# Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-gallium arsenide layer structure

код для вставкиСкачатьUNIVERSITY OF CALIFORNIA, IRVINE Tunable Wideband Microwave Band-Stop and Band-Pass Filters Using YIG/GGG-GaAs Layer Structure DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Electrical and Computer Engineering by Gang Qiu Dissertation Committee: Professor Chen Shui Tsai Professor Guann-Pyng Li Professor Ozdal Boyraz 2008 UMI Number: 3342926 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3342926 Copyright 2009 by ProQuest LLC. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 E. Eisenhower Parkway PO Box 1346 Ann Arbor, Ml 48106-1346 © 2008 Gang Qiu The dissertation of Gang Qiu is approved and is acceptable in quality and form for publication on microfilm and in digital formats: JT(JM J / IS'etc Committee Chair University of California, Irvine 2008 DEDICATION To My parents and my wife, Jing Chen, Without whose support it would never have been undertaken in TABLE OF CONTENTS Page LIST OF FIGURES viii LIST OF TABLES xv ACKNOWLEDGEMENTS xvi CURRICULUM VITAE xviii ABSTRACT OF THE DISSERTATION CHAPTER 1: xx INTRODUCTION 1 1.1 Introduction to Device Application 1 1.2 Microwave Interaction with Ferrimagnet 3 1.2.1 Equation of Motion of Magnetization 4 1.2.2 Polder Tensor Permeability 9 1.2.3 Ferromagnetic Resonance 13 1.2.4 Magnetic Properties of YIG/GGG Film 15 1.3 APPENDIX A l Research Objective and Thesis Organization 17 Maxwell's Equations in MKS and CGS System of Units 18 REFERENCES CHAPTER 2: 2.1 21 THEORETICAL MODELING AND ANALYSIS OF YIG/GGG-GAAS LAYER STRUCTURE 27 Theoretical Modeling 27 iv 2.2 2.1.1 Modeling Description 27 2.1.2 Full-Wave Method 28 Numerical Results and Analysis 2.2.1 APPENDIX 2 FMR Absorption and Its Band-Stop Filter Application 40 2.2.2. Wideband FMR Frequency Tunability 42 2.2.3 Material and Geometric Parameter Effect 45 2.2.4 Phase Shifter Applications 50 Ferromagentic Resonance (FMR) Linewidth 53 55 REFERENCES CHAPTER 3: 3.1 DEVICE SIMULATIONS OF MICROWAVE BAND-STOP FILTER USING YIG/GGG-GAAS LAYER STRUCTURE 57 Simulation Using Equivalent Circuit Method 57 3.1.1 Calculation of Radiation Resistance 59 3.1.2 Calculation of Values of Lumped Element 65 3.1.3 Simulation of Lumped Element Equivalent Circuit 3.2 67 Simulation using ANSOFT HFSS 69 3.2.1 Model and Parameter Assignments 69 3.2.2 Simulation Results and Discussion 73 75 REFERENCES CHAPTER 4: 40 TUNABLE WIDEBAND MICROWAVE BAND-STOP FILTER USING YIG/GGG-GAAS LAYER STRUCTURE v 77 4.1 4.2 Enhanced Microwave FMR Absorption Using Microstrip Step-Impedance Low-Pass Filter 78 4.1.1 Microstrip Step-Impedance LPF Design 79 4.1.2 AC Magnetic Field Simulation 85 4.1.3 Device Simulations 92 Experimental Results 94 4.2.1 Device Fabrication and Measurement 94 4.2.2 Device Performance of Tunable Wideband Microwave Band-Stop Filter 4.3 100 Band-Stop Filter with Large Stop-Band Bandwidth Using Microstrip Meander Line with Inhomogeneous Bias Magnetic Field 105 4.3.1 Inhomogeneous Bias Magnetic Field 105 4.3.2 Microstrip Meander Line Design 108 4.3.3 Experimental Results 111 REFERENCES CHAPTER 5: 113 TUNABLE WIDEBAND MICROWAVE BAND-PASS FILTER USING YIG/GGG-GAAS LAYER STRUCTRUES 115 5.1 Band-Pass Filter Architecture 116 5.2 Device Simulations 117 5.2.1 Simulation Using Equivalent Circuit Method 117 5.2.2 Simulation Using ANSOFT HFSS 121 5.3 Experimental Results 124 VI 5.3.1 Band-Pass Filter with Narrow Stop-Band Bandwidth 125 5.3.2 5.4 Band-Pass Filter with Large Stop-Band Bandwidthl27 Discussions 131 5.4.1 Electronic Tunability 131 5.4.2 Power Handling Capability 135 REFERENCES CHAPTER 6: 6.1 6.2 6.3 136 TUNABLE WIDEBAND FILTERS USING YIG/GGG-GAAS LAYER ON RT-DUROID SUBSTRATE 138 Band-Stop Filter on RT-Duroid6010LM 138 6.1.1. High Frequency Circuit Board Introduction 138 6.1.2 Band-Stop Filter Using 100 // m Thick YIG On RT-Duroid6010LM 140 An X-Band Tunable Band-Pass Filter 143 6.2.1 Design of An X-Band Composite Band-Pass Filter 144 6.2.2 Experimental Results and Discussion Future Works Outlined 156 157 REFERENCES CHAPTER 7: 151 CONCLUSIONS 158 vn List of Figures Figure 1.1 Spin Magnetic Dipole Moment and Angular Momentum for a Spinning Electron 4 Figure 1.2 Tuning of FMR Peak Absorption Frequency 15 Figure 2.1 The Multi-Layer Magnetic Structure 28 Figure 2.2 Outline of Analytical Analysis of the Multi-Layer Magnetic Structure Figure 2.3 29 Calculated Microwave Attenuation vs. rf Frequency when H = 2,200 Oe 41 Figure 2.4 Calculated FMR Frequencies vs. Biased Magnetic Field 43 Figure 2.5 Calculated FMR Peak Absorption Level vs. FMR Frequency 44 Figure 2.6 Calculated Attenuation vs. Microwave Frequency in 8 to 10 GHz 45 Figure 2.7 Effect of FMR Linewidth on Attenuation 46 Figure 2.8 Effect of GaAs Thickness on Attenuation 47 Figure 2.9 Effect of GGG Thickness on Attenuation 48 Figure 2.10 Effect of Air Layer Thickness on Attenuation 49 Figure 2.11 Effect of YIG Thickness on Attenuation 50 Figure 2.12 Calculated Propagation Constant (Real and Imaginary Parts) at H0=2,7lOOe Figure 2.13 51 Calculated Phase Shift at 9.66 GHz while H0 is Changed from 2,71 QOe to 3,42O0e Figure 3.1 Device Configuration of the Microwave Band-Stop viii 52 Filter using YIG/GGG-GaAs Layer Structure Figure 3.2 . 58 Lumped Element Equivalent Circuit Model of the Microwave Band-Stop Filter 59 Figure 3.3 Cross-Section View of MSSW Excitation Geometry 61 Figure 3.4 Calculated Radiation Resistance Rm versus Wavenumber k at t = 350^/w, d = 6.%/um, b = 256jum and if0 = 2,200Oe Figure 3.5 The Circuit Schematics in Microwave Office Simulator Figure 3.6 Simulated S-parameters (S21) of the Equivalent Circuit of Figure 3.5 Figure 3.7 65 68 68 The Physical Model of The Band-Stop Filter Configuration in HFSS Using a YIG/GGG-GaAs Layer Structure 70 Figure 3.8 Edit-material Interface of Ferrimagnetic Material in HFSS 71 Figure 3.9 Derivation Blocks of Relative Tensor Permeability [//] Using the Four Parameters Ms , AH, Figure 3.10 co, and H0 Simulated S-Parameter (S 2 l ) of the Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure Figure 3.11 72 73 Simulated H-field Pattern on the Surface of the YIG Layer at 8.28GHz 74 Figure 4.1 Design Outline of Step-Impedance LPF 78 Figure 4.2 Ladder Network for The Low-Pass Filter 80 Figure 4.3 A 10-Element Step-Impedance LPF 84 Figure 4.4 Simulated S-Parameters (S21 and S11) of the 10-Element Step-Impedance LPF and the 50 Q TML Figure 4.5 Simulated AC Magnetic Field (H-Field) Distributions at Frequency of 8.5 GHz along the 50 Q Microstrip Figure 4.6 84 Simulated AC Magnetic Field (H-Field) Distributions ix 87 at Frequency of 8.5 GHz along the 10-Element Step-Impedance LPF Figure 4.7 88 Simulated AC Magnetic Field (H-field) Intensities along the Y-Axis Center Lines of The 10-Segment Step-Impedance LPF and The 50 Q Microstrip Figure 4.8 89 Simulated Power Density Distribution at Frequency of 8.5 GHz on the Surface of GaAs of the 10-Segment Step-Impedance LPF Figure 4.9 90 Simulated Surface Power Density Distribution along The Cross-Section Direction (X-direction in Figure 4.8) over the TML, the Inductive Segment and Capacitive Segment of the Step-Impedance LPF Figure 4.10 91 Simulated Transmission Loss (S21) and Return Loss (Sn) of the YIG/GGG-GaAs-Based Microwave Band-Stop Filter at FMR Frequency of 8.5 GHz using the 50 TML and the 10-Segment Stepped-Impedance LPF Figure 4.11 93 The Flip-Chip Device Configuration of the Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure 94 Figure 4.12 Process Flow for Fabricating GaAs-based Microstrip Line 95 Figure 4.13 Layout of the Step-Impedance LPF with Two Mitered 90° Bends Figure 4.14 97 Photo of Fabricated GaAs-based Microstrip Step-Impedance LPF with Two Mitered 90° Bends together with Two 2.4 mm Connectors 98 Figure 4.15 Setup of the Microwave Power Measurement System 99 Figure 4.16 Setup of the Network Analyzer Measurement System 100 Figure 4.17 Measured S21 and S11 of the YIG/GGG-GaAs-Based x Microwave Band-Stop Filter at FMR Frequency of 8.5 GHz Using the 50 Q. Microstrip and the 10-Element Step-Impedance LPF 102 Figure 4.18 Measured S2i of the YIG/GGG-GaAs-Based Microwave Band-Stop Filter using the 50 Q Microstrip and the 10-element Step-Impedance LPF 103 Figure 4.19 Measured FMR Frequencies vs. Biased Magnetic Field 104 Figure 4.20 The Arrangement For Facilitating Non-Uniform Bias Magnetic Fields in YIG/GGG Layer Figure 4.21 105 Measured Magnetic Field Profiles Normalized to the Four Values of Magnetic Field at the Center of the Gap along the Y-Axis Figure 4.22 107 Measured Magnetic Field Profiles Normalized to the Four Values of Magnetic Field at the Center of the Gap along the X-Axis Figure 4.23 108 Layout of the Four-Segment Microstrip Meander Line using the Same 10-Element Step-Impedance LPFs 109 Figure 4.24 Miter Bend Layout in Microwave Office 110 Figure 4.25 Simulated S21 of a Microstrip with Two Miter Bend using Different Miter Coefficient Figure 4.26 110 A Wideband YIG/GGG/GaAs-Based Microwave Band-Stop Filter using Microstrip Meander-Line and Non-Uniform Bias Magnetic Field Figure 4.27 111 Measured S21 of the Tunable YIG/GGG-GaAs-Based Microwave Band-Stop Filter using a Meander Line with Four Segments of Step-Impedance LPF Figure 5.1 Realization of the Tunable Band-Pass Filter using a Pair of xi 112 Band-Stop Filters in Cascade Figure 5.2 Lumped Element Equivalent Circuit of the YIG/GGGGaAs-based Band-Pass Filter Figure 5.3 122 Simulated and Measured Transmission Losses (S21) of the Tunable Band-Pass Filter Figure 5.7 124 Photo of the Microwave Band-Pass Filter using Cascaded Band-Stop Filters Figure 5.8 121 Schematics of the Band-Pass Filter in HFSS 3-D Modeler Simulator Figure 5.6 119 Simulated S-parameters (S21) of the YIG/GGG-GaAs-based Microwave Band-Pass Filter Figure 5.5 117 Calculated Radiation Resistance ^ v e r s u s Wavenumber k for Band-Stop Filter (a) No.l, and (b) No.2 Figure 5.4 116 125 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs Based Microwave Band-Pass Filter with Narrow Stop-Band Bandwidth Figure 5.9 126 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs Based Microwave Band-Pass Filter with Large Stop-Band Bandwidth Figure 5.10 Measured 2-D Non-Uniform Bias Magnetic Field Profile Centered at (a) 2,750 Oe and (b) 4,150 Oe Figure 5.11 127 128 Measured Transmission Characteristics of the Tunable Band-Pass Filter in a Wide Frequency Range of 5.90-17.8 GHz 130 Figure 5.12 The Sketch of the Electromagnet 131 Figure 5.13 The Measured Changes of Magnetic Fields in the Air Gap versus the DC Current in the Coils with the Air Gap Distance xii as a Parameter 132 Figure 5.14 The Equivalent Circuit Used to Model the Coil 134 Figure 5.15 The Simulated and Measured Transient Voltages of the Coil when the Serial Resistors are 1.5 k Q , 270 Q and 47 Q Figure 5.16 135 Measured Transmission Characteristics of the Band-Stop Filter at Different Input Microwave Power Levels of (a) l m W (b) lOmW (c) lOOmW, and (d) 500mW Figure 6.1 The Layout (a), and the Simulated Transmission Loss (S21) (b), of the Step-Impedance LPF on Duroid 6010LM Figure 6.2 136 140 Measured S21 of the YIG/GGG-RT-Duroid-Based Microwave Band-Stop Filter at FMR Frequency of 8.5 GHz Using the 100 ju m Thick YIG Sample and the 6.8 ju m Thick YIG Sample Figure 6.3 142 A Scheme of Realizing an X-band (8 -12 GHz) Microwave Band-Pass Filter 143 Figure 6.4 BPF Using Quarter-Wave Short-Circuited Stubs 144 Figure 6.5 The Layout of the X-Band BPF 148 Figure 6.6 Simulated Transmission Loss (S21) of the X-Band BPF 148 Figure 6.7 The X-Band BPF (a), A Step-Impedance LPF (b), and the Composite X-Band BPF (c) 150 Figure 6.9 Simulated Transmission Loss (S21) of the Composite X-Band BPF Photo of Fabricated X-Band Composite BPF 150 151 Figure 6.10 Measured Transmission Loss (S21) of the Composite Figure 6.8 X-Band BPF 152 Figure 6.11 The Simulated Sensitivity of the S21 to the Shunt Stub Lengths Figure 6.12 The Simulated Sensitivity of the S21 to the Shunt Stub Grounding Resistance 154 xm 153 Figure 6.13 The High-End Stop-Band Tunability of the BPF by Applying Bias Magnetic Fields of 2,800 Oe and 2,450 Oe Figure 6.14 The Low-End Stop-Band Tunability of the BPF by Applying Bias Magnetic Fields of 990 Oe and 1,060 Oe xiv 155 156 List of Tables Table 2-1 Boundary Conditions of the Four-Layer Magnetic Layer Structure 36 Table 2-2 Field Independent Variables and Field Conversion Variables 37 Table 4-1 Specification of the Step-Impedance LPF 79 Table 4-2 Geometry of the 10-Element Step-Impedance LPF 83 Table 5-1 Geometric Parameters and Bias Magnetic Fields Used in the Simulation 118 Table 5-2 Values of Lumped Elements For Band-Stop Filter 1 and 2 120 Table 5-3 Measured Insertion Losses and Band-Widths of the Band-Pass Filter of Figure 5.11 Table 5-4 130 Measured Center Magnetic Fields and Maximum Change of Magnetic Field in the Center of the Air gap and the Maximum Tuning Ranges of the FMR Frequencies Table 5-5 133 The Comparison between the Simulated and Experimental Results of Figure 5-15 134 Table 6-1 Admittance and Impedance of the BPF 146 Table 6-2 Width and Length of Stubs and Connecting Lines in Figure 6.5 147 Table 6-3 Geometric Dimensions of The X-Band Composite BPF xv 149 ACKNOWLEDGEMENTS First of all, I would like to express my most sincere appreciation and deepest gratitude to my advisor, Professor Chen S. Tsai who has given me his instructive guidance, mentoring, full support, patience and encouragement throughout the course of my Ph.D. research. It has been a great honor to be able to study under his guidance, and his keen dedication to science and high standard to research have stimulated me during my whole study of Ph.D. research and will forever benefit me in my future life. I also like to express my gratitude to Professor G.P. Li who supported me for my first year of research and kindly guide me in my first teaching experience in his class. I like to thank both Professor G. P. Li and Professor Ozdal Boyraz for serving on my dissertation committee. The time and efforts they put in reviewing my dissertation are greatly appreciated. I would like to thank Dr. Hui Jae Yoo, and the former graduate Boh~Shun Chiu for their helps in the initial phase of this research. Professor Shirley C. Tsai has also been very encouraging throughout this work. I would also like to thank my fellow colleagues, Masatoshi M. Kobayashi, Chun-wei Chung, Yun Zhu and xvi Kai-Himg Chi for their helps and friendship provided in my research. I would like to thank the rest of Professor Tsai's research group, Ning Wang, Dr. Rong Wei Mao, Dr. Eugene Song, Shih-Kai Lin and Serhan Isikman. Financial support provided by the UC DISCOVERY Program is gratefully acknowledged. xvii CURRICULUM VITAE Gang Qiu 2000 B.S. in Electrical Engineering, Nanjing University, China 2003 M.S in Electrical Engineering, Nanjing University, China 2003-2008 Research Assistant and Teaching Assistant, University of California, Irvine Ph.D. in Electrical & Computer Engineering, University of California, Irvine 2008 FIELD OF STUDY Magnetic Thin-Film-Based Microwave Device Application PUBLICATIONS Journal Papers 1. C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y. Gulyaev. "Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41, pp.3568-3570, 2005. 2. G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low-pass filter in a yttrium iron garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103, 2008. 3. G. Qiu, C.S. Tsai, B. T. Wang, and Y. Zhu, "A YIG/GGG/GaAs-based magnetically tunable wideband microwave band-pass filter using cascaded xvm band-stop filters", IEEE Trans. Magn., vol.44, issue 11,2008. 4. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in flip-chip YIG-GaAs layer structures", accepted and to be published in IEEE Trans. Magn., vol. 45, 2009. Conference Papers 1. C.S. Tsai, G. Qiu, H. Gao, L.W. Yang, G.P. Li, and S.A. Nikitov, "Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs layer structures", IEEE International Magnetics Conference, Nagoya, Japan, April 2005. 2. G. Qiu, M. Kobayashi, B. T. Wang, and C.S. Tsai, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low pass filter in a yttrium iron garnet gallium arsenide layer structure", 52nd Annual Conference on Magnetism and Magnetic Materials, Paper EH-03, Nov 5-9, TAMPA, FLORIDA, 2007. 3. G. Qiu, B.T. Wang, C.S. Tsai, "A YIG/GGG/GaAs-based magnetically tunable wideband microwave band-pass filter using cascaded band-stop filters", IEEE International Magnetics Conference, Madrid, Spain, May 2008. 4. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in flip-chip YIG-GaAs layer structures", International Conference on Microwave Magnetics, Fort Collins, Coronado, September 2008. Oral Presentation 1. G. Qiu, M. Kobayashi, B. T. Wang, and C.S. Tsai, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low pass filter in a yttrium iron garnet gallium arsenide layer structure", Oral Presented at 52nd Annual Conference on Magnetism and Magnetic Materials, Nov 5-9, TAMPA, FLORIDA, 2007. xix ABSTRACT OF THE DISSERTATION Tunable Wideband Microwave Band-Stop and Band-Pass Filters Using YIG/GGG-GaAs Layer Structures by Gang Qiu Doctor of Philosophy in Electrical and Computer Engineering University of California, Irvine, 2008 Professor Chen Shui, Tsai Chair Magnetic thin-film-based microwave devices, in many applications, provide definite advantages of low cost, small size, and, in particular, enhanced compatibility with planar microwave circuit design such as monolithic microwave integrated circuits (MMIC). The ferromagnetic resonance (FMR)-based microwave filters have the advantages to possess the unique capability of potential high-speed electronic tunability, using magnetic field, for very high carrier frequency and very large bandwidth. In this dissertation research, a full-wave method of modeling and analysis of yttrium iron garnet (YIG)/ gadolinium gallium garnet (GGG)-gallium arsenide xx (GaAs) flip-chip layer structure was carried out predicting the device application as wideband tunable microwave band-stop filter utilizing the FMR absorptions of this magnetic layer structure in microwave frequency band. Detail simulations were then carried out aimed at optimal device performances of the microwave band-stop filter using YIG/GGG-GaAs layer structure. In the experimental studies, a magnetically-tuned microwave band-stop filter using YIG/GGG-GaAs flip-chip layer structure with wideband tunability of stop-band center frequency and bandwidth has been accomplished using a microstrip meander line together with non-uniform bias magnetic field. A microwave filter with tunable FMR absorption frequency range of 5.0 to 21 GHz, an absorption level of -35.5 dB and a corresponding 3 dB absorption bandwidth as large as 1.70 GHz, centered at 20.3 GHz, have been demonstrated. A magnetically-tunable wideband microwave band-pass filter with large tuning ranges for both the center frequency (5.90 -17.80 GHz) and the bandwidth (1.27 - 2.08 GHz) in the pass-band has also been realized using a pair of cascaded aforementioned band-stop filters. For example, the measured transmission characteristics of the band-pass filter at center frequency of 8.28 GHz, using 2-D non-uniform bias magnetic fields centered at 2,750 Oe and 4,150 Oe facilitated xxi by NdFeB permanent magnets, shows a - 3 dB bandwidth of 1.73 GHz, an out-of-band rejection of - 33.5 dB, and an insertion loss of - 4.2 dB. A good agreement between the simulation and experimental results for the band-pass filter in the center frequency and the bandwidths of the pass-band and the two guarding stop-bands has been accomplished. xxn Chapter 1 Introduction 1.1 Introduction to Device Applications Microwave ferrimagnetic materials and devices have been developed and constructed over the past five decades [1]. In contrast to ferromagnetic materials, a ferrimagnet is a magnetic dielectric that allows an electromagnetic wave to penetrate in the ferrimagnet, thereby permitting interactions between the rf magnetic field in the propagating microwave and the magnetization in the ferrimagnet. In the classical analysis within the linear regime under the smallsignal approximation, the behavior of the ferrimagnetic materials can be described by the Polder tensor permeability. This macroscopic description of the material property can then be incorporated in the Maxwell's equations to analyze wave propagation properties in a ferrimagnetic medium and in a ferrimagneticloaded waveguide and transmission lines. The magnetic anistropy of a ferrimagnetic material is induced by a dc biased magnetic field. This dc bias magnetic field aligns the magnetic dipoles in the ferrimagnetic materials to produce a non-zero magnetic dipole moment, and make the dipoles to precess about the axis of the dc bias magnetic field in the preferred right-hand circularly polarized (RHCP) manner. A microwave signal with RHCP rf magnetic field, therefore, will interact strongly with the dipole moments, while a signal with 1 left-hand circularly polarized (LHCP) rf magnetic field will interact much less strongly. Since the sense of the polarization changes with the direction of microwave propagation, a microwave signal will generally propagate in a ferrimagnet differently in different directions. This effect can be used to design and construct directional devices such as circulators and isolators. The other important characteristic of a ferrimagnet is that the interaction with applied microwave signal can be tuned by adjusting the strength of the dc bias magnetic field. This effect leads to a variety of tunable devices such as tunable resonators, filters, and phase shifters. Accordingly, the microwave ferrimagnetic devices can be divided into two categories based on whether directional property or tunability property is used in the applications. Conventional microwave ferrimagnetic devices have for long used bulk ferrimagnetic materials with non-planar waveguide structures [1-2]. However, for the microwave and millimeter-wave applications, there are increasing interests in using ferrimagnetic thin-film structures because, in many cases, thinfilm structures provide definite advantages of low cost, small size, and, in particular, enhanced compatibility with planar microwave circuit design such as monolithic microwave integrated circuits (MMIC). Although poly crystalline ferrimagnet are usually used in microwave directional (control) devices where a narrow ferromagnetic resonance (FMR) linewidth is not required, single crystalline ferrimagnet, almost always yttrium iron garnet (YIG), is necessary in the device applications of band-pass and band-stop filters and resonators where 2 a low FMR linewidth is a must [3]. The high-quality single crystalline liquid phase epitaxy (LPE)-grown YIG/ gadolinium gallium garnet (GGG) layers have been commercially available for many years. More recently, there has been increasing research activities in the ferromagnetic thin film-based [4-9], single crystalline hexagonal ferrite thin film-based [10-14], and ferrite-ferroelectric composite thin film-based [15-21] microwave devices in high frequency application. Although the monolithic integration combining these thin films with semiconductor in a system-on-a chip (SOC) is the ultimate goal, there are still some severe limitations in the development of ferri- and ferro-magnetic thin films and devices that are fully MMIC compatible, where the major problems are the high temperature process for growing ferrite thin film [3], and the required bulk external bias magnetic field [22]. Therefore, MMIC compatible ferrimagnetic devices with a hybrid structure using ferrimagnet and semiconductor fabricated separately and then combine in some device configuration is one of the key research focuses. 1.2 Microwave Interaction with Ferrimagnet The theoretical description of microwave interaction with ferromagnetic material starts with the derivation of equation of motion of magnetic moment of an electron in a dc magnetic field. The analysis is explored by introducing the Polder tensor permeability to be able to apply Maxwell's equation in the macroscopic level. It has been seen that, in the field of microwave magnetics, 3 researchers from physics and engineering preferred to use CGS system of units and MKS system of units respectively. The unit conversions are easy and clear when dealing with length, weight, or speed, but not the electrical and magnetic field quantities in the two systems [23]. A brief review of Maxwell equation in MKS units and CGS units is provided appendix A. 1.2.1 Equation of Motion of Magnetization Figure 1.1 Spin Magnetic Dipole Moment and Angular Momentum for a Spinning Electron The magnetic properties of a material are due to the existence of magnetic moments. The magnetic moment (m) of an electron is contributed by the orbital 4 angular momentum and spin angular momentum of an electron. There is a Lande g factor in quantum physics used to measure the relative contributions of the orbital momentum and the spin momentum to the total m . For most of microwave ferrimagnetic materials, the total m is due to spin momentum only while the Lande g factor is equal to 2. The m is, therefore, given by [24] m = -^S=—a me = -MBo- (MKS) (1.1) 2me where e is the electron charge, meis the mass of the electron, and Sis the spin angular momentum of an electron. The spin angular momentum ( S ) of an 2 electron is given by cr = ~S in equation (1.1) where Pi is the Planck's constant and h a is the Pauli Spin Operator [24]. The Bohr Magneton juB is then defined as -e%l2me (in MKS units) and its value is equal to 921x\0~1A A*m2. Since the charge of the electron is negative, equation (1.1) is given by m = JLs = -2&-S = -rS m„ (MKS) (1.2) ft where the constant y is the ratio of the magnetic moment to the angular momentum; y is called the gyromagnetic ratio or magnetogyric ratio and its value is equal to Inx2.8xlO10rad/(secxtesla) or 1.759xlOnra<i/(secxfes/a) (in MKS units). It is shown in equation (1.2) that the magnetic moment (m) of an 5 electron is proportional to its spin angular momentum ( S ) and the vector direction of m is opposite to the vector direction of S. We will now start to derive the Polder permeability tensor in both MKS and CGS unit used to describe the interaction between a microwave and a ferromagnetic material. Consider a free electron in a z-directed dc bias magnetic field as shown in Figure 1.1. The torque (T) will be exerted on the magnetic dipole and it is expressed by f = m x ^ = / / 0 m x ^ (MKSunits) f = mxW0 (CGSunits) (1.3) (1.4) since torque (T) acting on a body equals to the time rate of change of the angular momentum (S), equation (1.3) and (1.4) can be written as — = jU0mxH0 (MKSunits) dt (1.5) — -mxH0 dt (1.6) (CGSunits) combing equation (1.5) or (1.6) to (1.2) gives the equation of motion of magnetic dipole moment dfti —' —" = -ju0ymxH0 (MKSunits) (1.7) dt dm = -ym x H0 (CGS units) dt 6 (1.8) Now assuming the bias magnetic field is only at z direction as shown in Figure 1, i.e., H0=H0z. The equation (1.7) and (1.8) can be decomposed into its vector components as (1.9) and (1.10) dm dt dmY —-x dt dm,, •y dt dmT —-z dt dmY —-x dt dm,, —-y dt dm, —-z dt dm dt -w = -r x y m„ m„ 0 0 x mx 0 y my 0 z m. (MKS units) Hn z mz (CGS units) Hn (1.9) (1.10) The equation (1.9) and (1.10) are further developed to (1.11) and (1.12) dm dt dm = ju0ymxH0 dt dm =0 dt (MKS units) dm - = -ymyHG dt dm - = ymxH0 (CGS units) dt dm =0 dt 7 (1.11) (1.12) The equation (1.11) and (1.12) can be re-arranged to be the following differential equations (1.13) d2m 2 2^- + co mx=0 dt (MKS and CGS units) d2m 2 dt 2^ (1.13) + G) Qmy=0 where co0 is called Lamor precessing frequency and its value is given by G)Q = yjU0H0 (MKS units) or co0 = yH0 (CGS units). The y 2;rx2.8xl010rad/(secxfes/(3) (MKS units) or 2;rx2.8xl0 6 rad/(secx<3e) (CGS units). As an example, at the dc bias magnetic field of 10,000 Oe, the Lamor precessing frequency will be2;rx2.8xl0 10 rac//(sec). One solution for the equation (1.13) is as follows mx = A cos a>0t my=A sin co0t (1.14) m=C where A and C are arbitrary constants. The solution (1.14) shows that the x and y components of m is right-hand circular polarized (RHCP) and z component of m is determined by its initial value C. The magnitude of m is a constant equal to sA2 + C2 and the precessing angle 9 (see Figure 1.1) is given by Sin0 = 4A2+C2 8 (1.15) is In the absence of any damping forces, the m of the electron will precess about H0 at the angle 9 (see Figure 1.1) indefinitely and it is called free electron precessing. The equations (1.7) and (1.8) are the equation of motion of magnetic moment of a free electron. Now assuming, in a real magnetic material, there are N unbalanced electrons per unit volume. The magnetization is defined as the total magnetic moments per unit volume as M = Nm , and the equation of motion of magnetization is now given by — = -V0yMxH0 dt (MKS units) i^L = -YM x H0 (CGS units) dt (1.16) (1.17) In the ferrimagnetic materials, most of the magnetic dipole will be aligned by H0 and reach its limit value called saturation magnetization Ms. 1.2.2 Polder Tensor Permeability We will derive the Polder tensor permeability in this sub-section by adding a small rf magnetic field (induced by propagating microwave) to the precessing spinning system. Assuming H is the added rf magnetic field, the total magnetic field is lft=H0z + H 9 (1.18) where under the small signal approximation, L f t r « # 0 . This field produces a resultant total magnetization given by (1.19) Mt =Msz + M Where M is the induced magnetization by H. Here we will derive the Polder tensor permeability in MKS units. When combine equations (1.18) and (1.19) to the equation of motion of magnetization (1.16), it gives equation (1.20) dMt dt dMv dt dMy = -M»r dt dMz dt y X dMs dt K M Hx H y > z M2+Ms (1.20) H2+H0_ The equation (1.20) can be expanded to (1.21) dM„ = -WM(H0+Hz) + Moy(Ms+Mz)Hy dt dM.y -^^yMx{H, +Hz)-ju0r(Ms+Mz)Hx dt did. = -MQyMxHy+^yMyHx dt (1.21) Under small signal approximation, we can ignore MH product. Equation (1.21) will be arranged as 10 dM, = -co0My+amHy dt X dlfy (1.22) = a)0Mx-comHx dt d~Mz -n dt Where co0 = yjuGH0 (Lamor precessing frequency) and com = yn0Ms. The equation (1.22) can be further rearranged as d2M , dHv 2 ' + con M + G)ncoH„ x r = mm dt dt d2M.y + colM,, = -am — - + co.coH,, 0 m y 0^y I dt2 dt (1.23) J Assume the M and H are both relates to co as elM, i.e., — = jco and —- = -co2. dt dt1 The equation (1.23) can be written as (O (O H {CO2, ~ ®2)Mx =Q""m* 0 + mx 'X +J" "mJ^nF -*-y JK (coG -co)M= J (1.24) -jcocomHx + co0comH The equation (1.24) can be re-written with tensor susceptibility [%\ as M = [x]H = sCxx sCxy sCyx Xyy 0 0 0 0 H 0 (1.25) where the elements of [%\ are given by y Axx = y /lyy = G)0COm -—-— 2 ,,2 co0 — co 11 (1.26) Xxv X yx J<°®m 1 6D0 (1.27) 1 -CO To relate B and H, we have from equation (A1.5) (see Appendix Al) that B = ju0(H + M) = \fj\H and the resultant Polder tensor permeability [//] is given by M- JU JK 0 -JK fi 0 (z axis) 0 0 (1.28) M,_ where the elements of tensor permeability are then given by a M = Ml + Xxx) = Mo(l + Zyy) = Ml + ^m CO0 K <w»„ = -JMoXxy = JMoZy, = A) <»0 2 X 2 2 2 (1.29) -CD (1.30) -<y A material having this form of permeability is called gyrotropic, meaning that an x (ory) component of H gives both x and y components of B, with 90° phase difference between them. Please note that if the direction of bias magnetic field is reversed, both H0 and Ms will change signs, so co0 and com will both changed signs. From equation (1.28) it shows that ju will be unchanged, but K will change sign. We summarize for different /n w i t h respect to different bias magnetic field direction in equation (1.31) as follows 12 w= 0 0 0 -JK M 0 y"o 0 A>_ 0" 0 M JK 0 -J'K // 0 0 y" -y'* - p ]K If]' M- A, 0 0 J* 0 (-z axz's) (x axis) (-x axis) /* -JK 0 A> 0 (y axis) JK 0 ^ . 0 7'K" ' V 0 A) 0 (-y axis) [/<]• 0 M -JK /" M (1.31) This macroscopic Polder tensor permeability now is ready to be able to implement in Maxwell's equation to calculate the wave propagation properties in a ferrimagnetic media or ferrimagnet transmission lines. 1.2.3 Ferromagnetic Resonance As introduced previously, the total electron magnetic moment or magnetization in the ferromagnetic sample precess about the direction of the dc biased magnetic field and its precessing frequency is determined by the strength of the bias magnetic field. When adding an external rf transverse field, there is a strong resonance or coupling between the magnetization in ferromagnet and the rf transverse field when the frequency of the rf field is coincide to the precessing frequency of the magnetization. At this moment, the energy of the rf transverse 13 field will be strongly transferred to magnetic precessing system. This phenomena is called ferromagnetic resonance (FMR), and its corresponding peak absorption frequency is called FMR frequency. The Lamor precession frequency is just an ideal case of FMR frequency where a single magnetic dipole is in an infinite ferromagnetic medium. However, it is usually the case that the ferromagnetic sample is a finite sample with certain shape. As an example, the FMR frequency of a magnetic thin film layer is highly affected by the shape of the sample. The shape of the ferromagnetic sample plays an important role because the demagnetization field is large. The effect that the amount of internal magnetization in the ferromagnet depends on the shape of the sample is called the demagnetization. Kittel's equation [25] present the FMR frequency by adding the demagnetization f a c t o r ^ , Ny and7Vz. Then the FMR frequency can be generally defined as «o = r*J(H +(Ny-Nz)Ms)(H +(NX-NZ)MS) (CGSUnits) (1.32) For example, in a magnetic thin film layer, when the bias field is applied to the plane of the film (e.g., x-z plane), Nx=Nz=0; Ny=4x , then the FMR frequency is then given by co0 = yJ(H)(H +AnMs) (CGS Units) 14 (1.33) where y and Msare the gyromagnetic ratio and saturation magnetization of the sample. H is the internal biased magnetic field where any anisotropy of the sample should be considered. The tuning of the microwave FMR peak absorption frequency is clearly shown in equation (1.32) or (1.33) and it can be depicted in Figure 1.2 where FMR peak absorption frequency can be tuned in a wide frequency band by changing the bias magnetic field H. "\ 3 o Peak FMR Absorption Frequency / ^ T u n i n g by Magnetic Field H > CO o • / fres(H) Microwave Frequency Figure 1.2 Tuning of FMR Peak Absorption Frequency 1.2.4 Magnetic Properties of YIG/GGG Film Pure yttrium iron garnet (YIG) has cubic crystal structure with chemical formula Y3Fe50i2. Each unit cell contains eight formula units. The basic lattice point is 15 m3m and the lattice constant is 12.376 A [26]. Pure gadolinium gallium garnet (GGG) has the chemical formula GdsGasOn and also belongs to the cubic crystal structure. The lattice constant of GGG substrates which are prepared by Czochraliski crystal growth technique is 12. 383 A [22]. Single crystalline YIG thin films are most commonly grown on lattice-matched GGG substrate by liquid phase epitaxy (LPE) technique where a piece of polished GGG substrate was dipped into a bath of molten flux and garnet materials, i.e., YIG, for a short time. Typical film thickness ranges from 1 // m to 100 ju m. A 0.1 ju m transitional layer limits the purity of submicron thin films. Severe cracking of thick YIG films caused by the slight lattice mismatch between the epi-layer and the substrate places an upper limit on thickness of YIG films on GGG. The best quality YIG films are grown on [111] face GGG substrates with surface dislocation density of 1 defect/cm 2 . Single crystalline YIG thin film with its remarkable resonance properties has attracted a great deal of research efforts. The very low intrinsic damping of YIG film has made it an ideal vehicle for the study of fundamental relaxation properties, spin-wave excitations, and the contribution of inhomogeneities to the linewidth. In additional to its fundamental values in research, YIG has been found useful in many microwave applications [27]. Its gfactor of 2, narrow linewidth, and small anisotropy field make it especially suitable for microwave-frequency applications. In many microwave devices, such as ferromagnetic amplifier, resonance filters, harmonic generators, and passive limiters, YIG has been widely used because of its small resonance 16 linewidth. In the room temperature, the Lande g-factor of YIG is equal to 2, the saturation magnetization 4;rM s is near -1,700 Oe, and the Linewidth of polished single crystalline YIG at X-band can be well below a few Oe's [27]. YIG is a magnetic insulator where, in the room temperature, the electrical resistivity is ~ 109 CI/cm. 1.3 Research Objective and Thesis Organization Microwave tunable filters play critical roles in many microwave- and millimeterwave communication systems. For example, microwave band-stop filters are required in many applications for suppression of the frequency parasitics, undesired spurious bands or harmonics in microwave and millimeter-wave devices and modules. Traditional techniques based on the use of half-wavelength short-circuit stubs, chip capacitors or cascade rejection band filters are narrow band in principle [28]. More recently, the planar electromagnetic band-gap (EBG) structures have suggested some potential for wide stop-band band rejection applications [29-30]. The FMR-based microwave filters have the advantages to possess the unique capability of potential high-speed electronic tunability, using magnetic field, for very high carrier frequency and very large bandwidth [31]. In this dissertation research, a magnetically-tuned microwave band-stop filter using YIG/GGG- gallium arsenide (GaAs) flip-chip layer structure with wideband tunability of stop-band center frequency and bandwidth has been accomplished using a microstrip meander line together with non-uniform bias 17 magnetic field [32, 34]. A magnetically-tunable wideband microwave band-pass filter with large tuning ranges for both the center frequency and the bandwidth in the pass-band has also been realized using a pair of cascaded aforementioned band-stop filters [33, 34]. The thesis consists of 6 chapters. In Chapter 2, the theoretical modeling and analysis of YIG/GGG-GaAs layer structures are carried out, and the calculated results predict possible device application as wideband tunable microwave filters and phase shifters. Simulations of the microwave band-stop filter using equivalent circuit model and finite element analysis (FEA) method by ANSOFT High Frequency Structure Simulator (HFSS) are carried out in Chapter 3. Chapter 4 and 5 presents the experimental study of the magnetically-tuned wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs layer structures including device designs, fabrication, testing and measurement results. Chapter 6 concludes the thesis with the discussion and some future research topics. Appendix Al Maxwell's Equations in MKS and CGS System of Units The four Maxwell's equations supplemented by two constitutive relations are usually written in the form shown below. Equations (Al.l) to (A1.6) express the Maxwell equations in MKS system of units 18 dB ~~dt VxE = VxH = T dD J+ (Al.l) (A1.2) dt V»Z) = ~Pv (A1.3) V»2? = 0 (A1.4) B = /j0(H + M) = /iH (A1.5) D = s0E + T = sE (A1.6) where / = crE. The units of each field quantity are defined as E = Electrical Field Intensity (volt/m) D = Electrical Displacement (coulomb/ m2) H = Magnetic Field Intensity (amp/m) B = Magnetic Flux Density (weber/m 2 , tesla) J = Current Density (am/m 2 ) pv = Charge Density (coulomb/m 3 ) a = Conductivity (ohms/m) M = Magnetization (amp/m) P = Electric Polarization (coulomb/ m2) 19 ju0 = Free Space Permeability (henrys/m) e0 = Free Space Permittivity/Dielectric Constant (farads/m) ju and s are the material permeability and permittivity. Equations (A1.7) to (A1.12) express the Maxwell equations in CGS system of units V x ^ - I ^ c Bt (A1.7) vx^=i^ + i^ c V*D = -4xpv V»g = 0 B = H + 47TM = /JH D = £ +4^? = f£ The units of each field quantity are defined as E = Electrical Field Intensity (statvolts/cm) D = Electrical Displacement (statcoulomb/ cm2) H = Magnetic Field Intensity (oersted) B = Magnetic Flux Density (maxwell/cm 2 , gauss) pv = Charge Density (statcoulomb/cm 3 ) 20 (AL8) c dt (A 1.9) (ALIO) (ALU) (A1.12) a = Conductivity (l/(statohms/cm)) M = Magnetization (oersted) P = Electric Polarization (statcoulomb/ cm2) Mo= £ =1 o ju and s are the material permeability and permittivity. Reference 1. J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer "Ferrite devices and materials." IEEE Trans. MTT, vol.50, pp.721-737, Mar. 2002. 2. David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc., 2005. 3. J. D. Adam, S. V. Krishnaswamy, S. H. Talisa, and K. C. Yoo., "Thin-film ferrites for microwave and millimeter-wave applications," / Magn Magn Mater, vol.83, pp.419-424,1990. 4. V. S. Liau, T. Wong, W. Stacey, S. Ali, and E. Schloemann, "Tunable bandstop filter based on epitaxial Fe film on GaAs," IEEE MTT-S Dig., pp. 957960,1991. 5. C. S. Tsai, J. Su, and C. C. Lee, "Wideband electronically tunable microwave bandstop filters using iron film-gallium arsenide waveguide 21 structures/' IEEE Trans. Magn., vol.35, pp.3178-3180,1999. 6. B. Kuanr, I. R. Harward, D. L. Marvin, T. Fal, R. E. Camley, D. L. Mills, and Z. Celinski, "High-frequency signal processing using ferromagnetic metals," IEEE Trans. Magn., vol.41, pp. 3538-3543,2005. 7. E. Salahum, G. Tanne, P. Queffelec, M. Lefloc'h, A.-L. Adenot, and O. Acher "Application of ferromagnetic composite in different planar tunable microwave devices." Microwave and Optical Technology Letter, vol.30, Aug. 2001. 8. B. Kuanr, L. Malkinski, R. E. Camley, Z. Celinski, and P. Kabos, "Iron and permalloy based magnetic monolithic tunable microwave devices." /. Appl. Phys., vol.97, pp.8591-8593,2003. 9. N. Cramer, D. Lucie, R. E. Camley, and Z. Celinski. "High attenuation tunable microwave notch filters utilizing ferromagnetic resonance." /. Appl. Phys., vol.87, pp.6911-6913,2000. 10. V. G. Harris, Z. Chen, Y. Chen, S. Yoon, T. Sakai, A. Gieler, A. Yang, Y. He, K. S. Ziemer, N. X. Sun and C. Vittoria, "Ba-hexaferrite films for next generation microwave devices" /. Appl. Phys., vol.99, 08M911,2006. 11. Zhaohui Chen, Aria Yang, Anton Geiler, V. G. Harris, C. Vittoria, P. R. Ohodnicki, K. Y. Goh, M. E. McHenry, Zhuhua Cai, Trevor L. Goodrich and Katherine S. Ziemer, "Epitaxial growth of M-type Ba-hexaferrite films on MgO (111) | | SiC (0001) with low ferromagnetic resonance linewidths," Appl. Phys. Lett, vol. 91,182505,2007. 22 12. Yajie Chen, Anton L. Geiler, Taiyang Chen, Tomokazu Sakai, C. Vittoria and V. G. Harris, "Low-loss barium ferrite quasi-single-crystals for microwave application," /. Appl. Phys., vol.101, 09M501, 2007. 13. Y. Chen, I. Smith, A. L. Geiler, C. Vittoria, V. Zagorodnii, Z. Celinski, and V. G. Harris, "Realization of hexagonal barium ferrite thick films on Si substrates using a screen printing technique," /. Phys. D: Appl. Phys., vol. 41,2008. 14. Y. Y. Song, J. Das, Z. Wang, W. Tong, and C. E. Patton, "In-plane c-axis oriented barium ferrite films with self-bias and low microwave loss," Appl. Phys. Lett. Vol. 93,172503-1-3,2008. 15. M.I. Bichurin, LA Korner and V.M. Petrov, "Theory of magnetoelectric effects at microwave frequencies in a piezoelectric magnetostrictive multilayer composite", Physical Review B, vol. 64, 094409, 2001. 16. M.I. Bichurin and V.M. Petrov, "Theory of low-frequency magnetoelectric coupling in magnetostrictive-piezoelectric bilayers", Physical Review B, vol.68,054402,2003. 17. S. Shastry and G. Srinivasan, "Microwave magnetoelectric effects in single crystal bilayers of yttrium iron garnet and lead magnesium niobate-lead titanate", Physical Review B, vol.70, 064416, 2004. 18. Mirza I. Bichurin and Vladimir M. Petrov, "Composite magnetoelectrics: their microwave properties", Ferroelectrics, vol.162, pp.33-35,1995. 19. S. S. Kalarickal, D. Menard, J. Das, C. E. Patton, X. Zhang, L. C. Sengupta, 23 and S. Sengupta, J., "Static and high frequency magnetic and dielectric properties of ferrite-ferroelectric composite materials," /. Appl. Phys. Vol.100,084905-1-9,2006. 20. S. D. Yoon, C. Vittoria, Y. N. Srivastava, A. Widom, and V. G. Harris, "Magnetoelectric effects in composite of nanogranular Fe/Ti02-d films," Appl. Phys. Lett, vol.92, 042508, 2008. 21. Carl Pettiford, Saumitro Dasgupta, Jin Lou, Soack D. Yoon and N. X. Sun "Bias field effects on the microwave frequency behavior of a PZT/YIG magnetoelectric Mayer", IEEE Trans Magn., vol.43,3343,2007. 22. H. L. Glass, "Ferrite films for microwave and millimeter-wave devices," Proceeding of IEEE, vol.76, pp.151-158,1988. 23. Carmine Vittoria, Microwave Properties of Magnetic Films, World Scientific Inc., 1993. 24. Richard L. Liboff, Introductory Quantum Mechanics, 4th ed., Addison Wesley Inc., 2002. 25. C. Kittel, Introduction to Solid State Physics, 7th ed., John Wiley & Sons, Inc., 1996. 26. Gerhard Winkler, Magnetic Garnet, Vieweg Tract in Pure and Applied Physics, Friedr. Vieweg & Sohn Verlagsgesellschaft mbh, Braunschweig, 1981. 27. Wilhelm H. Von Aulock, Handbook of Microwave Ferrite Materials, Academic Press, New York and London, 1965. 24 28. F. Martin, F. Falcone, J. Bonache, R. Marques, and M. Sorolla, "Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators." IEEE Microwave and Wireless Components Letters, vol.13, pp.511-513, 2003. 29. V. Radisic, Y. X. Qian, and T. Itoh. "Broad-band power amplifier using dielectric photonic bandgap structure." IEEE Microwave and Guided Wave Letters, vol.8, pp.13-14,1998. 30. F. Falcone, T. Lopetegi, M. Irisarri, M. A. G. Laso, M. J. Erro, and M. Sorollaet. "Compact photonic bandgap microstrip structures." Microwave and Optical Technology Letters, vol.23, pp.233-236,1999. 31. C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y. Gulyaev. "Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41, pp.3568-3570,2005. 32. G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low-pass filter in a yttrium iron garnet-gallium arsenide layer structure", /. Appl. Fhys., vol.103, 2008. 33. Gang Qiu, Chen S. Tsail, Bert S. T. Wang, and Yun Zhu, "A YIG/GGG/GaAs-Based Magnetically Tunable Wideband Microwave Band-Pass Filter Using Cascaded Band-Stop Filters", IEEE Trans. Magn., vol.44, issue 11, 2008. 25 34. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in flip-chip YIG-GaAs layer structures", accepted and to be published in IEEE Trans. Magn., 2009. 26 Chapter 2 Theoretical Modeling and Analysis of YIG/GGG-GaAs Layer Structure In this chapter, the theoretical modeling and analysis of YIG/GGG-GaAs flipchip layer structure is carried out. A four-layer model and full-wave method are used to calculate the wave propagation property of the magnetic layer structure and the results show clearly maximum microwave energy absorptions at FMR frequency and the wideband FMR absorption frequency tunability when tuning the bias magnetic field. The theoretical results predict a potential device application as wideband tunable microwave band-stop filter utilizing the FMR absorption features of this magnetic layer structure in microwave frequency band. A tunable phase shifter in microwave frequency band, as another device application, is also discussed in this chapter. 2.1 Theoretical Modeling 2.1.1 Model Description The magnetic layer structure used in this theoretical study is shown in Figure 2.1. The analytical modeling and analysis method used in this chapter is based on a two-layer (magnetic/dielectric) model in [1]. In Figure 2.1, the magnetic layer structure consists of a YIG/GGG layer and a GaAs layer with thickness of d\, |<i2|-|Jl| and |J4| - |J3|, respectively. A thin air layer with thickness of |c/3| in 27 between is used to model the effect of the air gap due to the existence of the microstrip line in the experimental arrangement. The boundary between YIG film and air gap is set at y - 0 as shown in Figure 2.1. Both the internal bias magnetic field H0z and microwave propagation are in the z direction. The microwave is designated to propagate along z direction with propagation constant^. Because of the finite boundary on y direction, there is propagation constant k as well, but kx = 0 due to infinite dimension on the x direction. The propagation constant k2, for a given frequency of co, will be carried out to characterize the wave propagating properties along the magnetic layer structure. 1 d2 d1 0 -d3 -d4 Figure 2.1 the Multi-Layer Magnetic Structure 2.1.2 Full-Wave Method The method of theoretical analysis is outlined in Figure 2.2. 28 for a given co, A(j) findkztomake\M\-0 real(kz) Phase imag(kz) Attenuation t y PEC Ex,Ez=0aty = d2,-d4 d2 InYIG, Hx = Y,A(j)emyeJk-z EX,EZ,HX, Hz continuous dl 0 k -[01 Wl aty = Q,dl,-d3 HzHyExEyEz~A(j)(j Total16 B.C. Same for GaAs, GGG, Air, •• -d3 GaAs -d4 • • - PEC = lto4), Total 16 unkown indepentent variables. t plug in Maxwell Two CurlEqs. Vx£ = VX#: k=0 and \_ffi_ -cdt \8D for a given kz and a tensor[n\ jggk Vx(-Vxg) = -— £ C ^ OU [Q] = [0] when \Q\ = 0, there are four k solutions c dt Figure 2.2 Outline of Analytical Analysis of the Multi-Layer Magnetic Structure We will start with Maxwell's two curl equations to develop a relation involving the magnetic field component H, then k is determined by a given kz and frequency co. Each k gives an electromagnetic mode allowed in the layer and the superposition of all the modes with independent variables or coefficients represents the field in the layer. The analysis is carried out in the YIG layer first and the similar analysis is carried out for the remaining dielectric layers (GGG, GaAs, and air layer). Once all the field components are represented by their corresponding independent variables, i.e., four independent variables for each layer and the total are 16 independent variables, the boundary condition (B.C.) 29 will be used to write a matrix equation MV=0, where M is 16x16 B.C. matrix and V is the vector of the sixteen independent variables. There is only nontrivial solution if the determinant of M is equal to zero. Given a frequency co, we find kz to make determinant of M is zero. The CGS system of units is used in this section for the derivation. Starting from Maxwell's two curl equations and the two constitutive relations in (2.1) to (2.4) Vx£ = - I f (2.1) c dt VxJ? = I ^ (2.2) c at B = H + 4TTM = JUH (2.3) D = E + 4xP = sE (2.4) We obtain Vx(^-VxH) = --^pL s c dt In this derivation, the wave propagating is assumed in a form of Ae (2.5) j(kxx+ky+kzz-cot) d ., d ., d ., , d2 and, therefore, — = jkxx — = jky — = jkzz and -^-j = -co2 . Expanding left hand 2 dx dy 8z dt side, we have 30 Vx(-Vxtf) = x :(-kykxHy-kAH,+KH*+kM s +y -(-KkH -kxkHx k2H+k2Hy) + (2.6) -kykzHy+k2xHz+k2yHz) + z ~(-KKHx Note that kx=0 due to infinite dimension on the x direction. Equation (2.6) turns to 1 Vx(-VxH) = x (k2Hx+k2Hx) £ 2 +y -(-kzkyHz+k Hy) (2.7) -(-kykzHy+k2yHz) +z where e is the dielectric constant of the corresponding layer. The right hand side of equation (2.5) is expanded when plug in the tensor permeability [ju], we now consider the ferromagnetic material and [ju] is given as follows [2]. "1 + 4 % , [//] = [/] + 4 4 * ] = 4 ^ZyX 0 2 (yH0 + jcoa) A„; 4%, °" 1 + ^Zyy 0 2 - co . . 4n J - co (yH0 + jcoa) - co 0 = -jjUT 0 yMsco ——2 T (yH0 + jcoa) - co YMSQ> (yH0 + jcoa) A 0 1 0 7>r 0 //, 0 0 1 31 0 0 1 (2.8) Where y and a axe the gyromagnetic ratio and the Gilbert damping factor, respectively. The damping factor a is related to the ferromagnetic resonance AHv linewidth AH and frequency co as cx = — [3] (see Appendix A2). Expanding the 2co right hand side of equation (2.5), we have i a2 (juH) c2 dt2 —— JC 2 2 CO (0 -^Hx^+—HyMT 2 2 CO +y CO „ 2-HXMr+ — HyA c c (2.9) CO +z 2 a, Equate (2.7) and (2.9), we have this following matrix equation [£)][#] = 0, W> s s H .[iTco J c H £ KK 0 The equation KK \ v'] fh°> y Hz CO ~0~ = 0 0 (2.10) s (2.10) has nontrivial solution when the |£?| = 0 , that is Ak* + Bk2+C = 0, where A= 2 2 EC B= CO EC J(MI+MI2-VT2)—Tl-(1 2„4 C= 2M> EC* , ,k4 „ 2 > 2 2 EC + EC M) (2.11) ^ +-r(#r -M ) Therefore, given kz and co, there exist four solutions for k which corresponds to 32 four different electromagnetic modes allowed, k is given as i -B±(B2-4AC)2 :+ 2A MO ;=i to 4 (2.12) Now the /f is readily to be written as linear superposition of the four modes with different k . H now to be written as ^=XaO'Moy*' (0 v^ (2.13) j=i where X ( 0 2 . K2 -+£ a(i) = ju^2 S 2^ f .•Mr® 2 V C C J, ^(0 2 k2 £• S m- W> 2V K(i)2 • MTco Km (2.14) co 2 J The electrical field E can be represented in terms of Hby the Maxwell's curl • 1„ rr 1 QE . , , equation—V x H = , or equivalently s c 8t 33 c £ MkzHx-kxHz) = (2.15) C £ l(kxHy-kyHx) = £ £ C JSLEXk-*^,)--^ C £ C Now the E can be represent in terms of A(i) as follows E * =— £C0 j=\ L Z\(kM^-kyd)m)A(i)eJk^e^ k eJ y(i)y'eiK: (2.16) £CO~~? Now all E(Exx,E y,Ezz) and H(Hxx,H y,Hzz)aie written in terms of the four independent variables A(i)\. =lto4 The above derivations H(Hxx,Hyy,Hzz) are focused on calculating E(Exx,E y,Ezz) and in the ferromagnetic material. Now the similar analysis is to be carried out in the dielectric materials, i.e., GaAs, GGG and air layer. Since the permeability in dielectrics is simply represented by ju = I , so the matrix equation[g][i/] = 0 for dielectric material is (note that kx = 0) K K2 £ £ 0 0 a?2 0 0 c2 k2 co2 KK £ C2 £ KK £ 34 "o" Hy 0 0 y K co2 £ X" C2 Hz_ (2.17) We can determine the ky value by a given kz and co from the top left element of [Q] and lower right 2x2 elements of [Q], respectively. Both of them are turned out to be same mathematic condition as follows K2 k. +^ CO =0 r £ (2.18) C Therefore, k can be computed as 2 = ± Uco -k. K i Y2 (2.19) The block diagonal character of the [Q] means that we can not express H and H2 in terms of Hx. They are expressed separately as follows. Hy=jrC(i)eJk>(i)yeJk>z (2.20) Hz=fdS(i)C(i)e^'(i)yeJk-z r=l where r S(i) = e £ ,2 A CD C Kky(i)K Finally the E can be represent in terms of B(i) and C(i) as follows 35 (2.21) E*=—i[(*. -^o)^(o)c(/)^(°v^; SCO _ . kzB(i)ejkAi)yeJKz E =—-Y (2.22) scott Ez=-^-±-ky(i)B(i)eJkAi)ye^ £0) =1 The derivations above are applicable for the three different dielectric materials including GGG, GaAs and air. The differences are the material parameters and its k 's and, therefore, its corresponding independent variables. Now we should combine all E and //fields in dielectrics (in GaAs, GGG, and air layer) and ferromagnetic material (YIG) to the B.C.. The boundary conditions are summarized in Table 2-1. The notations of the field independent variables (e.g.,^(/),5(/)...) and field conversion factors (e.g.,a(/),/?(z)...) for each material is summarized in Table 2-2. Table 2-1 Boundary Conditions of the Four-Layer Magnetic Layer Structure y -axis Position y = d2 y = d\ Boundary Conditions (B.C.) = ^xGGG J-f n y=o — M ^xYlG ^xAlR **xAIR y = -d4 n = = = "' = • f-f ^zAIR zYIG » ~ -"zAIR' = ^zGaAs HxGaAs,nzAIR = n ~ ^ zAIR » ^xAIR'^zYlG ^xGaAs' ^zYIG' —M xYIG > " zGGG ~ ^xAIR •> &ZY1G ^xGaAs 36 ' ^zGGG ^xYIG •> ^iGGG xGGG **xYIG y = -c/3 u ^xGGG ^ ' ^zGaAs ' —tlzGaAs, = ^' Table 2-2 Field Independent Variables and Field Conversion Variables Material GGG Independent Variable Field Conversion Factor *(0L to2 ;C(0L o2 YIG ^•)L o 4 Air ^0L to2 ;£(0|, lto2 F (OL 2 ;G(o|, lto2 *(0L, 2 «(0|,=1/o4;A(0Llto4 tfOL* GaAs <PWLo2 There are total 16 B.C., and, according to those B.C., the following equations are given At y = dl ExGGG ~ 0 t [(*, - KGGG OW)) c ( * y W i ) V*< Z '= 0 e GGGG) EzGGG i=l = (2.23a) ^ ZU^'V^'V^o £ GGG<^ «'=1 At y - d\ ^xGGG ~ ^xYIG Z [(*. - W (0^(0) C(/y w ° V^ ^ £ GGGC0 >'=1 t[(K^)-kyY1G(i)m)meJkyY,Gii)ye^ SYJQCO , = I ^zGGG = ^zYIG k J ,GOG(')y ^kyGCG(i)B(i)ejk^a)y e 8 GGG® ikz: »=1 Jk,no(')y EWOAO**"8^ SYJQCO ajkzz i=\ rr " " xr/G TJ - " *GGG JkyBc(')yik^ i=i " zGGG i=i = HzYIG (2.23b) 1=1 1=1 37 At y = 0 ^xAIR ~ ^xYlG t[(kz-kyA!R(i)m)meJKA'R(i)yeJk>° £ 6) AIR <=1 X[(^«(0-V/ G 0')A0)^(0e 7VG<0 ^ Az YIG ^zAIR »=1 ~ ^zYlG fiyAIR^iy SWO^'V^e £ AIR0) JKZ i=l YKvomav^e Jkyna(')yoJKz £yjGG) ^zAIR ,=1 ~ ™zYIG Y,0(i)E(i)eJk^{i)yeJKz = Y^p^Aiiy^'e^ (2.23c) At y = - J 3 ^xAIR ^xGaAs -kyA1R(i)m)E{i)eJk^(i)ye^] t[(K e AIRCO i=\ E[(*,-WO*o)^i> w 'V S GaAs(D -^z^ffl = i=l ^zGaAs X^OPOVv<^ jk,Amii)y sATD a> AIR™ Jkzz i=l JkyGa.4s(')y jkzZ % ^ < ^ i=l **xAIR = tlxGoAs 2 2>o> JkyAmOv Jkzz 2 _ V J=l "z/lffi {t)y JKz i=l = **• zGaAs ^(/)£(/y (=1 k =£*•(»>J7{r\J y<*«* Vs(0 V M (2.23d) = XP(OG(0^ (=1 38 WO) V V y = -d* \ ^xGaAs ~ C Y(7/~ £ GaAsCO EzGaAs " /- d\m(i'\\G(i'\rikyaaA'{ji)yJk'z' = 0 (2.23e) (=1 = ^ - ^ t W O ^ W O V ' ' =o Now equations (2.23 a-e) are used to write a matrix equation MV=0, where M is B.C. matrix and V is the vector of the sixteen independent variables. A(l)' A(2) A(3) A(4) B(l) B(2) OT, 1,1 OT 1,2 ™1,16 w21 w,2,2 "h,l6 C(l) C(2) DO) ™16,1 ™16,2 ™16,16 = 0 D{2) E{\) E(2) F(l) F(2) G(l) G(2) (2.24) Equation (2.24) has nontrivial solution when the determinant of M is equal to zero. For a given frequency co, Mutter's method was applied to find kz which makes the determinant of M to be zero. The calculated k, is the wave 39 propagating constant containing the information regarding the attenuation and phase. The results are analyzed in detail in the next section. 2.2 Numerical Results and Analysis 2.2.1 FMR Absorption and Its Band-Stop Filter Application We re-write equation (1.32) here as (2.25) *>o = rJ(HMernal+(Ny -Nz)Ms)(Hinternal+(Nx-Nz)Ms) (CGS Units) (2.25) In the magnetic layer structure depicted in Figure 2.1, when the bias field is applied to the plane of the film (x-z plane), Nx=Nz=0; Ny=4n: , then the FMR frequency is *>0 = / M - — Win*™, +**K) (CGS Unite) (2.26) The FMR theory predicts that there will be a strong resonance at microwave frequency in the ferromagnetic layer structure described in Figure 2.1. Now we will calculate the wave propagation attenuation based on the full-wave method described in previous section to examine the FMR absorption in the layer structure in a wide microwave frequency regime. In this calculation, the material and geometric parameters used are in consistent with experimental arrangement, therefore, the thickness of GaAs substrate and YIG film are 350 jum and 6.8 jum, respectively. A 1.0 fim air layer is used to model the effect of the air gap due to the existence of the 1.0 jum thick microstrip line. The GGG substrate used to 40 epitaxial-grown YIG sample is ~ 350 jum. The AH and Ms of YIG sample are 1 Oe and l,160Oe , respectively, same as the material properties used in the experiments. The dielectric constant besGGG =14.7 and £GaAs=l\.l, of GGG and GaAs are set to respectively. As an example, a 2,200Oe field is applied to +z direction. The propagation distance along z direction was fixed at 0.57 cm for all the calculation in this chapter which is ready to be compared with experimental arrangement. The calculated microwave attenuation vs. rf frequency in the frequency of 8.0 to 8.5 GHz is shown in Figure 2.3. -i -10 \00 -20 C o 1 "iU -30 I -40 r i • r ~ O.O GaAs =350un Z-distance =0. H. t •4= 03 1 = 2,200 internal ' -50 FMR frequency = 8.2708 GHz -60 8.0 J 8.1 I . 8.2 I 8.3 . L 8.4 Frequency (GHz) Figure 2.3 Calculated Microwave Attenuation vs. rf Frequency when H = 2,200 Oe 41 8.5 Figure 2.3 shows clearly a maximum microwave power absorption at frequency of 8.2708 GHz. As a comparison, the predicted FMR frequency by equation (2.26) is 8.2645 GHz which are essentially the same to the peak absorption frequency shown in Figure 2.3. From the device application point of view, Figure 2.3 demonstrates a clear band-stop filtering function at microwave frequency regime, and, throughout this dissertation, the wideband tunable microwave band-stop and band-pass filters to be discussed are all based on this basic FMR absorption mechanism in this magnetic layer structures. 2.2.2 Wideband FMR Frequency Tunability By plug in different values of the bias magnetic fields, the calculations show that the frequencies of the maximum microwave power absorption associated with this magnetic layer structure were changed in a wide frequency band. The comparison between the calculated microwave power absorption frequency (0 to ~ 25 GHz) and the predicted FMR frequency by equation (2.26) vs. the bias magnetic field (0 to 8000Oe) is shown in Figure 2.4, while we see an excellent agreement between the calculated microwave peak absorption frequencies and the FMR frequency theory. Clearly, wideband tunability of FMR absorption frequency is shown in Figure 2.4. 42 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Internal Bias Magnetic Field (Oe) Figure 2.4 Calculated FMR Frequencies vs. Biased Magnetic Field From the application point of view, the maximum microwave power absorption level at FMR frequency is crucial when it is used as a microwave band-stop filter. Therefore, the FMR peak absorption level vs. FMR frequencies is calculated and shown in Figure 2.5. Clearly, Figure 2.4 and 2.5 combined predict a potential device application as a tunable microwave band-stop filter with large tuning range of peak absorption frequency with large peak absorption levels. 43 1 30 CD cz 1 I —-1 1 ' 1 • 40 45 1 1 1 1 1 1 - • \ •50 - - X -V. X •55 - ^•-^ ^•^ •60 - • i •65 1 YIG = 6.8um GGG = 350um Air= 1.0um GaAs =350um z-distance=0.57cm • 35 o 03 CD Q_ 1 • o CO < 1— " 1 6 • l 1 8 10 . 1 I 12 14 . I . 16 I . 18 20 FMR Frequency (GHz) Figure 2.5 Calculated FMR Peak Absorption Level vs. FMR Frequency As a typical example, the calculated attenuation vs. microwave frequency in a frequency range of 8 to 10 GHz is shown in Figure 2.6, where the bias magnetic fields used are from 2,200 Oe to 2,700 Oe. 44 -" n T " r~ '"" T ' 1 " 1 ' 1 ' 1 "^ ' i ' 1 1 ' ' ' 1 ' "\ ^ -10 ' - ' r -20 _ _ * CQ 3 ^ -30 c •2 -40 * - ^"-V II CO 13 0 H—» < - y 1 i i i l l 0U li II u I „ nnn „ -60 ~YIG = 6.8um 2,300 Oe 2' 400 Oe 2,500 Oe 1 : 2,200 Oe 2,600 Oe 2,700 Oe - • GGG = 350um Air^LOum -70 ~ GaAs =350um distance =0.57cm _«n 8.0 i 8.2 . i 8.4 . i 8.6 . i . 8.8 i . 9.0 i • 9.2 I 9.4 i I 9.6 . I . 9.8 10.0 Frequency (GHz) Figure 2.6 Calculated Attenuation vs. Microwave Frequency in 8 to 10 GHz 2.2.3 Material and Geometric Parameters Effect The microwave power absorption predicted in this magnetic layer structure is utilizing the strong coupling, at FMR frequencies, between the rf microwave field and the precessing magnetization in the magnetic layer. As with any resonance system, the effect of losses must be considered in its frequency response. The major parameter in the measurement of the loss in FMR system is the FMR linewidth (AH). Appendix A2 gives a brief introduction of FMR linewidth and its association with magnetic damping factor of the ferromagnet. AH is generally used to characterize the contribution of intrinsic loss mechanism and to 45 determine the role of magnetic inhomogeneities as well [5]. -10 CQ c o -20 •+= -30 I -40 CD 13 H. t = 2,200 Oe internal DeltaH=0.8Oe DeltaH=1 Oe DeltaH=2 Oe DeltaH=4 0e uaAs =JbiJum Ustance =0.57c -50 -60 8.0 8.1 8.2 8.3 8.4 8.5 Frequency (GHz) Figure 2.7 Effect of FMR Linewidth on Attenuation Figure 2.7 shows the effect of FMR linewidth ( AH = 0.8,1, 2, 4 Oe ) on the microwave attenuation at 8.2708GHz when H = 2,200Oe. As shown in Figure 2.7, the lower AH corresponds to higher FMR peak absorption level and a narrower FMR absorption bandwidth, holding all other parameters constant. The effects of dielectric layer thickness and ferromagnetic layer thickness on the microwave attenuation are also calculated. The thickness of the dielectric layers has a significant impact on the calculated attenuations. As shown in Figure 2.8, a 46 thickness of 150 urn GaAs layer provides much higher attenuation and slightly wider absorption bandwidth than others, holding all other parameters constant. The same effect happened on the GGG. As shown in Figure 2.9, a thickness of 150 um GGG layer also provides much higher attenuation and slightly wideband absorption bandwidth than others, holding all other parameters constant. The effects of thickness of GGG and GaAs are almost identical because they are nearly symmetric in the magnetic layer structure. 10 0 = 2,200 Oe te -10 h H,internal ^-v -20 DO /stance w -30 h GaAs Thickness t4 C —14 = 450 um o 14 = 350 um "ro -40 t4 = 200 um ZJ t4 = 150 um c _?> -50 -60 h -70 h 8.0 8.1 8.2 8.3 8.4 Frequency (GHz) Figure 2.8 Effect of GaAs Thickness on Attenuation 47 8.5 10 jgg|SS4SSaSS«£8SiffiSS!Sili«SS!aSfe -10 H., internal = 2,200 Oe '/L? - ' GaAs =350um Air- I.Oum -20 c o -30 =5 -40 C 5 -50 o.oum GGG Thickness t2 t2 = 450 urn t2 - 350 urn t2 = 200 urn t2 = 150 urn -60 -70 8.0 8.1 8.2 8.3 8.4 8.5 Frequency (GHz) Figure 2.9 Effect of GGG Thickness on Attenuation The air layer is used to model the thin air gap due to the existence of microstrip transmission line. It has a typical value of a few microns. As shown in Figure 2.10, the thickness of air layer has little effect on the propagation attenuation as expected. 48 -10 \- H. , internal 00 YIG = 6.8um GGG = 350um GaAs =350um ^-distance =0.5 = 2,200 Oe ' -20 c o •^3 - 3 0 CD C £ j -40 < -50 -60 8.0 Air Thickness t3 -t3 = 0um -t3= 1 urn t3 = 1.5 urn -t3 = 2um 8.1 8.2 8.3 8.4 8.5 Frequency (GHz) Figure 2.10 Effect of Air Layer Thickness on Attenuation The thickness of the YIG has a significant impact on the calculated attenuations. Unlike metallic thin film where increasing the thickness beyond skin depth has little effect on attenuation, the conductivity of magnetic insulator (i.e., YIG) is very low and the wave can penetrate and propagate inside the medium. As shown in Figure 2.11, for example, a thickness of 20.8 urn YIG layer provides much higher attenuation and much wider absorption bandwidth than a thickness of 6.8 um cases, holding all other parameters constant. 49 -10 f- H 1 = 2,200 Oe internal ' GO -20 c g -30 13 C -40 CD -50 5G = 35Gum ir= 1.0urn iAs =35 YIG Thickness t1 — tl = 2.8 urn 11 = 6.8 urn t1 = 8.8 urn t1 = 15.8 urn t1 =20.8 urn -60 8.0 8.1 8.2 8.3 8.4 8.5 Frequency (GHz) Figure 2.11 Effect of YIG Thickness on Attenuation 2.2.4 Phase Shifter Application Phase shifters find applications in test and measurement systems, but the most important use is in phased array antenna systems. In general, the change of the effective permeability under the bias magnetic field of single crystalline ferrite materials is more sensitive than the polycrystalline form. Therefore, in recent years, the microwave phase shifters based on single crystalline ferri- or ferromagnetic thin film structures have been actively studied [6-8]. 50 3* CO -i—> C/) c o O c o CD O) CD s_ Q. O u. 0_ 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 Frequency (GHz) Figure 2.12 Calculated Propagation Constant (Real and Imaginary Parts) at H0=2,7\0Oe The YIG/GGG-GaAs layer structure discussed in this chapter has possible device application as tunable phase shifters. Figure 2.12 shows the calculated propagation constant (both real and imaginary part) in 9.5 to 10 GHz while the bias magnetic field is 2,710 Oe. The wave is very dispersive (see Figure 2.12 real part ofkz) near the resonance. In the phase shifter application, in principle, the operating frequency is near the FMR frequency for maximum change of the phase with small bias magnetic field variation, and, in the meantime, the attenuation due to the change of the phase should remain low. In other words, 51 the operating frequency of the phase shifter should be near the FMR frequency which gives maximal dynamic range of the phase change and the minimum attenuation variations. For example, the possible operating frequency band for the phase shifter application of the magnetic layer structure when bias magnetic field is 2,710 Oe is indicated in Figure 2.12 (see the frequency range between blue lines). As an example, Figure 2.13 shows the calculated phase shifts at the operating frequency of 9.66 GHz with the bias magnetic field tuned from 2,710 Oe to 3,420 Oe, while the attenuation loss variation is within 0.3 dB. 500 400 0 300 D) CD CD 2 0 0 CO CD Q_ 100 0 9.50 J I 9.55 1 I 9.60 1 I I 9.65 I 9.70 1 I 9.75 1 I 9.80 1 I 9.85 I I 9.90 I I 9.95 L 10.00 Frequency (GHz) Figure 2.13 Calculated Phase Shift at 9.66 GHz while H0 is changed from 2,71OOeto3,42O0e 52 As a conclusion, the calculated wave propagation property of the YIG/GGGGaAs layer structure shown clearly maximum microwave power absorptions at FMR frequency and the wideband FMR absorption frequency tunability when tuning the bias magnetic field. The theoretical results predict a potential device application as a tunable microwave band-stop filter with large tuning range of peak absorption frequency with large peak absorption levels. Appendix A2 Ferromagnetic Resonance (FMR) Linewidth Laudau and Lifshitz introduced the equation of motion of magnetization with damping effect originally. — =W M x / / - n M x — dt \M\ dt (MKSunit) (A2.1) where: M: magnetization {A I m) H: bias magnetic field {A I m) y: gyromagnetic ratio, In x 2.8 xlO10 (rad /(sec* tesla))(MKS) /J0 : free space permeability a: damping coefficient We can begin with this lossy equation of motion of magnetization to derive the lossy tensor susceptibility \%\, and thus tensor permeability [//], or loss can be accounted for by making the resonant frequency complex co0 <- a>0 + jaco. 53 When we plug the complex resonant frequency co0 + jam into equation (1.26) and (1.27) in chapter 1, the complex tensor susceptibility [j] can be given as: stxx sCxx J si xx [AXF s^xy J /Cxy / A r\ r)\ where \jol -6>2(l + a 2 )] + 4<z>2<y2a2 [<y2-<y2] + 4a>lco2a2 acoa>m\a>Q+G)2(l + a2)\ aa>a>m\a)Q+G)2(l + a2)\ = Xxx = 2 ^— = —2 ^42.3(6) 2 2 2 2 2 2 2 2 [&>0 - <» (1 + a )] + 4o) a) a \col - a> ] + 4&>0Wa (a « 1 , 1 + a 2 2 1+ 2 2 2 2 a*»mM-» ( a )l coo)m\o) -co (l + a )] Xxy = ^ [<y02-a>2(l + a 2 )] = 2 = ^ 2 + 4c?0Wa l^o^a = 2 2 2 2 2 [(y0 -cj (l + a )] +46> ft> a 2 ^ -42.3(c) 2 2 + 4cv G) a 2_^a = 2 = 2 [<»02-<y2] 2 A 2 m 2 2 2 2 [<» -<» ] +4<» o a The damping coefficient a is related to the linewidth (AH) of the susceptibility curve near the resonance. The linewidth is defined as the width of the curve of Z^ vs. H0 where zlx has decreased to half of its peak value. The imaginary part zL w^ g ° t o maximal when co - co0 which is: acoa>m\(D2 + co2(l + a2)\ y = != [rt-m2] =L + 4co2co2a2 Assuming when*; = co02, x„ = - £ , m a x / so 54 i+«2=i —s ~> y „ = co __2L_ 2™ acocom a>l2 + a>2 1 2 2 2 [co 02-co ] + 4 f i 4 © V ffl. -X- 2 «« => <902 = coy[\ + 2a «<y(l + a ) => Aft>0 = 2(<»02 - <0O)« 2©(1 + a ) - 2<y = 2 a » . TT A<»n 2aco =>AH-—= ju0y MoT AHMnV CM or a = 2® (A2.5) Reference 1. R. J. Astalos and R. E. Camley, "Theory of a high frequency magnetic tunable filter and phase shifter", /. Appl. Phys., vol.83, pp.3744-3749, April 1998. 2. Carmine Vittoria, Microwave Properties of Magnetic Films, World Scientific Inc., 1993. 3. David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc., 2005. 4. C. Kittel, Introduction to Solid State Physics, 7th ed., John Wiley & Sons, Inc., 1996. 5. B. Heinrich and J. F. Cochran, "Ultrathin metallic magnetic film", Adv. Phys., vol.42, pp.523-549,1993. 6. H. How, P. Shi, L. C. Kempel, K. D. Trott, and C. Vittoria. "Single-crystal YIG phase shifter using composite stripline structure at X band." /. Appl. Phys, vol.87, pp.4966-4968,2000. 7. E. Salahum, G. Tanne, P. Queffelec, M. Lefloc'h, A. L. Adenot, and O. 55 Acher "Application of ferromagnetic composite in different planar tunable microwave devices." Microwave and Optical Technology Letter, vol.30, Aug. 2001. 8. Bijoy Kuanr, L. Malkinski, R. E. Camley, Z. Celinski and P. Kabos; " Iron and permalloy based magnetic monolithic tunable microwave devices." /. Appl. Phys, vol.97, pp.8591-8593,2003. 56 Chapter 3 Device Simulations of Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure The theoretical analysis of YIG/GGG-GaAs layer structure in Chapter 2 predicts the device application as a tunable wideband microwave band-stop filter. In this chapter, simulations aimed at device performance of the microwave band-stop filter using YIG/GGG-GaAs layer structure are carried out. A lumped element equivalent circuit method of the band-stop filter is presented first in this chapter. The advantage of a circuit model of the band-stop filter is the easy incorporation with commercial circuit simulator, and, therefore, an electronic subsystem, e.g., an oscillator, utilizing the band-stop filter (resonator) can be further simulated with a reliable equivalent circuit model. The simulations of finite element analysis (FEA) using ANSOFT High Frequency Structure Simulator (HFSS) is also discussed in this chapter. HFSS utilize 3-D full-wave FEA to conduct simulations for two-port parameter (S, Y, Z) extraction, and its capability of simulating em field distribution assist designs and optimizations of microstrip transmission line (transducer) in this YIG/GGG-GaAs-based microwave band-stop filter. 3.1 Simulations using Equivalent Circuit Method The basic device configuration of a tunable microwave band-stop filter using YIG/GGG-GaAs layer structure is shown in Figure 3.1. A YIG/GGG layer is laid 57 directly upon the GaAs-based microstrip line in a flip-chip configuration. An external bias magnetic field H0 is supplied along the z direction. The incoming microwave propagating along the microstrip is coupled into the flipped YIG/GGG layer and maximum coupling and, thus, the peak absorption of the microwave occurs when its carrier frequency coincides with the FMR frequency. YIG/GGG Layer X Microwave Ouput GaAs Substrate round Plane Transmission Line Microwave input Figure 3.1 Device Configuration of the Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure A theoretical modeling and analysis of this layer structure has been carried out in detail in Chapter 2. In this section, the simulation of the YIG/GGG-GaAs based microwave band-stop filter using a lumped element equivalent circuit model is presented [1]. As we stated before, once a circuit model of the microwave bandstop filter is available, it can be easily incorporated with commercial circuit 58 simulator, e.g., Advanced Design System (ADS) or Microwave Office by Applied Wave Research, Inc, and, furthermore, an electronic subsystem utilizing the bandstop filter (resonator) circuit model can be simulated. The simulation of the microwave band-stop will be presented by: (1) the calculation of the radiation resistance Rm of a YIG/GGG film in flip-chip coupling configuration, (2) FMR frequency knowledge and experimental data [2], and (3) the simulation of a lumped element equivalent circuit of the microwave band-stop filter using Microwave Office. The resulting lumped element equivalent circuit model [1] is shown in Figure 3.2. l:n Zo | CZI n:l 1 C Vin(V) j I L Zo R Figure 3.2 Lumped Element Equivalent Circuit Model of the Microwave BandStop Filter 3.1.1 Calculation of the Radiation Resistance As we studied in Chapter 1, when a ferrimagnet is bias by a large externally magnetic field, the ferrimagnet become magnetically saturated to produce a 59 saturation magnetization. Each individual magnetic dipole in the ferrimagnet will precess in a resonant frequency, e.g., Lamor precessing frequency. Due to the dipole-dipole coupling and quantum mechanical exchange coupling, the collective interactions among neighboring magnetic dipole moments produce a continuum spectrum of precessing modes or spin waves at frequency bands near the resonant frequency. Exchange-free spin wave spectrums obtained under the magnetostatic approximation are known as magnetostatic wave (MSW) [3-6]. In essence, MSW are relatively slow-propagating, dispersive, magnetically dominated electromagnetic (em) waves which exist in biased ferrites at microwave frequencies. It is well studied that three magnetostatic wave (MSW) modes can exist in a ferromagnetic layer depending on the orientation of the bias magnetic field relative to the ferromagnetic film and the propagating microwave direction [3-6]. These modes are magnetostatic surface wave (MSSWs); magnetostatic forward volume wave (MSFVWs); and magnetostatic backward volume waves (MSBVWs) [3-6]. In the microwave band-stop filter configuration shown in Figure 3.2, the external bias magnetic filed H0 is applied in the z direction in the plane of the YIG/GGG film and along the direction of the microwave propagation, and, therefore, MSSWs are to be excited in this configuration with propagation direction along the ±y axis [4]. 60 GGG Microstrip YIG d 1 dn b Substrate ///////// I IA Ground Figure 3.3 Cross-Section View of MSSW Excitation Geometry A theoretical analysis is developed in [4] for excitation of MSSWs with microstrip transmission line in flip-chip configuration as shown in Figure 3.3. Energy carried away in MSSWs propagating perpendicular to the microstrip (in ±y direction) is related to electromagnetic energy propagating along the microstrip line (in z direction) by an equivalent radiation resistance Rm. Here we will use the formulism developed in [4]. The Rm of the excited MSSWs with YIG/GGG film flip-chip coupling configuration is given by the expression. (3.1) Where A+ and A_ are the Rm associated with MSSW propagation along ±y directions, respectively. A+ and A_ are given as 61 A± = u^coR, sin(M 0 /2) 2 bkjl 2 1 - 4£07 exp(-2£0/) - exp(-4£0/) [2k0d{(ul2s + lf -Mn}]~ x[2 [l + exp(-2£00] x {{uns +1) sinh(^0J) + ux x cosh(&0<i) }2 + (uus + 2w, xk0d) {(ul2s+1)2 - u2n} (3.2a) - {ul2s[(ul2s+1)2 - Wj2 ] - 2w2j} cosh(2k0d) - w, x (u22 - 1 - u\x) sinh(2^0c/)] where i?t0 = (Wj j - w^s -1) exp(-£0 d) tanh(k0t) I AkQ (un-u12s + tanh(k0t)) Ak0=l + un(tf d)(l-tanh k0t)[un -(uns-tanhk0t) 2 -i-l ] (3.2b) (3.2c) The t, d and b axe defined in Figure 3.3 of the cross-sectional view of the excitation geometry. un and un are diagonal and off-diagonal components of the permeability tensor, respectively. s = ±\ represents the MSSWs propagating directions of ±y direction in Figure 3.3. a and the propagation constant k0 are related by dispersive equation of MSSWs in this configuration and will be calculated shortly. The formulism of co-k relation of excited MSSWs in the YIG/Dielectric layer is well developed in [5-6]. The relative permeability tensor uris given again as follows. The permeability tensor used here is in CGS units. ux -iu2 0 iu2 ux 0 where Q = o)/a)M, aH=coclcoM 62 0 0 1 (3.3) o)-27ixf is the wave angular frequency, coc = 2zr xyH0 is the gyromagnetic angular frequency (y = 2.SMHz/Oe is the gyromagnetic ratio, and the H0is the internal biased magnetic field), a>M = 2n x yAnMs ( AnMs is the saturation magnetization = l,760Oe). The dispersive equation for MSSWs written in terms of Q and Q.H is given by [5] ei\k]d 1 l + (fls + Q g ) [ l + tanh(-|fc|0] 2(Qs + Q„) + l l-(Qs-Q„)[l-tarJi(-|&|0] (3.4) The problem is now to find the value of k which, for a given frequency of / , satisfies the implicit dispersive equation (3.4). This is a root-finding problem requiring an initial guess at the value range of the root. In our case, the wavenumber k ranges over 10 <k<l05cm'1 . The range of / is the frequency range of excited MSSWs at ±y direction under this device configuration determined by the YIG intrinsic properties (e.g., Ms) and external bias magnetic field (H0). The lower frequency limit of the excited MSSWs is given as [5-6] -|l/2 /,=rt4*M,) £ (3.5) - -(—£- + 1) °>M ®M For the cases of dIt —» 0 (it is the usual case that the thickness of ferromagnet is much thinner than the dielectric substrate), the upper frequency limit of the excited MSSWs is given as [5-6] f2=r(4xMs)(^ +b ®M 2 63 (3.6) If we further expand equation (3.5) by plug in 6)c=2jrx yH0 and coM = In x y4nMs, equation (3.5) turns to -11/2 = yJ(H0)(H0+4xMs) /=K4*M,) (3.7) Now it is very interesting that the equation (3.7) is identical to equation (2.26) in Chapter 2. This relation is important and it is the bridge to understand the relation between the FMR absorption theory and the excited MSSWs in the ferromagnetic sample. Equation (2.26) is the FMR frequency derived from FMR theory with demagnetization effect (sample shape) considered. Equation (3.5) is the characteristic surface mode of a ferromagnetic sample magnetized in its plane obtained in the magnetostatic limit [6]. This relation states that the energy dissipated by the interaction between rf transverse magnetic field of propagating microwave and precessing magnetization of ferromagnet is transferred to the MSSWs propagating perpendicular to the microwave propagation, where the sample is magnetized in the plane of ferromagnet and also along the microwave propagation direction. Energy carried away in MSSWs is related to electromagnetic energy propagating along the microstrip line by an equivalent radiation resistance Rm. Radiation resistance Rm now can be readily calculated based on equation (3.1), (3.2) and (3.4). The parameters used in this Rm versus k diagram are consistent 64 with experimental arrangements as t-35Qfj,m , d = 6.8jum , b = 256/jm and H0 = 2,200Oe. The calculated Rm versus k diagram is 300 i—'—r i—•—r 250 i—•—r t=350um d=6.8um b=256um H=2,200Oe 3> 200 CD 150 O C CD •*—• CO 100 'co CD a: c 50 o "-1—< 03 T3 CD 0 Q^ 0 50 100 _L 150 J_ 200 _L 250 J_ 300 JL 350 400 _L 450 500 Propagation Constant (k) (cm"1) Figure 3.4 Calculated Radiation Resistance Rm versus Wavenumber kd&t = 350jum, d = 6.Sjum, b-256/im andH0 = 2,200Oe. Figure 3.4 will be used to calculate the values of lumped elements in the next subsection. 3.1.2 Calculation of Values of Lumped Elements 65 Figure 3.4 shows the Rm dependence of propagation constant k of MSSWs. In the device configuration with a constant bias magnetic field, different modes of MSSWs can be excited and propagate along the ±y direction. For lumped elements of equivalent circuit model, a dominant mode can be determined by the resonant property of MSSWs in the rectangle YIG sample. If ly,lz are the planar dimensions of the YIG sample in (y,z) I YITT wavenumber will be k = knm = | ( — ) 2 + ( V plane (see Figure 3.1), the resonance TTITT y ) 2 [7], and the wavenumber of the * main mode (n =l,m =1) is ku = n l(—)2 +(—)2 . In our simulations, the geometric parameters of YIG sample are also consistent with experimental arrangements as ly = 2.8mm and lz -9mm , therefore, the dominant mode is t u «12cm"' and the corresponding Rm is 12Q/cm. In the equivalent circuit model shown in Figure 3.2, the lumped element R , L and C are derived as R = Rm x/ , L = R/(yx AH) (y is the gyromagnetic ratio and Miis the linewidth of the YIG film), and C = l/(o^xL)(o)r =2xxfr, fr is the FMR frequency predicted in equation (2.26)). Values of the lumped element are now given as: R = RJy =336ohm , L = R/(yAH) = 191.05nH , and C = \l co2rL - 0.0019425pF, where linewidth AH is assumed to be a constant value 1 Oe . The Vin and the Z0 (see Figure 3.2) is the microwave signal and 66 characteristic impedance of the microstrip line, respectively. Two transformers are used by defining the turns ratio n , a value representing the connection with external circuit which can be estimated and by fitting experimental data [8]. n can be given as n = I—=$— , where (X = -^J— , Z0 = 50ohm (characteristic impedance of the microstrip transducer). The external quality factor Qext is a parameter counting for the microstrip as a coupling structure, and it can be defined as Qext = \ u0coMVK tm=\um [3] ( V = lyl2d and K = \n[(b + tm+2dQ)/(b + tm)]/4d0 is the thickness of the microstrip line). The resulting turns ratio is n « 2.5023. 3.1.3 Simulation of Lumped Element Equivalent Circuit We use Microwave Office to simulate the lumped element equivalent circuit. The circuit schematics are shown in Figure 3.5 and the simulated S-parameter (S21) is shown in Figure 3.6. It is shown in Figure 3.6 that the microwave band-stop filter has the stop-band peak absorption at frequency of 8.27 GHz with absorption level of more than -30 dB. The results are consistent with experimental data to be presented in next chapter. The equivalent circuit method will further be implemented in the calculation of microwave band-pass filter in Chapter 4. 67 SRLC ID=RLC1 R=3.36 Ohm L=191.1 nH C=0.001943pF XFMR ID=XF1 N=2.502 PORT P=1 Z=50 Ohm XFMR ID=XF2 N=2.502 PORT P=2 Z=50 Ohm 1 2 nl:l Figure 3.5 The Circuit Schematics in Microwave Office Simulator u —l | — •• • i -\ t=350um d=6.8um b=256um H=2,200Oe 11 il 11 -15 S CO _ u " - 11 IfII t r -20 CD <D • I1 CO -i—> • — i \\ 1f -5 2, ^—v — H „„ • 25 - E " CD s_ fi -30 - • - CO -35 8,27 GHz i .An 8.0 8.1 8.2 8.3 8.4 . 8.5 8.6 8.7 8.8 8.9 9.0 Frequency (GHz) Figure 3.6 Simulated S-parameters (S21) of the Equivalent Circuit of Figure 3.5 68 3.2 Simulation using ANSOFTHFSS 3.2.1 Model and Parameter Assignments ANSOFT Corporation's High Frequency Structure Simulator (HFSS) is an industry standard high-performance full-wave electromagnetic (em) field simulator for arbitrary 3D volumetric passive device modeling. HFSS utilizes the 3D full-wave Finite Element Method (FEM) to conduct simulations for two-port parameter (S, Y, Z) extraction, and it is also capable of generating visualizations of em field patterns. The HFSS simulation in this section for the microwave bandstop filter using YIG/GGG-GaAs layer structure is to simulate the microwave transmission characteristics (S-parameters) of the band-stop filter and the pertinent high frequency field (E-field and H-field) distributions in the multilayer structure. The simulation is particular useful when the electrical transducer (e.g., microstrip and step-impedance low-pass filter) are specifically designed for optimized device performances. One example is that the simulated H-field concentration on the inductive-elements of the designed step-impedance low pass filter, in contrast to a 50 Q microstrip, enhances the coupling of the microwave magnetic field into flipped YIG/GGG layer and, thus, increases the microwave power absorptions at the FMR frequencies (this part will be detailed in Chapter 4) The major procedures in the HFSS simulation of the microwave band-stop filter using YIG/GGG-GaAs layer structure is building up a physical model, 69 characterizing all associated materials including the ferromagnetic layer, adding solution setup, running the adaptive solver and generating plots. Radiation boundaries are at faces of cubic except the bottom one YIG/GGG Layer Waveport 1 mi Microstrip BiasH ;• X V id/ Waveport 2 GaAs Substrate \ Perfect E plan at bottom of substrate Figure 3.7 The Physical Model of The Band-Stop Filter Configuration in HFSS Using a YIG/GGG-GaAs Layer Structure The physical model was built as shown in Figure 3.7. The GaAs substrate, the silver microstrip, the YIG layer and the GGG layer are, respectively (in X Y Z axis), 10 4 X10 4 X350/WJ 3 , 104x256xl//w3 , 9000 x 6256 x6.8/W , and 9000 x 6256 x350//m3 . The material parameters for GaAs and silver are given in the material library of HFSS. The GGG was assigned as a perfect dielectric material with relative permittivity 14.7 (the same as YIG layer). The direction of the microwave propagation was assigned from waveport 1 to waveport 2. The 70 direction of the internal magnetic field, H0, was assigned in the same direction as microwave propagation shown in Figure 3.7. The bottom of the GaAs substrate was assigned as a perfect electrical, E, plane which serves as the signal ground plane. The parametric input data for the ferromagnetic YIG layer is the key step in this simulation. Figure 3.8 shows the edit-material box of ferrite materials in HFSS in which eight material parameters are shown. The relative permeability, magnetic loss tangent, magnetic saturation, Lande G factor, and Delta H (AH) are the five material parameters associated with the tensor permeability, [//], of the YIG layer. The five materials parameters together with co (frequency) and H0 (internal bias magnetic field) are used in HFSS to characterize a magnetic material. NOTS j Tp Value i Unta State 14.? f IRdative Permeability Simple 1 i ]8ylk Conductivity Simple 0,01 I {Dielectric Loss Tangent Simple 0 "t IMagnetic Loss Tangent Simple 0 I j Magnetic Saturation Simple^ 1760 _ Jaawt ' ItLandeGFactor^_ iilDeftaH.- . ... . . . ^ J j p l e ^ J ^ ._ Simple,, ! _ Sitmsni/m v _._ -i . _j . Q e _ . ... J Figure 3.8 Edit-material Interface of Ferrimagnetic Material in HFSS For most microwave ferrite materials, Lande G factor has a value in the range from 1.99 to 2.01 and it is safely to assign it as 2.00. The magnetic saturation, Ms , 71 and AH, together with frequency, co, and internal bias magnetic field, H0, are sufficient to assign the components in [ju]. Figure 3.9 shows the formulas that HFSS used to compute the [ju] from the four parameters (Ms , AH, co, and H0). This formulism is indeed agreed with the formulism discussed in Appendix A2. The actual assignment for the YIG layer in which the Ms =1,760 Oe and AH =1 Oe. The H0 was assigned to be 175070 A/m or 2,200 Oe in this simulation. The relative permeability and the magnetic loss tangent were assigned to be 1 and 0 in this simulation. «>|}W & = n Uh -JK }K jU o . ( w ' - f . ' 2 ) + M0<i>„,ar<r „2-«i»2)" + 4 a ^ V Mod),,, Ifti;I u = A n — A,t,t 0 JAxx <|J X» + «>:(1 + a2)) (ftij - <U2) + 4a'|cri>2rt2 A'jry ~ XXy "•" jXxy «%>,„(<«^-4> 2 {l + < r ) ) Xxif 0 0 ((Wjj-a)2) 1 + 4<<>Ju>2rt2 2(,)cni!,„in2<v A'ttf *~ (<ti^ - a) 2 ) + 4a>2l<i>2<l2 tl 10 Y = 2 JI X2.8X10 rad;nHz/Tesla «o = ,«o}'Ho Aff/V 26> Ho: Internal magnetic field Ms: Saturation magnetization to = 2 JI X applied ac signal frequency A H : Linewidth of the susceptibility curve near the resonance Figure 3.9 Derivation Blocks of Relative Tensor Permeability [ju] Using the Four Parameters Ms , AH, 72 co, and H0. 3.2.2 Simulation Results and Discussions Figure 3.10 shows the simulated S-parameter (S 2l ) of the microwave band-stop filter in the frequency range of 8.0 - 9.0 GHz. The simulated S2l shows that the microwave band-stop filter has the stop-band peak absorption at frequency of 8.28 GHz with absorption level of more than -30 dB. The FMR frequency of this band-stop filter occurred at 8.28 GHz agrees with the FMR frequency given in equation (2.26) and also consistent with the simulated FMR frequency in Figure 3.6. ctjo- 4M»- 8.4© Ff«q |6HteJ Figure 3.10 Simulated S-Parameter (S 2l ) of the Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure 73 Figure 3.11 Simulated H-field Pattern on the Surface of the YIG Layer at 8.28GHz The em field pattern is also studied in this simulation where Figure 3.11 shows the magnetic field (H-field) pattern on the surface of the YIG layer (contact surface to GaAs substrate) at the FMR frequency of 8.28 GHz. The major features in the Figure 3.11 are that the H-field pattern demonstrated a clear wave pattern which is propagates in the y-direction on the surface of the YIG layer (see Figure 3.11). These findings agree with the theoretical treatment in [9]. The magnetostatic surface waves (MSSW) was excited based on this configuration 74 and it is propagating on the surface the YIG layer in the direction of H0 x n, where n is the outwardly directed surface normal [9]. In this simulation, H0xn represent the xx(-z) = y direction shown in Figure 3.7 (-z is the surface normal of the surface contact to GaAs substrate). Both the simulated 521 and the H-field pattern agree with the expected results [9]. The HFSS simulations will further be implemented in the design of optimized transmission line in microwave band-stop filter in Chapter 4, and simulations of microwave band-pass filter in Chapter 5. Reference 1. G. Bartolucci, R. Marcelli, "A generalized lumped element modeling of magnetostatic wave resonators", /. Appl. Phys., vol.87, pp.6905-6907,2000. 2. C. S. Tsai, and Jun Su, "A wideband electronically tunable magnetostatic wave notch filter in yttrium iron garnet-gallium arsenide material structure", Appl. Phys. Lett, vol.74, pp.2079-2080,1999. 3. W. S. Ishak, "Magnetostatic wave technology: a review," Pro. IEEE., vol.76, pp.171-187,1988. 4. A.K, Ganguly and D.C. Webb, "Microstrip excitation of magnetostatic surface waves: theory and experiment", IEEE Trans, on MTT, vol.23, no.12, pp.998-1006,1975. 5. W. L. Bongianni, "Magnetostatic Propagation in a Dielectric Layered Structure", /. Appl. Phys., vol.43, pp.2541-2548,1972. 75 6. R. W. Damon and J. R. Eshbach, " Magnetostatic modes of a ferromagnet slab", /. Phys. Chem. Solids, vol. 19, pp.308-320,1961. 7. R. Marcelli, M. Rossi, P. De Gasperis, and Jun Su, "Magnetostatic wave single and multiple stage resonators", IEEE Trans, on Magn., vol.32, no.5, pp.4156-4161,1996. 8. J. Helszajn, YIG Resonators and Filters, Wiley, New York, pp.115,1985. 9. J. D. Adam and J.H. Collins, "Microwave magnetostatic delay devices based on epitaxial yttrium iron garnet", Proceedings of IEEE, vol.64, no.5, 1976. 76 Chapter 4 Tunable Wideband Microwave Band-Stop Filter Using YIG/GGG-GaAs Layer Structure The theoretical analysis of YIG/GGG-GaAs layer structure and device simulations of microwave band-stop filter using YIG/GGG-GaAs layer structure have been studied in Chapter 2 and 3. In this Chapter, the experimental study of tunable wideband microwave band-stop filter using YIG/GGG-GaAs layer structure is carried out in detail. Enhanced microwave FMR absorptions in YIG/GGG-GaAs layer structures using a microstrip step-impedance low-pass filter (LPF) are presented first. The field simulations of the step-impedance LPF show clearly that, in contrast to a 50 Q. microstrip, the ac magnetic fields of the propagating microwaves are heavily concentrated in its inductive elements. Stronger local ac magnetic fields at each inductive element of the step-impedance LPF facilitate enhanced coupling into the magnetic over-layer and, thus, significantly increase the microwave power absorptions at the FMR frequencies. The measured transmission loss (S21) and return loss (Sn) of -25.0 dB and -8.7 dB using the microstrip step-impedance LPF, at FMR frequency of 8.5 GHz, show a much higher level of microwave FMR absorption in the YIG/GGG-GaAs layer structure as compared to a 50 Q. microstrip with the measured S21 and Sn of -20.8 dB and -5.8 dB. The microwave transmission characteristics (S21) of the bandstop filter in a large base band of 2.0 - 20.0 GHz, using both the step-impedance 77 LPF and the 50 Q microstrip, were also measured and compared. The simultaneous enhancement of FMR absorption level and widening of absorption bandwidth has been accomplished in a microwave band-stop filter that utilizes a microstrip meander-line with step-impedance LPFs inserted in a non-uniform bias magnetic field. A microwave filter with tunable FMR absorption frequency range of 5.0 to 21 GHz, an absorption level of -35.5 dB and a corresponding 3 dB absorption bandwidth as large as 1.70 GHz, centered at 20.3 GHz, have been demonstrated. 4.1 Enhanced Microwave FMR Absorption Using Microstrip Step-Impedance Low-Pass Filter In this section, the design and simulations of the step-impedance LPF including the simulated ac magnetic fields (H-field) of the propagating microwaves in the two types of transmission lines and the overall device simulation are presented. Filter Specification I Low-Pass Filter Prototype I Conversion of Impedance and Frequency I Implementation by Microstrip Figure 4.1 Design Outline of Step-Impedance LPF 78 4.1.1 Microstrip Step-Impedance LPF Design The design procedures of the microstrip step-impedance LPF is outline in Figure 4.1. We start with the filter specification to design the prototype low pass filter. The design specification of the low pass filter is listed in Table 4-1. Table 4-1 Specification of the Step-Impedance LPF Filter Response Substrate Metal Material Cut-off „ Frequency Band-Reject _ Frequency Off-band ... .. Attenuation „ ^ ., Materials _,. . Thickness 35 GHz 45 GHz 20 dB GaAs 350 urn Ag , Impedance T 50 ohm The insertion loss method is employed to characterize the filter response for the low-pass filter design [1-2]. The insertion loss, or power loss ratio (PLR), is defined as the ratio of the power available from the source to the power delivered to the load. In our specific application, a minimal insertion loss over the passband is important because the designed step-impedance LPF is used as a transmission line to guide the microwaves in the magnetic layer structures. A binomial or Butterworth response is used to characterize the filter design which provides the flattest possible passband region for a given filter complexity. For the low-pass filter with Butterworth response, PLR is specified by [1-2]: \2N f ^,=1 + CO \<°cj 79 (4.1) where a and coc are the microwave frequency and the cutoff frequency, respectively, and N is the order of the low-pass filter. The passband of the lowpass filter extends from co = 0 to co = coc where the PLR is - 3 dB, and the attenuation increases monotonically as the frequency increases beyond the cutoff frequency. The ladder circuit that provides the power loss characteristics of this filter type with shunt capacitors (C i , i = \to 5) and series inductors (L t , i = 1 to 5) is shown in Figure 4.2. Figure 4.2 Ladder Network for The Low-Pass Filter The element values of the ladder circuit, normalized with respect to the source impedance and the cutoff frequency, can be calculated as [1-2]: gk =2 sin 2k-l 2N "\ •n k = l,2,...,N (4.2) where gk are the normalized element values of the shunt capacitors and the series inductors. The order of the low pass filter N is determined by the filter response of design specification, specifically TV = 10 in our design in order to achieve more than 20 dB off-band attenuation at 45 GHz band-reject frequency 80 with 30 GHz cut-off frequency. The actual values of the capacitors and inductors can be readily computed from the normalized element values using the source impedance and the frequency transformations [1-2]. (4.3a) Ct = T & - * = l,3,5,7,9 Z 0®c Lk=-^t k = 2,4,6,8,10 (4.3b) where Z0 is the load impedance of the ladder circuit. The microstrip implementation of shunt capacitors and series inductors is realized using alternating segments of low and high characteristic impedance lines (or low-Z and high-Z lines). A short microstrip with high characteristic impedance can be approximate as a serial inductor, and a short microstrip with low characteristic impedance can be approximate as a shunt capacitor [1-2], specifically, in our filter design, high-Z of 75 Q a n d low-Z of 30 Q were used. The characteristic impedance of the microstrip is determined by the ratio of the width of microstrip, W, to the thickness of the substrate, d. One of the wellW established experience formulas for calculating the — ratio is given by [2] d W_ d %eAd e2A-2 2d B - 1 - ln(25 -1) + ^-^-Qn(B -1) + 0.39 - — ) 71 £„ 2s„ where 81 — <2 d W_< 2 d (4.4a) 6 °V 2 ^+1 *' (4.4b) and Z is the desired characteristic impedance of the microstrip, i.e., 75 fi and 30 Q in our design for serial inductors and shunt capacitors. From equation (4.4a-b), the widths of the 50£2 , 75Q and 30Q microstrip are calculated to be 256jum ,&0jum and 670jum respectively based on the 350jum thick GaAs substrate. The length of each segment are calculated by Z r _ gk bk^LL k,capacitor r> y lr — \ l a ^ 7 Q ' J ' ^' ' ' (4.5) h,inductor=^ * = 2,4,6,8,10 Where gk are prototype element values for serial inductors and shunt capacitors, ZL and ZH are low and high characteristic impedance of the microstrip, i.e., 30 Q and 75 Q. respectively, Z0 = 50 Q is the characteristics impedance of the load system. In I— The effective propagation constant J3e is given by j5e =—•s]se , K where Xc is the wavelength at the cutoff frequency and the effectively permittivity se is given by s=——2 + —2 , V 82 f^l W (4.6) With the above equations, the microstrip implementation of the 10-element, i.e., five capacitor and five inductor, step-impedance LPF is shown in Figure 4.3. Note that the 256 jum wide line serves as a 50 Q line, and the 670 fj,m and 80 jum wide lines are the low and high characteristic impedance lines of 30 Q and 75 Q , corresponding to the shunt capacitors and the series inductors, respectively. The width, W, and length, L, of each element of the 10-element step-impedance LPF indicated in Figure 4.3 are listed in Table 4-2. The thickness of the metal, t, was chosen to be 1.0 jum for the experimental consideration. Table 4-2 Geometry of the 10-Element Step-Impedance LPF Cj C2 C3 C4 C5 Vf(jum) 670 670 670 670 670 L(jum) 84 221 232 232 190 A W (jum) 80 80 80 80 80 L (jum) 486 635 659 624 278 83 256 urn 670 urn WM Jr 8 0 urn Figure 4.3A 10-Element Step-Impedance LPF Frequency (GHz) Figure 4.4 Simulated S-Parameters (S21 and Sn) of the 10-Element StepImpedance LPF and the 50 QTML The simulated S-parameters (S2land Sn) of the step-impedance LPF and the 50 84 Q. microstrip transmission line (TML) using Microwave Office is shown in Figure 4.4. The simulated S21 and Sn greater than -0.3 dB and less than -16.0 dB, respectively, up to 30 GHz shows that the 10-segment stepped-impedance LPF can be efficiently act as a TML over a large span of base band frequency. 4.1.2 AC Magnetic Field Simulations In this section, the ac magnetic field components of the propagating microwave in the YIG/GGG-GaAs layer structure are simulated using ANSOFT HFSS. Utilization of such step-impedance LPF in lieu of a 50 Q microstrip for enhancement of the FMR power absorption in the layer structure has been clearly demonstrated by the simulated ac magnetic field (H-field) components of the propagating microwaves along the two types of transmission lines. Figure 4.5 and Figure 4.6 are, respectively, the simulated magnitude of ac magnetic fields (H-field) on the surface of the GaAs substrate at 8.5 GHz along the 10-element step-impedance LPF and the 50 Q microstrip. Figure 4.6 clearly shows that the ac magnetic fields of the propagating microwaves are heavily concentrated in each inductive element (note that the narrow microstrip segments are the high characteristic impedance lines corresponding to the series inductors). Specifically, the H-field intensity in the inductive line segments is seen to be greater than 70 A/m in contrast to a much lower H-field intensity of 30 A/m along the 50 n microstrip (see Figure 4.5 and 4.6). The heavily concentrated magnetic fields in each inductive element are more clearly shown in Figure 4.7 where the simulated 85 ac magnetic field intensities along the center lines of the step-impedance LPF and the 50 Q microstrip were extracted. The five peak and notch regions in Figure 4.7 correspond to the H-field intensities in the five inductive and capacitive elements of the LPF, respectively, and they show clearly that much stronger local H-fields exist at each inductive line segment. 86 H-Field [A/m] I 5.5000e+001 5.1563e+001 4.8125e+001 4.4688e+001 4.1250e+001 3.7813e+001 3.4375e+001 3.0938e+001 2.7500e+001 2.4063e+001 2.0625e+001 1.7188e+001 1.3750e+001 1.0313e+001 6.8750e+000 3.4375e+000 O.OOOOe+000 30 A/m I y i X Center Line Figure 4.5 Simulated AC Magnetic Field (H-Field) Distributions at Frequency of 8.5 GHz along the 50 Q Microstrip 87 H-Field [A/m] I 8.0000e+001 7.5000e+001 7.0000e+001 6.5000e+001 6.0000e+001 5.5000e+001 5.0000e+001 4.5000e+001 4.0000e+001 3.5000e+001 3.0000e+001 2.5000e+001 2.0000e+001 1.5000e+001 1.0000e+001 5.0000e+000 O.OOOOe+000 = 70 A/m y A X Center Line Figure 4.6 Simulated AC Magnetic Field (H-Field) Distributions at Frequency of 8.5 GHz along the 10-Element Step-Impedance LPF 88 E c o (0 2 Y-Axis Distance [mm] Figure 4.7 Simulated AC Magnetic Field (H-field) Intensities along the Y-Axis Center Lines of The 10-Segment Step-Impedance LPF and The 50 Q. Microstrip The surface power density distribution on GaAs substrate by computing the power density as ExH is also simulated over the 10-element step-impedance LPF and shown in Figure 4.8. As shown in Figure 4.8, the surface power density is also much higher concentrated in the inductive segment than the capacitive segment. A comparison between the surface power density on GaAs substrate along the cross-section direction (X-direction in Figure 4.8) at 8.5 GHz over the step-impedance LPF and 50 Q microstrip are plotted in Figure 4.9. 89 Power (W/m2) Density 5.0000e+005 4.6875e+005 4.3750e+005 4.0625e+005 3.7500e+005 3.4375e+005 3.1250e+005 2.8125e+005 2.5000e+005 2.1875e+005 1.8750e+005 1.5625e+005 1.2500e+005 9.3750e+004 6.2500e+004 3.1250e+004 0.0000e+000 :-S:# INDUCTIVE CAPACITIVE y X Figure 4.8 Simulated Power Density Distribution at Frequency of 8.5 GHz on the Surface of GaAs of the 10-Segment Step-Impedance LPF 90 50 50 45 -45 LPF:INDUCTIVE ELEMENT \l E 40 s.> 35 u ^* +J "55 c 0) -40 -35 30 -30 TML 25 -25 0) 20 -20 5 o a. 15 Q a> o 10 t(0 3 5 </5 -15 I LPF:CAPACITIVE \ ELEMENT -10 -5 0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 0 1.0 Distance along the Cross Section [mm] Figure 4.9 Simulated Surface Power Density Distribution along The CrossSection Direction (X-direction in Figure 4.8) over the TML, the Inductive Segment and Capacitive Segment of the Step-Impedance LPF A final note on the above field and power simulations is that the input power used in HFSS is normalized to 1 W for all the simulations. From above simulation results, the much stronger ac magnetic fields at each inductive line segment of the LPF will facilitate stronger coupling into the magnetic over-layer during the microwaves propagation, and, thus, enhance the interaction between the ac magnetic fields of the microwaves and the precessing magnetic dipoles in 91 the magnetic layer. Enhanced FMR power absorption, therefore, will occur if the frequency of the propagating microwaves coincides with the FMR frequency of the magnetic layer. 4.1.3 Device Simulations The HFSS is used again for the overall device performance simulation. The physical model is same as the model shown in Figure 3.7 except for different geometry. The GaAs substrate, the YIG layer and the GGG layer are, respectively (in X Y Z axis) 10 4 xl0 4 x350//w 3 ,9000x6256x6.8//w 3 and 9000 x 6256 x350//m3 . The 50Q microstrip line are 256jum wide and the geometry of the 10-elment step-impedance LPF are in Table 4-2. The material parameters for GaAs and silver are given in the material library of HFSS. The GGG was assigned as a perfect dielectric material with relative permittivity 14.7 (the same as YIG layer). The direction of the internal magnetic field, HQ =2,3OO0e, was assigned in the same direction as microwave propagation. The bottom of the GaAs substrate was assigned as a perfect electrical, E, plane which serves as the signal ground plane. The assignment of the material property of YIG is the same as Section 3.2. The simulated transmission loss (S21) and return loss (Sn) of the YIG/GGG-GaAsbased band-stop filter at FMR frequency of 8.5 GHz using the 50 Q microstrip and that using the step-impedance LPF are shown in Figure 4.10. The S21 and Sn of -30.0 dB and -6.0 dB, respectively, using the microstrip step-impedance LPF clearly show a significantly higher level of microwave power absorption in the 92 magnetic layer structure as compared to the 50 Q microstrip with the simulated S21 and Sn of —22 dB and -5.0 dB, respectively. The large tunable range of FMR frequency and the corresponding S21 and Sn parameters measured have verified the simulation results and will be shown in Section 4.3. Stepped-lmpedance LPF ko Stepped-lmpedance LPF -40 -i 8.0 1 8.1 1 1 8.2 1 1 8.3 1 1 8.4 1 1 8.5 1 1 8.6 1 1 8.7 1 1 8.8 1 1 8.9 •40 r> 9.0 Frequency (GHz) Figure 4.10 Simulated Transmission Loss (S21) and Return Loss (Sn) of the YIG/GGG-GaAs-Based Microwave Band-Stop Filter at FMR Frequency of 8.5 GHz using the 50 TML and the 10-Segment Stepped-lmpedance LPF 93 4.2 Experimental Results 4.2.1 Device Fabrication and Measurements The basic flip-chip device configuration of the microwave band-stop filter using YIG/GGG-GaAs layer structure is shown in Figure 4.11 where the 10 element step-impedance LPF was used as the microstrip transmission line. The single-crystalline YIG sample was furnished by Shin-Etsu Chemical Co., Japan. The YIG film is grown on lattice-matched GGG sample on [111] face by liquid phase epitaxy (LPE) technique. The thickness of the YIG sample is 6.8 fim. The measured 4?rMs and AH are 1,760 Oe and 1 Oe at 9.2 GHz, respectively, according to the data sheet provided. YIG/GGG Layer Step-impedance Low-Puss Filter Microwave Output Microwave Input GaAs Substrate Ground Plane Figure 4.11 The Flip-Chip Device Configuration of the Microwave Band-Stop Filter using YIG/GGG-GaAs Layer Structure 94 The metallization/photolithography/etching process is used to fabricate the GaAs-based microstrip line, i.e., the step-impedance LPF and 50 Q TML, as shown in Figure 4.12. A 1.0//m silver is deposited onto GaAs using e-beam evaporation deposition technique. The process started with the photo-resist spinning coating of Shipley 1827® at a thickness of 2.7 jum . Iron masks are produced in a separate procedure and aligned to the substrate in a Karl Suss Aligner. Near-UV exposure defines resolutions with ~4 um. The exposed sample then is developed in Microposit 319®. The electrode patterns are hard baked at 95° C for 30 min. A chemical etching is followed to remove silver. The chemical enchant is a room temperature 1:1:10 dilution of NH4OH, H2O2 and DI- H2O solutions. The final step is an acetone bath to strip the photo-resist. Near UV light UUUUIU Mask PR Substrate Preparation Metalization Photo-Resist (PR) Spin Mask Align and Exposure I PR Strip Chemical Etching Develop PR and Bake Figure 4.12 Process Flow for Fabricating GaAs-based Microstrip Line 95 Once the YIG/GGG sample and the GaAs-based microstrip line are ready, the flip-chip technique is used to assembly the YIG/GGG sample to the microstrip line. Although flip chip components are predominantly in semiconductor devices, passive components, e.g., filters and MEM devices, can also be used in flip chip assembly. In the device packaging, the GaAs-based microstrip line was bonded to an aluminum holder using Transene® silver-based surface mount adhesive. The 2.4 mm connectors are used to connect the microstrip to the coaxial cable. The 2.4 mm connectors are designed to be operated up to 50 GHz. The microstrip/stepimpedance LPF is designed with right-angle bends for easy supply of bias magnetic field to be same as the microwave propagation direction. The optimized bend design will be discussed in Section 4.3. The layout of the stepimpedance LPF with two mitered 90° bends is shown in Figure 4.13. The photo of the actual fabricated device including the 2.4 mm connected is shown in Figure 4.14. 96 Figure 4.13 Layout of the Step-Impedance LPF with Two Mitered 90° Bends The fabricated device then was inserted into the external bias magnetic field facilitated by a pair of neodymium (Nd 2 Fe 14 B) permanent magnets (0.75" in diameter and 0.5" in thickness). The magnetic field intensities in the center of the YIG/GGG sample were varied by tuning the gap, d, between the permanent magnet pair (see Figure 4.19). The non-uniformity of the biased magnetic field provide by this arrangement will be discussed in detailed in Section 4.3. 97 Figure 4.14 Photo of Fabricated GaAs-based Microstrip Step-Impedance LPF with Two Mitered 90° Bends together with Two 2.4 mm Connectors Two measurement systems are used in this device measurement as shown in Figure 4.15 and Figure 4.16. The microwave power measurement system has a Signal Generator (HP83630B 0-26.5GHz) to send microwave to the DUT through a directional coupler (HP 87301E) where the coupled power from the directional coupler is the reference power that is captured by a power sensor (HP 8487D) and fed into one channel o f the power meter (Agilent E4419A). The output of the directional coupler will be sent to DUT and the output of DUT enters the other directional coupler and fed to the other channel of the power meter. The 98 microwave power consumption by the DUT can be obtained by comparing the two power input to the power meter (see Figure 4.15). HP 83630B Signal Gen GPIB HP S7301E Coupler HP 87301E Coupler IOUT Signal DUT Agilent 4419A Power Meter GPIB —j 5Qohm " | -10dBl 10dBl (Probe HP 8487D power Sensor HP 8487D Power Sensor CH_B CH A BELL 620 Gaussmeter GPIB Work Station Figure 4.15 Setup of the Microwave Power Measurement System The network analyzer measurement system consists of the 8510C Network Analyzer, the 8517B S-parameter Test Set, and the 83621A Signal Generator (up to 20GHz). The network analyzer system is a standard instrument measurement the microwave transmission characteristics to (S-parameters) including the magnitude and phase information. For both of the system, the bias magnetic field intensity was measured by BELL620 Gaussmeter. The BELL620 Gaussmeter is a precision magnetic flux measuring instrument, featuring high stability with Hall Effect magnetic field probes. Measurement range extends from 1 mG per scale division to 30 kG full scale. 99 HP 8510C Network Analyzer GPIB HP 83621A Signal Gen ,GPIB OUT HP 8514B Test Set GPIB Port 1 Port 2 w W DUT f 4 ^ 1 Probe ^ ^ 1 1 1 S M %. 1 % BELL 620 Gaussmeter IN GPIB Work Station Figure 4.16 Setup of the Network Analyzer Measurement System 4.2.2 Device Performance of Tunable Wideband Microwave Band-Stop Filter In the experiments, the YIG film used is 6.8 jum in thickness with dimension of 2.8x9.0mm2 in the X and Y directions (see Figure 4.11). The 256 //w wide 50 Q microstrip and the 10-element step-impedance LPF (see Figure 4.13) presented in Section 4.1 were used to compare the microwave power absorptions at the FMR frequencies. The bias magnetic field (HQ) supplied by a pair of NdFeB permanent magnets was set in the same direction as the microwave propagation. The 100 transmission characteristics were then measured using HP 8510C Network Analyzer (see Figure 4.16). The measured transmission loss (S21) and return loss (Sn) of the YIG/GGGGaAs-based band-stop filter at FMR frequency of 8.5 GHz using the 50 Q microstrip and that using the step-impedance LPF are presented in Figure 4.17. Bias magnetic field of 2,100Oe was applied to set the FMR frequency at 8.5 GHz [3-4]. Note that the measured FMR absorption frequency of 8.5 GHz in Figure 4.17 is identical to the simulated carrier frequency in Figure 4.10. The S21 and Sn of -25.0 dB and -8.7 dB, respectively, using the microstrip step-impedance LPF clearly show a significantly higher level of microwave power absorption in the magnetic layer structure as compared to the 50 Q microstrip with the measured S21 and Sn of -20.8 dB and -5.8 dB, respectively. As we studied in Chapter 2 and Chapter 3, the peak FMR absorption frequency of the band-stop filter can be tuned in a wide frequency band by varying the bias magnetic fields [3-4]. The microwave transmission characteristics of the bandstop filter in the frequency range of 2.0-20.0 GHz using the two types of transmission lines were also measured and compared in Figure 4.18. Clearly, enhanced peak FMR absorptions in the YIG/GGG-GaAs flip-chip layer structure were accomplished in a base band as large as 2.0 to 20.0 GHz using the stepimpedance LPF. 101 Step-Impedance LPF (/) iw -25 -25 -30 I- -30 Step-Impedance LPF -35 6.5 7.0 7.5 8.0 8.5 9.0 -35 9.5 10.0 10.5 Frequency (GHz) Figure 4.17 Measured S21 and Sn of the YIG/GGG-GaAs-Based Microwave BandStop Filter at FMR Frequency of 8.5 GHz Using the 50 Q Microstrip and the 10Element Step-Impedance LPF. 102 -10 ST *~L -20 CM 1020 Oe 1440 Oe O) - t 2100 Oe •30 t / / N f 2670 Oe k « 50 Ohm Microstrip . 3250 Oe J r P ' -40 8 10 f 3850 Oe I Step-Impedance LPF 6 -30 4gQg Q 6 5 3 0 0 Oe 12 14 16 18 -40 20 Frequency (GHz) Figure 4.18 Measured S21 of the YIG/GGG-GaAs-Based Microwave Band-Stop Filter using the 50 Q Microstrip and the 10-element Step-Impedance LPF The magnetic field (H0) dependence of the FMR frequency (fr) is given by equation (4.7) [3-4] and also be verified in the measurement. MH0) = y[(H0 2 +Han)(H0+Han+4xMs)J (4.7) In equation (4.7), AnMs (1,76O0e) and Han are, respectively, the saturation magnetization and the anisotropy field of the YIG film. The value of the Hm of 103 YIG sample can be determined by fitting the experimental results to the equation. Figure 4.19 shows a good agreement between the FMR theory in equation (4.7) and measured FMR frequency when Han is fitted to be 100 Oe. 1000 2000 3000 4000 5000 6000 7000 20 • N fM=r>IW0+Ha)(H0+Ha+4xM,) 20 y = 2.SMHz/Oe,Ha=100Oe AnM =1150 Gauss X o 15 ~15-l o C O I- 10 £ O • i • i • i • i \- 5 Calculated Measured « • i • 1000 2000 3000 4000 5000 6000 7000 External Bias Magnetic Field (Oe) Figure 4.19 Measured FMR Frequencies vs. Biased Magnetic Field 104 4.3 Band-Stop Filter with Large Stop-Band Bandwidth Using Microstrip Meander Line with Inhomogeneous Bias Magnetic Field 4.3.1 Inhomogeneous Bias Magnetic Field Microwave band-stop filters with desirable device performances, i.e. wideband frequency selectivity with high peak absorption level and large absorption bandwidth, were discussed in this section using a four-segment microstrip meander-line constructed by the same 10-element step-impedance LPFs together with a 2-D non-uniform bias magnetic field [4-5]. tMmnn' Microwave Output Figure 4.20 The Arrangement For Facilitating Non-Uniform Bias Magnetic Fields in YIG/GGG Layer 105 The non-uniform bias magnetic field in the YIG/GGG layer was facilitated by the a pair of NdFeB permanent magnets as shown in Figure 4.20, and the intensity of the non-uniform bias magnetic field distribution desired was set by adjusting the separation of the gap, d, in between. The non-uniform field distributions are clearly shown in the measured magnetic field profiles normalized to the four values of magnetic field at the center of the gap along the Y-axis and X-axis in Figure 4.21 and 4.22, respectively. Figure 5.10 (a) and 5.10 (b) show the measured 2-D non-uniform bias magnetic fields in the 8.0 x8.0mm2 YIG/GGG sample (see Figure 4.20), centered at 2,750 Oe and 4,150 Oe, respectively, in which the field non-uniformity is clearly shown. Since the FMR frequency for peak absorption depends on the bias magnetic field, the different bias magnetic fields at the separate locations of the four segments of the meander-line would result in a large widening of the peak absorption bandwidth. 106 160* 150140- A d=18.0mm H=3,700 Oe d=28.5mm, H=1,940 Oe d=35.0mm, H=1,325 0 e d=42.0mm, H=990 Oe A • v A • • • / v • < 130- A • « 4 A • V A AV * ^ • A 4 • 4 A \ A * ';, 120- *A ^ * V A A , •^••^ 110- # # • •« * < V * ^ AA « < ''« v . V* « **••<« A NS& • Center . ^ *>J&k T ^P^* ^ 4 ^ 10090-2 ^# j • % • A A • •* A 0 2 4 6 8 10 12 14 16 18 Position along Y-axis (mm) ure 4.21 Measured Magnetic Field Profiles Normalized to the Four Values of Magnetic Field at the Center of the Gap along the Y-Axis 107 6^ ] _ ive Magi tic ield to the Cen 3 100- ^^^•*^l^. 95< ^ V 90- A v • % A.*? • ^* V • > -4 85" * 80°. 75- A A * * -, ^ • • < A A A A 70- A A 652 " 1 ' 0 1 2 i d=18.0mm H=3,700 Oe d=28.5mm, H=1,940Oe d=35.0mm, H=1,325 0e d=42.0mm, H=990 Oe i 4 i i i 6 i 8 i i i i 4 • \ v W « A A 1? O 'v A ± v CD r- <9 v£\ »V . A A LL *-* «S Center » & V • \ \ A \ i i i i i 10 12 14 16 18 Position along x-axis (mm) Figure 4.22 Measured Magnetic Field Profiles Normalized to the Four Values of Magnetic Field at the Center of the Gap along the X-Axis 4.3.2 Microstrip Meander Line Design In order to fully utilize the non-uniformity of the 2-D bias magnetic field, a multisegment microstrip meander line was designed and implemented in the experiments. The same 10-element step-impedance LPFs were used to construct a four-segment microstrip meander-line shown in Figure 4.23. 108 2.0mm 2.0mm Figure 4.23 Layout of the Four-Segment Microstrip Meander Line using the Same 10-Element Step-Impedance LPFs One of the key designs of a meander line is the mitered 90° bends that fold each microstrip line side by side. These bend segments are actually a microstrip discontinuity that can introduce parasitic reactance [6]. In order to minimize the parasitic effect, simulation was carried out using Microwave Office to look for the optimal design. Microwave Office introduces a new parameter called the Miter Coefficient (MC) to distinguish different miter bends [7]. The definition of the miter bend segment is shown in Figure 4.24 where the MC is defined as M =d 109 (4.8) Clearly, M can only have a value between 1 > M > 0. I "Is JL. W i - ^ l 4^W^I Figure 4.24 Miter Bend Layout in Microwave Office 0.0 -0.2 M = 0.8: Lowest Overall Loss CQ T3 -0.4 A s_ 0 CD E 2 -0.6 J M M M M M M = 0.0 = 0.2 = 0.5 = 0.7 = 0.8 = 0.9 CO Q_ W -0.8 4 -1.0 8 12 Frequency (GHz) Figure 4.25 Simulated S21 of a Microstrip with Two Miter Bend using Miter Coefficient 110 Microwave Office was used again to simulate the transmission loss (S21) of a microstrip line with two miter bend using different MCs. Figure 4.25 shows clearly M=0.8 corresponds to the lowest loss transmission, and the corresponding Wx and a of the miter are 204.8 jum and 651.7 fitn, respectively, when the W = 256 //m. 4.3.2 Experimental Results Figure 4.26 shows the device configuration of the YIG/GGG-GaAs-based microwave band-stop filter with wideband tunability of stop-band center frequency and bandwidth utilizing a four-segment microstrip meander-line with 2-D non-uniform bias magnetic fields. Ground Plane ^ j l • ''\\ H^M^'^^W v^ Substrate Figure 4.26 A Wideband YIG/GGG/GaAs-Based Microwave Band-Stop Filter using Microstrip Meander-Line and Non-Uniform Bias Magnetic Field 111 QQ •a w w • O c o "55 £ (A C re 1)940 O -45 J i i j 7 5 0 Oe3.700 O e 4 ' 8 5 0 L 8 0 e 1.70GHz J t 6,100 Oe L _ I 10 12 14 16 i_ 18 20 22 24 Frequency (GHz) Figure 4.27 Measured S2i of the Tunable YIG/GGG-GaAs-Based Microwave Band-Stop Filter using a Meander Line with Four Segments of Step-Impedance LPF The measured transmission loss (S21) of the tunable band-stop filter just described is shown in Figure 4.27. The experimental data demonstrated a large tunable absorption frequency range of 5 to 21 GHz and an absorption level of 35.5 dB together with a corresponding 3 dB absorption-bandwidth as large as 112 1.70 GHz at 20.3 GHz. Clearly, the desirable capability of the band-stop filter for wideband frequency selectivity with high peak absorption level and large absorption bandwidth has been accomplished. Reference 1. G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, ImpedanceMatching Networks, and Coupling Structures, Artech House, Dedham, Mass., 1980. 2. David M. Pozar, Microwave Engineering, 3rd ed., John Wiley & Sons, Inc., 2005. 3. C. S. Tsai, G. Qiu, H. Gao, L. W. Yang, G. P. Li, S. A. Nikitov, and Y. Gulyaev, "Tunable wideband microwave band-stop and band-pass filters using YIG/GGG-GaAs layer structures." IEEE Trans. Magn., vol.41, pp.3568-3570, 2005. 4. G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low-pass filter in a yttrium iron garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103, 2008. 5. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in flip-chip YIG-GaAs layer structures", accepted and to be published in IEEE Trans. Magn., 2009. 6. B. C. Wadell, Transmission Line Design Handbook. Artech House, 1991. 113 7. Advanced Wave Research, Microwave Office User's Manual. 114 Chapter 5 Tunable Wideband Microwave Band-Pass Filter Using YIG/GGG-GaAs Layer Structure Chapter 4 discussed in detail the experimental study of the tunable wideband microwave band-stop filter using YIG/GGG-GaAs layer structure. In this Chapter, the microwave band-pass filter using YIG/GGG-GaAs layer structure with large tuning ranges for the center frequency (5.90 - 17.80 GHz) and the bandwidth (1.27 - 2.08 GHz) in the pass-band using a pair of aforementioned microwave band-stop filters in cascade is presented. The design and simulation of the band-pass filter were carried out using equivalent circuit method and ANSOFT HFSS, specifically the simulation that incorporates multi-segment microstrip meander-lines and 2-D non-uniform bias magnetic fields was carried out using ANSOFT HFSS. The measured transmission characteristics of the bandpass filter at center frequency of 8.28 GHz, using 2-D non-uniform bias magnetic fields centered at 2,750 Oe and 4,150 Oe facilitated by NdFeB permanent magnets, shows a - 3 dB bandwidth of 1.73 GHz, an out-of-band rejection of - 33.5 dB, and an insertion loss of - 4.2 dB. A good agreement between the simulation and experimental results for the band-pass filter in the center frequency and the bandwidths of the pass-band and the two guarding stop-bands has been accomplished. 115 5.1 Band-Pass Filter Architecture B i a s ?VWe7 Microwave Input Hoz(jlo2>Hoi) Microwave Output Band-Stop Band-Stop Filter No.1 +*A Filter No.2 sie Pass-band freq freq High-«»nc8 Stop-band -end! Stos-bana •f :lr(t3Qi J i n 1 Figure 5.1 Realization of the Tunable Band-Pass Filter using a Pair of Band-Stop Filters in Cascade As discussed in Chapter 4, the YIG/GGG-GaAs-based microwave band-stop filter with wideband tunability of stop-band center frequency and bandwidth has demonstrated a large tuning range in peak absorption frequency of 5.0 to 21.0 GHz and an absorption level of - 35.5 dB together with a corresponding 3 dB bandwidth as large as 1.70 GHz (see Figure 4.26) [1]. It is clear that by using a pair of such band-stop filters in cascade (Figure 5.1) in which different nonuniform bias magnetic fields (H02 > H0l) are applied, a band-pass filter with large tuning ranges for both the center frequency and the bandwidth in the pass-band 116 can be realized by properly programming the low-end and the high-end values of the bias magnetic fields (Hmand H02) [2-3]. Figure 5.1 shows the scheme of realizing the tunable band-pass filter using a pair of band-stop filter in cascade. 5.2 Device Simulations 5.2.1 Simulation Using Equivalent Circuit Method YIG Band-stop Filter No.2 YIG Band-stop Filter No.1 Figure 5.2 Lumped Element Equivalent Circuit of the YIG/GGG-GaAs-based Band-Pass Filter As we presented in Chapter 3, the equivalent circuit method was used to simulate the band-stop filter, and the same method is implemented here in this chapter to simulate the device performance of the band-pass filter. Figure 5.2 shows the lumped element equivalent circuit of the YIG/GGG-GaAs-based microwave band-pass filter. Please note that, in this equivalent circuit method, 117 the microstrip line for each band-stop filter (no.l and no.2) is the 50 Q transmission line. The Vin and the Z0 (Z0 =50iQ) are, respectively, the input microwave and the characteristic impedance of the transmission line. The formulism used to calculate the values of the lumped elements, namely, Ri, R2, Li, L2, Ci, C2 and the returns ratio ni and m, are derived in Chapter 3. The geometric parameters and the applied bias magnetic fields which are used to in this simulation for the band-stop filter no.l and no. 2 are listed in the Table 5-1. Please note that those parameters are the same as our experimental arrangement, and the simulation results will be compared with the experimental data shown in Section 5.3. The calculated radiation resistance Rm versus wavenumber k for the band-stop filter no.l and no.2 are shown in Figure 5.3 (a) and (b) respectively. Table 5-1: Geometric Parameters and Bias Magnetic Fields Used in the Simulation YIG Band-stop Filter 1 t d " 350 um 6.8 um "~"" YIG Band-stop Filter 2 350 um 6.8 um b 256 um 256 um H 1,300 Oe 2,050 Oe 118 • "P i i i i 180 1 ' 1 i • -, i i , i i i O > * ~ 160 t=350um d=6.8um b=256um H =1,300 Oe "O 140 '>—^ Q : S 120 8 100 c 80 B CO 0 K. c '_ _ . - 60 40 O « T3 CO Q: 20 ^ ^ g ^ ^ ^ ^ 0 -90 . i c • i i 100 150 200 • 50 . i I 250 300 . I . I 350 . I 400 . 5C 450 1 Propagation Constant (k) (cm ) (a) • i ' I i i • i • 1 i l i 1 i l i ^ - . 250 E .o "p £ • 200 £ ° ^ 150 0 O c CD -*i 100 w "to CD * 50 C . \ i t=350um d=6.8um b=256um H=2,030 Oe \ I \ - I \ i - g *^—i CO "•5 CO CC o • _i_ i 50 100 i i 150 200 . i 250 • i 300 i i 350 i i 400 i i 450 i 500 Propagation Constant (k) (cm1) (b) Figure 5.3 Calculated Radiation Resistance Rm versus Wavenumber k for Band-Stop Filter (a) No.l, and (b) No.2 119 Two identical YIG samples are used both in experiments and in simulations where / = 2.%mm and lz =9mm (ly,lzxe the planar dimensions of the YIG sample in (y,z) plane (see Figure 3.3). Therefore, the wavenumber of the main mode (n=l, m=l) of the MSSWs is approximately equal to klA& 12crrT1 and the corresponding radiation resistance Rm I cm and other values of lumped elements are listed in Table 5-2 as follows: Table 5-2 Values of Lumped Elements For Band-Stop Filter 1 and 2 YIG Band-stop Filter 1 YIG Band-stop Filter 2 Rm/cm 12 14.5 R(ohm) 3.36 4.06 L(nH) 382.11 461.71 C(pF) 1.9287E-3 0.82617E-3 n 5.4 7.0 Microwave Office is used again to simulate the lumped element equivalent circuit whose parameters are given in Table 5-2. The simulated S-parameter (S21) plot directly from Microwave Office is shown in Figure 5.4. These simulated results have been compared to the experimental results in Figure 5.7 in Section 5.3. As we can see in Figure 5.7, a good agreement between the experimental results and the simulation results has been achieved. 120 Graph 1 u I -10 I -20 lil- ^DB(IS[2,1]|) -30 ; YIG_1 I i j -40 2 4 6 8 Frequency (GHz) 10 12 Figure 5.4 Simulated S-parameters (S21) of the YIG/GGG-GaAs-based Microwave Band-Pass Filter 5.2.1 Simulation Using ANSOFT HFSS The simulation of the band-pass filter that incorporates four-segment microstrip meander-lines and 2-D non-uniform bias magnetic fields have been carried out using ANSOFT HFSS in this section. The HFSS can simulate the exact design of your device including the multi-segment microstrip line. More importantly, we incorporate two-dimension non-uniformity of the bias magnetic field into simulation, specifically, the non-uniform bias magnetic field with sixteen (4x4) 121 discrete values that was taken from measurement data are implemented into the simulation. The results showed a good agreement between the simulation and experimental results for the band-pass filter in the center frequency and the bandwidths of the pass-band and the two guarding stop-bands. Figure 5.5 Schematics of the Band-Pass Filter in HFSS 3-D Modeler Simulator A physical model of a band-pass filter with exact design of the two four-segment microstrip meander-lines, the YIG/GGG layer and the GaAs substrate were first built as shown in Figure 5.5. In this simulation, we keep the two four-segment microstrip meander-line structure exactly the same as design, but the trace distance between the two band-stop filter are not exactly the same as the 122 experiments. The main reason here is that the longer distance of the trace between the two band-stop filters will result in a much large side of device, and consequently, a much longer simulation time. The effects of the trace difference between the simulation and real measurements will only be the small differences of the transmission loss (S21) which has been neglected here in the simulation. The material property of the YIG sample has been assigned where the Linewidth AH = 1.0 Oe, the Lande G Factor = 2, the Saturation Magnetization AnMs = 1,760 Oe, and the relative permittivity sr = 14.7. For the 2-D non-uniform bias magnetic field, we directly implemented the experimental data into the simulations, namely, we used 16 discrete values (4x4) from the measured 2-D non-uniform bias magnetic field data. The measured non-uniform bias magnetic fields centered at 2,750 Oe and 4,150 Oe will be shown shortly in next section in Figure 5.8. With all aforementioned assignments ready, the microwave transmission loss (S21) of the band-pass filter are simulated and the results is shown Figure 5.6. As you will see shortly in Figure 5.8, a good agreement between the experiment results and the simulation results has been achieved for the band-pass filter in the center frequency and the bandwidths of the pass-band and the two guarding stop-bands. 123 "i—•—r s S f f l *^ra^«aa3s&vj^ 3 .- a s ( a , CO •D ex tn H-4,22<3Hz t w=2,75p..Oa. (centered) 11 H 12 13 w01 *4 T 150Oe (centered) 15 14 16 17 Frequency (GHz) Figure 5.6 Simulated and Measured Transmission Losses (S21) of the Tunable Band-Pass Filter 5.3 Experimental Results In the band-pass filter experiments, two band-stop filters are cascaded externally through coaxial cable to realize this band-pass filter. A photo of the real device is shown in Figure 5.7. 124 Figure 5.7 Photo of the Microwave Band-Pass Filter using Cascaded Band-Stop Filters 5.3.1 Band-Pass Filter with Narrow Stop-Band Bandwidth In the experiments, without incorporating the multi-segment microstrip line where each of the band-stop filter only contain single-segment 50 Q microstrip line, a pair of identical YIG/GGG samples 2.8 x 9.0mm2 (same as simulation in Section 5.2.1) was placed in separate bias magnetic fields supplied by two pair of permanent magnets (see Figure 4.20 for the bias magnetic field arrangement) for 125 band-stop no.l and no.2. For the bias magnetic fields of 1,300 Oe and 2,050 Oe, the measured transmission characteristics of the band-pass filter (black circle in Figure 5.8) at the passband center frequency of 7.1 GHz shows a 3 dB bandwidth of 1,450 MHz, out-of-band rejection of 33dB, and an insertion loss of 1.5 dB. Clearly, good agreement between the experimental results and the simulation results (red dot in Figure 5.8, same as Figure 5.4) has been achieved. Insertion Loss= -1.5dB BW(-3dB)=1450 MHz Shape Factor 1.56 (30dB/3dB) -h (M "*«Ham*. -1(H PI 00 S -20 CM CO c -30 o "55 w g -40w c w o a m is Measurec Simulatec t O O o o i± -50 J -60 & o O o sn o CO T 3 T" 1 1 4 6 7 CM 1 8 r 9 10 11 12 Frequency (GHz) Figure 5.8 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs Based Microwave Band-Pass Filter with Narrow Stop-Band Bandwidth 126 5.3.2 Band-Pass Filter with Large Stop-Band Bandwidth The microwave band-stop filter with wideband tunability of stop-band center frequency and bandwidth utilizing the four-segment microstrip meander-line is used to construct the band-pass filter with large stop-band bandwidth. The experimental arrangement for facilitating the 2-D non-uniform bias magnetic field was shown in Figure 4.20. 10 Central Frequency=12.28 GHz BW(-3dB)=1.73GHz Insertion Loss =-4.2 dB Measured Simulated ••""IITI'I"* — 1.22 GHz -40 Hn =2,750 Oe 01 H 0 ,=4,150Oe (centered) ' (centered) 10 11 12 13 14 15 16 17 Frequency (GHz) Figure 5.9 Comparison of the Simulated and Measured S21 of a YIG/GGG-GaAs Based Microwave Band-Pass Filter with Large Stop-Band Bandwidth 127 Measured Non-uniform Magnetic Field 3100 3000 2900 2600 2700 2600 (a) Measured Non-uniform Magnetic Field Figure 5.10 Measured 2-D Non-Uniform Bias Magnetic Field Profile Centered at (a) 2,750 Oe and (b) 4,150 Oe 128 In the experiments, two YIG/GGG samples each with the dimension of 8.0mmx8.0mmx6.8//m in X, Y and Z-directions (see Figure 5.5) were used. The measured transmission characteristics (see circle line in Figure 5.9) at the center frequency of 12.28 GHz shows a - 3dB bandwidth as large as 1.73 GHz, an out-ofband rejection of - 33.5 dB, and an insertion loss of - 4.2 dB. As clearly shown in Figure 5.9, a good agreement between the experiment results and the simulation results has been achieved for the band-pass filter in the center frequency and the band widths of the pass-band and the two guarding stop-bands. The large stopband at each end of the pass-band was realized by the two band-stop filters in which the non-uniform bias magnetic fields were centered at 2,750 Oe (H0,) and 4,150 Oe (H02). The highly non-uniformity of the bias magnetic fields centered at 2,750 Oe (Hm) and 4,150 Oe (H02) are measured and shown in Figure 5.10 (a) and (b), respectively. Large tuning ranges in the pass-band center frequency (5.90-17.80 GHz) and the bandwidth (1.27-2.08GHz) of the band-pass filter were also measured and shown in Figure 5.11. Note that the measured S21 lower than the low-end stop-band and higher than the high-end stop-band are not plotted in the figure, i.e. only the two stop-bands and the pass-band are plotted. The measured pass-band bandwidths and insertion losses are listed in Table 5-3. 129 8 10 12 14 16 18 20 Frequency (GHz) Figure 5.11 Measured Transmission Characteristics of the Tunable Band-Pass Filter in a Wide Frequency Range of 5.90-17.8 GHz TABLE 5-3 Measured Insertion Losses and Band-Widths of the Band-Pass Filter of Figure 5.11 Pass-Band Center 5.90 9.00 12.28 17.80 BW@-3dB (MHz) 1,270 1,300 1,730 2,080 Insertion Loss (dB) -3.1 3.9 -4.2 -6.6 130 5.4 Discussions 5.4.1 Electronic Tunability Air Gap (d) Solenoids NdFeB Permanent Magnets NdFeB Permanent Magnets Steel Yoke Figure 5.12 The Sketch of the Electromagnet The magnetic circuit that incorporates inductive coils for high-speed electronic control of bias magnetic field within the YIG/GGG sample and, thus, the peak FMR absorption frequency will be discussed in this section [3]. Figure 5.12 shows the components of the magnetic circuit that were used to facilitate electronic tuning of the band-stop and band-pass filter. Each of the disk-shape NdFeB permanent magnet has the dimensions of 0.5" in thickness and 0.75" in diameter. The electric wire used for the solenoids is of the size of 28 a.w.g. and the number 131 of turns in each coil is 820. The pair of solenoids was wrapped around the NdFeB permanent magnets to facilitate electronic tuning of the magnetic field in the air gap. The measured changes of magnetic fields in the air gap versus the DC currents in the coils, with the air gap distance as a parameter, are shown in Figure 5.13. CD O CD Air Gap Distances • 11.0mm A 17.1mm 500• 24.1mm ^ 30.6mm • 600- • • • O 400"0 c: • • CO CO o 200- o • • C/5 0 CD 100C CO x: A H • A A A • + 9 • 0 • • ^ • 9 9 1* * 0- A I A A 9 0 0.0 • A • 300- • A • i 0.1 i | 0.2 . | 0.3 i i i i i i i i i i 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 DC Current (Amp) Figure 5.13 The Measured Changes of Magnetic Fields in the Air Gap versus the DC Current in the Coils with the Air Gap Distance as a Parameter Table 5-4 lists the measured magnetic fields and maximum in the center of air gap at four discrete air gaps of 11,17.1, 24.1, and 30.6 mm, and its corresponding maximum tuning ranges of the FMR frequencies. Using different combinations of 132 the air gap and the current in the coils, a tuning range as large as 5.5-18.8 GHz for the FMR absorption frequencies was realized. TABLE 5-4 Measured Center Magnetic Fields and Maximum Change of Magnetic Field in the Center of the Air gap and the Maximum Tuning Ranges of the FMR Frequencies Air Gap(mm) ~" Center Magnetic Field (Oe) Change of H @ DC 11.0 17.1 241 30.6 5,200 3,250 2,000 1,425 + 590 ±470 ±325 ±245 15.4-18.8 10.2-12.9 7.0-9.0 5.5-7.0 Current= ±1.2 Amp Maximum Tuning Range (GHz) It is of interest to determine the time it would take to tune electronically the dc magnetic field, and thus the tuning speed of the FMR absorption frequency. The electrical parameters of the coils were measured by using Agilent 4294A impedance analyzer. The measured values of the inductance, capacitance, and resistance are 12.2 mH, 165.5 pF, and 20 Q (from 40Hz to 100 kHz), respectively, as shown in Figure 5.14 where the major electrical parameters are the inductance and the resistance by the coil together with a very small parasitic capacitance. In the experiments, a step-function voltage (0-2Vpp) from a function generator was used to drive the coil to measure the transient voltages of the coils. A serial resistance is used to control the response time (time constant) of the circuit. The OrCAD Pspice is used to simulate the circuit and the results are used to compare 133 with experimental results in Figure 5.15. The measured response time was found to be in good agreement with the calculated values based on the measured inductance, capacitance, and resistance of the coil. The comparisons of the response times and static voltages between the simulated results and measured results are shown in Table 5-5. It is clearly shown in Table 5-5 that the higher series resistor will result in a faster response (small time-constant) and lower static voltage, and therefore, the lower static-state current. J prrrs R \Mr * Figure 5-14 The Equivalent Circuit Used to Model the Coil Table 5-5 The Comparison between the Simulated and Experimental Results of Figure 5-15 Simulation Experiments Series Resistor Response Time (//s) Static Voltage (mV) 47 270 1,500 47 270 160 43.3 9.4 209 69.5 1,500 12 360 118 30 360 120 70 134 2.2 m Measured 1.5K ohm — Simulated 1.5K ohm 2.0 1.8 > CO 1.6 o o 1.4 .c -*-» c o 1.2 CD 0 D) CD ,4—1 o > A — Measured 270 ohm Simulated 270 ohm • Measured 47 ohm Simulated 47 ohm 1.0 0.8 0.6 0.4 0.2 0.0 T — • — i — • — i — • — i — • — i — ' — i — ' — i — ' — i — ' — i — 0 50 100 150 200 250 300 350 r ~ 400 450 500 Times(us) Figure 5-15 The Simulated and Measured Transient Voltages of the Coil when the Serial Resistors are 1.5 k Q , 270Q. and 47 Q 5.4.2 Power Handling Capability The power handling capability of the band-stop and band-pass filter are also interested and measured in a wide frequency range [3]. A typical measurement results is shown in Figure 5-16 where the microwave transmission characteristics (S21) of the band-stop filter using one segment microstrip SILPF were measured at different microwave power input levels in the range of 1 - 500 mW. The measurement data (see Figure 5-16) shows no obvious changes at the four discrete microwave power input levels (lmW, 10mW, 100mW, and 500mW) in 135 the important quantities of FMR frequencies, power absorption levels, and FMR absorption spectrums. o -5 -10 -15 CQ 860 Oe 1,325 Oe S -20 S OJ -25 1,940 Oe -30 K Input Power = 1 m W -35 -40. 3 4 1,940 Oe 2,750 Oe Input Power = 10 m W • 5 6 7 8 9 10 11 12 13 Frequency (GHz) (a) 3 0 1 8 1X T ° -10 2,750 Oe • 5„ 6 7 8 9 10 11 12 13 Frequency (GHz) 4 3 -20 -30 tff-25 5 A? ° I y Y P 1,940 Oe -35 Input Power = 500 mW -35 .Input Power = 100 mW 4 Q 0 -30 2,750 Oe 3 \Y 860 Oe t W 1,325 Oe | S-20 860 Oe ' V 1,325 Oe t 1,940 Oe yj -25 • ^-15 . -15 2 - -5 -10 -40. • 0 -5 ^ - | 6 7 8 9 10 11 12 13 -402 Frequency (GHz) (c) 3 4 t 2,750 Oe 5 6 7 8 9 10 11 12 13 Frequency (GHz) (d) Figure 5-16. Measured Transmission Characteristics of the Band-Stop Filter at Different Input Microwave Power Levels of (a) l m W (b) lOmW (c) lOOmW, and (d) 500mW Reference 1. G. Qiu, C. S. Tsai, M. M. Kobayashi, and B. T. Wang, "Enhanced microwave ferromagnetic resonance absorption and bandwidth using a microstrip meander line with step-impedance low-pass filter in a yttrium 136 iron garnet-gallium arsenide layer structure", /. Appl. Phys., vol.103,2008. 2. Gang Qiu, Chen S. Tsail, Bert S. T. Wang, and Yun Zhu, "A YIG/GGG/GaAs-Based Magnetically Tunable Wideband Microwave Band-Pass Filter Using Cascaded Band-Stop Filters", IEEE Trans. Magn., vol.44, issue 11, 2008. 3. C. S. Tsai, and G. Qiu, "Wideband microwave filters using FMR tuning in flip-chip YIG-GaAs layer structures", accepted and to be published in IEEE Trans. Magn., 2009. 137 Chapter 6 Tunable Wideband Filters using YIG/GGG Layer on RTDuroid Substrates Chapter 2 to 5 presented theoretical and experimental studies of FMR-based tunable wideband microwave band-stop and band-pass filters using YIG/GGGGaAs layer structure. In this Chapter, the filter counterparts using YIG/GGG layer on RT-Duroid substrate are presented. The band-stop filtering using YIG/GGG layer with a YIG film thickness of 100 ju m on RT-Duroid 6010LM substrate is demonstrated first showing a much wider FMR absorption bandwidth and a higher absorption level compared to the results obtained with YIG thickness of 6.8 jum. A scheme for realizing an X-band microwave bandpass filter with tunable center frequency and pass-band bandwidth using YIG/GGG layer on Duroid 6010LM is discussed. A composite X-band (8-12GHz) band-pass filter (BPF) which employs a quarter-wave short-circuited stubs-based X-band BPF and a 9-element step-impedance LPF as the transmission line is proposed, designed and simulated. Finally, the experimental results and some future works outlined. 6.1 Band-Stop Filter on RT-Duroid 6010LM 6.1.1 High-Frequency Circuit Board Materials 138 The market of RF/microwave circuit board has greatly evolved over the past several decades from military applications using waveguides to commercial applications using low-cost substrates. The conventional circuit board materials such as FR-4 were developed as a way of supporting conductors to replace cable connections as a means for conducting electrical current. The combination of metal conductor and supporting material had the primary purpose of providing a reliable connection between any two points. This approach came about as a way of reducing the cost and size of electrical circuits. The requirements for these conventional materials were simplicity, good adhesion of the conductor to the substrate material, substrate material to be rigid and low cost. However, the board material at high frequency, e.g., higher than 500MHz, is much more than just a support for the conductor; it also forms part of the circuit by dictating the length, width and spacing of the traces as well as the way in which the resulting circuit function. It is important to understand that at RF /microwave frequency, a signal trace becomes an element by itself with distributed resistance, capacitance, and inductance. At such high frequencies, the dimensions of the circuit play a vital role in its function. Changing dimensions of the traces and spaces with better utilization of the board can drastically improve the performance. In general, high-frequency applications require circuit board materials with many special properties and electrical characteristics that are not critical for DC but are essential for high frequency analog circuitry and high speed digital circuitry. When selecting circuit board materials for RF/ microwave 139 applications, proper control of the dielectric constant, low dissipation factor or loss tangent, and thicknesses of the substrate is particularly important. Rogers Corporation, Advanced Circuit Materials Division has an extensive selection of high frequency laminates for many types of applications that include linear power amplifiers and antennas for cellular and PCS base stations, phased array antennas, radar systems and high performance wireless components. Potential application of RT-Duroid circuit board materials for linear power amplifier using photonic band gap structure [1-2], and planar microwave circulator applications [3] have been demonstrated. 6.1.2 Band-Stop Filter using 100 ju m Thick YIG on Duroid 6010LM -10 QQ •o 5.70 mm s -30 -40 -50 -60 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) (a) (b) Figure 6.1 The Layout (a), and the Simulated Transmission Loss (S21) (b), of the Step-Impedance LPF on Duroid 6010LM 140 In this section, a band-stop filter using the same basic device configuration of Figure 4.11 but with the 350//m GaAs substrate replaced by the Duroid 601OLM substrate is presented. The RT-Duroid 6010LM substrate has the desirable features of high and stable dielectric constant of 10.5 for circuit size reduction, low loss (loss tangent of 0.0023) for operation at X-band, and well-controlled thickness of 254 ju m. The layout and the simulated transmission loss (S21) of the 9-element step-impedance LPF on Duroid 601 OLM substrate are shown in Figure 6.1 (a) and (b), respectively. Note that the design methodology has been presented in Chapter 4. In the measurements, the YIG films used are 6.8 jum and 100 jum in thickness with dimension of 6.0x8.0mm2 in the X and Y directions (see Figure 4.11 for device coordinates). Two band-stop filters, one with 6.8 jum thick YIG sample and the other with 100 jum thick YIG sample, were used in the experiments to compare the microwave power absorptions at the FMR frequencies. The bias magnetic field (H0) supplied by a pair of NdFeB permanent magnets was set in the same direction as the microwave propagation. The transmission losses (S21) were then measured using the power meter measurement system (see Figure 4.15 for the measurement system). The measured S21 of the two band-stop filters shows that a much wider FMR absorption bandwidth and greater absorption level occurred when using the 100 / / m thick YIG sample as compared to that 141 using the 6.8 ju m thick YIG sample. These experimental findings are indeed in line with the theoretical prediction presented in Chapter 2. •> 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 r Frequency (GHz) Figure 6.2 Measured S21 of the YIG/GGG-RT-Duroid-Based Microwave BandStop Filter at FMR Frequency of 8.5 GHz Using the 100 ju m Thick YIG Sample and the 6.8 ju m Thick YIG Sample For example, the measured S21 of the two band-stop filters at the FMR frequency of 8.5 GHz are shown in Figure 6.2. The bias magnetic field of 2,100Oe was applied to set the FMR frequency at 8.5 GHz. The measured S21 of -35.5 dB using the 100 ju m thick YIG sample clearly shows a significantly greater level of 142 microwave power absorption as compared to that using the 6.8 ju m thick YIG sample with the measured S21 of -20.0 dB. A much wider FMR absorption bandwidth is also seen in Figure 6.2. 6.2 An X-Band Tunable Band-Pass Filter 8 GHz Microwave Input GHz y I 12 GHz -/ / Band-Stop Filter ".TV Band-Stop Filter #1 #2 fre Tunable X-Band BPF S21 Microwave Output GHz 12 GHz fre Figure 6.3 A Scheme of Realizing an X-band (8 -12 GHz) Microwave Band-Pass Filter A scheme for realizing an X-band (8-12 GHz) microwave band-pass filter (BPF) with tunable center frequency and pass-band bandwidth using YIG/GGGDuroid 6010LM is shown in Figure 6.3. The basic idea of the BPF using cascaded band-stop filters is the same as that shown in Figure 5.1 of Chapter 5 except that the X-band BPFs were used here to replace the step-impedance LPFs in the band-stop filter #1 and #2. A microwave BPF with the pass-band of 8 to 12 GHz was designed first as transmission line structure for band-stop filters #1 and #2. 143 As shown in Figure 6.3, an X-band BPF with tunable center frequency and passband bandwidth can be realized by simultaneously tuning the low-end and highend stop-bands and varying the bias magnetic fields of the band-stop filters #1 and #2, respectively. 6.2.1 Design of an X-Band Composite Band-Pass Filter Figure 6.4 BPF Using Quarter-Wave Short-Circuited Stubs Shunt quarter-wave short-circuited stubs were used to design and construct the X-band BPF (see Figure 6.4). In this configuration, the filter is comprised of shunt short-circuited stubs (shown as ln in Figure 6.4) that are Xg / 4 long with connecting lines (shown as ln_ln in Figure 6.4) that are also X / 4 long, where A is the guided wavelength in the medium of propagation at the mid-band frequency of the BPF. This shunt quarter-wave short-circuited stubs configuration has the unique advantages that can combine with step-impedance LPF to form a compact composite BPF [4]. This BPF was designed by using Chebyshev (or equal ripple referred to in the literature) LPF as its prototype filter which has a sharp cut off response and then 144 transformed to the band-pass response to form a BPF [5]. In the prototype filter design, four stubs (n=4) and pass-band ripple lower than 0.1 dB were specified. The corresponding prototype element values are listed as follows [5]. The four shunt quarter-wave short-circuited stubs were subsequently inserted into the four inductive elements of the step-impedance LPF. gi=1.1088; g2=1.3061; #=1.7703; g4=0.8180; g5=1.3554; go=l Note that for a given filter degree n, the stub BPF characteristics will depend on the characteristic admittances of the stub lines denoted by Yi (i = 1 to n) and the characteristic admittances of the connecting lines denoted by Yy+i (i = 1 to n - 1). The normalized Yi (i = 1 to n) and Yy+i (i = 1 to n - 1) are determined using equations (6.1). 4,2 Am Yo Mt t++1 T t ' /%! = 4-l,„ = j fel&,-H h 8og Vg;g/+1 for i = 2 to n - 2 fo -=Ito«-1 VUTi \~~T-l Yi =goYJ( l~^)gilm()+ YolNui- -y- Yn = Y0[ g„gn+i -gogi -r Jtanl? + F 0 ^«-i,« - ~ ? J ^ '0 WUWiw^-^| Y "';,!+1 i,H-i = Y0[ — p — J fcl-2B,-. for / = 1 to n - 1 (6.1) 145 f where 9 = — 2 a02 j , o)2 =\2GH2,Q\ =%GHz,G)0 =\OGHz, gi is the prototype element values, and h is a dimensionless constant that can be set to 2. The resulting normalized Yi (i = 1 to n ) , Yy+i (i = 1 to n - 1) and the corresponding impedances transformed Zi (i = 1 to n) and Zy+i (i = 1 to n - 1) are listed in Table 6-1. Table 6-1 Admittance and Impedance of the BPF Admittance(Y) Yo Yi Y12 Y2 Y23 Y3 Y 34 Y4 Impedance (Z) 1 2.0103 1.303 3.9295 1.4584 4.117 1.0123 2.1977 Z0 50 Zi Z12 24.8719 38.3729 12.7243 34.2841 12.1447 49.3924 22.7510 z2 Z23 Z3 Z34 z4 The width (W) of each stub in the BPF was computed using Equation (6.2) (a-d) [51. 's.+0 60 V ^ J s-\ f *r" V +-e+lr l 0.23 + 0.11 ,Wld<2 W _ SxeA W_ <2 d ~ e1A-2' d 5= W low = dx7T (B-l)-hi(2B-l) 60TT 2 + (6.2a) "r J ,Wld>2 0.61 e-l l n ( 5 - l ) + 0.392e„ (6.2b) (6.2c) W ,^->2(6.2d) d where Z. are the impedances in Table 6-1, £,.= 10.5 is the relative dielectric constant of Duroid 6010LM substrate, and d - 254jum is the substrate thickness. 146 The length (L - Ag / 4 ) of each stub in the BPF was computed using equation (6.3) (a-b), >L __h 4 75 (mm) f(GHz)^e 4 ^ £•+1 £.„ = - £ - 1f -a* 1+ V u J •+ - w4 + a = lH 10 (6.3a) In uJ v52y 4 w +0.432 49 + 18.7 - -In 1 + 18.1 (6.3b) V / f s 0.053 6 = 0.564 e - 0 . 9 ^ v ^+3 Finally, the dimensions of the width (W) and length (L) of each stub and the connecting line of the BPF are listed in Table 6-2. The layout of the X-band BPF thus designed is shown in Figure 6.5. The designed BPF was then simulated using AWR Microwave Office Simulator. The simulated transmission loss (S21) is shown in Figure 6.6. Table 6-2: Width and Length of Shunt Stubs and Connecting Lines in Figure 6.5 Width (W)(um) 231.6 Wo Wi 762.8 383.4 W12 1837.4 w2 463.4 W23 1944.1 w3 237.5 W34 865.6 w Length (L)(um) 3157 Lo Li 2972.6 3085.4 L12 2828.2 U 3055.5 L23 2819.7 3153.8 L34 2951.1 u u 4 147 wo Figure 6.5 The Layout of the X-Band BPF 1 0 ^ ^ ^ M « *• 8.0GHz A pa M ^ ^ l ' r T " 1'" ^ A 12.4 GHz 1 -10 CD -d O) +•> 1 % -20 -30 \ M -40 f -50 -fin \ ¥ 2 , ^k 1 1 1 4 6 8 .X 10 12 14 16 18 Frequency (GHz) Figure 6.6 Simulated Transmission Loss (S21) of the X-Band BPF 148 Subsequently, the designed X-band BPF (see Figure 6.7 (a)) was combined with a step-impedance LPF (see Figure 6.7(b)) to realize a composite X-band BPF (Figure 6.7 (c)) having compact structure and used as the transmission structure for the cascaded band-stop filters #1 and #2. In this design, the four shunt stubs in Figure 6.7 (a) were inserted into the four inductive elements ( 4 0 ' = 1,2,3,4) in Figure 6.7(b)) of the step-impedance LPF, and the length of each stubs (Ll,L2,L3,L4) and length of each inductive elements (LH,L12,L13,L14) are tuned to form the desired frequency responses. The width of each shunt stub and that of the capacitor and inductor in the step-impedance LPF were keep constant. The width of each shunt capacitor and serial inductor are 757.1 ju m and 153.1 ju m, respectively, as shown in Figure 6.7 (b). AWR Microwave Office Simulator was used for the tuning and optimization in the simulation. The dimensions of the composite X-band BPF are listed in Table 6-3. The simulated S21 of the X-band composite BPF are shown in Figure 6.8. Table 6-3: Geometric Dimensions of The X-Band Composite BPF Wl W2 W3 W4 LI L2 L3 L4 762.8 jum 1837.4//m 1944.1//m 865.6//m 3106 ju m 3439//m 3424 jum 3176 jum Lcl Lc2 Lc3 Lc4 Lc5 Lll L12 L13 L14 149 111.5 /urn 492 jum 642.3 jum 492 jum 111.5 /jm 957.3 jum 1997 /um 2199.3 jum 1190.6 /um (c) Figure 6.7 The X-Band BPF (a), The Step-Impedance LPF (b), and the Composite X-Band BPF (c) T—•—r 1 7.9 GHz ' 12.2GHz 1 r A -\ -10 -20 \- Figure 6.8 Simulated Transmission Loss (S21) of the Composite X-Band BPF 150 6.2.2 Experimental Results and Discussion The designed X-band composite BPF was fabricated using the same photolithograph process as described in Chapter 4. A photo of the device fabricated is shown in Figure 6.9. The transmission characteristics of the composite BPF is measured using the Power Meter Measurement System (see Figure 4.15 for the measurement system) and the measured S21 is shown in Figure 6.10. >•_«. <*-: Figure 6.9 Photo of Fabricated X-Band Composite BPF 151 — • — i — ' — i — ' — i — ' • -5 -10 -15 i ' i —>—r"' i 6.5 GHz " J • i • i • i i l i 1 i 10.5 G H z • „ ^ * ^ ^ - -20 £T -25 Afc -35 U - -40 -45 i -50 3 4 5 6 7 I 8 9 10 11 12 , I 13 1 1 14 1 1 15 1 16 Frequency(GHz) Figure 6.10 Measured Transmission Loss (S21) of the Composite X-Band BPF Two major discrepancies between the measured and simulated transmission characteristics are identified. First, the measured pass-band of 6.5 -10.5 GHz is seen to shift towards the low frequency region as compared to the simulated pass-band of 8-12 GHz shown in Figure 6.8. This pass-band frequency shift is attributable to the stub length inaccuracy during the experimentation. In the experiments, four holes at the end of each shunt stub (see Figure 6.9) were drilled manually and filled with Transene® silver-based surface mount adhesive. As a result, it is difficult to accurately control the length of each stub. As a verification, the sensitivity of the S21 to the shunt stub lengths was simulated and shown in 152 Figure 6.11. It is clearly seen that the pass-band frequency shifts greatly towards the high- or low- frequency end when the lengths of the stubs are deviated from their ideal values by 1,000 ju m. T — ' — i — ' — i — ' — i — ' — i — ' — i — ' — i — « — r 2 4 6 8 10 12 14 16 18 Frequency (GHz) Figure 6.11 The Simulated Sensitivity of the S21 to the Lengths of Shunt Stubs The second discrepancy between the measurement and simulation result is that the measured insertion loss of ~-7dB is much higher than the simulation results. This higher insertion loss in the pass-band is attributable to the imperfect grounding of the shunt stubs. The measured average resistance of each shunt stub to ground is about 1.0 ohm. The sensitivity of S21 to the shunt stub grounding resistance was simulated and shown in Figure 6.12. It is seen that, the 153 insertion loss in the pass-band increases by more than 6dB as the shunt stub grounding resistance increases from 0 to 1.6 Q.. 5 0 1 1 1 1 1 1 1 1 Ground Resistance 0.6Ohm r 1 ' 1 r - Perfect Ground -5 -10 -15 T5 C/5 -20 -25 -30 -35 -40 -45 18 Freuqency (GHz) Figure 6.12 The Simulated Sensitivity of the S21 to the Shunt Stub Grounding Resistance Encouraged by the preliminary results presented above, the same X-band composite BPF was used to demonstrate its low- and high-end tunability. In the experiments, the YIG films used were 100 pirn in thickness with dimension of 6.0x8.0WOT2 in the X and Y directions (see Figure 4.11). The bias magnetic field was again supplied by a pair of NdFeB permanent magnets in the same direction as the microwave propagation. Again, the S21 was then measured using the 154 Power Meter Measurement System. As illustrated in Figure 6.3, the pass-band bandwidth of the BPF can be changed by tuning the bandwidth of the low- and high-end stop-bands. The measured high-end and low-end stop-band tunability of the BPF by applying the bias magnetic fields of 2,800 Oe and 2,450 Oe, and 990 Oe and 1,060 Oe, respectively, are shown in Figure 6.13 and 6.14. Figure 6.13 and 6.14 clearly show that both the low- and high-end stop-bands could be shifted downward or upward by applying appropriate external bias magnetic fields. CO 7 8 9 10 11 12 13 14 15 16 Frequency(GHz) Figure 6.13 The High-End Stop-Band Tunability of the BPF by Applying Bias Magnetic Fields of 2,800 Oe and 2,450 Oe 155 0 -i—|—i—|—i—[—i—|—i—|—i—|- 1 •<—i—'—r i ' i Original -5 -10 PQ 73 CD .45 L_i I i_l i L 7 8 9 10 11 12 13 14 15 16 Frequency(GHz) Figure 6.14 The Low-End Stop-Band Tunability of the BPF by Applying Bias Magnetic Fields of 990 Oe and 1,060 Oe 6.3 Future Works Outlined As discussed in the previous section, realization of the composite X-band BPF with desired center frequency and pass-band bandwidth together with greatly reduced insertion loss was one of the objectives of this research. For this purpose, the approach involving accurate control of the shunt stub lengths and the minimization of the grounding resistances need to pursued 156 Following realization of the X-band composite BPF just described, the meandertyped BPF can be realized by using two or more such composite BPFs and then incorporated in the band-stop filters to simultaneously enhance the FMR peak absorptions levels and broaden the absorption bandwidths. Finally, a pair of band-stop filters each with the meander-type BPF can be cascaded as shown in 6.3 to realize the proposed X-band tunable band-pass filters. Reference 1. V. Radisic, Y. X. Qian, and T. Itoh. "Broad-band power amplifier using dielectric photonic band-gap structure", IEEE Microwave and Guided Wave Letters, vol.8, pp.13-14,1998. 2. Maite Irisarri, Miguel A. G. Laso, Maria J. Erro, and Mario Sorolla. "Compact photonic band-gap microstrip structures", Microwave and Optical Technology Letters, vol.23, pp.233-236,1999. 3. S. D. Yoon, Jianwei Wang, Nian Sun, C. Vittoria and V. G. Harris, "Ferritecoupled line circulator simulations for application at X-band frequency," IEEE Trans. Magn., vol. 43, pp.2639,2007. 4. C. Hsu, F. Hsu, and J. Kuo, "Microstrip bandpass filters for ultrawideband (UWB) wireless communications," in IEEE MTT-S Int. Dig., pp. 679-682, June 2005. 5. G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures, Artech House, Dedham, 1980. 157 Chapter 7 Conclusions Wideband communication and radar systems require high-speed electronicallytunable wideband microwave band-stop and band-pass filters. FMR-based microwave devices possess the unique capability of high-speed electronic tunability, using magnetic field, for very high carrier frequency and very large bandwidth. Various types of FMR-based microwave filters using bulk ferrimagnetic yttrium iron garnet (YIG) materials have long been constructed and utilized in system applications. In recent years, tunable FMR absorption in YIG thin film structures has also been investigated for broadband microwave device applications. Although the monolithic integration combining magnetic thin film structure with semiconductor substrate in a system-on-a chip (SOC) is the one of the most important goal of magnetoelectronics, there are currently still some severe limitations in the development of ferri- and ferro-magnetic thin films and devices that are fully MMIC compatible. Therefore, MMIC compatible ferrimagnetic semiconductor devices with fabricated a hybrid separately structure using ferrimagnet and then combine in some and device configuration is one of the current research directions. In this dissertation research, the FMR-based microwave band-stop filter and band-pass filter using YIG/GGG-GaAs layer structure have been throughout studied. A full-wave method of modeling and analysis of the YIG/GGG-GaAs 158 flip-chip layer structure was first carried out for the device application as wideband tunable microwave band-stop filter utilizing the FMR absorptions of this magnetic layer structure in microwave frequency band. Detail simulations were then carried out aimed at optimal device performances of the microwave band-stop filter using YIG/GGG-GaAs layer structure. In the experimental studies, a magnetically-tuned microwave band-stop filter using YIG/GGGgallium arsenide (GaAs) flip-chip layer structure with wideband tunability of stop-band center frequency and bandwidth has been accomplished using a microstrip meander line together with non-uniform bias magnetic field. A magnetically-tunable wideband microwave band-pass filter with large tuning ranges for both the center frequency and the bandwidth in the pass-band has also been realized using a pair of cascaded aforementioned band-stop filters. The filters application using the same YIG/GGG layer on high frequency circuit board materials, i.e., RT-Duroid 6010LM, has also been studied and demonstrated in this thesis, and the results shows promising filter application on those high frequency laminate materials. Both of the band-stop and band-pass filters studied in this thesis, when fully developed, should find applications in frequency-hopping wideband microwave communication and signal processing systems. 159

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