves the zero phase

without the need for large values by either of its two terms, i.e. +2π by the NRI section

as in a traditional high-pass design, or -2π by the PRI section as in a traditional low-

pass design. Alternatively, the zero phase is achieved by having two small and equal

contributions from the NRI and PRI sections, which eventually cancel-out due to the

negative sign in Eq.(6.12). Now looking at the group delay expression of Eq.(6.13), in

which the two terms add-up, one can see that the small phase contributions by the

NRI and PRI sections will automatically result in a small group delay.

The phase response of the PRI/NRI phase shifter is tuned by simultaneously chang-

ing the values of both the loading elements L and C. This is achieved by using both

TAIs and varactors, and results in a larger phase tuning range compared to varying C

only as was demonstrated in chapter 4. Furthermore, changing L and C simultaneously

according to the following equation,

Zo =

√2L

C(6.14)

where Zo is the microstrip TL characteristic impedance, will result in a constant phase

shifter impedance, i.e. ZPS = Zo, and consequently result in a low return loss across

the entire phase tuning range.

6.3 Antenna Array Design

A 4-element series-fed array is designed to operate in the 2.4GHz ISM band. The array

is based on the proposed alternating architecture of Fig. 6.3, and uses the TL tunable

PRI/NRI phase shifters of chapter 4 to implement the three interstage phase shifters.

Four identical λ/2 resonant rectangular patches are used as the antenna elements.

Although patch antennas have a relatively small impedance bandwidth, they are used

here for their simplicity. In order to be able to integrate the patches and the beam

steering network onto the same PCB, the interstage phase shifter and the two λ/4

transformers have to fit between each pair of consecutive patches, which might imply

increasing the inter-element distance, dE, to accommodate them. On the other hand,

it is important to avoid capturing grating lobes in the radiation pattern, which can be

Page 202: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.3. ANTENNA ARRAY DESIGN 179

guaranteed if the following condition is satisfied:

dE ≤ λo

2, (6.15)

where λo is the free-space wavelength. Eq.(6.15) is a fundamental equation, since it

sets the maximum distance between each two consecutive patches. Consequently, this

sets tight limitations on the interstage phase shifter dimensions. In this design, the

inter-element distance was chosen to be λo/2 in order to avoid capturing any grating

lobes in the radiation pattern, and at the same time provide the maximum allowable

space, which corresponds to an inter-element distance dE of 6.25cm at 2.4GHz.

To increase the phase tuning range and consequently the scan-angle range, two unit-

cells of the TL PRI/NRI phase shifter shown in Fig. 6.6 are cascaded to form each

interstage phase shifter. This will double the phase tuning range, while having a minor

effect on the phase shifter return loss S11. However, this will increase the interstage

phase shifter insertion loss. The average insertion loss of the PRI/NRI phase shifter

unit-cell was extracted from simulations to be 0.77dB, resulting in an average interstage

phase shifter loss of 1.55dB. This estimated loss was used in the design of the feed

network by using Eq.(6.7)-Eq.(6.10) to size the transformers.

Integrating the antenna array, feed network, and phase shifters onto a single-layer

PCB prevents us from designing each one of them independently, and forces us to treat

their design as three coupled designs. For instance, if one would design the patches

separately, a low substrate relative permittivity, εr, and would be desirable in order to

increase the patch bandwidth and at the same time its radiation efficiency. On the other

hand, one has to trade-off between the patch bandwidth and efficiency when choosing

the substrate thickness, h [102]. However, a lower εr entails longer λ/4 impedance

transformers and longer PRI/NRI phase shifters, as now we require a longer microstrip

TL to compensate for the positive phase shift from the NRI section. This becomes

evident by re-writing the phase shift expression of the PRI/NRI unit-cell as:

φ ≈√

2

ω√

LC− ωdPS

c

√εeff , (6.16)

where εeff is the effective relative dielectric constant of the phase shifters’s microstrip

Page 203: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.3. ANTENNA ARRAY DESIGN 180

TLs [24], and is given by:

εeff =εr + 1

2+

εr − 1

2× 1√

1 + 12h/W. (6.17)

In Eq.(6.17), h and W are the substrate height and the microstrip TL width, respec-

tively. Now by looking at Fig. 6.3, one can see that the λ/4 impedance transformers

and the interstage phase shifter have to fit in a fixed distance, dE, to avoid meandering

the lines. Consequently, εr can not take an arbitrarily small value. Furthermore, we

will show that for a given value of the positive phase shift, φNRI , from the NRI section,

there exists an optimum value for εr, that will allow centering the radiation around

the broadside direction, and at the same time satisfy the physical constraints imposed

by the requirement for a single PCB implementation. This physical constraint simply

requires that the sum of the lengths of the two λ/4 transformers and the interstage

phase shifter to be λo/2, i.e.:

dE =λo

2=

λ

4× 2 + 2dPS, (6.18)

where λ = λo/√

εeff is the guided wavelength, and the factor 2 in the second term is

added to account for the cascading of two PRI/NRI unit-cells for each interstage phase

shifter. However, this assumes that the two λ/4 transformers have the same εeff , which

neglects the change in their width. For the sake of simplicity, all the microstrip TLs

are assumed to have an equal εeff , which represents an average value for the different

width TLs. Equating Eq.(6.16) to zero and solving it with Eq.(6.18) results in the

following expression for the optimum substrate dielectric constant:

εeff =

(1 + 2

φNRI

π

)2

, (6.19)

where φNRI is the average phase shift generated by the NRI section, which is expressed

as:

φNRI =

√2

ω√

LC. (6.20)

Now substituting the result of Eq.(6.19) in Eq.(6.16), one can obtain the length of the

TL PRI/NRI phase shifter unit-cell required for broadside radiation. This results in

Page 204: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.3. ANTENNA ARRAY DESIGN 181

the following expression:

dPS = λoφNRI

2π√

εeff

. (6.21)

As Eq.(6.19) and Eq.(6.21) indicate, the design parameters εeff and dPS are a func-

tion of the NRI section’s phase shift, φNRI . The value of φNRI can be calculated

using the average TAI inductance and varactor capacitance. The average inductance

generated by the TAI chips is obtained from the measurements presented in chapter

3. However, a fixed 2.7nH inductance is added to the inductance values reported in

chapter 3 to account for the parasitic bond wire and package inductance. The varactor

capacitance values can be obtained from the matching condition, given by Eq.(6.14),

which results in C = 2L/Z2PS. In this design, the impedance of the PRI/NRI phase

shifters, ZPS, was not set to 50Ω, but was chosen as 75Ω. This choice was made in

order to extend the phase tuning range of the phase shifters, which can be expressed

as:

|∆φPS| = ZPS

2ωL

(∣∣∣∣∆C

C

∣∣∣∣ +

∣∣∣∣∆L

L

∣∣∣∣)

. (6.22)

Eq.(6.22) indicates that, for a fixed inductance value, the phase tuning range can be

increased by designing the phase shifters to exhibit a high impedance level. Note that

the matching at the higher impedance level requires smaller capacitance values.

Now we can substitute in Eq.(6.19) to evaluate the optimum εe, which results in a

value of 3.44. Using Eq.(6.17), one can use the value of εeff to calculate the optimum

substrate εr. This, however, this requires knowledge of the substrate height and the

average TL width. A 125mil thick substrate is chosen for the design. From simulations,

this thickness allows us to achieve a reasonable trade-off between the patch bandwidth

and its radiation efficiency. As for the average microstrip TL width, a reasonable

assumption is to equate it to the desired width of the middle section TLs (i.e. ZT3

and ZT4 in Fig. 6.3), which was chosen as 2.5mm. Now one can use the correction

factor h/W in Eq.(6.17) to obtain the optimum substrate relative permittivity εr,

which turns out to be 4.9. If the value of εr obtained does not result in an adequate

radiation efficiency or an adequate bandwidth for the patches, one can change the value

of φNRI by picking different lumped-element values. In this design, the value of φNRI

was dictated by the inductance values obtained from the fabricated TAI chips. Based

on these calculations, a 125mil TMM4 Rogers ceramic substrate with an εr of 4.5 was

Page 205: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 182

selected for the design of the steerable array. This results in a length of 14.41mm for

each of the TL PRI/NRI phase shifters. Electro-magnetic simulations were carried-out

in Agilent-Momentum, and the results show that the length of the TL PRI/NRI phase

shifters should be 14mm. This shows very good agreement between the value obtained

from the theoretical expression of Eq.(6.21) and the value obtained from simulations.

6.4 Physical Implementation and Experimental Results

The proposed steerable antenna array was fabricated on a 125mil TMM4 Rogers ce-

ramic substrate. In order to characterize the electronically steerable array, one first

needs to determine the appropriate control voltages required to obtain the different

scan angles. To this end, a separate prototype of the TL PRI/NRI interstage phase

shifter was fabricated using the same substrate material and characterized.

6.4.1 Interstage Phase Shifter

A picture of the fabricated interstage phase shifter prototype is given in Fig. 6.7. It is

composed of a cascade of two tunable TL PRI/NRI phase shifters. Each stage is com-

posed of a microstrip TL loaded with 2 series SMV1232 silicon hyper-abrupt junction

varactor diodes from Skyworks, and the TAI chip which uses a 4mm×4mm high-speed

QFN (Quad Flat-Pack No Lead) package to minimize the package parasitics. The in-

put and output of the interstage phase shifter are connected through the surface mount

right-angled SMA connectors to the left and right sides of the board, whereas the bias

and control lines going to the varactors and the TAI chips are supplied from the upper

and lower sides of the board. Printed RF chokes are used to provide the varactor con-

trol voltages to the main TL while providing a high impedance at 2.4GHz for the signal

on the main TL. This is achieved by connecting radial stubs through high-impedance

λ/4 TLs. The minimum reliable trace width (100µm) allowed by the fabrication pro-

cess was used for these λ/4 TLs to provide high isolation. Also, a set of three parallel

de-coupling capacitors, 68pF each, are used to stabilize each of the bias and control

voltages by providing a low-impedance path to the ground plane. The interstage phase

shifter roughly occupies an area of 3.6cm×6cm. As previously mentioned in section 6.3,

the interstage phase shifters are designed to exhibit an impedance of 75Ω, so in order

Page 206: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 183

3.6cm

6cm

Printed

RF choke

De-coupling

capacitors

Tunable active

inductor (TAI) chips

Varactors

Bias & control

inputs

Figure 6.7: Photograph of the fabricated tunable TL PRI/NRI interstage phase shifter.

Page 207: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 184

2 2.5 3

−200

−100

0

100

200

300

Frequency (GHz)

Inse

rtio

n ph

ase

φP

S (

deg)

φPS

= −97o→ +100o

at 2.4GHz

VVAR

increases

Figure 6.8: The measured insertion phase φPS vs. freq. for different bias conditions.

to characterize the phase shifters in a 50Ω environment, two printed λ/4 transformers

were added before and after the phase shifter to match it to the 50Ω equipment. How-

ever, the phase shift due to these transformers together with the connectors response

were de-embedded by characterizing a TL through connection fabricated on the same

substrate material.

Figure 6.8 shows the measured phase response of the TL PRI/NRI interstage phase

shifter when both the varactor capacitance and the TAI inductance are varied. To

generate these different phase responses the varactor control voltage Vvar was swept

from 3V to 15V, and for each case, the appropriate TAI control voltages that result

in the desired inductance, given by Eq.(6.14), are determined. This, however, requires

the characterization of the TAI chips, which was presented in chapter 3. At the design

frequency of 2.4GHz, the insertion phase can be varied from -97o to +100o passing

through the zero-phase point by changing the varactor control voltage from 3V to 15V,

respectively. The interstage phase shifter is capable of achieving both positive and

negative phase shifts at the design frequency without going through an entire 360o

rotation. Furthermore, across this entire phase tuning range, the matching condition

is satisfied, and the return loss, S11, is maintained below -15dB at 2.4GHz. Figure 6.9

shows the measured S11 and S21 at 2.4GHz versus the interstage phase shift. Across the

Page 208: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 185

−100 −75 −50 −25 0 25 50 75 100−6

−5

−4

−3

−2

−1

S21

at 2

.4G

Hz

(dB

)

Insertion phase at 2.4GHz (deg)

−100 −75 −50 −25 0 25 50 75 100−30

−25

−20

−15

−10

−5

S11

at 2

.4G

Hz

(dB

)

Figure 6.9: Measured S21 and S11 at 2.4GHz versus the insertion phase of the interstagephase shifter.

entire phase tuning range S11 varies from -27.5dB to a worst case of -15dB at the two

extremes. Also the interstage phase shifter S21 changes from -1.6dB to a worst case of

-2.4dB at the two extremes. The phase shifter achieves a bandwidth of 0.44GHz across

which S11 is less than -10dB. Across the phase tuning range, the interstage phase shifter

dissipates an average DC current of approximately 116mA from a 1.5V supply, which

corresponds to an average power consumption of 174mW.

Page 209: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 1866.4

.2Ste

era

ble

Ante

nna

Arr

ay

22

.6cm

7.1

cm

PR

I/N

RI

inte

rsta

ge

ph

ase

sh

ifte

rs

RF

RX

/TX

po

rt

De-

cou

pli

ng

cap

aci

tors

Bia

s &

co

ntr

ol

inp

uts

ZT

1Z

T2

ZT

3Z

T4

ZT

5Z

T6

ZT

7

y

xz

Fig

ure

6.10

:P

hot

ogra

ph

ofth

efa

bri

cate

del

ectr

onic

ally

stee

rable

seri

es-fed

pat

char

ray

uti

lizi

ng

the

tunab

leT

LP

RI/

NR

Iin

ters

tage

phas

esh

ifte

rs.

Page 210: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 187

A picture of the fabricated 2.4GHz electronically steerable antenna array is given in

Fig. 6.10. As shown in the figure, the antennas, the feed network, and the TL PRI/NRI

interstage phase shifters are all fabricated on a single-layer PCB and the bottom con-

ductor acts as the ground plane. The core of the antenna array occupies an area of

22.6cm×7.1cm and is fabricated on a 125mil TMM4 Rogers ceramic substrate with

an εr of 4.5. The RF transmit/receive signal is connected through the surface mount

right-angled SMA connector on the left side of the PCB, whereas the bias and control

lines going to the interstage phase shifters are supplied from the upper and lower sides

of the PCB. Note that the array is fed only from one end, making it truly electronically

steerable, and it does not require switching the feeding and terminating ports as in

the other array designs presented in [98]- [100], where the switching is necessary to

center their radiation about the broadside. The proposed array uses four identical al-

ternating rectangular patches. The size of each patch antenna is 2.7cm(L)×3.7cm(W).

The patch’s width is chosen to be longer than the length to decrease the real part of

the patch impedance at resonance. This, however, is not enough to bring the patch

impedance to the desired value and the inset feeding technique, which was briefly de-

scribed in chapter 2, is used to achieve a patch impedance ZA of 190Ω. To provide good

power matching, the patches are then connected to the main feed line through 190Ω

microstrip TLs. Using a characteristic impedance equal to ZA allows us to maintain

good matching at the design frequency regardless of the length of these interconnecting

lines, which are 7.5mm long measured from the center of the feed line to the patch edge.

The value of the patch impedance was dictated by the PCB fabrication process, which

allows us to use a minimum trace width of 100µm. This, in turn, results in a maximum

realizable microstrip TL characteristic impedance of 190Ω.

As evident in Fig. 6.10, the width of the λ/4 impedance transformers decrease as

we move away from the RF port, which accounts for the increasing characteristic

impedances computed from Eq.(6.7)- Eq.(6.10). To avoid having a very wide microstrip

TL for the left-most λ/4 impedance transformer ZT7, the array is designed to have a

75Ω input impedance (i.e. Zo in Eq.(6.10) is set to 75Ω), and another tapered trans-

former placed right at the SMA connector is designed to match the array impedance to

the 50Ω environment. Also one can see from Fig. 6.10 that the array uses identical TL

PRI/NRI interstage phase shifters. The DC bias and control voltages are supplied to

the TL PRI/NRI interstage phase shifters using a ribbon cable which runs underneath

Page 211: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 188

the PCB, and a small 2.5mm×40mm rectangular-shaped cut in the bottom conductor

(i.e. the ground plane) allows us to connect these DC voltages to the bias lines on the

top side of the PCB. Another set of four parallel de-coupling capacitors (91pF, 1nF,

0.1µF, 10µF) are used to stabilize each of the bias and control voltages in Fig. 6.10 by

providing a low-impedance path to the ground plane. Printed RF chokes are used to

provide the varactor control voltages to the main TL, while providing a high impedance

at 2.4GHz for the signal on the main TL.

Gain Patterns

The fabricated antenna array was characterized in an antenna anechoic chamber while

operating in the receive mode. The measured co- and cross-polarization gain patterns

and the simulated co-polarization gain patterns in the azimuth plane (i.e. the x-z plane)

are presented in Fig. 6.11 for different bias conditions. To generate these different plots,

the control voltages of the varactors, Vvar, and of the TAI chips were obtained from the

characterization of the TL PRI/NRI interstage phase shifter. For each set of control

voltages, the interstage phase shifters generate a different phase while maintaining low

return and insertion losses. The results in Fig. 6.11 show that the proposed array is

capable of continuously steering its main beam from an angle of -27o to an angle of

+22o passing through the broadside direction by simply changing Vvar from 15V to 3.5V

and accordingly adjusting the control voltages going to the TAI chips to achieve the

desired inductance level. As previously explained in section 6.2, the ability to achieve

both negative and positive scan angle is due to the use of the tunable PRI/NRI phase

shifters. Across this entire 49o scan angle range, the gain of the antenna array varies

from a maximum of 8.4dBi to a worst case of 6.9dBi and the side-lobes are at least

10dB lower than the the main-lobe. Furthermore, the cross-polarization gain is always

less than that of the co-polarization by at least 14.7dB measured at the peak angles.

It is worth noting that, in the proposed design, the gain variation across the entire 49o

scan angle range is less than 1.5dB compared to more than 10dB gain degradation in

the leaky-wave design reported in [101] when its beam is merely scanned beyond ±6o

off the broadside direction.

Note that the radiation patterns are not perfectly symmetric for both positive and

negative scan angles. For example Fig. 6.11-b and Fig. 6.11-f have slightly different

Page 212: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 189

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

(a) (b)

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

(c) (d)

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

0° 15°30°

45°

60°

75°

90°

105°

120°

135°150°

165°±180°−165°−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°−30°

−15°

−20

−10

0

10

(e) (f)

Figure 6.11: Measured co- and cross-polarization and simulated co-polarization gainpatterns in the azimuth plane (x-z plane) for different bias conditions:(a)Vvar=15V, (b)Vvar=9.5V, (c)Vvar=7V, (d)Vvar=6.5V, (e)Vvar=5V,(f)Vvar=3.5V. Solid line: measured co-polarization, dashed line: measuredcross-polarization, dash dot line: simulated co-polarization.

Page 213: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 190

gain and side-lobe levels. This can be attributed to two main factors; first of all, one

can clearly see from Fig. 6.10 that the antenna array is not fully symmetric around the

y-z plane, due to the tapering of the feed line and due to having a single input/output

port. Secondly, as indicated by Fig. 6.9, the interstage phase shifters do not have the

exact same insertion and reflection losses for both positive and negative phase shifts.

Consequently, this would lead to different values for the gain and side-lobe levels.

Figure 6.11 also compares the measured co-polarization gains with the results ob-

tained from simulations. The figure shows good agreement between the simulated and

measured results for the different bias conditions. The good agreement between the

measurements and simulations was achieved by adopting a two step simulation process.

First, the patches were simulated together with the feed network using the full-wave

simulator of Agilent-Momentum. However, the tunable PRI/NRI phase shifters were

excluded from this simulation, and instead, each end of a λ/4 transformer was termi-

nated with a port impedance equal to that of the phase shifter ZPS (i.e. 75Ω), and the

following λ/4 transformer was excited by another port with a 75Ω source impedance,

and so on. But to obtain the array’s radiation pattern, we still need to determine the

appropriate amplitudes and phases for the different ports. To obtain this information,

the measured S-parameters of the TL PRI/NRI interstage phase shifter, presented in

section 6.4.1, were used to obtain an accurate estimate of the phase shifter’s magnitude

and phase responses. One can use this information together with the power splitting

ratios at the three junctions of the feed network to calculate the amplitude and phase

excitation at each of the ports. These results were provided to the full-wave simulation

of the patches and the feed network to obtain the radiation patterns of the array. This

two step process was adopted here to obtain accurate simulation results, and more im-

portantly, to avoid having to include the patches, the feed network, and the tunable TL

PRI/NRI phase shifters into one simulation. This separation is important since it was

not possible to obtain the radiation patterns using Agilent-Momentum in the presence

of the active lumped-element components, specifically, the varactors and the CMOS

TAIs. The simulation procedure which was used to obtain the radiation patterns of

the steerable antenna array is briefly summarized in Fig. B-2 in Appendix B.

The measured peak gain of the antenna array and the HPBW are plotted in Fig. 6.12

versus the scan angle. The proposed array has a relatively constant gain across its entire

49o scan angle range, with a peak gain of 8.4dBi and a maximum gain variation of 1.5dB.

Page 214: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 191

−30 −25 −20 −15 −10 −5 0 5 10 15 20 250

2

4

6

8

Pea

k G

ain

at 2

.4G

Hz

(dB

i)

Scan angle θ (deg)

−30 −25 −20 −15 −10 −5 0 5 10 15 20 2515

20

25

30

35

40

HP

BW

at 2

.4G

Hz

(deg

)

Figure 6.12: Measured peak gain of the antenna array and the half-power beamwidthversus the scan angle.

0° 15°

30°

45°

60°

75°

90°

105°

120°

135°

150°

165°±180°−165°

−150°

−135°

−120°

−105°

−90°

−75°

−60°

−45°

−30°

−15°

−20

−10

0

10

Figure 6.13: Measured co- and cross-polarization and simulated gain patterns in they-z plane. Solid line: measured co-polarization, dashed line: measuredcross-polarization, dash dot line: simulated co-polarization.

Page 215: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 192

2 2.2 2.4 2.6 2.8−40

−30

−20

−10

0

10

Frequency (GHz)

Ant

enna

ret

urn

loss

S11

(dB

)→ ←

S11

< −10dB BW = 70MHz

Figure 6.14: Input return loss, S11, of the antenna array versus frequency for all thedifferent bias conditions given by Fig. 6.11.

This flat gain is a consequence of using the constant-impedance tunable TL PRI/NRI

interstage phase shifters employing both varactors and TAIs. The constant-impedance

feature is important to minimize reflections and also to minimize the mismatch in the

power level feeding the different antennas, since the power splitting ratios depend on

the phase shifters’ impedances. Figure 6.12 also shows that the HPBW changes from

a nominal value of 25o at broadside to a worst case of 29o for positive scan angles.

The measured co- and cross-polarization gain patterns of the antenna array in the y-z

plane are plotted in Fig. 6.13 together with the simulated co-polarization gain pattern.

These patterns were obtained with the array biased for broadside radiation.

Return Loss

Figure 6.14 shows the measured input return loss of the antenna array, S11, for all the

different bias conditions given by Fig. 6.11. Across the entire 49o scan angle range the

antenna array return loss changes from a best case of -24dB to a worst case of -10dB.

This low return loss is a consequence of combining the use of varactors and TAIs to

design the constant-impedance tunable PRI/NRI interstage phase shifters. However,

the variation in the value of the antenna array return loss for different scan angles can

Page 216: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.4. PHYSICAL IMPLEMENTATION AND EXPERIMENTAL RESULTS 193

2.1 2.2 2.3 2.4 2.5 2.6 2.7−40

−30

−20

−10

0

10

20

30

Mai

n Lo

be A

ngle

θp (

deg)

Frequency (GHz)

→ ←θ = ±2o

BW = 0.3GHz

2.1 2.2 2.3 2.4 2.5 2.6 2.7−30

−25

−20

−15

−10

−5

0

5

10

Pea

k G

ain

Gp (

dBi)

Figure 6.15: Beam squinting characteristics: antenna array main-lobe angle, θp, andthe peak gain, Gp, versus frequency.

be attributed to two main factors; first, as indicated by Fig. 6.9 the input impedance

of the interstage phase shifters slightly varies for different phase shifts. Another source

of variation for the reflection coefficient of the antenna array is the mutual coupling

between the antenna array elements, as typically characterized by the active reflection

coefficient. However, this design uses alternating patch antennas which minimizes the

coupling between the adjacent array elements.

Figure 6.14 also shows that the return loss of the array is less than -10dB across a

bandwidth of 70MHz, which corresponds to a fractional bandwidth of approximately

3%. The relatively small bandwidth of the proposed design, is attributed to the narrow-

band characteristics of the patch antennas and can be extended by using a more broad-

band antenna element.

Beam Squinting

To demonstrate the low beam squinting capability of the proposed series-fed antenna

array, the array was biased to produce its main beam at the broadside direction for

the design frequency (2.4GHz). Then the frequency of the transmitter was swept

Page 217: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.5. ANTENNA ARRAY LINEARITY 194

from 2 to 2.8GHz, and for each frequency point the co-polarization gain pattern was

measured, and these results were used to find the angle of the main lobe, i.e. the peak

gain angle θP , and the corresponding peak gain Gp. The resulting main lobe angles

and peak gains are shown in Fig. 6.15 versus the transmitter frequency. Figure 6.15

shows that the angle of the main beam, θp, remains within ±2o across a relatively wide

bandwidth of 0.3GHz, confirming that the beam squinting is low within this bandwidth.

To be precise, the beam squints by an angle of 1.3o for each 100MHz change in the

input frequency around the 2.4GHz design frequency, which, as mentioned earlier, is

due to the small group delay of the TL PRI/NRI phase shifters used in the design

of the series-fed array. The beam squinting can also be estimated from Eq.(A-3) in

Appendix A. The value of the group delay, Tgd, of the TL PRI/NRI phase shifters can

be obtained by evaluating the derivative of the measured phase responses in Fig. 6.8.

For the broadside case, the measured group delay at 2.4GHz is 0.5ns. Using this value

for Tgd, the theoretical expression of Eq.(A-3) results in an estimated beam squinting

of 1.29o/100MHz. This shows the very good agreement between the theoretical and

measured beam squinting, as well as the accuracy of Eq.(A-3).

Also, Fig. 6.15 shows the measured peak gain Gp versus the transmitter frequency.

The peak gain drops at a faster rate compared to the changes occurring in the main

lobe angle θp. This, however, is attributed to the narrow band characteristics of the

patch antennas, and can be solved by using more wide band antenna elements.

6.5 Antenna Array Linearity

Combining the use of the varactors and the 0.13µm CMOS TAIs to build the TL

PRI/NRI interstage phase shifters allowed increasing the scan angle range as opposed

to a varactor-based implementation [98–100]. Furthermore, tuning both the inductance

and capacitance allowed the antenna array to achieve a low return loss and maintain

a relatively flat gain response across this wide scan angle range. However, using these

active components imposes limitations on the antenna array’s linearity, especially since

the CMOS TAIs operate from a 1.5V supply voltage. To this end, the TAIs have been

designed to achieve good linearity by selecting appropriate transistor sizes and bias

points, and the linearity performance of the TAIs was reported in chapter 3.

To characterize the linearity of the proposed antenna array, the setup shown in

Page 218: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.5. ANTENNA ARRAY LINEARITY 195

f1

Agilent E4403B

Spectrum Analyzer~6m

Antenna Anechoic

Chamber

RF signal

sources

TX:

Antenna array

RX:

Horn Antenna

f2

+

RF signal

combiner

Figure 6.16: Experimental setup used to characterize the linearity of the steerable an-tenna array.

−15 −10 −5 0 5 10−60

−55

−50

−45

−40

−35

−30

P1−dB

= 4.54dBm

Array input power Pin

(dBm)

Hor

n ou

tput

pow

er P

out (

dBm

)

Figure 6.17: Measured output power, Pout, of the horn antenna at 2.4GHz versus theantenna array input power Pin.

Page 219: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.5. ANTENNA ARRAY LINEARITY 196

−15 −10 −5 0 5 10−110

−100

−90

−80

−70

−60

−50

−40

−30

IIP3 = 8.85dBm

Pout

at f1

Pout

at 2f1−f

2

Array input power (dBm)

Hor

n ou

tput

pow

er (

dBm

)

Figure 6.18: Measured horn output power at the fundamental frequency f1 and at third-order intermodulation frequency 2f1 − f2 versus the antenna array inputpower.

Fig. 6.16 was used. The antenna array was used as a transmitter, and a standard horn

antenna was used as a receiver. For the IIP3 measurement, two input tones at f1 and

f2 were applied to the antenna array though an RF signal combiner. On the other

hand, for the 1-dB compression point measurement, only one input tone was required,

and hence the RF signal combiner was removed. For both measurements, the received

signal by the horn antenna was detected using a spectrum analyzer to measure the

power at the different frequency components.

A single tone at 2.4GHz was used for the 1-dB compression point measurement,

and the input signal power was swept from -15dBm to 10dBm. Figure 6.17 shows the

measured output power Pout, received by the horn antenna, versus the input power

of the antenna array Pin. The measured results shows that the output power of the

antenna array reaches its 1-dB compression point at 4.5dBm, which corresponds to a

1.1Vpp signal swing at the antenna array input. Note that, not all of this signal swing is

seen at the TAI input port, as part of the input power is radiated by the first patch.This

points out the fact that the linearity of the proposed antenna array is mainly limited by

the low supply voltage of the CMOS TAI chips, as it sets a limit on the maximum peak-

to-peak signal swing at the TAI input port. For the IIP3 measurement the antenna

Page 220: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.6. DISCUSSION AND COMPARISON 197

array is used to transmit two tones f1 and f2 at 2.4GHz and 2.41GHz, respectively,

and the intermodulation products in the received signal are analyzed. The frequency

separation was selected to put the two tones and their third-order intermodulation

products within the antenna array bandwidth. The measured output power at the

fundamental frequency f1 and at the third-order intermodulation product at 2f1 − f2

are plotted in Fig. 6.18 versus the input power level. By extrapolating the measured

results, one can show that the antenna array achieves an IIP3 of 8.8dBm.

6.6 Discussion and Comparison

In the fabricated prototype of the steerable antenna array, the varactors’ and the TAIs’

control voltages going to each of the interstage phase shifters are supplied manually

in order to achieve the desired scan angle. However, if this steerable array is used in

a practical transceiver, a look-up table together with multiple DACs can be used to

set the control voltages for each interstage phase shifter according to a single control

voltage. Here, one can see the importance of having identical interstage phase shifters,

as all the stages can share a single control voltage. Furthermore, the look-up tables

and the DACs can be integrated on the same die with the TAI circuit, which is one of

the main advantages of using a standard CMOS technology for the TAIs as opposed

to using other high ft technologies such as GaAs.

Page 221: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.6. DISCUSSION AND COMPARISON 198

Tab

le6.

2:C

ompar

ison

Bet

wee

nT

he

Pro

pos

edSte

erab

lePat

chA

rray

And

Oth

erP

ublish

edSer

ies-

Fed

Ste

erab

leA

nte

nna

Arr

ays.

Spec

ifica

tion

[98]

[99,

100]

[101

]T

his

wor

k

Ant

enna

elem

ents

4Pat

ches

5Pat

ches

30ce

llLea

ky-W

ave

4Pat

ches

Sing

leP

CB

impl

.X

√√

Bro

adsi

desc

anni

nga

XX

√√

Ope

rati

ngfr

eque

ncy

2.45

GH

z5.

8GH

z3.

33G

Hz

2.4G

Hz

Ele

ctro

nic

scan

-ang

lera

nge

0o⇒

+30

o+

10o⇒

+32

o-3

9o⇒

+21

o-2

7o⇒

+22

o

Max

gain

–11

.3dB

i18

dBi

8.4d

Bi

Gai

nva

riat

ionb

–0.

4dB

13dB

1.5d

B

HP

BW

24o

–22

o⇒

35o

25o⇒

29o

Rel

.si

de-lob

e-9

dB-1

0dB

-5.5

dB-1

0dB

Rel

.cr

oss-

pol.

–-1

2dB

–-1

4.7d

B

Ret

urn

loss

(S11)

-13d

B⇒

-17d

B-1

8dB⇒

-22d

B-6

dB⇒

-12.

5dB

-10d

B⇒

-24d

B

Frac

tion

alba

ndw

idth

c1.

02%

4.6%

N/A

3%

Max

cont

rolvo

ltag

e3.

5V30

V18

V15

V

Ave

.po

wer

diss

ipat

ion

00

045

0mW

@1.

5V

Size

1.55

λo×0

.49λ

o(A

nt.

PC

B)

2.9λ

o×1

.35λ

o4.

26λ

o×0

.33λ

o1.

81λ

o×0

.57λ

o

+0.

31λ

o×0

.16λ

o(P

SP

CB

)

aT

his

isba

sed

onth

eab

ility

toel

ectr

onic

ally

scan

inbo

thdi

rect

ions

offth

ebr

oads

ide,

i.e.

wit

hout

phys

ical

lysw

itch

ing

the

inpu

tan

dte

rmin

atin

gpo

rts.

bG

ain

vari

atio

nis

defin

edhe

reas

the

chan

gein

the

peak

gain

acro

ssth

een

tire

scan

angl

era

nge.

cB

andw

idth

mea

sure

men

tcr

iter

ion:

S11

<-1

0dB

acro

ssth

een

tire

scan

angl

era

nge.

Ban

dwid

thw

asno

tre

port

edfo

rth

ede

sign

of[1

01]

sinc

eS

11

>-1

0dB

for

som

eof

the

repo

rted

scan

angl

es.

Page 222: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.6. DISCUSSION AND COMPARISON 199

Table 6.2 summarizes the performance of the proposed electronically steerable patch

array with other series-fed steerable arrays presented in the literature [98–101]. The

proposed design is capable of centering its radiation about the broadside direction as

opposed to the designs in [98–100], which can only achieve this by physically switching

the input and terminating ports. Furthermore, the proposed antenna array achieves a

much wider electronic scan-angle range compared to the designs presented in [98–100].

This is due to the use of both varactors and TAIs to design the interstage phase

shifters. To the author’s knowledge, the proposed antenna array is the first resonant

antenna-element structure that demonstrates electronic beam steering utilizing tunable

PRI/NRI phase shifters. Consequently, this series-fed design is capable of centering

its radiation at the broadside direction without the need for physically switching the

input and terminating ports. Moreover, in this PRI/NRI-based design, the compact

size of the TL PRI/NRI phase shifters allows them to fit between the antenna elements,

resulting in a compact, planar, PCB implementation. Although the leaky-wave design

in [101] achieves a wider scan angle range compared to the proposed resonant antenna

design, the proposed design has a relatively flat gain and HPBW across its entire scan

angle range. On the other hand, the leaky-wave design in [101] has very large variations

in both gain and HPBW as its beam is steered. In addition, the proposed antenna array

has a much lower relative side-lobe level and input return loss across its entire scan

angle range compared to the design in [101].

The idea of minimizing beam squinting by using PRI/NRI phase shifters for the feed

network of series-fed antenna arrays was originally proposed in [103]. Following that,

this principle was demonstrated in [6, 104] for a microstrip series-fed dipole antenna

array, and then in [105, 106] for a coplanar strip-line leaky-wave antenna array. Table

6.3 summarizes the achieved beam squinting by the proposed antenna array and other

published designs in the literature. It is worth mentioning that achieving a lower

beam squinting is more challenging at lower frequencies, as evident from Eq.(A-3) in

Appendix A. The beam squinting reported in the Table 6.3 is defined as the variation in

the main beam angle in degrees for a 100MHz change in the frequency centered around

the operating frequency. Compared to the other designs, the proposed design achieves

the lowest beam squinting. However, to be fair, note that in the proposed design, the

slope of the main beam angle, θp, increases beyond the 300MHz bandwidth, which

is evident from Fig. 6.15. Nonetheless, this should not be a big concern since the

Page 223: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.6. DISCUSSION AND COMPARISON 200

Table 6.3: Comparison Between The Measured Beam Squinting Of The Proposed ArrayAnd Other Published Antenna Arrays.

Design Array type Squintinga Oper.

(deg/100MHz) freq.

[100] Series-fed patch array 9.5o 5GHz

[101]b Leaky-wave array 8o 3.3GHz

[104] Series-fed dipole array 5.7o 5.2GHz

[106] Leaky-wave array 3.1o 5GHz

This work Series-fed patch array 1.3o 2.4GHz

aBeam squinting is reported as degrees/100MHz variation in frequency centered at the operatingfrequency.

bFor this design, the beam squinting is theoretically estimated by differentiating Eq.(10) in [101].This is carried-out using the extracted parameters provided in Table I of [101] at a varactor voltageof 5V.

bandwidth of the proposed design is limited to 70MHz by its input impedance.

The 1-dB compression of the proposed antenna array, as it stands, makes it capable

of handling the transmit power for only short range wireless devices. For example it,

can be used for wireless devices using Bluetooth or ZigBee. One potential solution

to extend the power handling capability of the proposed antenna array is to couple

the input signal to the TAI circuits using an on-chip transformer that steps down the

voltage swing by the turns ratio. The corresponding increase in the TAI input current

swing can be accommodated by increasing the TAI’s bias currents. This, however, will

increase the value of the TAI inductance with the square of the turns ratio. But this

could be accounted for during the design of the TAI circuit. A related approach has

been recently proposed in [107] to couple the outputs of four CMOS power amplifiers

to achieve a higher voltage swings than that allowed at the drain of each transistor

before breakdown occurs.

As described in chapter 3, noise is one of the critical performance limits which should

be quantified for TAI-based applications. This was carried out for the 2-port phase

shifters in chapter 4 and the 4-port coupler in chapter 5. However, antennas converts

electrical signals into electro-magnetic radiation and vise versa. Therefore, from an

Page 224: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

6.6. DISCUSSION AND COMPARISON 201

electrical point of view, antennas can be considered 1-port devices. To the author’s

knowledge, there is no standard procedure for the experimental characterization of the

noise performance of active antennas. However, it is worth mentioning that, in the

proposed steerable antenna array, the effect of the added noise generated by the TAIs

can be counterbalanced, from a system’s point of view, by having a highly-directive

antenna. This highly-directive antenna, when compared to an omni-directional one,

would result in a higher signal to noise and interference ratio, and consequently in a

lower bit error rate since it minimizes the effect of interference with undesired signals.

To know which one of the two effects would dominate, and determine if using TAIs

improves the the overall performance requires knowledge of the environment in which

the antenna is used and is outside the scope of this thesis.

Page 225: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

CHAPTER 7

Conclusion

T his chapter summarizes the thesis and outlines its main contributions. In addition,

some areas are suggested for future research.

7.1 Summary

This thesis presented the design of RF CMOS TAIs and their applications towards

the design of RF metamaterial-based tunable phase shifters, directional couplers, and

series-fed steerable antenna arrays for 2.4GHz ISM band applications. The design of

the CMOS TAIs was based on a modified gyrator-C architecture utilizing a feedback

resistance, which allows independent control over the inductance and quality factor.

The TAI was fabricated in the 1.5V, 0.13µm CMOS process, and its inductance can

be tuned from 0.93nH to 2.7nH at 2.4GHz, with a peak-Q of 100 across the entire

inductance tuning range. Furthermore, the Q of the TAI can be tuned from a value of

10 to 200 at 2.4GHz with less than 6.7% variation in its inductance.

Chapter 4 presented a variety of implementations for bi-directional phase shifters

utilizing varactors and TAIs. The focus was directed more towards PRI/NRI phase

shifters, which are capable of achieving positive, negative and zero phase shifts without

202

Page 226: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

7.1. SUMMARY 203

going through an entire 360o rotation. Hence, they have the capability to achieve low

group delays compared to standard low-pass or high-pass phase shifters, which is a

necessary feature to minimize the beam squinting in series-fed antenna arrays. Both

printed and 0.13µm CMOS, fully-integrated implementations were presented. The for-

mer synthesizes the PRI section using microstrip TLs, whereas the latter replaces the

TL sections with lumped L−C sections; thus, allowing for a single MMIC implementa-

tion. Compared to other implementations having only one tunable element, using var-

actors and TAIs extended the phase tuning range and at the same time maintained the

input and output matching of the phase shifters. The TL PRI/NRI phase shifter pre-

sented in this thesis achieved an electronically tunable phase of -40o to +34o at 2.5GHz

with less than -19dB return loss from a single stage occupying 10.8mm×10.4mm. On

the other hand, the MMIC PRI/NRI phase shifter achieved a phase of -35o to +59o at

2.6GHz with less than -19dB return loss from a single stage occupying 550µm×1300µm.

Furthermore, a passive fully-integrated PRI/NRI phase shifter was presented to ad-

dress some of the drawbacks of the active designs (DC power consumption, noise, and

linearity) by eliminating the TAI and using instead a shunt varactor. The resulting

topology still exhibits phase compensation properties, which allows one to center its

phase response around the zero-degree mark while having a small group delay. Fur-

thermore, it is also capable of maintaining the phase shifter matching. The passive

MMIC PRI/NRI phase shifter achieved an electronically tunable phase from -25.5o to

27o at 2.6GHz, from a single stage, with better than -21dB return loss across the entire

tuning range, while occupying an area of 700µm×1300µm.

In chapter 5, a compact, metamaterial-inspired, highly-reconfigurable directional

coupler was presented. The coupler was implemented in a standard 0.13µm CMOS

process and operates from a 1.5V supply. A lumped-element approach is used to

build the directional coupler, which makes it possible to integrate the entire coupler

onto a single MMIC. The MMIC coupler occupies an area of 730µm×600µm, which

is much smaller compared to printed designs operating at the same frequency range.

The MMIC coupler is based on the high-pass architecture and utilizes both varactors

and tunable active inductors, which allows simultaneous electronic control over the

coupling coefficient as well as the operating frequency of the coupler, while insuring a

low return loss and a very high isolation. Furthermore, the symmetric configuration

of the coupler allows it to electronically switch from forward to backward operation

Page 227: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

7.2. CONTRIBUTIONS 204

by simply exchanging the bias voltages applied across the varactors. The different

modes of operation of the proposed MMIC coupler were experimentally verified, and

the measured results show that the coupler is capable of achieving a tunable coupling

coefficient from 1.4dB to 7.1dB, while maintaining the isolation higher than 41dB. The

MMIC coupler is also capable of operating at any center frequency over the 2.1GHz-

3.1GHz frequency range with higher than 40dB isolation. The linearity of the proposed

MMIC coupler was experimentally characterized.

Chapter 6 of this thesis presented a planar electronically steerable series-fed patch

array for 2.4GHz ISM band applications. The proposed steerable array used the zero-

degree tunable TL PRI/NRI phase shifters to center its radiation about the broad-

side direction and allow scanning in both directions off the broadside. Also, using the

PRI/NRI phase shifters minimizes the squinting of the main beam across the operating

bandwidth. The feed network of the proposed array used λ/4 impedance transformers.

This allows using identical interstage phase shifters, which share the same control volt-

ages to tune all stages. Furthermore, using the impedance transformers in combination

with the CMOS-based constant-impedance TL PRI/NRI phase shifters guarantees a

low return loss for the antenna array across its entire scan angle range. The antenna

array was fabricated, and is capable of continuously steering its main beam from -27o

to +22o off the broadside direction with a gain of 8.4dBi at 2.4GHz. This was achieved

by changing the varactors’ control voltage from 3V to 15V. Across this 49o scan angle

range, the array return loss is less than -10dB across a bandwidth of 70MHz, and the

side-lobe level is always 10dB lower than the main lobe. Furthermore, the proposed

design achieves very low beam squinting of 1.3o/100MHz at broadside and a 1-dB

compression point of 4.5dBm.

7.2 Contributions

The main contributions of this thesis are summarized as follows:

1. Development of a novel generalized method, based on the gyrator-C architecture,

to design grounded TAIs with independent L and Q tuning capability.

2. Evaluation of the performance of the proposed modified gyrator-C architecture,

by presenting the design and experimental characterization of a grounded 0.13µm

CMOS TAI.

Page 228: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

7.3. FUTURE WORK 205

3. Design and implementation of four novel wide tuning range phase shifters,

a) Fully-integrated, tunable, active high-pass phase shifter.

b) Tunable, active, TL PRI/NRI phase shifter.

c) Tunable, active, MMIC PRI/NRI phase shifter.

d) Tunable, passive, MMIC PRI/NRI phase shifter.

4. Design and implementation of a novel highly-reconfigurable directional coupler,

which is simultaneously capable of operating with a variable coupling coefficient

and a variable center frequency. As well as switching the input power among the

through and isolated ports.

5. Design and implementation a 4-element, PCB, electronically steerable, series-fed

antenna array. The array is capable of centering its radiation about the broadside

direction, and achieves very low beam squinting by utilizing the TL PRI/NRI

phase shifters.

7.3 Future Work

There are many areas that can be further investigated. First of all, the generalized

gyrator-C architecture with resistive feedback, which was presented in this thesis, can

be applied to the different TAI circuit topologies discussed in chapter 2 to obtain a

variety of new TAI designs with independent L and Q tuning capability.

Secondly, metamaterials is a relatively new research area. In this thesis only two of

its applications were extensively investigated; phase shifters and directional couplers.

However, there is a broad range of different applications that can use metamaterial

concepts and combine them with the capabilities offered by active circuits. For instance,

one may replace the fixed capacitors and inductors in the series power divider presented

in [13] to make it operate at an arbitrary frequency. Also, TAIs and/or varactors can be

used to electronically control the resonance frequency of an antenna. For example, this

can be used to electronically tune the resonance of a planar inverted F antenna (PIFA),

enabling the design of re-configurable antennas for multi-standard applications. The

series-fed patch array presented in this thesis can be very easily modified to achieve a

wider bandwidth by replacing the narrow-band patch antennas with more wide-band

antenna elements, such as stacked patches. Another possibility is to replace the bulky

patch antennas with small metamaterial-based antennas [19,20].

Page 229: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

7.3. FUTURE WORK 206

Furthermore, another area that has not been fully investigated yet is the integration

of the entire phased antenna array transceiver on-chip. Scaling-up the operating fre-

quency to the millimeter-wave region allows shrinking the antenna dimensions and the

inter-element distance of the array making it feasible to fit onto a single MMIC. One

such attempt was reported in [108], where a 16-element 30-50GHz transmit phased ar-

ray is integrated with the beam forming network on a single chip. However, in order to

scale-up the operating frequency appropriate technology nodes with higher transistor

fts would be required. For instance, the 30-50GHz design in [108] is fabricated in a

0.18µm SiGe BiCMOS technology, which offers transistors with peak fts of 155GHz.

Another example of frequency scaling is the 12.7GHz and 30GHz metamaterial phase

shifter designs which were recently presented in [109] and [110,111] respectively. Since

the phase shifters published in [109–111] mostly relay on passive devices such high oper-

ating frequencies were possible to achieve using a standard 0.18µm CMOS technology.

The majority of the circuits presented in this thesis use the TAI circuit, which will be-

come the design bottleneck when it comes to scaling-up the operating frequency. The

0.13µm CMOS technology provides transistors with peak fts close to 80GHz, which

indicates that there should be some room for speed improvement. However, note that

other specifications such as the inductance tuning range or the power handling ca-

pability might be the limiting factors that determine the speed of the TAI circuit in

a specific technology node. In this case, migrating to new technologies with smaller

feature sizes and higher fts would be beneficial.

In addition, techniques to extend the linearity and noise limitations of TAIs have

yet to be investigated. One potential solution to extend the power handling capability

of TAIs is by coupling the input signal to the TAIs using an on-chip transformer that

steps down the voltage swing by the turns ratio. The corresponding increase in the

TAI input current swing can be accommodated by increasing the TAI’s bias currents.

This, however, will increase the value of the TAI inductance with the square of the

turns ratio, but could be accounted for during the design of the TAI circuit. A similar

approach was proposed in [107] to couple the outputs of four CMOS power amplifiers

to achieve a higher voltage swing than that allowed at the drain of each transistor

before breakdown occurs.

Also, a detailed sensitivity analysis of the TAI, and the subsequent circuits presented

here using the TAI, would be necessary for determining whether these circuits are

Page 230: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

7.3. FUTURE WORK 207

sufficiently robust for use in commercial applications. Any limitations, once identified,

could be the subject of further research for developing new tuning and compensation

techniques.

Finally, the contribution of this thesis has been to establish the feasibility of meta-

material-inspired circuits for wireless applications. This work has demonstrated the

strengths of these circuits in enhancing tunability and matching. At the same time,

this work has characterized to some extent, some of the limitations of these circuits in

terms of noise and distortion. In doing so, this work has laid the foundation for future

research aimed at identifying specific, wireless applications that can benefit from these

circuits.

Page 231: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Appendix A: Beam Squinting Analysis For

The Proposed Series-Fed Antenna Array

T his appendix analyzes the relationship between the squinting of the main beam

of the proposed series-fed alternating antenna array and the group delay of the

interstage phase shifters. The scan angle, θ, of the series-fed antenna array having an

inter-element spacing dE can be expressed as:

θ = sin−1(−c× π + φTL + φPS

ωdE

), (A-1)

where c is the speed of light, φTL is the interconnecting λ/4 TLs phase shift, and φPS

is the phase shift of the interstage phase shifters. For broadside radiation, the antenna

elements of the alternating architecture should be fed out-of-phase, i.e. φTL = −π and

φPS = 0o. To evaluate the beam squinting around the broadside direction, Eq.(A-1) is

used to find the derivative of θ with respect to frequency. For small variations in the

scan angle, one can approximate the rate of change of the scan angle as:

dω≈ c

dE

(π + φPS

ω2+

Tgd

ω), (A-2)

where Tgd is the group delay of the interstage phase shifters. Evaluated at broadside,

208

Page 232: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Appendix A: Beam Squinting Analysis 209

i.e. φPS = 0o, the expression of Eq.(A-2) results in the following:

∣∣∣∣broadside

≈ c

dE

ω2+

Tgd

ω). (A-3)

Hence, feeding the antenna elements with interstage phase shifters that have small

group delays will result in less beam squinting.

Page 233: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Appendix B: Simulation Procedure

T his appendix presents two flow charts to demonstrate the method used to simulate

and consequently design the TL PRI/NRI metamaterial phase shifter and the

steerable antenna array. Figure B-1 shows the procedure used to simulate the single

stage and the 2-stage TL PRI/NRI metamaterial phase shifters. Whereas, Fig. B-2

shows the procedure used to obtain the simulated radiation patterns of the steerable

antenna array.

210

Page 234: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

Appendix B: Simulation Procedure 211

TAI S-parameters files for

different bias conditions

(obtained from experimental

characterization)

Model the printed structure of the TL

phase shifter with a multi-port S-

parameter file (using the ADS EM/

Circuit co-simulation tool)

Combine the S-parameters of TAIs with SPICE models of

the varactors and the S-parameters of the printed

structure of the TL phase shifter in ADS’s circuit simulator

SPICE models of discrete

varactors (obtained from

vendor)

Obtain phase response,

insertion, and return loss of TL

metamaterial phase shifters

Electromagnetic

simulations

Experimental

characterization

Circuit

simulations

Simulate the printed structure of the

TL phase shifter in Momentum ADS

(without varactors and TAI)

Figure B-1: Flow chart showing the procedure used to simulate the TL PRI/NRI meta-material phase shifters.

Obtain the phase response,

insertion, and return loss of the

2-stage TL PRI/NRI

metamaterial phase shifters

Model the entire printed structure

with a multi-port S-parameter file

(using the ADS EM/Circuit co-

simulation tool)

Combine the 2-stage PRI/NRI phase shifters with the S-

parameters of the steerable array in ADS’s circuit

simulation, and obtain the antenna array’s return loss and

the maximum and minimum phase states.

Electro-magnetic

simulations

EM/Circuit co-simulations

plus measurements

Simulate the feed network of the

steerable array together with the patch

antennas in Momentum ADS, but

without the PRI/NRI phase shifters

Using the information on the maximum and minimum

phase states to feed the input ports of the steerable array

with the appropriate signal amplitudes and phases in an

EM simulation to obtain the radiation patterns

Circuit

simulations

Electromagnetic

simulations

Figure B-2: Flow chart showing the procedure used to simulate the steerable antennaarray.

Page 235: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References

[1] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a nega-tive index of refraction,” Science, vol. 292, pp. 77–79, April 2001.

[2] A. K. Iyer, P. C. Kremer, and G. V. Eleftheriades, “Experimental and theoreticalverification of focusing in a large, periodically loaded transmission line negativerefractive index metamaterial,” Optics Express, vol. 11, no. 7, pp. 696–708, April2003.

[3] G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractiveindex media using periodically L-C loaded transmission lines,” IEEE Trans. Mi-crow. Theory Tech., vol. 50, no. 12, pp. 2702–2712, Dec. 2002.

[4] A. Lai, T. Itoh, and C. Caloz, “Composite right/left-handed transmission linemetamaterials,” IEEE Microw. Mag., vol. 5, no. 3, pp. 34–50, Sept. 2004.

[5] M. A. Antoniades and G. V. Eleftheriades, “Compact linear lead/lag metamate-rial phase shifters for broadband applications,” IEEE Antennas Wireless Propa-gat. Lett., vol. 2, pp. 103–106, 2003.

[6] M. A. Antoniades and G. V. Eleftheriades, “A metamaterial series-fed lineardipole array with reduced beam squinting,” in Proc. IEEE Int. Symp. Antennasand Propagat., Albuquerque, NM, Jul. 2006, pp. 4125–4128.

[7] V. G. Veselago, “The electrodynamics of substances with simultaneously negativevalues of ε and µ,” Sov. Phys.Usp., vol. 10, no. 4, pp. 509–514, Jan. 1968.

[8] J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Magnetism fromconductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. TheoryTech., vol. 47, pp. 2075–2084, Nov. 1999.

212

Page 236: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 213

[9] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,“Composite medium with simultaneously negative permeability and permittiv-ity,” Phys. Rev. Lett., vol. 84, no. 18, pp. 4184–4187, May 2000.

[10] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., vol. 85,no. 18, pp. 3966–3969, Oct. 2000.

[11] A. K. Iyer and G. V. Eleftheriades, “Negative refractive index metamaterialssupporting 2-D waves,” in Proc. IEEE MTT-S Int. Microw. Symp., IMS, vol. 2,2-7 June 2002, pp. 1067–1070.

[12] C. Caloz and T. Itoh, “Application of the transmission line theory of left-handed(LH) materials to the realization of a microstrip LH line,” in Proc. IEEE Int.Symp. Antennas and Propagat. Society, vol. 2, 16-21 June 2002, pp. 412–415.

[13] M. A. Antoniades and G. V. Eleftheriades, “A broadband series power divider us-ing zero-degree metamaterial phase-shifting lines,” IEEE Microw. Wireless Com-ponents Lett., vol. 15, no. 11, pp. 808–810, Nov. 2005.

[14] I.-H. Lin, C. Caloz, and T. Itoh, “A branch-line coupler with two arbitrary op-erating frequencies using left-handed transmission lines,” in Proc. IEEE MTT-SInt. Microw. Symp., IMS, vol. 1, 8-13 June 2003, pp. 325–328.

[15] R. Islam and G. V. Eleftheriades, “A planar metamaterial co-directional couplerthat couples power backwards,” in Proc. IEEE MTT-S Int. Microw. Symp., IMS,vol. 1, 8-13 June 2003, pp. 321–324.

[16] L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena betweenartificial left-handed transmission lines,” J. of Appl. Phys., vol. 92, no. 9, pp.5560–5565, Nov. 2002.

[17] R. Islam and G. V. Eleftheriades, “Phase-agile branch-line couplers using meta-material lines,” IEEE Microw. Wireless Components Lett., vol. 14, no. 7, pp.340–342, July 2004.

[18] A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-waveradiation from a negative refractive index metamaterial,” J. of Appl. Phys.,vol. 92, no. 10, pp. 5930–5935, Nov. 2002.

[19] F. Qureshi, M. A. Antoniades, and G. V. Eleftheriades, “A compact and low-profile metamaterial ring antenna with vertical polarization,” IEEE AntennasWireless Propagat. Lett., vol. 4, pp. 333–336, 2005.

Page 237: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 214

[20] Y.-S. Wang, M.-F. Hsu, and S.-J. Chung, “A compact slot antenna utilizing aright/left-handed transmission line feed,” IEEE Trans. Antennas & Propagat.,vol. 56, no. 3, pp. 675–683, March 2008.

[21] V. M. Lubecke, B. Barber, E. Chan, D. Lopez, M. E. Gross, and P. Gammel,“Self-assembling MEMS variable and fixed RF inductors,” IEEE Trans. Microw.Theory Tech., vol. 49, no. 11, pp. 2093–2098, Nov. 2001.

[22] S. Chang and S. Sivoththaman, “A tunable RF MEMS inductor on silicon in-corporating an amorphous silicon bimorph in a low-temperature process,” IEEEElectron Device Lett., vol. 27, no. 11, pp. 905–907, Nov. 2006.

[23] T. M. Hancock and G. M. Rebeiz, “A 12-GHz SiGe phase shifter with integratedLNA,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 977–983, March2005.

[24] D. M. Pozar, Microwave Engineering, 3rd ed. New York: John Wiley, 2005.

[25] R. Mukhopadhyay, Y. Park, P. Sen, N. Srirattana, J. Lee, C.-H. Lee, S. Nuttinck,A. Joseph, J. D. Cressler, and J. Laskar, “Reconfigurable RFICs in Si-based tech-nologies for a compact intelligent RF front-end,” IEEE Trans. Microw. TheoryTech., vol. 53, no. 1, pp. 81–93, Jan. 2005.

[26] Y. Wu, X. Ding, M. Ismail, and H. Olsson, “RF bandpass filter design based onCMOS active inductors,” IEEE Trans. Circuits & Systems II: Analog & DigitalSignal Processing, vol. 50, no. 12, pp. 942–949, Dec. 2003.

[27] L.-H. Lu and Y.-T. Liao, “A 4-GHz phase shifter MMIC in 0.18µm CMOS,”IEEE Microw. Wireless Components Lett., vol. 15, no. 10, pp. 694–696, Oct.2005.

[28] L.-H. Lu, Y.-T. Liao, and C.-R. Wu, “A miniaturized Wilkinson power dividerwith CMOS active inductors,” IEEE Microw. Wireless Components Lett., vol. 15,no. 11, pp. 775–777, Nov. 2005.

[29] B. D. Tellegen, “The gyrator, a new electric network element,” Philips ResearchRepts., vol. 3, pp. 81–101, April 1948.

[30] A. S. Morse and L. P. Huelsman, “A gyrator realization using operational ampli-fiers,” IEEE Trans. Circuits & Systems, vol. 11, no. 2, pp. 277–278, June 1964.

[31] R. M. Inigo, “Gyrator realization using two operational amplifiers,” IEEE Journalof Solid-State Circuits, vol. 6, no. 2, pp. 88–89, April 1971.

Page 238: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 215

[32] G. Sharpe, “The pentode gyrator,” IRE Trans. Circuit Theory, vol. 4, no. 4, pp.321–323, Dec. 1957.

[33] B. Shenoi, “Practical realization of a gyrator circuit and RC-gyrator filters,”IEEE Trans. Circuits & Systems, vol. 12, no. 3, pp. 374–380, Sept. 1965.

[34] A. Thanachayanont, “CMOS transistor-only active inductor for IF/RF applica-tions,” in Proc. IEEE Int. Conf. Industrial Tech., ICIT, vol. 2, Dec. 2002, pp.1209–1212.

[35] S. Hara and T. Tokumitsu, “Monolithic microwave active inductors and theirapplications,” in Proc. IEEE Int. Symp. Circuits and Systems, ISCAS, vol. 3,11-14 June 1991, pp. 1857–1860.

[36] C. Yong-Ho, H. Song-Cheol, and K. Young-Se, “A novel active inductor andits application to inductance-controlled oscillator,” IEEE Trans. Microw. TheoryTech., vol. 45, no. 8, pp. 1208–1213, Aug. 1997.

[37] C. Leifso, J. Haslett, and J. McRory, “Monolithic tunable active inductor withindependent Q control,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 6, pp.1024–1029, June 2000.

[38] C. Leifso and J. W. Haslett, “A fully integrated active inductor with indepen-dent voltage tunable inductance and series-loss resistance,” IEEE Trans. Microw.Theory Tech., vol. 49, no. 4, pp. 671–676, April 2001.

[39] C.-C. Hsiao, C.-W. Kuo, C.-C. Ho, and Y.-J. Chan, “Improved quality-factor of0.18-µm CMOS active inductor by a feedback resistance design,” IEEE Microw.Wireless Components Lett., vol. 12, no. 12, pp. 467–469, Dec. 2002.

[40] A. I. Karsilayan and R. Schaumann, “A high-frequency high-Q CMOS activeinductor with DC bias control,” in Proc. IEEE 43rd Midwest Symp. Circuits andSystems, vol. 1, 8-11 Aug. 2000, pp. 486–489.

[41] R. Akbari-Dilmaghani, A. Payne, and C. Toumazou, “A high Q RF CMOS dif-ferential active inductor,” in Proc. IEEE Int. Conf. Electronics, Circuits andSystems, vol. 3, 7-10 Sept. 1998, pp. 157–160.

[42] A. Thanachayanont and A. Payne, “VHF CMOS integrated active inductor,”Electronics Letters, vol. 32, no. 11, pp. 999–1000, May 1996.

[43] A. Thanachayanont and A. Payne, “CMOS floating active inductor and its ap-plications to bandpass filter and oscillator designs,” IEE Proceedings Circuits,Devices and Systems, vol. 147, no. 1, pp. 42–48, Feb. 2000.

Page 239: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 216

[44] B. Razavi, Design of Analog CMOS Integrated Circuits. Boston: McGraw-Hill,2000.

[45] M. Ismail, R. Wassenaar, and W. Morrison, “A high-speed continuous-time band-pass VHF filter in MOS technology,” in Proc. IEEE Int. Symp. Circuits andSystems, ISCAS, vol. 3, 11-14 June 1991, pp. 1761–1764.

[46] T. Y. K. Lin and A. J. Payne, “Design of a low-voltage, low-power, wide-tuningintegrated oscillator,” in Proc. IEEE Int. Symp. Circuits and Systems, ISCAS,Geneva., vol. 5, 28-31 May 2000, pp. 629–632.

[47] W. Yue, M. Ismail, and H. Olsson, “A novel CMOS fully differential inductorlessRF bandpass filter,” in Proc. IEEE Int. Symp. Circuits and Systems, ISCAS,Geneva, vol. 4, 28-31 May 2000, pp. 149–152.

[48] Y.-H. Cho, S.-C. Hong, and Y.-S. Kwon, “A novel active inductor and its appli-cation to inductance-controlled oscillator,” IEEE Trans. Microw. Theory Tech.,vol. 45, no. 8, pp. 1208–1213, Aug. 1997.

[49] G. M. Rebeiz, RF MEMS Theory, Design, and Technology. New Jersey: Wiley-Interscience, 2003.

[50] R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microw. TheoryTech., vol. 20, no. 5, pp. 314–323, May 1972.

[51] F. Ellinger, R. Vogt, and W. Bachtold, “Ultracompact reflective-type phaseshifter MMIC at C-band with 360o phase-control range for smart antenna com-bining,” IEEE Journal of Solid-State Circuits, vol. 37, no. 4, pp. 481–486, April2002.

[52] F. Ellinger, R. Vogt, and W. Bachtold, “Compact reflective-type phase-shifterMMIC for C-band using a lumped-element coupler,” IEEE Trans. Microw. The-ory Tech., vol. 49, no. 5, pp. 913–917, May 2001.

[53] B. Williams and F. J. Taylor, Electronic Filter Design Handbook: LC, Active,and Digital Filters, 2nd ed. New York: McGraw-Hill, 1988.

[54] F. Ellinger, R. Vogt, and W. Bachtold, “Ultra compact, low loss, varactor tunedphase shifter MMIC at C-band,” IEEE Microw. Wireless Components Lett.,vol. 11, no. 3, pp. 104–105, March 2001.

[55] F. Ellinger, H. Jackel, and W. Bachtold, “Varactor-loaded transmission-line phaseshifter at C-band using lumped elements,” IEEE Trans. Microw. Theory Tech.,vol. 51, no. 4, pp. 1135–1140, April 2003.

Page 240: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 217

[56] C. Damm, M. Schussler, M. Oertel, and R. Jakoby, “Compact tunable periodi-cally LC loaded microstrip line for phase shifting applications,” in Proc. IEEEMTT-S Int. Microw. Symp., IMS, 12-17 June 2005, pp. 2003–2006.

[57] H. Kim, A. B. Kozyrev, A. Karbassi, and D. W. van der Weide, “Linear tun-able phase shifter using a left-handed transmission line,” IEEE Microw. WirelessComponents Lett., vol. 15, no. 5, pp. 366–368, May 2005.

[58] A. Mahmud, T. S. Kalkur, A. Jamil, and N. Cramer, “A 1-GHz active phaseshifter with a ferroelectric varactor,” IEEE Microw. Wireless Components Lett.,vol. 16, no. 5, pp. 261–263, May 2006.

[59] D. Kuylenstierna, A. Vorobiev, P. Linner, and S. Gevorgian, “Compositeright/left handed transmission line phase shifter using ferroelectric varactors,”IEEE Microw. Wireless Components Lett., vol. 16, no. 4, pp. 167–169, April2006.

[60] R. W. Vogel, “Analysis and design of lumped- and lumped-distributed-elementdirectional couplers for MIC and MMIC applications,” IEEE Trans. Microw.Theory Tech., vol. 40, no. 2, pp. 253–262, Feb. 1992.

[61] K. Chang, I. Bahl, and V. Nair, RF and Microwave Circuits and ComponentDesign for Wireless Systems. New York: Wiley-Interscience, 2002.

[62] R. Islam, F. Elek, and G. V. Eleftheriades, “Coupled-line metamaterial couplerhaving co-directional phase but contra-directional power flow,” Electronics Let-ters, vol. 40, pp. 315–317, March 2004.

[63] C. Caloz, A. Sanada, and T. Itoh, “A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth,” IEEETrans. Microw. Theory Tech., vol. 52, no. 3, pp. 980–992, March 2004.

[64] R. Islam and G. V. Eleftheriades, “Printed high-directivity metamaterialMS/NRI coupled-line coupler for signal monitoring applications,” IEEE Microw.Wireless Components Lett., vol. 16, no. 4, pp. 164–166, April 2006.

[65] H. V. Nguyen and C. Caloz, “Generalized coupled-mode approach of metama-terial coupled-line couplers: coupling theory, phenomenological explanation, andexperimental demonstration,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5,pp. 1029–1039, May 2007.

[66] R. C. Frye, S. Kapur, and R. C. Melville, “A 2-GHz quadrature hybrid im-plemented in CMOS technology,” IEEE Journal of Solid-State Circuits, JSSC,vol. 38, no. 3, pp. 550–555, March 2003.

Page 241: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 218

[67] Y.-C. Chiang and C.-Y. Chen, “Design of a wide-band lumped-element 3-dBquadrature coupler,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 3, pp.476–479, March 2001.

[68] Federal Standard 1037C. Definition of Phased Array, United States.

[69] C. A. Balanis, Antenna Theory Analysis and Design, 3rd ed. New Jersey: Wiley-Interscience, 2005.

[70] G. Xiang, H. Hashemi, and A. Hajimiri, “A fully integrated 24-GHz eight-elementphased-array receiver in silicon,” IEEE Journal of Solid-State Circuits, vol. 39,no. 12, pp. 2311–2320, Dec. 2004.

[71] A. Natarajan, A. Komijani, and A. Hajimiri, “A fully integrated 24-GHz phased-array transmitter in CMOS,” IEEE Journal of Solid-State Circuits, vol. 40,no. 12, pp. 2502–2514, Dec. 2005.

[72] A. Babakhani, X. Guan, A. Komijani, A. Natarajan, and A. Hajimiri, “A 77GHz 4-element phased array receiver with on-chip dipole antennas in silicon,” inProc. IEEE Int. Solid State Circuits Conf., ISSCC, Feb. 2006, pp. 629–638.

[73] A. Babakhani, X. Guan, A. Komijani, A. Natarajan, and A. Hajimiri, “A 77-GHz phased-array transceiver with on-chip antennas in silicon: Receiver andantennas,” IEEE Journal of Solid-State Circuits, vol. 41, no. 12, pp. 2795–2806,Dec. 2006.

[74] A. Natarajan, A. Komijani, X. Guan, A. Babakhani, and A. Hajimiri, “A 77- GHzphased-array transceiver with on-chip antennas in silicon: Transmitter and localLO-path phase shifting,” IEEE Journal of Solid-State Circuits, vol. 41, no. 12,pp. 2807–2819, Dec. 2006.

[75] J. Huang and D. M. Pozar, Advances in Microstrip and Printed Antennas,K. F. Lee and W. Chen, Eds. Wiley-Interscience, 1997.

[76] A. Derneryd, “Linearly polarized microstrip antennas,” IEEE Trans. Antennas& Propagat., vol. 24, no. 6, pp. 846–851, Nov. 1976.

[77] T. Metzler, “Microstrip series arrays,” IEEE Trans. Antennas & Propagat.,vol. 29, no. 1, pp. 174–178, Jan. 1981.

[78] J. Huang, “A parallel-series-fed microstrip array with high efficiency and lowcross-polarization,” Microw. & Optical Technology Lett., vol. 5, no. 5, pp. 230–233, Jan. 2007.

[79] R. C. Hansen, Phased Array Antennas. New York: Wiley-interscience, 1998.

Page 242: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 219

[80] M. A. Y. Abdalla, G. V. Eleftheriades, and K. Phang, “A differential 0.13µmCMOS active inductor for high-frequency phase shifters,” in Proc. IEEE Int.Symp. Circuits and Systems ISCAS, Kos, Greece, 21-24 May 2006, p. 4pp.

[81] E. Alarcon, H. Martinez, E. Vidal, J. Madrenas, and A. Poveda, “D-MRC: dig-itally programmable MOS resistive circuit,” in Proc. 44th IEEE Midwest Symp.Circuits and Systems, MWSCAS, vol. 1, 14-17 Aug. 2001, pp. 215–218.

[82] D. Johns and K. Martin, Analog Integrated Circuit Design. Toronto: John Wiley& Sons, 1997.

[83] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuit, 2nd ed.Cambridge, UK: Cambridge University Press, 1998.

[84] S. Hara, T. Tokumitsu, and M. Aikawa, “Lossless broad-band monolithic mi-crowave active inductors,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 12,pp. 1979–1984, Dec. 1989.

[85] C. Damm, M. Schubler, J. Freese, and R. Jakoby, “Artificial line phase shifterwith separately tunable phase and line impedance,” in Proc. 36th IEEE EuropeanMicrow. Conference, EuMC, 10-15 Sept. 2006, pp. 423–426.

[86] H.-H. Hsieh, Y.-T. Liao, and L.-H. Lu, “A compact quadrature hybrid MMICusing CMOS active inductors,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6,pp. 1098–1104, June 2007.

[87] D. Kuylenstierna, E. Ash, A. Vorobiev, T. Itoh, and S. Gevorgian, “X-band lefthanded phase shifter using thin film Ba0.25SR0.75TiO3 ferroelectric varactors,” inProc. IEEE 36th European Microw. Conf., EuMC, Sept. 2006, pp. 847–850.

[88] E. E. Djoumessi, E. Marsan, C. Caloz, M. Chaker, and K. Wu, “Varactor-tuned dual-band quadrature hybrid coupler,” IEEE Microw. Wireless Compo-nents Lett., vol. 16, no. 11, pp. 603–605, Nov. 2006.

[89] C.-S. Kim, C.-S. Yoon, J.-S. Park, D. Ahn, J.-B. Lim, and S.-I. Yang, “A design ofthe novel varactor tuned directional coupler,” in Proc. IEEE MTT-S Int. Microw.Symp., IMS, vol. 4, 13-19 June 1999, pp. 1725–1728.

[90] C.-S. Kim, J.-S. Park, D. Ahn, and J.-B. Lim, “Variable directional coupler withLC resonator,” Electronics Letters, vol. 36, no. 18, pp. 1557–1559, 31 Aug. 2000.

[91] E. A. Fardin, K. Ghorbani, and A. S. Holland, “A varactor tuned branch-linehybrid coupler,” in Proc. Asia-Pacific Microw. Conf., APMC, vol. 3, 4-7 Dec.2005.

Page 243: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 220

[92] E. A. Fardin, A. S. Holland, and K. Ghorbani, “Electronically tunable lumpedelement 90o hybrid coupler,” Electronics Letters, vol. 42, no. 6, pp. 353–355,March 2006.

[93] S. Toyoda, “Variable coupling directional couplers using varactor diodes,” inProc. IEEE MTT-S Int. Microw. Symp., IMS, vol. 82, no. 1, Jun 1982, pp. 419–421.

[94] S.-M. Wang, C.-Y. Chang, and J. Lin, “A software configurable coupler withprogrammable coupling coefficient,” in Proc. IEEE MTT-S Int. Microw. Symp.,IMS, June 2007, pp. 185–188.

[95] L. Marcaccioli, C. Lugo, M. M. Tentzeris, J. Papapolymerou, and R. Sorrentino,“A novel reconfigurable coupler for intelligent sop rf front-ends,” in Proc. IEEEEuropean Microw. Conf., EuMC, vol. 1, 4-6 Oct. 2005.

[96] K.-K. M. Cheng and F.-L. Wong, “A novel approach to the design and imple-mentation of dual-band compact planar 90o branch-line coupler,” IEEE Trans.Microw. Theory Tech., vol. 52, no. 11, pp. 2458–2463, Nov. 2004.

[97] J. Reed and G. J. Wheeler, “A method of analysis of symmetrical four-portnetworks,” IEEE Trans. Microw. Theory Tech., vol. 4, no. 4, pp. 246–252, Oct1956.

[98] M. Tsuji, T. Nishikawa, K. Wakino, and T. Kitazawa, “Bi-directionally fedphased-array antenna downsized with variable impedance phase shifter for ISMband,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 7, pp. 2962–2969, July2006.

[99] S. Cheng, E. Ojefors, P. Hallbjorner, and A. Rydberg, “Compact reflective mi-crostrip phase shifter for traveling wave antenna applications,” IEEE Microw.Wireless Components Lett., vol. 16, no. 7, pp. 431–433, July 2006.

[100] E. Ojefors, S. Cheng, K. From, I. Skarin, P. Hallbjorner, and A. Rydberg, “Elec-trically steerable single-layer microstrip traveling wave antenna with varactordiode based phase shifters,” IEEE Trans. Antennas & Propagat., vol. 55, no. 9,pp. 2451–2460, Sept. 2007.

[101] S. Lim, C. Caloz, and T. Itoh, “Metamaterial-based electronically controlledtransmission-line structure as a novel leaky-wave antenna with tunable radiationangle and beamwidth,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp.161–173, Jan. 2005.

Page 244: Metamaterial-Inspired CMOS Tunable Microwave … · Metamaterial-Inspired CMOS Tunable Microwave Integrated ... Metamaterial-Inspired CMOS Tunable Microwave Integrated Circuits For

References 221

[102] D. M. Pozar, A review of bandwidth enhancement techniques for microstrip an-tennas, Microstrip Antennas, D. M. Pozar and D. H. Schaubert, Eds. New York:IEEE Press, 1995.

[103] G. V. Eleftheriades, M. A. Antoniades, A. Grbic, A. K. Iyer, and R. Islam, “Elec-tromagnetic applications of negative-refractive-index transmission-line metama-terials,” in Proc. 27th ESA Antenna Technology Workshop on Innovative PeriodicAntennas, Santiago de Compostela, Spain, Mar. 2004, pp. 21–28.

[104] G. V. Eleftheriades, M. A. Antoniades, and F. Qureshi, “Antenna applications ofnegative-refractive-index transmission-line (NRI-TL) structures,” IET Microw.,Antennas and Propagat., Special Issue on Metamaterials, vol. 1, no. 1, pp. 12–22,Feb. 2007.

[105] M. A. Antoniades and G. V. Eleftheriades, “A negative-refractive-indextransmission-line (NRI-TL) leaky-wave antenna with reduced beam squinting,”in Proc. IEEE Int. Symp. Antennas and Propagat., Honolulu, HI, Jun. 2007, pp.5817–5820.

[106] M. A. Antoniades and G. V. Eleftheriades, “A CPS leaky-wave antenna withreduced beam squinting using NRI-TL metamaterials,” IEEE Trans. Antennas& Propagat., vol. 56, no. 3, pp. 708–721, Jun. 2007.

[107] I. Aoki, S. Kee, R. Magoon, R. Aparicio, F. Bohn, J. Zachan, G. Hatcher, D. Mc-Clymont, and A. Hajimiri, “A fully integrated quad-band GSM/GPRS CMOSpower amplifier,” in Proc. IEEE Int. Solid State Circuits Conf., ISSCC, Feb.2008, pp. 570–571.

[108] U. of California San Diego, “World’s most complex silicon phased-array chipdeveloped,” Science Daily, Nov. 4, 2007.

[109] S. Podilchak, B. Frank, A. Freundorfer, and Y. Antar, “A positive/negative re-fractive index coplanar transmission line in CMOS for controlled insertion phase,”Microw. & Optical Technology Lett., vol. 50, no. 8, pp. 2227–2229, Aug. 2008.

[110] S. Podilchak, B. Frank, A. Freundorfer, and Y. Antar, “Composite right/lefthanded artificial transmission line structures in CMOS for controlled insertionphase at 30 GHz,” in Int. Journal of RF & Microw. Computer-Aided Eng., Aug.2008.

[111] S. Podilchak, B. Frank, A. Freundorfer, and Y. Antar, “Metamaterial artificialtransmission line structures in CMOS for tunable insertion phase at 30 GHz,” in1st Microsystems & Nanoelectronics Research Conf., MNRC, Oct. 2008.