RECONFIGURABLE PASSIVE RF/MICROWAVE COMPONENTS. Dissertation. Submitted to. The School of Engineering of the UNIVERSITY OF DAYTON

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1 RECONFIGURABLE PASSIVE RF/MICROWAVE COMPONENTS Dissertation Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Doctor of Philosophy in Engineering By Hailing Yue Dayton, Ohio August, 2016

2 RECONFIGURABLE PASSIVE RF/MICROWAVE COMPONENTS Name: Yue, Hailing APPROVED BY: Guru Subramanyam, Ph.D. Advisory Committee Chairman Professor and Chair Department of Electrical and Computer Engineering Partha P. Banerjee, Ph.D. Committee Member Professor Electro-Optics Graduate Program and Department of Electrical and Computer Engineering Monish R. Chatterjee, Ph.D. Committee Member Professor Department of Electrical and Computer Engineering Robert P. Penno, Ph.D. Committee Member Professor Department of Electrical and Computer Engineering Robert J. Wilkens, Ph.D., P.E. Associate Dean for Research and Innovation Professor School of Engineering Eddy M. Rojas, Ph.D., M.A., P.E. Dean, School of Engineering ii

3 ABSTRACT RECONFIGURABLE PASSIVE RF/MICROWAVE COMPONENTS Name: Yue, Hailing University of Dayton Advisor: Dr. Guru Subramanyam Passive devices are the key elements in various Radio Frequency and microwave communication systems for functions such as switching, filtering and impedance matching. Passive devices realized with lumped elements exhibit losses from resistive and reactive parasitic behavior at higher frequencies, while distributed elements can achieve superior high frequency performance at a sacrifice of increased electrical lengths. In recent years, novel ideas have emerged for the design of RF/microwave components composed of transmission lines loaded with reactive elements (inductors, capacitors, and/or both of them in the form of resonators). These structures have been extensively shown to exhibit high controllability in their passband or stopband characteristics and electrical lengths. iii

4 In this study, novel passive RF/microwave components in the form of ferroelectric varactors, subwavelength resonators, and Defected Ground Structures (DGS) are explored with an eye to design innovative RF/microwave devices such as filters and phase shifters. Specifically, main contributions are: Analog phase shifters realized with a cascade of thin film Barium Strontium Titantite (BST) varactors are demonstrated with a FOM of 24.5 degrees/db at 8 GHz in an area of 0.45 by 3.3 mm 2 with a maximum DC bias of 8 V. A capacitive tuning ratio of 4:1 is achieved by apply 0-10 V dc bias on a single varactor unit with loss tangent under 0.01 up to 40 GHz. Capacitive loading capability is integrated to subwavelength resonators, making it possible for varactor loading. Resulting design is exhibits a notch depth of 48 db at 116 MHz within an area of 6.1 by 9.65 cm 2, demonstrating its exceptional compactness without sacrificing the performance of band-rejection behavior. Modified Spiral-shaped DGS are presented with superior stopband performance and suppressed harmonics. Resulting design showed enhanced band-rejection behavior of around -50dB notch depth and less than 3dB insertion loss at 3.64 GHz within an area of 1.5 by 13 mm 2 with no higher order harmonics up to 10 GHz. In conclusion, this dissertation represents a successful demonstration of passive electrical small components with improved performance for RF/microwave applications. iv

5 DEDICATION Dedicated to my son, my husband, and my parents. v

6 ACKNOWLEDGEMENTS First and foremost I offer my sincerest gratitude to my supervisor and chair of my doctoral committee, Professor Guru Subramanyam, who has supported me throughout my graduate study with his patience and knowledge whilst allowing me the room to develop my interests. I attribute the level of my Doctoral degree to his advice, insight, encouragement and effort. I would also like to thank Professor Partha P. Banerjee, Professor Monish R. Chatterjee, and Professor Robert P. Penno for being my Ph. D. committee members and attending each cornerstone event, which defines the progress of my doctoral study. I also would like to thank Dr. Weisong Wang and Dr. Eunsung Shin who provided the supplies, advice, and effort in fabricating the samples for my research work; my current colleagues, Kuangchang Pan and Dr. Shu Wang, for their help in doing the measurements, fabrications, and part of my teaching duties. vi

7 My thanks are also extended to my past colleagues, Dustin Brown, Hai Jiang, Mark Patterson, and Henry Zhang, who trained me with the skills in operating Vector Network Analyzer, Pulsed Laser Deposition (PLD) system, as well as the Electromagnetic simulation software. I would also like to extend my thanks to Dr. Temesguen M. Kebede and Professor Russell C. Hardie who trained me in teaching ECE401 Communication Systems course and ECE401L Communication Systems laboratory. This experience is definitely another important branch of my skill set, which also extends my career choices. My completion of all the projects cannot be accomplished without the support of the Department of Electrical and Computer Engineering at the University of Dayton, which provided me the platform that I needed to produce and complete my dissertation and funded my studies. Finally, I thank my father Han Yue, and my husband Jian Gao for supporting me all the way through my studies at University of Dayton at all possible angles. vii

8 PREFACE All of the work presented henceforth was conducted in the Kettering Laboratory at the University of Dayton. All projects and associated methods were approved by the Laboratory supervisor Professor Guru Subramanyam. A version of Chapter 3 has been published, which is a continued work from my Master thesis. I was the lead investigator, responsible for all major areas of concept formation, data collection and analysis, as well as manuscript composition. Professor Subramanyam was the supervisory author on this project and was involved throughout the project in concept formation and manuscript composition, who is also the inventor of the varactor model with patent ( Ferroelectric varactors suitable for capacitive shunt switching. US B2). Fabrication of the test structures was done by Dr. Eunsung Shin and Dr. Shu Wang. Part of the testing was performed by Dr. Shu Wang. I was the lead investigator for the projects located in Chapters 4 and 5 where I was responsible for all major areas of concept formation, data collection and analysis, as well as the majority of manuscript composition. Professor Subramanyam was involved in viii

9 the early stages of concept formation and contributed to manuscript edits. Device fabrication was done by Dr. Eunsung Shin. To integrate all the aforementioned structures for a single set of mask production, I was also designated to design a four-layer mask set to adapt all the fabrication requirements on four-inch diameter wafers including alignment marks, device arrangement and layout, polarity and minimum feature check, and ordering process ix

10 TABLE OF CONTENTS ABSTRACT... iii DEDICATION... v ACKNOWLEDGEMENTS... vi PREFACE... viii LIST OF ILLUSTRATIONS... xiv LIST OF TABLES... xxiv CHAPTER 1 INTRODUCTION Motivations Objectives Contributions Outline... 7 CHAPTER 2 LITERATURE REVIEW Basics of Ferroelectric Material Applications in Ferroelectric (polar) Phase Applications in Paraelectric (non-polar) Phase Barium Strontium Titanate Thin Film and Bulk Ferroelectric Material MIM and Planar Ferroelectric Varactors x

11 2.5 Figure of Merits Other Varactor Technologies RF-MEMS Varactors Semiconductor Varactor Diodes Ferroelectric Varactors Comparison and Discussion Ferroelectric Varactors in This Work CHAPTER 3 CHARACTERIZATION OF THIN FILM BST VARACTORS Structure and Operation Equivalent Schematic Model Quality Factor Formulation Step 1: Parallel to Series Conversion Step 2: Equivalent Schematic Circuit of the Varactors Step 3: Calculation of Circuit Q Fabrication Measurements Results and Discussion Varactor Measurements without DC Bias and Thin Film Thickness Estimation Varactor Measurement with DC Bias Quality Factor Versus DC Bias Quality Factor Versus Frequency CHAPTER 4 VARACTOR BASED ANALOG PHASE SHIFTERS Methodology xi

12 4.2 Maximum Transmission Loss of Varactor-based Phase Shifters Phase Control Range of Varactor-based Phase Shifters FOM of Varactor-based Phase Shifters Mathematical Modeling ABCD Matrix of a Single Varactor Section ABCD Matrix of a CPW Section ABCD Matrix of N-cell Phase Shifter Structure Conclusion CHAPTER 5 CAPACITIVE LOADED SUBWAVELENGTH RESONATORS Structure and Operation Printed Circuit Board Realization Experimental Results and Analysis CHAPTER 6 NOVEL CPW DEFECTED GROUND STRUCTURES Overview DGS Characteristics DGS Equivalent Circuit Structure and Operation Parametric Study Fabrication and Testing Measurements of Single DGS Units Measurement of Cascaded DGS Conclusion CHAPTER 7 PHOTO MASK LAYOUT DESIGN xii

13 7.1 Mask Template Mask Layout Device Layout Alignment Mark Design CHAPTER 8 CONCLUSION AND FUTURE WORK BIBLIOGRAPHY APPENDIX A Meaurement Data of Varactors APPENDIX B Measurement Data of Phase Shifters APPENDIX C Additional Data of DGS APPENDIX D Additional Data of Subwavelength Resonators APPENDIX E Mathematical Model of Phase Shifters xiii

14 LIST OF ILLUSTRATIONS Figure 1 Reconfigurable RF frontend with tunable microelectronic components... 2 Figure 2 (a) the P (E) response of a linear capacitor, in (b) a nonlinear capacitor in the ferroelectric phase (with hysteresis) and in (c) a nonlinear capacitor in the paraelectric phase (without hysteresis)... 9 Figure 3 BST in the ferroelectric phase structure Figure 4 Parallel Plate versus IDC Figure 5 Cross-section of a planar RF-MEMS electro-static switched capacitor Figure 6 Cross-section of a Schottky varactor diode and the equivalent circuit model Figure 7 Cross-section of a ferroelectric varactor and the equivalent circuit model Figure 8 Parallel plate equivalent schematic model Figure 9 3D view of the single unit varactor device Figure 10 Top view the parallel-plate single unit varactor device. Dimensions are in μm Figure 11 Equivalent schematic model for shunt varactor unit cell Figure 12 Parallel RC to series RC conversion Figure 13 Modified equivalent schematic using parallel RC to series RC transformation Figure 14 On-wafer measurement on ferroelectric varactors by Vector Network Analyzer with a set of GSG microprobes xiv

15 Figure 15 On-wafer measurement setup with GSG microprobes Figure 16 2-port scattering parameters obtained from VNA measurements Figure 17 Locations of the measured varactors on 4 inch sapphire wafer named as UDBST Figure 18 Measured scattering parameters of 9 varactors at each location on wafer UDBST115 from 0-40 GHz at 0 V bias (solid curve), matched with schematic model shown in dotted curve. Extracted equivalent capacitances Cp of varactor device R1C1 (corner), R1C2 (top), R2C2 (center), R3C3 (corner) are: pf (C1), pf (C3), pf (C4), pf (C2) Figure 19 Comparison between electromagnetic model simulation (blue dashed curve) and measurements of varactor device R1C1 (red solid curve), matched by schematic model (green dotted curve) with C=0.748 pf, L=0.01 nh, Rp=849 Ω, Rs=2.57 Ω Figure 20 S21 magnitudes of varactor device R1C1 on wafer UDBST115 from 0-40 GHz. The insertion loss at 10 GHz is decreased from -4 db to 0.6 db from 0-10 V Figure 21 S21 phase of varactor device R1C1 on wafer UDBST115 from 0-40 GHz. The phase shifted from degrees to degrees at 10 GHz Figure 22 S11 magnitudes of varactor device R1C1 on wafer UDBST115 from 0-40 GHz Figure 23 S11 phase of varactor device R1C1 at 0-8 V on wafer UDBST115 from 0-40 GHz Figure 24 Extracted capacitance and estimated dielectric constant versus bias voltage Figure 25 Comparison between Total Quality Factor and dielectric Quality Factor versus DC bias Figure 26 Comparison between total Quality Factor Qt and dielectric Quality Factor Qp versus frequency Figure 27 Dielectric Quality Factor Qp and loss tangent of the varactor device from 0-10 V Figure 28 Top view of single varactor units. Dimensions are labeled in μm xv

16 Figure 29 Top and 3D view of analog phase shifter cascaded by 10 varactor units. Dimensions are labeled in μm Figure 30 Comparison of measured S21 angles of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 31 Comparison of measured S21 magnitudes of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 32 Comparison of S21 magnitudes of phase shifters cascaded by 20 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 33 Comparison of S21 angles of phase shifters cascaded by 20 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 34 Comparison of maximum transmission loss in terms of the differences between S21 magnitudes at highest bias voltage (8 V) and S21 magnitudes at 0 volt bias for phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz Figure 35 Comparison of phase control range in terms of the differences between S21 angles at highest bias voltage (8 V) and S21 magnitudes at 0 V bias for phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz Figure 36 Comparison of Figure-Of-Merit in terms of the phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz Figure 37 Modeling by ABCD matrix Figure 38 Modeled and measured S21 phases of 20-section phase shifter Figure 39 Modeled and measured S21 magnitudes of 20-section phase shifter Figure 40 3D view of the CPW sub-wavelength resonator Figure 41 Top view of the resonator with dimensioning in cm Figure 42 Top views of three variations of the bottom metal layer named as C_Loading_V1, C_Loading_V2, and C_Loading_V3 from left to right with increasing overlapping areas xvi

17 Figure 43 3D views of three variations of the bottom metal layer named as C_Loading_V1, C_Loading_V2, and C_Loading_V3 from left to right with increasing overlapping areas Figure 44 Simulated S21 magnitudes of C_Loading_V1, C_Loading_V2, and C_Loading_V3 using ADS Figure 45 EM field distribution at DC and resonance of C_Loading_V Figure 46 PCB Layout of the CPW sub-wavelength resonator. The red layer is the top metal layer and the green layer is the bottom metal layer which has three variations. The five-hole combination on either side of the CPW signal line of each device were patterned to adapt SMA connectors Figure 47 Comparison of simulated and measured frequency response of CPW sub-wavelength resonator in terms of magnitudes of S21 C_Loading_V1, C_Loading_V2, and C_Loading_V Figure 48 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V3 in terms of magnitudes of S Figure 49 Top views of C-DGS (left) cell with 10 full spiral turns and corresponding M-DGS (right) cell. Dimensions are in μm Figure 50 CPW (left) and Microstrip (right) Dumbbell-shaped DGS structure Figure 51 Equivalent circuit for dumbbell-shaped DGS section Figure 52 Comparison of simulated S21 magnitudes of C-DGS cell with 10 full spiral turns and five removed inner spiral turns Figure 53 Comparison of simulated S21 magnitudes of C-DGS cell with 10 full spiral turns and only outer spiral turns Figure 54 Electromagnetic field distribution of M-DGS at dc (left) and resonance (right) Figure 55 DGS On 4 inch Sapphire Wafer Figure 56 Top views of C-DGS cells with full 10 spiral turns, only outermost spiral turn (M-DGS), 7 removed spiral turns, and 5 removed spiral turns Figure 57 Measured S21 magnitudes of C-DGS cells with 6 to 10 spiral turns xvii

18 Figure 58 Measured S21 magnitudes of M-DGS cells (With only outermost turns of 6-turn to 10-turn C-DGS cells) Figure 59 Measured S21 magnitudes of C-DGS cells with full 10 spiral turns, 5 removed spiral turns, 7 removed spiral turns, and only outermost spiral turn Figure 60 Top view of cascaded C-DGS with 5 removed inner spiral turns and M-DGS cell (10-turn C-DGS with its outermost spiral turn) Figure 61 Measured and simulated S21 magnitudes of cascaded M-DGS cells Figure 62 Measured and simulated S21 magnitudes of cascaded C-DGS cells with 5 removed inner spiral turns Figure 63 Photo mask Template with four 1 by 1 units inside 4 inch diameter circumference. Number units are in μm unless specified Figure 64 Mask layout for device shared same fabrication process Figure 65 Single and cascaded Varactor layout Figure 66 Completed Photo Mask Layout Figure 67 3D View (left) and Top view (right) of the alignment marks at each layer. Dimensioning units are in μm Figure 68 Top view of the alignment marks at each layer Figure 69 Overlapping of alignment marks for all possible combinations (Big). Dimensioning units are in μm Figure 70 Tunable coupled-resonator filter with shunt resonators enhanced by DGS and varactors Figure 71 Tunable coupled-resonator filter with serial resonators enhanced by DGS and varactors Figure 72 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.748 pf, L=0.01 nh, Rp=849Ω, Rs=2.57 Ω Figure 73 Measured scattering parameters of varactor R1C1 in terms of xviii

19 magnitudes of S21 and S11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.714 pf, L=0.01 nh, Rp=849 Ω, Rs=1.9 Ω Figure 74 Measured scattering parameters of varactor R1C2 in terms of magnitudes of S21 and S11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.608 pf, L=0.01 nh, Rp=849 Ω, Rs=1.25 Ω Figure 75 Measured scattering parameters of varactor R2C2 in terms of magnitudes of S21 and S11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.548 pf, L=0.01 nh, Rp=669 Ω, Rs=1.62 Ω Figure 76 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.748 pf, L=0.01 nh, Rp=849 Ω, Rs=2.57 Ω Figure 77 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 1 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.652pF, L=0.008 nh, Rp=849 Ω, Rs=2.25 Ω Figure 78 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 2 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.54 pf, L=0.008 nh, Rp=849 Ω, Rs=2.25 Ω Figure 79 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 3 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.46 pf, L=0.006nH, Rp=849 Ω, Rs=2.25 Ω Figure 80 Measured scattering parameters of varactor R1C1 in terms of xix

20 magnitudes of S21 and S11 from 0-10V shown in solid curve. The dotted green curve is the matched curved to 4 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.374 pf, L=0.006 nh, Rp=849 Ω, Rs=2.25 Ω Figure 81 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 5 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.33 pf, L=0.006 nh, Rp=849 Ω, Rs=2.25 Ω Figure 82 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 6 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.304 pf, L=0.006 nh, Rp=849 Ω, Rs=1.69 Ω Figure 83 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 7 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.27 pf, L=0.003 nh, Rp=849Ω, Rs=1.69 Ω Figure 84 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 8 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.252 pf, L=0.003 nh, Rp=849 Ω, Rs=1.69 Ω Figure 85 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 9 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.226 pf, L=0.03 nh, Rp=849 Ω, Rs=1.69 Ω Figure 86 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S21 and S11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 10 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.208 pf, L=0.002 nh, Rp=849 Ω, Rs=2.25 Ω Figure 87 Comparison of S21 magnitudes of phase shifters cascaded by 10 single xx

21 units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 88 Comparison of S21 angles of phase shifters cascaded by 10 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 89 Comparison of S21 magnitudes of phase shifters cascaded by 15 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 90 Comparison of S21 magnitudes of phase shifters cascaded by 10 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 91 Comparison of S21 magnitudes of phase shifters cascaded by 25 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V Figure 92 Comparison of S21 angles of phase shifters cascaded by 25 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. There is no obvious phase change as DC bias increases from 7 V to 8 V at all frequencies Figure 93 Comparison of measured S21 angles of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 94 Comparison of measured S21 magnitudes of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 95 Comparison of measured S21 angles of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 96 Comparison of measured S21 magnitudes of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 97 Comparison of measured S21 angles of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 98 Comparison of measured S21 magnitudes of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz Figure 99 Standard Dumbbell-Shaped DGS Unit Top view (All dimensions are xxi

22 in µm) Figure 100 Standard Dumbbell-shaped DGS on CPW. As L increases from 300 µm to 700 µm, inductance increases from 0.42 nh to 0.61 nh, while capacitance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters Figure 101 Standard Dumbbell-shaped DGS on CPW. As G increases from 5 µm to 20 µm, capacitance decreases from pf to pf, while inductance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters Figure 102 Metal Loaded Dumbbell-Shaped DGS Unit Top view (All dimensions are in µm) Figure 103 Metal-Loaded Dumbbell-shaped DGS on CPW. As L increases from 500 µm to 900 µm, inductance increases from 0.21 nh to 0.33 nh, while the capacitance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters Figure 104 Metal-loaded Dumbbell-shaped DGS on CPW. As G increases from 10 µm to 30 µm, capacitance decreases from 0.75 pf to 0.58 pf, while inductance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters Figure 105 Spiral-shaped DGS Top View Figure 106 Magnitudes of S21 parameters of Spiral-shaped DGS units with varying widths W Figure 107 PCB Layout for preliminary DGS study with variations of dumbbell-shaped DGS and spiral-shaped DGS Figure 108 Measured (blue solid) and simulated (green dotted) S21 magnitudes of metal-loaded dumbbell DGS. The ratio between the largest dimension of the DGS L to its guided wavelength λ is Figure 109 Measured (blue soild) and simulated (green dotted) S21 magnitudes of metal-loaded dumbbell DGS. The ratio between the largest dimension of the DGS L to its guided wavelength λ is 1/ Figure 110 Measured (blue soild) and simulated (green dotted) S21 magnitudes of spiral-shaped DGS. The ratio between the largest dimension of the DGS L to xxii

23 its guided wavelength λ is 1/ Figure 111 Measured (blue soild) and simulated (green dotted) S21 magnitudes of cascaded spiral-shaped DGS with enhanced selectivity Figure 112 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V1 in terms of magnitudes of S Figure 113 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V2 in terms of magnitudes of S Figure 114 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V3 in terms of magnitudes of S Figure 115 Planar Spiral-In-Spiral-Out topologies for CPW subwavelength resonators Figure 116 Simulated S21 and S11 magnitudes of 30 Turn SISO resonator with 20 μm spiral traces and 10 μm gaps Figure 117 Top view of planar Spiral-In-Spiral-Out CPW subwavelength resonators with spiral turns Figure 118 Simulated S21 and S11 magnitudes of 30 Turn SISO resonator with 20 μm spiral traces and 10 μm gaps Figure 119 PCB layout for a cascade of four SISO resonators with 12 and 16 spiral turns Figure 120 Simulated (dotted) and measured (solid) S21 and S11 magnitudes of cascaded 12 and 16 Turn SISO resonators shown in Figure Figure 121 Measured S21 phases of a cascade of 20 varactor units from 0-8V Figure 122 Modeled S21 phases of a cascade of 20 varactor units from 0-8V Figure 123 Measured S21 magnitudes of a cascade of 20 varactor units from 0-8V Figure 124 Modeled S21 phases of a cascade of 20 varactor units from 0-8V xxiii

24 LIST OF TABLES Table 1 The ferroelectric and paraelectric phase comparison of ferroelectric material Table 2 Comparison with other tunable ferroelectric filters Table 3 Varactor Fabrication Specifications Table 4 Extracted capacitances of varactors and estimated thickness of BST thin film Table 5 Extracted Electrical Parameters of a varactor device and Quality Factors versus DC bias Table 6 Calculated dielectric and total Quality Factors of Varactors device versus frequency Table 7 Measured S21 magnitudes of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8V at 5, 6, 7, 8, 9 GHz Table 8 Measured S21 angles of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8V at 5, 6, 7, 8, 9 GHz Table 9 Maximum Transmission Loss of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz Table 10 Phase Control Range of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz Table 11 FOM of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz Table 12 Equivalent electrical parameters extracted from schematic model Table 13 Comparison of three variations of the capacitive-loaded sub-wavelength resonators xxiv

25 Table 14 9 sets of device designed on a photo mask set of 4 layers Table 15 Device set with same layer definitions Table 16 Photo Mask Layer Specifications Table 17 Measured S21 magnitudes of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 18 Measured S21 angles of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 19 Measured S21 magnitudes of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 20 Measured S21 angles of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 21 Measured S21 magnitudes of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 22 Measured S21 angles of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz Table 23 Left half: Increasing 100 µm in L results in ~0.1 nh increase in inductance. Right half: Increasing 10 µm in G results in ~0.01 pf decrease in capacitance Table 24 Left half: Increasing 200 µm in L results in ~0.05 nh increase in inductance. Right half: Increasing 10 µm in G results in ~0.01 pf decrease in capacitance Table 25 Comparison between Standard and Metal-loaded Dumbbell DGS unit Table 26 Both C and L increase as W increases. 150 µm increase gives ~0.4 pf capacitance and ~0.05 nh inductance Table 27 Notch performance of each DGS configuration xxv

26 CHAPTER 1 INTRODUCTION 1.1 Motivations The era of wireless communications began when Guglielmo Marconi successfully transmitted radio signals across the Atlantic Ocean in 1901 [1]. From that moment on wireless communications has become one of the fastest growing industries in the world. Each new generation of wireless technologies have brought new features and more complexity. At the same time, the semiconductor industry has provided circuit implementation to communication devices with better performance and reduced sizes and costs. Existing solutions for wireless communications offer reliable voice and video communication, digital picture exchange and internet accessibility with the capability for fast download of music, video clips and news. In addition, new services supported by new standards and high performance electronic devices are announced every day. When a new service is offered, customers would not only like to access different services using only one 1

27 electronic device, but also like to use the same service on all communication devices (personal computer, tablets, and smart phone). Therefore, a major part of the research activity is related to multi-standard solutions for wireless communications. In line with this trend, this work investigates tunable and compact passive devices related to the design and implementation of multi-band RF frontends, exploring the possibility to navigate between different mobile phone standards and different communication devices, and to re-adjust to the environment for optimum performances [2]. 1.2 Objectives Figure 1 Reconfigurable RF frontend with tunable microelectronic components An RF transceiver is incorporated in each communication device that allows wireless communication, which consists of at least a Digital Signal Processing (DSP) unit which performs control and monitoring functions, and a frontend circuit that processes analog signals. A simplified view of a reconfigurable RF frontend is shown in Figure 1. The frontend circuit consist of a receiver and a transmitter. The basic function of a 2

28 receiver is to condition and amplify received signals, to down-convert these high frequency modulated signals to a lower Intermediate Frequency (IF), to demodulate them and convert them into digital signals. The transmitter, on the opposite side, converts digital base-band signals into the analog domain first and modulate them, up-converts them to high frequencies and amplifies them before sending. The reconfigurability of this transceiver is embedded in each of the passive components. Band-pass filters with tunable resonant frequencies can replace the traditional filter-banks and realize the multi-band function with one single unit. Band-stop filters with adjustable resonance and bandwidths can be used to suppress undesired spectrum from the image stations or other unwanted signals at certain frequencies. Tunable matching networks can intelligently compromise the impedance variation due to environmental changes. Voltage-controlled oscillator (VCO) is functioned by an output signal with variable output resonant frequency based on the applied input, which can be realized by varying one of the reactive components (inductance or capacitance). It is extensively used in RF transceiver circuitry such as clock circuitry, Phase Locked Loop (PLL), FM modulator, and Analog-to-Digital Converter (ADC) [3], [4]. Analog phase shifters can offer a continuous linear phase shift with a simple DC bias, which can also be easily implemented with VCO. It has typical applications in analog modulation schemes such as Quadrature Amplitude Modulation (QAM) and Quadrature Phase Shift Keying (QPSK). 3

29 As a result, the reconfigurability of these frontend circuitry roots in the fundamental passive components like capacitors, inductors, and a combination of both in the form of resonators. The simplest and cheapest resonators based on lumped L and C elements have limited applications due to low quality factors. To handle many standards and increasing bandwidth requirements, a large number of filters and switches are used in frontends, making the cost, size, performance, and power consumption critical issues [5]. Subwavelength resonators is featured by its compact sizes and high selectivity, which is also known as a compromise between resonators realized by lumped elements and distributed elements. On the other hand, variable capacitors, also called varactors, can be integrated with subwavelength resonators to realize filters, impedance matching networks, oscillators, phase shifters with tunable parameters. The performance of integrated device can be enhanced by a third degree of freedom called Defected Ground Structure (DGS), which can be easily implemented for transmission line based structures without increasing device area. The objective of this study is to design and characterize thin film ferroelectric varactors, subwavelength resonators, and DGS on Coplanar Waveguide (CPW) Transmission lines as independent projects and ultimately to integrate the three technologies on the same platform that can be employed in reconfigurable RF frontend circuitry. CPW is chosen to load these components because it facilitates shunt and series surface mounting of active and passive devices and its characteristic impedance can easily be tailored by adjusting the distance between two ground pads and 4

30 width of center signal line [6]. 1.3 Contributions This dissertation provides a guidance for designing and optimizing reconfigurable and miniaturized passive RF/microwave components in the form of thin film ferroelectric varactors, capacitive loaded subwavelength resonators, and modified DGS. Metal-Insulator-Metal (MIM) varactors made with thin film Barium Strontium Titanate (BST) material with high tuning ratio, low control voltage, and moderate losses are characterized and implemented as analog phase shifters. Capacitive loading capability is integrated to subwavelength resonators on CPW transmission lines, making it possible for varactor loading and therefore realizing reconfigurable filters. Optimized DGS topologies on CPW transmission lines are presented with superior stopband performance suppressed harmonics. Specifically, four projects are presented to address each technology, Single units of thin film BST MIM varactors are characterized with a capacitive tuning ratio of 4:1 by apply 0-10 V dc bias on with loss tangent under 0.01 up to 40 GHz. An expression for the total quality factor involving parasitic effects is presented and a total quality factor around 10 at 10 GHz is achieved for the single unit varactor without DC bias [7], [8]. Analog phase shifters realized with a cascade of thin film BST MIM varactors are demonstrated with a FOM of 24.5 degrees/db at 8 GHz in an area of 0.45 by 3.3 mm 2 with a maximum DC bias of 8 V [8]. 5

31 Subwavelength resonators are designed with capacitive loading capability, achieving a notch depth of 48 db at 116 MHz within an area of 6.1 by 9.65 cm 2. The ratio between the largest dimensions of structure to its guided wavelength at resonance is less than 0.05, demonstrating its exceptional compactness without sacrificing the performance of band-rejection behavior (Submitted for publication to Microwave and Optical Technology letters in March 2016). Modified spiral-shaped DGS (M-DGS) is proved with spurious-free band-stop performance up to 10 GHz with an exploration on the relationship between inner and outer turns of the spiral topology and their effects on the band-stop behavior. The final testing structure cascaded six M-DGS cells to enhance the band-rejection behavior with a notch depth greater than -50 db at 3.64 GHz within an area of 1.5 by 13 mm 2. Insertion loss is under 3 db with no higher order modes up to 10 GHz [9]. In conclusion, each project addressed above is demonstrated with improved performance for RF/microwave applications. 6

32 1.4 Outline A literature review in the fundamentals and implementations of ferroelectric varators are addressed in Chapter 2. In Chapter 3, attention is given to thin-film BST MIM varactors loaded on CPW transmission lines. By analyzing the performance of single varactor cells, its application is demonstrated in Chapter 4 as analog phase shifters. In Chapter 5, capacitive loading capability is integrated to subwavelength resonators on CPW transmission lines, making it possible to realize compatible and reconfigurable filters. DGS is another degree of freedom explored aiming to enhance filter performance in Chapter 6. Fabrication of all three sets of structures mentioned above, thin film ferroelectric varactors, sub-wavelength resonators, and DGS, involves in designing a set of patterned photomasks for each layer that is to be fabricated for each set of structures. In other words, the same photomask set is designed to adapt to produce all sets of device but each set of device only uses a certain combination of photomasks. The device layout, arrangement, pattern polarity, minimum feature size, and tolerances are presented in Chapter 7, as well as a set of alignment marks that are designed for alignments of all layer combinations. Chapter 8 summarizes the study with future perspectives 7

33 CHAPTER 2 LITERATURE REVIEW Characterization of thin film BST MIM varactors requires an understanding of the tuning mechanism of BST material, the reasons for choosing BST as the tuning dielectric in the thin film form and MIM configuration, the Figure Of Merits (FOM) of varactors, and a knowledge of other popular varactor technologies. This chapter gives an overview of aforementioned area and clarifies certain definitions that are used throughout Chapter Basics of Ferroelectric Material Ferroelectrics are a class of dielectrics with a spontaneous polarization, which can be reversed by an electric field. In parallel plate capacitors the dielectric layer is located in between two electrodes. Unlike conventional dielectrics used in the integrated circuit technology, the relative permittivity (εr) of ferroelectric material is a nonlinear function of the electric field E [10]. An applied voltage results in an orientation of the electric dipoles in the ferroelectric material. After the applied voltage is removed, the polarization P(E) in ferroelectrics is remnant, reversible and saturates with increasing E. 8

34 The P(E) curves of a linear capacitor, and that of a ferroelectric capacitor in the ferroelectric and the paraelectric phases are depicted in Figure 2 [10]. P P P P E E E Figure 2 (a) the P (E) response of a linear capacitor, in (b) a nonlinear capacitor in the ferroelectric phase (with hysteresis) and in (c) a nonlinear capacitor in the paraelectric phase (without hysteresis) As shown in Figure 2 (a), a linear capacitor has a constant εr with varying electric field, since the slope of polarization P(E) remains unaltered. The dielectric constant εr of a nonlinear capacitor reduces with increasing E due to the saturation of the polarization as shown in both ferroelectric (polar) and paraelectric (non-polar) states (Figure 2 (b) and Figure 2 (c)). The hysteresis occur in ferroelectric phase when the non-linear capacitor is operated above the phase transition temperature. When the ferroelectric capacitor is operated below phase transition temperature, the crystal structure changes shape from tetragonal to cubic and the polarization curve is monotonic (paraelectric state). The actual phase transition point, which also affects the εr, is modeled by the Curie-Weiss relation for small-signals at 0 Vdc in the paraelectric phase, 9

35 0C r = T -T Curie where ε0 = F/m is the permittivity of free space, CCurie is the Curie constant, and T0 the Curie-Weiss phase transition temperature. T0 is equal to or a few degrees Celsius less than the Curie temperature Tc [10]. A brief summary of various properties of the two crystal phase structures is given in Table 1 [11]. Table 1 The ferroelectric and paraelectric phase comparison of ferroelectric material. Phase Ferroelectric Paraelectric Temperature Range T<Tc T>Tc Crystal structure Tetragonal Cubic Hysteresis(Pe) Yes No Relative Permittivity εr Higher Higher Tuning ratio η and loss tan δ Higher Lower Applications in Ferroelectric (polar) Phase Ferroelectrics may be in polar (ferroelectric) or non-polar (paraelectric) phases. In ferroelectric phase the P(E) dependence is characterized by a hysteresis loop. The ferroelectric/dielectric properties of the ferroelectrics are associated with the electric dipoles in the crystal. Memory cells are one of the main applications of ferroelectrics in polar (ferroelectric) phase, where the hysteresis loop with two equilibrium states of the spontaneous polarization is used to store binary information in non-volatile memory cells [12] [14]. In spite of the larger dielectric constant, ferroelectrics in polar phase have not 10

36 been considered for applications in tunable microwave devices because most ferroelectrics in polar phase are also piezoelectric whose transformation cause large losses at relatively low microwave frequencies (<10 GHz). Domain wall movements may also cause additional losses at low frequencies [10] Applications in Paraelectric (non-polar) Phase In the paraelectric (non-polar) phase the ferroelectric is characterized by a high dielectric permittivity which depends strongly on temperature, applied external electric field and mechanical stress. The dependence of the permittivity on the applied electric field in paraelectric phase is the main character used in phase, frequency and amplitude agile microwave devices. A variable capacitor using a paraelectric phase ferroelectric as a dielectric, also called a varactor, is the basic building block of these systems. Components like switches, phase shifters, tunable bandpass/bandstop filters etc. based on ferroelectric varactors are the main interest subject in this dissertation and may have advantages over competing technologies in RF/microwave performance, reduced control power consumption, sizes and cost [15] [18]. 2.2 Barium Strontium Titanate The ferroelectric varactors are an emerging technology which relies on the variable permittivity of ferroelectric materials by applying an external electric field. Over the years Barium-Strontium-Titanate BaxSr1 xtio3, or namely BST, has shown promising 11

37 material properties with respect to tuning ratio, dielectric loss, good temperature behavior, size and integration. By mixing BaTiO3 with SrTiO3 a BST composition is created. Bulk single crystalline BaTiO3 has a Tcurie = 388 K, is in the ferroelectric phase at room temperature, and has a high tuning ratio. Solid solutions of BaTiO3 and SrTiO3 shift the transition temperature close to room temperature to tailor the tuning ratio and loss [11], [19]. Figure 3 BST in the ferroelectric phase structure For BST in the ferroelectric phase as shown in Figure 3. The titanium (Ti) is in the center of the octahedron, is shifted relative to the oxygen atoms in the ferroelectric phase and is relatively free to move in the octahedron. When the Ti moved from the center, a permanent dipole moment is formed, and the domains are formed in the ferroelectric [20]. An external electric field changes the direction of the polarity and more domains will be aligned towards the direction of the electric field. The ferroelectric phase induces 12

38 a hysteretic P(E) behavior which is dominated by the movement of domain walls. Hysteresis causes an increase in dielectric loss and a steeper P(E) slope compared to a capacitor in the paraelectric phase, which increases the εr(0vdc) and Cmax. On the other hand, the paraelectric phase exhibits a centro-symmetric cubic crystal structure without any spontaneous polarization nor hysteresis, resulting in a lower dielectric loss and εr [10]. 2.3 Thin Film and Bulk Ferroelectric Material Ferroelectric materials in thin film and bulk ceramic form exhibit very different properties. Bulk BST material (thickness > 1 μm) has much higher unbiased dielectric constant (εr>1000) and the dielectric constant is highly temperature dependent. The ferroelectric behavior and paraelectric behavior of bulk film are clearly identified by setting the operating temperature below or above Curie temperature [21]. On the other hand, thin film BST, of which the thickness is less than 1 μm, has less than 5% temperature dependence, meaning that the dielectric constant is stable and relatively temperature-insensitive. Experimental results have shown that thin film BST has lower the relative permittivity εr, the tuning ratio η, and the phase transition temperature Tcurie, and the phase transition temperature region becomes wider compared to bulk ceramics. A positive side-effect in thin films is that the dielectric constant εr is much less sensitive to temperature and these are therefore preferred in RF applications. A lower maximum εr compared to bulk materials is not important at high frequencies where capacitance values 13

39 are typically small. The tuning ratio of thin films can already be sufficient for low-voltage applications [22]. Thin film BST in this work has an unbiased dielectric constant ranging from , which is more than enough applications in RF/Microwave components that requires a capacitance of a few pico-farads. 2.4 MIM and Planar Ferroelectric Varactors Figure 4 Parallel Plate versus IDC Varactors can be implemented in both interdigitated (IDC) form and parallel plate (MIM) form (Figure 4). IDC is a planar structure which requires only one photo mask process but it requires a higher control voltage and large fringing capacitances that compromises the tunability. Parallel plate configuration, also called MIM configuration, is a more popular choice in spite of its addition bottom electrode because of low control voltages, maximum utilization of film tunability, and very small fringing capacitance [20]. 14

40 2.5 Figure of Merits In RF/microwave applications low losses and low hysteretic effects are preferred. Therefore, thin film ferroelectric capacitors in the paraelectric phase are often desired with the advantages of tuning ratio (up to 4:1 or more), high tuning speed (<1.0 ns), small leakage currents, DC control power, and low temperature dependence. The main challenge is that for most of applications the loss and selectivity requirements are quite strict. For example, RF filters should have very low losses in the pass-band and high selectivity (Q-factor) which is not easy to fulfill, especially for narrow band (bandwidth less than 5%) filters. In the literature the performance of ferroelectric varactors operating at microwave frequencies is assessed by several Figure of Merits. One of the commonly performance parameters for ferroelectric varactors is the dielectric quality factor [19], Q d = 1 tan 2-2 which is inversely related to the total loss tangent tan δ of the ferroelectric material alone at 0 V DC bias. To characterize the varactors at all DC bias voltages, the concept of Commutation Quality Factor (CQF) is introduced [23], h -1 2 CQF = 2-3 h tan tan 1 2 where tan δ1 is the loss tangent at 0 V and tan δ2 is the loss tangent at the bias voltage V, 15

41 and η is the tuning ratio, h (0 V ) ( V ) C C = r dc = r, MAX = MAX 2-4 r dc r, MIN MIN with the maximum capacitance Cmax at 0 Vdc and the minimum capacitance Cmin at the applied DC voltage (typically at near breakdown voltage) [19]. However, there are also losses caused by the interface between electrode and substrate, which can lead to the expression for the total quality factor QT, real Z Q - = = wr C( V ) = tan T T s T imag ZT where ZT is the total impedance of electrical equivalent circuit of the varactor unit which can be expressed in terms of lumped circuit parameters, Rs is the Equivalent Series Resistance (ESR), and tan δt is the total loss tangent of the varactor [19]. 2.6 Other Varactor Technologies Increasing research efforts in a variety of varactor technologies are being made to develop high performance tunable components for RF frontend applications. In this section three contemporary varactor technologies are introduced: micro-machined capacitors (RF-MEMS), semiconductor varactor diodes, and dielectric (ferroelectric) varactors. The concentration is on the trade-off between tuning ratio η and quality factor Q since it is the most-concerning issue for varactor technologies. For each technology, parallel-plate configuration is employed. The capacitance is 16

42 expressed by, C = d 0 r A 2-6 where the relative permittivity of the dielectric material between the two plates εr, the permittivity of free space ε0= F/m, the overlap area between two metal plates A and the thickness of the dielectric material d. The capacitance can be varied in, 1. RF-MEMS capacitors: through a change in the distance h between two electrodes for planar capacitors or effective electrode overlapping area A for comb-like structures, or by a movable dielectric ; 2. Semiconductor varactor diodes: through a change in the depletion layer width h in the semiconductor; 3. Dielectric (ferroelectric) varactors: through a change in dielectric constant εr of the dielectric material. 17

43 2.6.1 RF-MEMS Varactors Figure 5 Cross-section of a planar RF-MEMS electro-static switched capacitor RF-MEMS varactors contain movable parts and can be configured as continuously tunable capacitors (Figure 5) [24]. Such devices are usually large in physical sizes, compared to other devices discussed due to the actuator that moves the mechanical parts and low εr of the dielectric material. One way to realize a RF MEMS varactor is to use the electrostatic actuation method as shown in Figure 5, which is based on the mechanical stability of parallel-plate capacitors under an electrostatic force [25]. In the equivalent circuit model, Re is the resistance of the electrode and CMEMS is the MEMS capacitance. Using the fact that the top plate can be moved to a gap height hmems =2g/3 before it collapses on the bottom plate. The tuning ratio can be written as, C h= C MEMS, MAX MEMS, MIN = A C 2 g / 3 A C f g f

44 where Cf if the fringing-field and parasitic capacitance to ground of the MEMS structure and input/output transmission line [24]. There is no fundamental difference in gap tuning, area tuning and movable dielectric tuning, since the dielectric layer (air or vacuum) is basically lossless and the electrode losses dominant performance of unpackaged planar RF-MEMS capacitively switched devices. The dielectric losses for common substrates such as SiO2 and Si3N4 are negligible (tanδ<0.003). Therefore the losses mainly come from the resistive electrodes, whereas in other discussed technologies the inherent losses often dominate over the electrode losses. Parasitic effects, such as coupling to the substrate, can be reduced by isolating substrates. For a best estimate these effects are neglected and the quality factor as a function of η, Q(η) can be expressed as, Q -1 = w R e C MEMS,MAX = w R e C MEMS,MIN C MEMS,MAX C MEMS,MIN = w R e C MEMS,MIN h 2-8 where ω is the angular frequency, Re is the resistance of the electrode, CMEMS,MAX and CMEMS,MIN are the maximum and minimum MEMS capacitance, and tuning ratio η= CMEMS,MAX/ CMEMS,MIN [26] Semiconductor Varactor Diodes A varactor diode is a P-N junction diode that changes its capacitance through the variation of the diode depletion layer width with applied DC voltage (Figure 6). The 19

45 diode is operated under reverse bias conditions and this gives rise to three regions. At either end of the diode are the P and N regions where current can be conducted. However around the junction is the depletion region where no current carriers are available. As a result, current can be carried in the P and N regions, but the depletion region acts like an insulator. In the case of the varactor diode, it is possible to increase and decrease the width of the depletion region by changing the level of the reverse bias. This has the effect analogous to changing the distance between the plates of the capacitor. Figure 6 Cross-section of a Schottky varactor diode and the equivalent circuit model As shown in Figure 6, the depletion layer hvc is controlled by the electric field and determines the capacitance value. To explore the relationship between Q and η for semiconductor diode, following equations from [27] are used for calculations. The equivalent lumped-element model is shown on the right of Figure 6. The interconnect losses and electrode losses are given by Re, the depletion region capacitance of the p-n 20

46 junction by Cvc and the resistance of the semiconductor by Rsemi. Therefore the ratio between maximum and minimum depletion layer width also equals to the tuning ratio, C C h = max = vc,max 2-9 min h h vc,min Where the minimum depletion layer width, h vc,min 2 2kT qn q 0 s = ( bi - ) 2-10 where εs is the relative permittivity of the semiconductor, q= C, N is the doping concentration in cm -3, the built-in voltage ϕbi=0.75, the Boltzman constant κ= J/K, and the temperature T=300 K [27]. The maximum depletion layer, h 2 2kT = ( V - ) qn q 0 s vc,max bi r,max 2-11 where Vr,max is the maximum reverse breakdown voltage calculated by, V r,max, Si E h E = = 2 2qN 2 c, vc, Si vc,max 0 r, Si c, vc, Si 2-12 where εr,si=11.7 in case of uniformly doped Si[27]. The maximum dielectric field at breakdown in Si for a uniform doping concentration. can be described as, 21

47 E c, vc, Si = 1 N 1 log Generally, a heavily doped single-sided (hyper-abrupt) varactor diode with high carrier concentration is employed to support a large change in depletion-width leading to a higher Q and η. To achieve a higher breakdown voltage, low carrier concentration is required and thus a large-series resistance, resulting in a low Q due to lowly doped semiconductor, hvc,max 1 0 r w semi vc,max w( ( ) ) h h vc,min vc,min - Q = R C = x dx 2-15 where Cvc,max is the maximum capacitance of the varactor diode at hvc,min, Rsemi is the resistance of the semiconductor which is obtained by integrating the resistivity ρ(x) from hvc,min to hvc, max. In summary, increasing the dopant concentration increases the quality factor, but lowers the breakdown voltage and tuning range. If the dopant concentration is very high, tunneling can occur at the junction, further reducing the tuning range [28] Ferroelectric Varactors Ferroelectrics are a class of dielectrics with a spontaneous polarization which can be reversed in an electric field. Unlike conventional dielectrics used in the integrated circuit technology, the relative permittivity εr of ferroelectric material can be changed when a DC voltage is applied to the capacitor. Therefore the tuning ratio η can be 22

48 expressed by, h C C max = = min r,max r,min 2-16 Ferroelectric varactors are smallest in physical sizes because of its high permittivity εr ( ) compared with the permittivity of semiconductor materials (~12). Figure 7 Cross-section of a ferroelectric varactor and the equivalent circuit model Under a fixed dc bias, the varactor device can be modeled as a conventional parallel plate capacitor using lumped elements as shown in Figure 7, which includes the capacitance Cfe of the dielectric material between two parallel plate, a shunt resistor Rp which represents the dielectric loss of the ferroelectric material, a series resistor Rs which represents the parasitic conductor and interconnect/electrode resistance, and an series inductor Ls which represents the parasitic conductor inductance. 23

49 Figure 8 Parallel plate equivalent schematic model For the best estimation result, parasitic coupling Ls and dielectric loss Rp are eliminated as shown in Figure 8, leading to the total impedance and the Q factor as, Q wr C - 1 = 2-17 s max The mathematical approximation loosely follows the measurement due to the thin film processing variation and operating conditions, which is not discussed here. Data on thin film ferroelectrics, using different deposition techniques and substrates, which have resulted in a high tunability and low loss for BaxSr1-xTiO3 at 1-10 GHz [29] [33]. The Q factor differs from with maximum tuning ratio η between 2 and Comparison and Discussion The trade-off between losses and tuning ratio of three varactor technologies for RF/Microwave applications has been discussed. All technologies show an increased loss for higher tuning capability. The above discussion excludes the packaging and 24

50 interconnects effects on the performance, which must be optimized for each of the technologies. In general, RF MEMS switches are preferred at millimeter-wave frequencies since they provide low loss and high linearity. However, their switching speed, which is typically in the microsecond range, does not allow them to be implemented for applications that require fast re-configurability [34] [36]. Semiconductor varactor diodes are featured for fast tuning (in nanoseconds) and low-loss levels at frequencies lower than 5 GHz [37], [38]. However, the increase of their series resistance, resulting in high insertion loss, limits their performance at higher frequencies. At present, for continuous, moderate tuning performance (η=1-3) at RF frequencies, highly-doped GaAs varactor diodes could offer the best performance [27]. Compared to these technologies above, ferroelectric varactors provide switching speed in the nanosecond range and low loss at high frequencies [16], [39]. Thin film BST-on-sapphire technology enables the fabrication of low-loss planar capacitors, simplifies the fabrication process, and results in lower metal losses [33], [40], [41]. In addition, the innovative capacitor structure allows the varactor to operate at low bias voltages [19], [42]. By selecting different frequencies with analog-switching low-voltages, ferroelectric filters provide a low-cost solution, with a small size, low power consumption, a simple fabrication process and a sub-microsecond switching speed at radio frequencies. Table 2 gives a comparison of existing tunable ferroelectric filters using thin film 25

51 BST varactors. It can be seen that these filters all have low insertion loss (<10 db), highest tuning range of 20%, and at least 30 V dc bias for microwave application (>10 GHz). Table 2 Comparison with other tunable ferroelectric filters References Frequency(GHz) Insertion Loss(dB) Tuning Bias(V) [43] at 26K 10% 320 [44] % 30 [45] % 100 [15] % 30 [46] % 13 [17] % Ferroelectric Varactors in This Work Ferroelectric varactors operate on the variable permittivity of ferroelectric materials by applying an external electric field. Among the various choices for ferroelectric material, BST is featured by a high permittivity, adequate tunability, low dielectric loss, and low leakage current, which are ideal for compact passive tunable devices. On the other hand, BST can be utilized in several forms like ceramic thick-film/crystal thin-film and parallel plate (MIM)/planar (IDC), which can be flexibly adapted to applications. Thin film BST MIM varactors discussed in the next two chapters are designed on CPW transmission lines which is featured by its low control voltage (<10 V), high tuning ratio (~4:1), moderate loss (tanδ < 0.01), and good temperature stability. 26

52 CHAPTER 3 CHARACTERIZATION OF THIN FILM BST VARACTORS In this chapter single-unit thin-film BST MIM varactors designed with an unbiased capacitance of 0.8 pf are characterized. A tuning ratio of 4:1 is achieved by apply 0-10 V DC bias with loss tangent under 0.01 up to 40 GHz calculated from the extracted electrical parameters from an equivalent schematic model. A dielectric quality factor of 40 is achieved at 10 GHz. 3.1 Structure and Operation The building block of the phase shifter is based on the single unit shunt varactor device. The single unit structure has a layer of thin film BST material sandwiched between two metal layers. As shown in Figure 9, the top metal layer adopts CPW transmission line configuration where the middle part of the horizontal CPW signal line is tapered to form a tiny effective overlapping area with the vertical shunt line in the bottom metal layer. The bottom metal layer has two identical CPW ground pads as the ones in the top metal layer but are shorted by a tapered vertical shunt line. 27

53 Figure 9 3D view of the single unit varactor device The top view of the single unit shunt varactor is shown in Figure 10, the cell area is 450 µm by 500 µm. The CPW Ground-Signal-Ground dimensions in top metal layer are 150 µm/50 µm/150 µm. The spacing between CPW signal line and two ground pads is 50µm. Previous publication has proved that the voltage dependent capacitance C(V) can be approximated using the standard parallel plate capacitance formula [16], 0 r( ) C( V ) = V A 3-1 d where ε0 is the permittivity of free space, εr(v) is the relative dielectric constant of the ferroelectric BST thin film at dc bias V. A is the effective overlapping area of the varactor, and d is the thickness of the ferroelectric BST thin film. Because of the high dielectric constant of BST material, the overlapping area A is chosen to be 5 μm by 5μm, 28

54 resulting in an overall effective capacitance of 0.8 pf when the thin film thickness is around 0.2 μm and BST permittivity of 650 at 0 V dc bias. Figure 10 Top view the parallel-plate single unit varactor device. Dimensions are in μm When there is no bias voltage on the CPW signal line, the effective capacitance of the varactor device will be at the highest, resulting in the signal shunted to the ground instead of going into the output port. As the dc bias voltage increases, the capacitance of the varactor is decreased, allowing more signal to pass through from the input port to the output port. This behavior also causes a change in the transmission phase. When multiple single units are cascaded, the amount of phase shift is expected to reach more than 360 degrees without significant increase in transmission loss between 5 and 10 GHz, resulting in a voltage-controlled analog phase shifter, which is discussed in Chapter 4. 29

55 3.2 Equivalent Schematic Model Figure 11 Equivalent schematic model for shunt varactor unit cell The equivalent schematic model for the varactor single unit is shown in Figure 11, the signal line connects the port 1 (input) to port 2 (output), represented by two CPW transmission lines in between, with the varactor unit modeled as four lumped electrical parameters shunted to the ground. The capacitor C(V) models the effective capacitance of the varactor calculated using Equation 3-1. The shunt resistor Rp(V) is in parallel with C to model the leakage conductance of the varactor, R p 2 fc( V ) tan -1 = 3-2 where f is the operating frequency and tanδ is the loss tangent of the BST thin film. The series resistor Rs and the inductance of the line Ls model the parasitic effects can be calculated as, 30

56 R s l = 3-3 wt where σ is the conductivity of the bottom metal electrode, w is the width of the conductor, l is the length of the line shunting to ground, and t is the thickness of the conductor. The expression for the parasitic inductance, L s = Z0 2 l sin( ) 2 f 3-4 g where Z0 is the characteristic impedance of the CPW transmission line, f is the operating frequency, λg is the guided wavelength. An expression for total quality factor is obtained by taking into account all four electrical parameters mentioned above, Q T 2 Q p 1 wls 2 1 Q p wc p = 3-5 R Rs 1 Q p 2 p Where Qp=ωRpCp is the quality factor of the dielectric material alone. This equation is obtained from the process detailed in section Quality Factor Formulation Equation 3-5, taking account into all four electrical parameters in the equivalent schematic model, gives a more accurate estimation on the Quality Factor of the varactor device over a wide range of frequencies. The derivation of Equation 3-5 is presented in this section by converting the equivalent circuit into a series configuration. 31

57 3.3.1 Step 1: Parallel to Series Conversion A parallel RC circuit can be forced to have the same impedance as the series RC circuit, at lease at one frequency as shown in Figure 12. This conversion is valid for only a narrow frequency range, which is the limitation of this method. Figure 12 Parallel RC to series RC conversion The impedance of the parallel circuit is 1 R jwc Z Z R jx p p RP p = = = s = s _ EQ s _ EQ 1 R 1 jwc prp p jwc p 3-6 The dielectric quality factor Qp for a parallel RC circuit is, Q wc p wc p = = = wc R G 1 R p p p p The equivalent series resistance and reactance in terms of Qp,

58 R X R = p s _ EQ 2 1 Qp X Q = = P p s _ EQ 2 wcs _ EQ 1 Qp Step 2: Equivalent Schematic Circuit of the Varactors. The schematic of the parallel-plate varactor device shown in Figure 13 left is matched to the equivalent schematic shown in Figure 13 right using parallel RC to series RC transformation. The modified equivalent schematic is a series RLC circuit. The value of the new total series resistance is the sum of the matched resistance Rs_EQ from the capacitance and the parasitic resistance Rs, R R = R R = R 3-9 p ST s s_ EQ s 2 1 Qp Figure 13 Modified equivalent schematic using parallel RC to series RC transformation 33

59 3.3.3 Step 3: Calculation of Circuit Q An approximate value for total quality factor QT can be found by calculating the impedance of the modified series RLC equivalent schematic, 1 R p 1 ZT = RST jwls = Rs j wl 2 s - jwc s _ EQ 1 Q p wc s _ EQ 3-10 The total quality factor QT for the modified circuit can be expressed in terms of Rs, Rp, Ls, Cp, and Q p=ωr pc p, Q T X Q Q wl wl wl = = = R R R p R R s 2 s R 1 Q 1 Q 1 p P p p 1 s - s 2 s 2 wcs _ EQ 1 Qp 1 Qp wc p p p 2 s 2 p Qp Fabrication Table 3 Varactor Fabrication Specifications Layer Material Thickness Method Layer 4 Passivation Si3N4 250 nm Layer 3 Metal2 Ti(20nm)/Pt/ Au nm E beam evaporation followed by standard photolithography process Layer 2 Dielectric BST (patterned) 250 nm Pulsed Laser Deposition with KrF beam followed by etching. Layer 1 Metal1 Ti(20 nm)/au/pt nm E beam evaporation followed by standard photolithography process Substrate Sapphire/HR Silicon Based on the EM topology and the layer-by-layer material specifications 34

60 illustrated in Table 3, the fabrication process started with a bottom metal stack of a 500 nm of Ti//Au/Pt deposition on Sapphire substrate. This metal contact stack was fabricated using standard positive photoresist liftoff photolithography and e-beam evaporation of the metal stack. A layer of BaxSr1-xTiO3 thin-film was deposited on the entire surface by PLD method using a KrF excimer laser (248 nm wavelength) and annealed at 600 ºC with oxygen pressure of 500 mt for 30 minutes in the chamber. The thickness of BST layer is about 250 nm. After the BST deposition, the top metal layer of 500 nm of Ti/Pt/Au was patterned using the same liftoff technique and deposited using e-beam evaporation. 3.5 Measurements On-wafer measurements are performed on each Device Under Test (DUT) using Agilent 8720 Vector Network Analyzer (VNA) with a frequency sweep up to 40 GHz and at least 800 points data are collected each sweep (Figure 14). All DUT on the mask set are designed with CPW configuration so that they can be probed using a pair of planar GSG microprobes (Figure 15). Calibration is done manually using standard Short-Open-Load-Through scheme with a calibration substrate. Bias Tee is installed on one of the ports of VNA to provide desired DC bias on the varactor device. 35

61 Figure 14 On-wafer measurement on ferroelectric varactors by Vector Network Analyzer with a set of GSG microprobes Figure 15 On-wafer measurement setup with GSG microprobes Data is collected in terms of 2-port scattering parameters defined as Sij where subscript j indicates incident port and i indicates receiving port. Specifically, S11 is the input reflection coefficient, S21 is the forward transmission coefficient, S12 is the reverse transmission coefficient and S22 is the output reflection coefficient when both input port 1 is considered as input port and port 2 is the output port. 36

62 Figure 16 2-port scattering parameters obtained from VNA measurements 3.6 Results and Discussion Varactor Measurements without DC Bias and Thin Film Thickness Estimation Because of the non-uniformity of the BST thin film, thicknesses at different locations on the wafer can be different (Figure 17). To proceed with further analysis, device that has a thin film thickness closest to the designed value of 0.2 um should be chosen. Nine identical varactor device are measured at zero volts on the same wafer and named after their locations. Therefore, thin film thicknesses of each device can be estimated using the extracted capacitances at 0 V DC bias, C A A 0V = 0 r 0V d = 0 r 0V d C 0V 3-12 Where C(0V) is the extracted capacitance of each device without DC bias, ε0 is the permittivity of free space, εr(0v)=650 is the relative dielectric constant of the ferroelectric BST thin film at 0 V DC bias. A=25 μm 2 is the effective overlapping area of the varactor, and d is the estimated thickness of the ferroelectric BST thin-film. 37

63 UDBST115 Figure 17 Locations of the measured varactors on 4 inch sapphire wafer named as UDBST115 Extracted zero bias capacitances of all 9 varactors and their matched frequency response are shown in Figure 18 and summarized in Table 4 with corresponding estimated thicknesses calculated using Equation It is not difficult to see that device at center (R2C2) has the smallest capacitance hence the thickest ferroelectric film among all nine device, while device at corners (R3C1, R3C1, R1C3, R3C3) have thinner films than all other device. As a result, device at the corner, which have an estimated thin film thickness of around um, are closest to the designed value of 0.8 pf. Following analysis therefore is conducted using measured results from varactor device R1C1, which has a 0 V capacitance of pf and estimated thin film thickness of um (Figure 19). All other extracted electrical parameters matched by the schematic model at 0 V of each device are shown in Figure in Appendix A. 38

64 Figure 18 Measured scattering parameters of 9 varactors at each location on wafer UDBST115 from 0-40 GHz at 0 V bias (solid curve), matched with schematic model shown in dotted curve. Extracted equivalent capacitances Cp of varactor device R1C1 (corner), R1C2 (top), R2C2 (center), R3C3 (corner) are: pf (C1), pf (C3), pf (C4), pf (C2). Table 4 Extracted capacitances of varactors and estimated thickness of BST thin film Device Location Capacitance Estimated Thickness (pf) (um) R3C3/R1C3/R1C R3C R1C2/R3C2/R2C1R2C R2C

65 Figure 19 Comparison between electromagnetic model simulation (blue dashed curve) and measurements of varactor device R1C1 (red solid curve), matched by schematic model (green dotted curve) with C=0.748 pf, L=0.01 nh, R p=849 Ω, R s=2.57 Ω Varactor Measurement with DC Bias The measurement of nine varactor device without DC bias concludes that device R1C1 has a thin film thickness of μm and extracted capacitance of pf, which best meets the designed parameters of 0.2 μm thin film thickness and 0.8 pf capacitance. This is also verified by a good agreement between electromagnetic simulation results and measurement, and matched by the schematic model in Figure 11. In this section, measurements of device R1C1 with DC bias from 0-10 V is presented Figure Insertion loss at 10 GHz are reduced from around -4 db to around -0.6 db (Figure 20) while the transmission phase angle is reduced from around 60 40

66 degrees to around 26 degrees (Figure 21) as the dc bias is increased from 0 to 10 V. The C-V characteristics of device R1C1 is also shown in Figure 24. Estimated dielectric constant is also plotted and shows a tuning from 650 (0V) to 180 (8V). Figure 20 S 21 magnitudes of varactor device R1C1 on wafer UDBST115 from 0-40 GHz. The insertion loss at 10 GHz is decreased from -4 db to 0.6 db from 0-10 V. Figure 21 S 21 phase of varactor device R1C1 on wafer UDBST115 from 0-40 GHz. The phase shifted from degrees to degrees at 10 GHz. 41

67 Figure 22 S 11 magnitudes of varactor device R1C1 on wafer UDBST115 from 0-40 GHz. Figure 23 S 11 phase of varactor device R1C1 at 0-8 V on wafer UDBST115 from 0-40 GHz. 42

68 C-V Plot of a single unit varactor 1.4 Er(V) C(V) <pf> C(V) Relative permitivitty DC Bias (V) 0 Figure 24 Extracted capacitance and estimated dielectric constant versus bias voltage Quality Factor Versus DC Bias The dielectric quality factors Qp and total quality factors Qt are calculated using Equation 3-7 and Equation 3-11 using the extracted electrical parameters of varactor R1C1 measured at 0-10 V DC tabulated in Table 4. As shown in Table 5 and Figure 25, Qp is much higher than Qt of the device at all voltage levels, which are predictable since metallic losses are not considered in Qp calculations. By taking into account the parasitic inductance and resistance, the total quality factor Qt is worsened. As the DC bias increases, the dielectric Quality Factor is worsened by more than 50% while the total Quality Factor is maintained above

69 Dielectric Quality Factor Qp Qt Voltage(V) Total Quality Factor Figure 25 Comparison between Total Quality Factor and dielectric Quality Factor versus DC bias Table 5 Extracted Electrical Parameters of a varactor device and Quality Factors versus DC bias Q Energy Stored Energy Dissipated Q Voltage C p R s L s R p GHz (Q Nominator) (Q Denominator) GHz (V) (pf) (Ω) (nh) (Ω) Quality Factor Versus Frequency The Quality Factors can also be analyzed as a function of frequency shown in Table 6 and Figure 28. As frequency increases, parasitic inductance Ls begins to take 44

70 effect and lower total quality factor Qt. By involving all four electrical components into Quality Factor calculation in Equation 3-11, the results became more realistic at higher frequencies. To examine the quality factor of BST thin film alone, Qp calculated using Equation 3-7 at each voltage level is plotted with loss-tangent in Figure 26. Table 6 Calculated dielectric and total Quality Factors of Varactors device versus frequency Frequency (GHz) Q p Energy Stored (Q Numerator) Energy Dissipated (Q Denominator) Qt

71 Quality Factor Frequency (GHz) Qp Qt Figure 26 Comparison between total Quality Factor Qt and dielectric Quality Factor Q p versus frequency Dielectric Quality Factor Dielectric Q Factor Loss Tangent at 10GHz Voltage(V) Loss Tangent Figure 27 Dielectric Quality Factor Q p and loss tangent of the varactor device from 0-10 V. 46

72 CHAPTER 4 VARACTOR BASED ANALOG PHASE SHIFTERS Beam-steering antennas are the ideal solution for collision avoidance radars, traffic control, and smart base station antennas for cellular communication [18]. Beam-steering is commonly achieved by using phased arrays, where phase shifters are used to control the relative phase of the main-beam [47]. An ideal analog phase shifter changes the insertion phase (phase of S21) of a network while keeping the insertion gain (magnitude of S21) constant. The requirements of an analog phase shifter can be summarized as large phase-control range (360⁰), low insertion loss (or even gain), low power consumption, occupying small area, and easiness to control. Technologies available for the phase shifters such as PIN diodes, GaAs varactors, or field-effect transistor (FET) switches which suffer from relatively high power consumption and losses especially at millimeter wave frequencies [48][49]. On the other hand, phase shifters based on ferroelectric varactors offer significant reduction in the power consumption and high speed control. By simply applying a DC bias on the varactors, the change in capacitance can result in a phase shift. 47

73 Ferroelectric materials, such as BST, have a dielectric permittivity that is a function of the electric field. Tunable microwave device such as electronically tunable impedance matching networks, delay lines, filters and phase shifters can be realized due to this property. This chapter presents a loaded line phase shifter using ferroelectric varactors as tunable loading element to periodically load a CPW transmission line, allowing for phase velocity and phase shift to be continuously varied. S-parameter measurements are used to evaluate the performance of the thin film ferroelectric varactor in terms of its capacitance-voltage relationship. At 8-V dc-biasing voltage, the varactor-loaded phase shifter exhibits a differential phase shift of 360 degrees with an insertion loss of -12 db. This chapter details the process for evaluation on the performance of a cascade of 10, 15, 20, 25 varactor cells for phase shifter applications. Section 4.1 presents the methodology as well as the characterization of 20-section phase shifter. Comparison between all four variations in terms of the maximum transmission loss, phase control range, and FOM is given in section 4.2, 4.3, and 4.4. A mathematical model using cascaded ABCD parameters is developed in section 4.5 to characterize the design. Section 4.6 concludes the chapter. 4.1 Methodology A CPW line with an unloaded characteristic impedance of 50Ω is used as the base transmission line. The line has a 50 µm wide center signal conductor and 50 µm gaps between the signal line and ground pads (Figure 28). Each varactor has an effective 48

74 overlapping area of 5 by 5 µm 2 between the center tapered signal conductor on the top electrode (M1) and a shunt line on the bottom electrode (M2). This line is then loaded with 10, 15, 20, 25 varactor units, spaced 200 µm apart to form a distributed loaded transmission line of 2.245, 3.3, 4.3, 5.5 mm lengths (Figure 29). Each device is replicated by five times at different locations on the same mask and fabricated on a 4 inch diameter Sapphire substrate with the same process explained in Chapter 3. Figure 28 Top view of single varactor units. Dimensions are labeled in μm. Figure 29 Top and 3D view of analog phase shifter cascaded by 10 varactor units. Dimensions are labeled in μm. 49

75 Figure 30 and Figure 31 show the measured S21 phases and magnitudes for the 20-section device, respectively. Maximum transmission losses, phase control range and FOM can be computed using Equation 4-5, 4-6, and 4-7 from extracted data from measurements at 5, 6, 7, 8, 9 GHz (Tabulated in Table 7 and 8, and plotted in Figure 32, 33, and 34), Maximum Transmission Loss ( f ) = S (0 V, f ) - S (8 V, f ) db 21 0 Phase Control Range ( f ) = S (0 V, f ) - S (8 V, f ) Phase Control Range ( f0) FOM = degree / db 4-7 Maximum Transmission Loss ( f ) 0 It was found that the differential phase shift gradually increases as the voltage increases from 0 V to 8 V, which is due to the tunability of BST films variation with applied dc field. At the same time, the insertion loss also increases as DC bias increases. The same process is repeated for other phase shifters cascade by 10, 15, and 25 varactor units (Appendix B). db 50

76 Figure 30 Comparison of measured S 21 angles of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. Figure 31 Comparison of measured S 21 magnitudes of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. 51

77 Phase Shifter With 20 Cascaded Varactors S21 Magnitude (db) Control Voltage S21 at 5GHz S21 at 6GHz S21 at 7GHz S21 at 8GHz S21 at 9GHz Figure 32 Comparison of S 21 magnitudes of phase shifters cascaded by 20 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. Phase Shifter With 20 Cascaded Varactors S21 Phase (degree) Control Voltage <S21 at 5GHz <S21 at 6GHz <S21 at 7GHz <S21 at 8GHz <S21 at 9GHz Figure 33 Comparison of S 21 angles of phase shifters cascaded by 20 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. 52

78 Table 7 Measured S 21 magnitudes of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8V at 5, 6, 7, 8, 9 GHz. SP20 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz Voltage S 21 S 21 S 21 S 21 S Δ S Table 8 Measured S 21 angles of the phase shifter cascaded by 20 varactor units as the DC bias increases from 0 to 8V at 5, 6, 7, 8, 9 GHz. SP20 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz Voltage <S21 <S21 <S21 <S21 <S Δ<S FOM

79 4.2 Maximum Transmission Loss of Varactor-based Phase Shifters The maximum transmission loss at f0 for each device shown in Table 9 are calculated using Equation 4-7. Table 9 Maximum Transmission Loss of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz ΔS 21(dB) 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz SP SP SP SP At each frequency, the 10-unit device has the least transmission loss (5-7 db from 5-9 GHz) and the increase in transmission losses is more significant between 20 and 25 unit device than between 10/15 and 15/20 unit device. As the number of cascaded units increases, transmission losses increase but each device has a relative stable gain (under 5 db in the frequency range of 5-9 GHz). As shown in Figure 34, transmission losses are slightly higher in the frequency range 8-9 GHz than transmission losses between 5 and 8 GHz for all four device. Specially, the 25-unit device has a higher transmission loss than the other three device between 7-9 GHz. Change in S21 amplitudes are within only 2 db for 10, 15, and 20 unit device from 6-8 GHz. For all four device, transmission losses are less frequency dependent at higher frequencies. 54

80 S21 Magnitude (db) Maximum Transmission Loss Frequency (GHz) 25 Section 20 Section 15 Section 10 Section Figure 34 Comparison of maximum transmission loss in terms of the differences between S 21 magnitudes at highest bias voltage (8 V) and S 21 magnitudes at 0 volt bias for phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz. 4.3 Phase Control Range of Varactor-based Phase Shifters The differential phase shift at frequency f0 for each device shown in Table 10 are obtained by calculating the difference between S21 angles at 0 V and S21 angles at 8 V (Equation 4-8). Table 10 Phase Control Range of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz <S21(degree) 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz SP SP SP SP At each frequency, the 10-unit device has the smallest phase shift ( ⁰ from 5-9 GHz). The phase shift increases as the number of cascaded units increases from 5 to 9 GHz. Phase change of each device are more significant at higher frequencies (7-9 GHz). 55

81 A phase shift of 360⁰ can be reached for 25 unit device at around 8.5 GHz as shown in Figure Phase Control Range S21 Angle (degree) Section 20 Section 15 Section 10 Section Frequency (GHz) Figure 35 Comparison of phase control range in terms of the differences between S 21 angles at highest bias voltage (8 V) and S 21 magnitudes at 0 V bias for phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz. 4.4 FOM of Varactor-based Phase Shifters The FOM at f0 for phase shifter in Table 11 are calculated by taking the ratio between the phase control range and maximum transmission loss (Equation 4-9). As shown in Figure 36, FOM of each device is higher at 8 and 9 GHz than that between 5-7 GHz. The FOM of 25-unit device is comparable to 15-unit device at lower frequencies but even lower at 8 and 9GHz because of its high transmission loss at higher frequencies. In consequence, FOM of 20-unit device is the highest among all four device at all measured frequencies. The highest FOM of around 25 degree/db is measured at 8 GHz for the 20-unit device. 56

82 Table 11 FOM of 10,15,20,25 unit varactors at 5, 6, 7, 8, 9 GHz FOM(degree/dB) 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz SP SP SP SP Figure Of Merit FOM (degree/db) Section 20 Section 15 Section 10 Section Frequency (GHz) Figure 36 Comparison of Figure-Of-Merit in terms of the phase shifters cascaded by 10, 15, 20, 25 single units in a frequency range between 5 and 9 GHz. 4.5 Mathematical Modeling Figure 37 Modeling by ABCD matrix Transmission line loaded reactive components can be modeled by dividing the structure into N cells and cascading ABCD matrices for each cell. To model a phase 57

83 shifter with a cascade of N varactors, each cell is modeled as another cascade of two CPW transmission line sections and a varactor section in between as shown in Figure ABCD Matrix of a Single Varactor Section The varactor section is modeled as a shunt impedance based on the equivalent electrical model discussed in chapter 3 [50], 1 0 ABCD_Varactor= 1/ Z T Where ZT is the total impedance of the varactor unit calculated by Equation 3-10, consisting all four circuit parameters C(V), Rp, Rs, and Ls which can be calculated using Equation.3-1 through Equation ABCD Matrix of a CPW Section The CPW section for varactor loading consists of a double-layered dielectric substrate with conductors on the top surface. The conductors formed a center signal strip separated by a narrow gap from two ground planes on either side. The dimensions of the center signa strip, the gap between the center strip and ground planes, the thickness and permittivity of the dielectric substrate determined the effective dielectric constant, characteristic impedance and attenuation constant of the line and is modeled as [51], cosh(( +j )L) Z0sinh(( +j )L) ABCD_CPW= c(1/z )sinh(( +j )L) cosh(( +j )L) where L is the length of the transmission line section, α is the attenuation constant and β 58

84 phase constant which are expressed as, = a +a = 0 (Lossless) 4-10 c d = 2 f eff c 4-11 In this analysis, conformal mapping methods are used to obtain the effective permittivity εeff of the CPW section [6]. Resulting effective permittivity is expressed with elliptical integrals [6], eff ( -1) K ( k ) K ( k ) ( - ) K ( k ) K ( k ) 2 K ( k ') K ( k ') 2 K ( k ') K ( k ') r1 1 0 r 2 r1 0 2 = Where the k parameters are function of CPW geometry, k 0 = s s g 4-13 k 1 sinh( s / 2 h1 ) = sinh( ( s g) / 2 h ) k 2 sinh( s / 2 h2 ) = sinh( ( s g) / 2 h ) k = 1- k 4-16 ' 2 n n ABCD Matrix of N-cell Phase Shifter Structure Therefore each cell shown in Figure 44 is modeled as, ABCD_Cell=ABCD_CPW ABCD_Varactor ABCD_CPW 4-16 As a result, an N-cell phase shifter structure can be modeled as, 59

85 ABCD_ N = ABCD_Cell n 4-17 Once the ABCD_N is obtained, a simple transformation from ABCD parameters to scattering parameters is used to generate modelled results that can be compared with the measurement. Figure 38 Modeled and measured S 21 phases of 20-section phase shifter Figure 39 Modeled and measured S 21 magnitudes of 20-section phase shifter This model is realized with Matlab and the comparison between the modelled S21 results and measurements of the 20-section phase shifter are shown in Figure The 60

86 Matlab script that generates the modelled results for 10, 15, and 25 sectioned phase shifters is attached in Appendix E. 4.6 Conclusion In this study single varactor units are demonstrated to be a potential candidate for continuous analog phase shifter application. A tuning ratio of 4:1 is achieved by apply 0-10 V dc bias with a loss tangent under 0.01 up to 40 GHz calculated from the extracted electrical parameters. An expression for the total quality factor involving parasitic effects is presented and the single cell varactor gives a total quality factor from around 10 to 6.4 under 0-10 V. Phase shifters cascaded by 10, 15, 20, 25 varactor units are realized with FOM of degrees/db in an area of by 0.4 mm 2 with a maximum DC bias of 8 V in the frequency range of 7-9 GHz. A mathematical model is also developed to validate the phase shifter design. 61

87 CHAPTER 5 CAPACITIVE LOADED SUBWAVELENGTH RESONATORS Compactness is one key driving force in designing electronic components for modern RF frontend applications. Various sub-wavelength resonators have been explored with the ratio between the largest dimensions of the device to their free space wavelengths less than 1/10 [52] [55]. One popular choice is to use spiral-shaped resonators due to the fact that spiral-shaped topology can achieve exceptional performance with a much smaller electrical length than that of other sub-wavelength topologies [56] [59]. Capacitive loading capability can also be easily integrated into spiral-shaped resonators by modifying the spiral topology or coupling with other unit cells, but this always requires increasing the circuit size [60], [61]. Another way of incorporating capacitive loading capability is proposed this study by introducing a second metal layer on the other side of the substrate to form an overlapping area between metal layers. A capacitive loaded resonator is therefore realized without increasing the size of the structure and resonance can be achieved at lower frequencies than that of spiral-shaped structures alone. In addition, tuning capabilities can be imported to this type of structure by inserting ferroelectric thin 62

88 films between the two metal layers [62] [64]. This chapter explores novel designs of miniaturized capacitive loaded band-stop structures with spiral-shaped sub-wavelength components fed by CPW transmission line.three variations are explored in this study, leading to increased effective capacitances, lowered resonant frequencies, steeper band-rejection, and smaller electrical sizes. The design methodology and operation mechanism is explained in section 5.1. Device were fabricated using commercial Printed Circuit Board technology from a third party detailed in section 5.2. Measurements of scattering parameters were obtained and compared with simulation results in section 5.3. This work is summarized in section 5.4 with a forecast on future study. 5.1 Structure and Operation The 3D view of the proposed design is shown in Figure 40. The top metal layer is a planar CPW resonator with a spiral-shaped input signal line and two adjacent ground pads. The bottom metal layer consists of an output signal line patterned for capacitive loading and a couple of identical ground pads as on the top metal layer. By introducing a second metal layer to the planar CPW resonator and splitting the signal line into two portions on both metal layers, an overlapping area is formed between the input and output signal lines and capacitive loading capability is incorporated to the resonator without increasing the circuit area. As a result, signal enters input port is transmitted through the 63

89 spiral inductor and capacitive coupled to the output signal line on the bottom metal layer. At resonance, the amount of signal transmitted to the output is suppressed based on the choice of effective inductance and capacitance given by the designed structure parameters. Spiral Signal Line Three effective overlap areas Top Metal Layer Input Port Bottom Metal Layer Ground Ground Ground Ground Straight Signal Line Output Port Figure 40 3D view of the CPW sub-wavelength resonator The structure parameters of the spiral structure (spiral turn width, number of spiral turns, gap between adjacent spiral turns) determines the inductive behavior, while the topology of bottom metal layer determines the effective overlapping area of two metal layers, which controls the capacitive behavior of the resonator. Therefore a resonating structure is realized by the inductive and capacitive component whose resonance can be 64

90 controlled by the spiral topologies and effective overlapping area. Figure 41 Top view of the resonator with dimensioning in cm. In this design, an 8-turn spiral topology is adopted with non-uniform spacing between adjacent spiral turns on the top metal layer (Figure 41). The signal line on the bottom metal layer is patterned with three topologies with increasing overlapping areas (Figure 42, 43) to prove that the proposed design can be further miniaturized with lower resonances under the same circuit area without sacrificing the resonating behavior. Electromagnetic simulation is performed on proposed structures, C_Loading_1, C_Loading_2, and C_Loading_3 (Figure 40) and capacitive loading behavior is evidenced by decreased resonance. 65

91 Figure 42 Top views of three variations of the bottom metal layer named as C_Loading_V1, C_Loading_V2, and C_Loading_V3 from left to right with increasing overlapping areas. Figure 43 3D views of three variations of the bottom metal layer named as C_Loading_V1, C_Loading_V2, and C_Loading_V3 from left to right with increasing overlapping areas. Figure 44 Simulated S 21 magnitudes of C_Loading_V1, C_Loading_V2, and C_Loading_V3 using ADS 66

92 Figure 45 EM field distribution at DC and resonance of C_Loading_V1 5.2 Printed Circuit Board Realization Figure 46 PCB Layout of the CPW sub-wavelength resonator. The red layer is the top metal layer and the green layer is the bottom metal layer which has three variations. The five-hole combination on either side of the CPW signal line of each device were patterned to adapt SMA connectors. To verify the concept, the electromagnetic model presented in the previous section has to be tailored for Printed Circuit Board fabrication through PCBexpress.com with mm thick of copper for both metal layers and 1.57 mm thick of FR4 as the dielectric material in between. The PCB layout with both metal layers is shown in Figure 67

93 46. The five-hole combination placed at the input and output ports of the CPW signal line of each device were patterned to adapt to SMA connectors for measurement and additional vias are placed on the CPW ground pads to ensure the connections. Three identical boards were received for each PCB layout and measured using Agilent FieldFox N9914A portable RF Analyzer through SMA connection. The measurement were obtained with a frequency sweep from 30 khz -1 GHz and 500 data points were recorded for each sweep. All measured results presented in the following section are tested for repeatability. 5.3 Experimental Results and Analysis Figure 47 Comparison of simulated and measured frequency response of CPW sub-wavelength resonator in terms of magnitudes of S 21 C_Loading_V1, C_Loading_V2, and C_Loading_V3. 68

94 As shown in Figure 47, device named as C_Loading_V1 with the least overlapping area achieved over 48 db at 138 MHz, while C_Loading_V2 and C_Loading_V3 show resonances at MHz and MHz with narrowed rejection bandwidths and improved passband insertion loss (under 5 db) within the same device area. Simulation results represented by the dotted curve show a good agreement with the measured data indicated by the solid curve. An equivalent schematic model using three cascaded parallel RLC cells are used to characterize the resonance behavior. The matching between electromagnetic simulation, schematic, and measured data of C_Loading_V3 is shown in Figure 48. The three RLC cells model the DC, resonance, and the harmonic, respectively. Figure 48 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V3 in terms of magnitudes of S

95 The electrical parameters that model the dominating resonance of all three device are summarized in Table 12. As expected, the high inductance values are contributed by the spiral structure. However, as the equivalent capacitances increase with expanded overlapping areas, inductance values are at the same time decreased by the enhanced capacitive coupling between two metal layers. It can be seen that the sizes of effective overlapping area can be tailored to shift the resonances, giving miniaturization to the proposed structure without sacrificing the band-rejection behavior. Table 12 also compared the miniaturization of each design in terms of the ratio between the largest dimensions of the PCB device L and its guided wavelength λg at resonance. The PCB device has an area of 6.1 by 9.65 cm 2 for all three variations. The V3 topology revealed smallest L/λg ratio (0.03) where L equals to 9.65 cm. Table 12 Equivalent electrical parameters extracted from schematic model C_Loading_V1 C_Loading_V2 C_Loading_V3 L 0 (nh) C 0 (pf) Measured Resonance (MHz) L/λ g Three variations of capacitive loaded sub-wavelength resonators are represented in this study. The band-stop performance is well demonstrated by the agreement between 70

96 the measurements obtained from PCB realization and simulated results. By keeping the same inductive spiral structures on the top metal layer, the capacitive loading capability is revealed by varying bottom metal topologies which controls the effective overlapping areas, giving rise to further miniaturization and a promising aspect for varactor loading (Table 13). Table 13 Comparison of three variations of the capacitive-loaded sub-wavelength resonators Notch depth (db) Resonance (MHz) L (cm) Guided Wavelength λ g (m) C_Loading_V L/λ g C_Loading_V C_Loading_V

97 CHAPTER 6 NOVEL CPW DEFECTED GROUND STRUCTURES The core module of today s wireless communication system is the RF frontend, consisting of at least a power amplifier, a mixer, a voltage control oscillator, band-pass/band-stop filters, and antennas. The filter is located at the next stage of an antenna. Signal received by the antenna is transmitted to the filter, and the filter keeps the signal of required band and isolates the signal of unnecessary bands. Therefore, the quality of the frequency response of the filter directly influences correctness of signal processing of post-end circuits, and the performance of the filter determines the quality of the wireless communication system. Resonating structures with compact size and prominent stopband realized by Defected Ground Structures (DGS) can be used to enhance filter performance. Implemented in the ground planes of the transmission lines, DGS offers substantial flexibility in integration with other technologies and simple fabrication processes. Spiral-shaped resonating structures are featured by its steep band-rejection characteristics, low insertion loss, and exceptional compactness [65], [66]. When the spiral topology is 72

98 implemented as DGS, multiple harmonics occur at integer numbers of resonant frequency when three or more spiral turns are adopted [67] [69]. Spiral-shaped DGS in [67] shows a spurious-free band-stop behavior up to 10 GHz with a resonance of 3.8 GHz when two spiral turns are used. However, the same structure with three spiral turns has a resonance frequency of 1.3 GHz with steeper band rejection slope and a harmonic at 2.6 GHz, resulting in a clean pass-band only up to 2 GHz. Consequently an increase in spiral turns enhances the band-stop performance at a sacrifice of unwanted harmonics. Hence a modification to the spiral-shaped structure is proposed to suppress the harmonics while preserving the desired band-rejection behavior. It is shown that spiral-shaped resonating structures are featured by its steep band-rejection characteristics, low insertion loss, and exceptional compactness [65], [66]. When this type of structure is implemented as DGS, multiple harmonics occur at integer numbers of resonant frequency when three or more spiral turns are adopted [67] [69]. Spiral-shaped DGS in [67] shows a spurious-free band-stop behavior up to 10GHz with a resonance of 3.8 GHz when two spiral turns are used. However, the same structure with three spiral turns has a resonance frequency of 1.3 GHz with steeper band rejection slope and a harmonic at 2.6 GHz, resulting in a clean pass-band only up to 2 GHz. Consequently an increase in spiral turns enhances the band-stop performance at a sacrifice of unwanted harmonics. 73

99 Figure 49 Top views of C-DGS (left) cell with 10 full spiral turns and corresponding M-DGS (right) cell. Dimensions are in μm. The conventional spiral-shaped DGS (C-DGS) and the modified spiral-shaped DGS (M- DGS) are both single-layer planar structures shown in Figure 49. Both structures are composed of a standard CPW line and DGS etched on both ground planes. The defected areas give rise to a rejection for a certain frequency band, which can be represented by equivalent L-C components [70]. The band-rejection characteristics of DGS can simply be controlled by the geometric parameters of the defected areas. Previous study has explored the effects of various spiral finger lengths, widths, and gaps on the resonate frequencies and bandwidths for C-DGS cells [67]. In this chapter, the relationship etween the inner and outer spiral turns and their impacts on the resonances, rejection bandwidths, and number of harmonics are explored. An overview is first presented in section 6.1 with an introduction of DGS operating mechanism followed by a parametric study of proposed DGS structures in section

100 Design methodology of M-DGS is explained in section 6.3. Comparison between C-DGS and M-DGS cells with different numbers of full spiral turns and removed inner spiral turns is presented in section 6.4 and 6.5. Test structures with cascaded units are analyzed in section 6.6. Section 6.7 summarizes the study. 6.1 Overview By definition, DGS is an etched periodic or non-periodic cascaded configuration defect in the back ground metallic plane of a planar transmission line (e.g., micro-strip, coplanar and conductor backed coplanar wave guide) which disturbs the shield current distribution in the ground plane because of this defect. This disturbance, or any defect etched in the ground plane, can give rise to increasing effective capacitance and inductance. When an electromagnetic wave propagates on the DGS with periodic obstacles, energy (or frequency) thereof only appears at some specific wave vectors, so that the energy is suppressed at some frequency bands to achieve a special band-stop effect. Such characteristic of the DGS is widely used for designing microwave band-pass/stop filters. In another words, DGS could be another tool that we can integrate into our device to modify and enhance our varactor-based device DGS Characteristics The basic element of DGS is a resonant gap or slot in the ground metal plates, placed above and below the center signal line and aligned for efficient coupling to the 75

101 line when using CPW configuration, and placed underneath the signal line when using Micro-strip transmission lines. Figure 50 shows the classic dumbbell-shaped DGS structure using CPW (left) and Micro-strip (right) transmission lines. The etched dumbbell shape can differ in occupied area, equivalent L-C ratio, coupling coefficient, and other electrical parameters. There are also various topologies. In this study, DGS with potential varactor loading capabilities and compact sizes are of interests. DGS ground CPW signal line DGS ground plane Figure 50 CPW (left) and Microstrip (right) Dumbbell-shaped DGS structure DGS Equivalent Circuit The equivalent circuit for a DGS is a parallel RLC circuit in series with the transmission line to which it is coupled to (Figure 51). The input and output impedances are that of the transmission line section, while the equivalent values of L, C and R are determined by the dimension of the DGS structure and its position relative to the 76

102 transmission line. The range of structures arises from different requirements for bandwidth (Q) and center frequency, as well as practical concerns such as a size/shape that does not overlap other portions of the circuit, or a structure that can be easily trimmed to the desired center frequency. Figure 51 Equivalent circuit for dumbbell-shaped DGS section DGS allows the designer to place a notch (zero in the transfer function) almost anywhere. When placed just outside a band-pass filter s pass-band, the steepness of the roll-off and the close-in stop-band are both improved. A classic characteristic of distributed filters is higher order responses, with the most troublesome being at twice the center frequency. If the application requires elimination of this second pass-band, additional filter elements are required. This can be accomplished simply by adding another DGS element resonant at the second harmonic frequency. The rejection of this resonant notch will greatly reduce the filter s unwanted response. 6.2 Structure and Operation C-DGS and M-DGS cells are designed with identical overall area of 1.5 by

103 mm 2 and fixed spiral geometric parameters (gap length = 1 mm, gap width = 20 μm, spiral finger width = 20 μm) on CPW transmission line (Figure 49). The changing parameters are the number of overall spiral turns and removed spiral turns. At first, C-DGS cells are designed with 6 to 10 full spiral turns and corresponding M-DGS cells are simply the same set of C-DGS cells with only the outermost spiral turns. The shifts in resonant frequencies and variations in bandwidths between C-DGS cells and M-DGS set are compared. After that, C-DGS with 10 full spiral turns is modified with reduced number of inner spiral turns to demonstrate the phenomenon of suppressed harmonics. 6.3 Parametric Study Simulated transmission characteristics of C-DGS of 10 full spiral turns shows 4 higher order modes from 0-15GHz (Figure 52, Figure 53). Compared with C-DGS, higher order modes are eliminated and reduced in M-DGS and C-DGS with removed spiral turns. 78

104 Figure 52 Comparison of simulated S 21 magnitudes of C-DGS cell with 10 full spiral turns and five removed inner spiral turns. Figure 53 Comparison of simulated S 21 magnitudes of C-DGS cell with 10 full spiral turns and only outer spiral turns. 79

105 Figure 54 Electromagnetic field distribution of M-DGS at dc (left) and resonance (right) 6.4 Fabrication and Testing Figure 55 DGS On 4 inch Sapphire Wafer 80

106 Figure 56 Top views of C-DGS cells with full 10 spiral turns, only outermost spiral turn (M-DGS), 7 removed spiral turns, and 5 removed spiral turns. All the testing structures were fabricated on four inch diameter Sapphire wafers followed by a 0.3 μm gold as the metal layer. Measurement results presented in the following sections were conducted on at least three replications for each cell using Agilent 8720 Vector Network Analyzer with a frequency sweep from 1-10GHz and 800 points. 6.5 Measurements of Single DGS Units Measurements of scattering parameters are shown in Figure 57 for C-DGS with 6-10 spiral turns and in Figure 58 for corresponding M-DGS cells. It can be seen that all C-DGS cells have two or more harmonics between 1-10 GHz. The C-DGS with 10 spiral turns has a resonance at 1.9 GHz and two harmonics at 5.1 GHz and 8.1 GHz (Figure 57). Increase in spiral turns also causes decreased notch depths and narrowed bandwidths, which can be explained by the coupling effect between inner spiral turns. With only outermost spiral turns, notch depths and bandwidths of corresponding M-DGS cells have little variations without the inner spiral turns. A clean passband is achieved for all 81

107 M-DGS cells at a sacrifice of shifts in resonances and wider rejections bandwidths than equal-sized C-DGS cells (Figure 64). The comparison between the two sets of DGS cells confirms that theory that the resonant frequency of a C-DGS cell is dominantly controlled by the outermost spiral structure and each inner spiral turn contributes to the harmonics as well as some effect on the resonant frequencies and bandwidths. To eliminate the harmonics, inner spiral turns can be reduced or removed to achieve a spurious-free band-stop performance. Figure 57 Measured S 21 magnitudes of C-DGS cells with 6 to 10 spiral turns. 82

108 Figure 58 Measured S 21 magnitudes of M-DGS cells (With only outermost turns of 6-turn to 10-turn C-DGS cells). To explore how the harmonics are suppressed by eliminating the inner spiral turns, C-DGS with 10 full spiral turns and reduced spiral turns are analyzed. Measurements on the four cells in Figure 66 show that the removal of 5 inner spiral turns from full 10 spiral turns reduces 2 harmonics to only 1 harmonic at 6.5 GHz (Figure 59). Removal of 7 inner spiral turns pushes the closest harmonic to even higher frequency at 9.8 GHz. Eventually the M-DGS cell which has the only outermost spiral turn has no harmonics up to 10 GHz. Shifts in the resonating frequencies from 1.8 GHz to 4 GHz as inner spiral turns are reduced can be adjusted by varying the sizes of the defected area. A deeper rejection and sharp transition from passband to stopband can be obtained by cascading M-DGS cells which is presented in the next section. 83

109 Figure 59 Measured S 21 magnitudes of C-DGS cells with full 10 spiral turns, 5 removed spiral turns, 7 removed spiral turns, and only outermost spiral turn. 6.6 Measurement of Cascaded DGS C-DGS cell with five removed inner spiral turns and an equal sized M-DGS cell are cascaded to explore their impacts on the band-rejection behavior (Figure 60). The number of cells in the cascaded DGS section controls the sharpness and the widths of the stopband. The center frequency of the stopband is determined by the resonance of the single DGS cell. 84

110 Figure 60 Top view of cascaded C-DGS with 5 removed inner spiral turns and M-DGS cell (10-turn C-DGS with its outermost spiral turn). The measured and simulated performances of the test structures cascaded by 6 sections are shown in Figure 61 for M-DGS and for C-DGS with removed spiral turns in Figure 62. Obviously, the cascaded M-DGS achieves more than -50 db rejection at 3.64 GHz with no harmonics up to 10 GHz (Figure 61). The cascaded C-DGS with five removed inner spiral turns, on the other hand, only reaches -12 db rejection at 2.19 GHz and the first harmonic occur at 6.4 GHz (Figure 62). A good agreement between the measurement and the simulation results is achieved for the M-DGS unit but not the C-DGS unit due to the intense coupling effect between inner spiral turns. 85

111 Figure 61 Measured and simulated S 21 magnitudes of cascaded M-DGS cells Figure 62 Measured and simulated S 21 magnitudes of cascaded C-DGS cells with 5 removed inner spiral turns. 86

112 6.7 Conclusion The relationship between the inner and outer turns of the C- DGS cells and their impacts on the band-rejection characteristics are explored by comparisons between C-DGS cells with different numbers of full spiral turns and removed spiral turns. Proposed M-DGS cells are proved to have spurious-free passbands and less than 3 db insertion losses up to 10 GHz. Removing inner spiral turns also eliminates the coupling effects between spiral turns. Test structures with cascaded M-DGS cells on CPW has an improved band-stop performance of a notch depth greater than -50 db at 3.64 GHz with insertion loss under 3 db and no other harmonics up to 10 GHz. Because of the extensive coupling effect between the spiral turns, cascading of C- DGS cells with removed spiral turns does not expose enhanced band-rejection behavior. 87

113 CHAPTER 7 PHOTO MASK LAYOUT DESIGN A photo mask set designed for microelectronic devices consists of all device patterns and alignment marks at each mask layer. The minimum feature size of the device patterns on each layer has to be specified to choose a reasonable resolution for mask production. Often times etching layer for dielectric materials and passivation layers require less accuracy than metallic patterns. The polarity of each mask layer has something to do with the fabrication method, thus device layer with same or similar fabrication techniques can often share the same mask layer. To efficiently utilize the space on a photo mask set with least number of mask layers, all device have to be categorized by specifying the material, fabrication techniques and minimum feature sizes at each layer to decide which mask layer can be shared. Table 13 listed the all the design that are to be fabricated using the same mask set UD12. Four mask layers are designed to adapt all layer combinations for 9 sets of designs. 88

114 Table 14 9 sets of device designed on a photo mask set of 4 layers 89

115 7.1 Mask Template The mask layout is designed for on-wafer measurements for wafers of 2, 3 or 4 inch in diameters (Figure 63). The mask template is first generated with a 4-inch diameter circumference with alignment marks arranged to form a 2 inch by 2 inch square inside the circumference. The 2 inch by 2 inch unit is further divided into four 1 inch by 1 inch quadrants. Figure 63 Photo mask Template with four 1 by 1 units inside 4 inch diameter circumference. Number units are in μm unless specified. 7.2 Mask Layout From Table 15, all 9 sets of device can be simplified as 5 sets of device which share the same mask layers in Table 15 and updated layer specifications showing shared layers is shown in Table 16. Each new set is then arranged and filled in the further divided mask template shown in Figure

116 Table 15 Device set with same layer definitions Name Description Layer Combination BST Varactor based structures Metal-BST-Metal VO2 Vanadium Dioxide based structures VO2-Metal MEM Memristors Metal-Insulator-Metal CAL Calibration structures Metal only SUB Sub-wavelength resonators SiO2-Metal Air Table 16 Photo Mask Layer Specifications Material Thickness Polarity Description Layer 4 Passivation Si3N4 250 nm Drawing area are to be etched. Layer 3 Metal2 Ti/Pt/ Au nm Drawing area are to be deposited. Top electrode Layer 2 Dielectric BST/VO2/SiO 2/Oxide 200 nm/150 nm/250 nm/20-50 nm Drawing area are to be etched. Dielectric Layer 1 Metal1 Ti//Au/Pt 300 nm-500 nm Drawing area are to be deposited. Bottom electrode Substrate Sapphire/HR Silicon 91

117 Figure 64 Mask layout for device shared same fabrication process 7.3 Device Layout Within each quadrant, each test structure are aligned and spaced by at least 500 μm to facilitate on-wafer measurements (Figure 65). The full view of the entire mask layout is shown in Figure 66. Figure 65 Single and cascaded Varactor layout 92

118 Figure 66 Completed Photo Mask Layout 7.4 Alignment Mark Design Since each set of device only uses 1, 2, or 3 out of 4 photo masks, a set of new alignment marks are designed for each layer to assure accurate alignment between any possible combinations (Figure 67). The alignment mark pattern on each layer shown in Figure 68 is designed in a ways that corner features can be used to align in a zoom-out view (rough alignment for location), while the center features can be used for alignment in a close-in view (accurate alignment). This set of alignment marks can adapt all possible layer combinations (Figure 69). 93

119 Figure 67 3D View (left) and Top view (right) of the alignment marks at each layer. Dimensioning units are in μm. Figure 68 Top view of the alignment marks at each layer Figure 69 Overlapping of alignment marks for all possible combinations (Big). Dimensioning units are in μm. 94

120 CHAPTER 8 CONCLUSION AND FUTURE WORK Four projects are investigated in designing reconfigurable and miniaturized passive RF/Microwave components. Thin-film BST varactors are characterized with high tunability (~4:1), low control voltage (8-10V), and moderate loss (<0.01). Analog phase shifters realized with a cascade of thin film BST varactors are demonstrated with a FOM of 24.5 degrees/db at 8 GHz in an area of 0.45 by 3.3 mm 2 with a maximum DC bias of 8 V. The subwavelength resonators and the modified spiral shaped DGS are novel contributions from this dissertation work. Capacitive loading capability is integrated to subwavelength resonators on CPW transmission lines, making it possible for varactor loading. A notch depth of 48 db at 116 MHz within an area of 6.1 by 9.65 cm 2 is achieved and can be adjusted by adjusting the amount of loaded capacitance. Optimized DGS topologies on CPW transmission lines are presented with superior stopband performance suppressed harmonics up to 10 GHz with an exploration on the relationship between inner and outer turns of the spiral topology and their effects on the band-stop behavior. The final testing structure cascaded six M-DGS cells to enhance the band-rejection behavior with a 95

121 notch depth greater than -50 db at 3.64 GHz within an area of 1.5 by 13 mm 2. Insertion loss is under 3 db with no higher order modes up to 10 GHz. In conclusion, each project addressed above is demonstrated with improved performance for RF/microwave applications. For future work, a model of coupled-resonator filter that combines all the addressed technologies is shown in Figure 70, where two shunt subwavelength resonators are capacitive coupled through a varactor unit and DGS units can be used to suppress the higher order modes generated by the subwavelength resonators. Figure 71 shows another model that has cascaded shunt varactor units and serial resonators. Although there is not enough time to experiment and validate these models, a solid understanding in each technology is developed through this study which is a valuable experience for RF/microwave industry. Figure 70 Tunable coupled-resonator filter with shunt resonators enhanced by DGS and varactors 96

122 Figure 71 Tunable coupled-resonator filter with serial resonators enhanced by DGS and varactors 97

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131 APPENDIX A MEASUREMENT DATA OF VARACTORS Figure 72 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.748 pf, L=0.01 nh, R p=849ω, R s=2.57 Ω. 106

132 Figure 73 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.714 pf, L=0.01 nh, R p=849 Ω, R s=1.9 Ω. Figure 74 Measured scattering parameters of varactor R1C2 in terms of magnitudes of S 21 and S 11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.608 pf, L=0.01 nh, R p=849 Ω, R s=1.25 Ω. 107

133 Figure 75 Measured scattering parameters of varactor R2C2 in terms of magnitudes of S 21 and S 11 at 0 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.548 pf, L=0.01 nh, R p=669 Ω, R s=1.62 Ω. Figure 76 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 0 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.748 pf, L=0.01 nh, R p=849 Ω, R s=2.57 Ω. 108

134 Figure 77 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 1 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.652pF, L=0.008 nh, R p=849 Ω, R s=2.25 Ω. Figure 78 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 2 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.54 pf, L=0.008 nh, R p=849 Ω, R s=2.25 Ω. 109

135 Figure 79 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 3 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.46 pf, L=0.006nH, R p=849 Ω, R s=2.25 Ω. Figure 80 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10V shown in solid curve. The dotted green curve is the matched curved to 4 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.374 pf, L=0.006 nh, R p=849 Ω, R s=2.25 Ω. 110

136 Figure 81 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 5 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.33 pf, L=0.006 nh, R p=849 Ω, R s=2.25 Ω. Figure 82 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 6 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.304 pf, L=0.006 nh, R p=849 Ω, R s=1.69 Ω. 111

137 Figure 83 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 7 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.27 pf, L=0.003 nh, R p=849ω, R s=1.69 Ω. Figure 84 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 8 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.252 pf, L=0.003 nh, R p=849 Ω, R s=1.69 Ω. 112

138 Figure 85 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 9 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.226 pf, L=0.03 nh, R p=849 Ω, R s=1.69 Ω. Figure 86 Measured scattering parameters of varactor R1C1 in terms of magnitudes of S 21 and S 11 from 0-10 V shown in solid curve. The dotted green curve is the matched curved to 10 V measurements using the equivalent schematic model. Extracted electrical parameters show that C=0.208 pf, L=0.002 nh, R p=849 Ω, R s=2.25 Ω. 113

139 APPENDIX B MEASUREMENT DATA OF PHASE SHIFTERS Phase Shifter With 10 Cascaded Varactors S21 Magnitude (db) Control Voltage S21 at 5GHz S21 at 6GHz S21 at 7GHz S21 at 8GHz S21 at 9GHz Figure 87 Comparison of S 21 magnitudes of phase shifters cascaded by 10 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. Phase Shifter With 10 Cascaded Varactors S21 Magnitude (db) Control Voltage S21 at 5GHz S21 at 6GHz S21 at 7GHz S21 at 8GHz S21 at 9GHz Figure 88 Comparison of S 21 angles of phase shifters cascaded by 10 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. 114

140 Phase Shifter With 15 Cascaded Varactors S21 Magnitude (db) S21 at 5GHz S21 at 6GHz S21 at 7GHz S21 at 8GHz S21 at 9GHz -25 Control Voltage Figure 89 Comparison of S 21 magnitudes of phase shifters cascaded by 15 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. Phase Shifter With 15 Cascaded Varactors S21 Phase (degree) <S21 at 5GHz <S21 at 6GHz <S21 at 7GHz <S21 at 8GHz <S21 at 9GHz -600 Control Voltage Figure 90 Comparison of S 21 magnitudes of phase shifters cascaded by 10 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. 115

141 Phase Shifter With 25 Cascaded Varactors S21 Magnitude (db) S21 at 5GHz S21 at 6GHz S21 at 7GHz S21 at 8GHz S21 at 9GHz -35 Control Voltage Figure 91 Comparison of S 21 magnitudes of phase shifters cascaded by 25 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. Phase Shifter With 25 Cascaded Varactors S21 Phase (degree) Control Voltage <S21 at 5GHz <S21 at 6GHz <S21 at 7GHz <S21 at 8GHz <S21 at 9GHz Figure 92 Comparison of S 21 angles of phase shifters cascaded by 25 single units at frequencies 5, 6, 7, 8, 9 GHz as DC bias increases from 0 to 8 V. There is no obvious phase change as DC bias increases from 7 V to 8 V at all frequencies. 116

142 Figure 93 Comparison of measured S 21 angles of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. Figure 94 Comparison of measured S 21 magnitudes of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. 117

143 Figure 95 Comparison of measured S 21 angles of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. Figure 96 Comparison of measured S 21 magnitudes of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. 118

144 Figure 97 Comparison of measured S 21 angles of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. Figure 98 Comparison of measured S 21 magnitudes of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V in the frequency range of 1 to 10 GHz. 119

145 Table 17 Measured S 21 magnitudes of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP10 5GHz 6GHz 7GHz 8GHz 9GHz Voltage S21 S21 S21 S21 S Δ S Table 18 Measured S 21 angles of the phase shifter cascaded by 10 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP10 5GHz 6GHz 7GHz 8GHz 9GHz Voltage <S21 <S21 <S21 <S21 <S Δ<S FOM

146 Table 19 Measured S 21 magnitudes of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP15 5GHz 6GHz 7GHz 8GHz 9GHz Voltage S21 S21 S21 S21 S Δ S Table 20 Measured S 21 angles of the phase shifter cascaded by 15 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP15 5GHz 6GHz 7GHz 8GHz 9GHz Voltage <S21 <S21 <S21 <S21 <S Δ<S FOM

147 Table 21 Measured S 21 magnitudes of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP25 5GHz 6GHz 7GHz 8GHz 9GHz Voltage S21 S21 S21 S21 S Δ S Table 22 Measured S 21 angles of the phase shifter cascaded by 25 varactor units as the DC bias increases from 0 to 8 V at 5, 6, 7, 8, 9 GHz. SP25 5GHz 6GHz 7GHz 8GHz 9GHz Voltage <S21 <S21 <S21 <S21 <S Δ<S FOM

148 APPENDIX C ADDITIONAL DATA OF DGS L W G Figure 99 Standard Dumbbell-Shaped DGS Unit Top view (All dimensions are in µm) Table 23 Left half: Increasing 100 µm in L results in ~0.1 nh increase in inductance. Right half: Increasing 10 µm in G results in ~0.01 pf decrease in capacitance. Varying L(µm) Capacitance (pf) Inductance (nh) Varying G(µm) Capacitance (pf) Inductance (nh)

149 Figure 100 Standard Dumbbell-shaped DGS on CPW. As L increases from 300 µm to 700 µm, inductance increases from 0.42 nh to 0.61 nh, while capacitance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters. Figure 101 Standard Dumbbell-shaped DGS on CPW. As G increases from 5 µm to 20 µm, capacitance decreases from pf to pf, while inductance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters. 124

150 L W G Figure 102 Metal Loaded Dumbbell-Shaped DGS Unit Top view (All dimensions are in µm) Table 24 Left half: Increasing 200 µm in L results in ~0.05 nh increase in inductance. Right half: Increasing 10 µm in G results in ~0.15 pf decrease in capacitance. Varying L(µm) Capacitance (pf) Inductance (nh) Varying G(µm) Capacitance (pf) Inductance (nh) Table 25 Comparison between Standard and Metal-loaded Dumbbell DGS unit. Standard Dumbbell Metal-loaded Dumbbell L=700 µm, G=10 µm, W=1000 µm L (nh) C (pf) R (Ω)

151 Figure 103 Metal-Loaded Dumbbell-shaped DGS on CPW. As L increases from 500 µm to 900 µm, inductance increases from 0.21 nh to 0.33 nh, while the capacitance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters. Figure 104 Metal-loaded Dumbbell-shaped DGS on CPW. As G increases from 10 µm to 30 µm, capacitance decreases from 0.75 pf to 0.58 pf, while inductance and resistance unchanged. The green dotted line is obtained by tuning the schematic model parameters. 126

152 Figure 105 Spiral-shaped DGS Top View Table 26 Both C and L increase as W increases. 150 µm increase gives ~0.4 pf capacitance and ~0.05 nh inductance Varying W(µm) Capacitance (pf) Inductance (nh) R (Ω) Figure 106 Magnitudes of S 21 parameters of Spiral-shaped DGS units with varying widths W 127

153 Table 27 Notch performance of each DGS configuration Standard Dumbbell Metal-loaded Dumbbell Spiral Top View 3dB Quality Factor NA dB Quality Factor NA Notch Depth NA Notch Frequency(GHz) Above DGS unit Size (µm 2 ) 1000* * *220 Figure 107 PCB Layout for preliminary DGS study with variations of dumbbell-shaped DGS and spiral-shaped DGS. 128

154 Figure 108 Measured (blue solid) and simulated (green dotted) S 21 magnitudes of metal-loaded dumbbell DGS. The ratio between the largest dimension of the DGS L to its guided wavelength λ is 0.5 Figure 109 Measured (blue soild) and simulated (green dotted) S 21 magnitudes of metal-loaded dumbbell DGS. The ratio between the largest dimension of the DGS L to its guided wavelength λ is 1/6. 129

155 Figure 110 Measured (blue soild) and simulated (green dotted) S 21 magnitudes of spiral-shaped DGS. The ratio between the largest dimension of the DGS L to its guided wavelength λ is 1/16. Figure 111 Measured (blue soild) and simulated (green dotted) S 21 magnitudes of cascaded spiral-shaped DGS with enhanced selectivity. 130

156 APPENDIX D ADDITIONAL DATA OF SUBWAVELENGTH RESONATORS Figure 112 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V1 in terms of magnitudes of S

157 Figure 113 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V2 in terms of magnitudes of S 21. Figure 114 Comparison of frequency response matched by the equivalent schematic model (green dashed curve) with simulated and measured results of device C_Loading_V3 in terms of magnitudes of S

158 Figure 115 Planar Spiral-In-Spiral-Out topologies for CPW subwavelength resonators (db) Figure 116 Simulated S 21 and S 11 magnitudes of 30 Turn SISO resonator with 20 μm spiral traces and 10 μm gaps. 133

159 Figure 117 Top view of planar Spiral-In-Spiral-Out CPW subwavelength resonators with spiral turns (db) Figure 118 Simulated S 21 and S 11 magnitudes of 30 Turn SISO resonator with 20 μm spiral traces and 10 μm gaps. 134

160 Figure 119 PCB layout for a cascade of four SISO resonators with 12 and 16 spiral turns Figure 120 Simulated (dotted) and measured (solid) S 21 and S 11 magnitudes of cascaded 12 and 16 Turn SISO resonators shown in Figure

161 APPENDIX E MATHEMATICAL MODEL OF PHASE SHIFTERS 136

162 137

163 138

164 Figure 121 Measured S21 phases of a cascade of 20 varactor units from 0-8V Figure 122 Modeled S21 phases of a cascade of 20 varactor units from 0-8V 139

165 Figure 123 Measured S21 magnitudes of a cascade of 20 varactor units from 0-8V Figure 124 Modeled S21 phases of a cascade of 20 varactor units from 0-8V 140