# Planar Tunable RF/Microwave devices with magnetic, ferroelectric and multiferroic materials

код для вставкиСкачатьPlanar Tunable RF/Microwave devices with magnetic, ferroelectric and multiferroic materials A Dissertation Presented by Jing Wu To The Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Electrical Engineering Northeastern University Boston, Massachusetts August, 2012 UMI Number: 3527638 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent on the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3527638 Copyright 2012 by ProQuest LLC. All rights reserved. This edition of the work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 UMI Number: 3527638 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent on the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3527638 Copyright 2012 by ProQuest LLC. All rights reserved. This edition of the work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 NORTHEASTERN UNIVERSITY Graduate School of Engineering Thesis Title: Planar Tunable RF/Microwave devices with magnetic, ferroelectric and multiferroic materials Author: Jing Wu Department: Electrical and Computer Engineering Approved for Dissertation Requirement for the Doctor of Philosophy Degree ______________________________________________ ____________________ Dissertation Advisor: Professor Nian-Xiang Sun Date ______________________________________________ ____________________ Thesis Reader: Professor Philip Serafim Date ______________________________________________ ____________________ Thesis Reader: Professor Edwin Marengo Date ______________________________________________ ____________________ Department Chair: Ali Abur Date Graduate School Notified of Acceptance: ______________________________________________ ____________________ Director of the Graduate School: Date 2 Acknowledgments I would like to thank my advisor, Prof. Nian-Xiang Sun, for his constant help and support during the time that I spent on my research. His patient guidance and novel approach to the problems that I encountered was invaluable for my exploration and learning, which help me become a better researcher. I am grateful to Prof. Yuri K. Fetisov and Prof. Igor Zavislyak for their helpful discussion on magnetostatic wave propagation, which helps me build in-depth understanding of the physic concepts behind these RF devices. I would also like to thank Prof. Philip Serafim and Prof. Edwin Marengo for agreeing to be on my dissertation committee. Their advices on my thesis and dissertation defense are invaluable. Additionally, I would like to acknowledge the other members of our group. Without the friendly help from the lab personnel and the scholarly and constructive work environment within the group this process would have taken much longer. In particular, I would like to thank Xi Yang, Ming Li, Ogheneyunume Obi, Xing Xing, Ming Liu, Jing Lou, Yuan Gao, Tianxiang Nan and Shawn Beguhn for their invaluable help and collaboration with my research. Finally a special thank goes out to my family, who have always been behind me whatever my goal at the time happened to be. Their love and support has helped me to achieve my goals, and I will forever appreciate it. 3 Abstract Modern ultra wideband communication systems and radars, and metrology systems all need reconfigurable subsystems that are compact, lightweight, and power efficient. At the same time, isolators with a large bandwidth are widely used in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. Conventional Isolators based on the non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide. However, these approaches are usually bulky. This dissertation focuses on theoretical study, numerical evaluation and measurement verification of novel planar RF/microwave devices with magnetic substrates and superstrates, demonstrating tunable and non-reciprocal characteristics, so that size, weight and cost of systems can be reduced. The combination of ferrite thin films and planar microwave structure constituted a major step in the miniaturization of such a non-reciprocal devices. A novel type of tunable isolator was presented, which was based on a polycrystalline yttrium iron garnet (YIG) slab loaded on a planar periodic serrated microstrip transmission line that generated circular rotating magnetic field. The non-reciprocal direction of circular polarization inside the YIG slab leads to over 19dB isolation and < 3.5dB insertion loss at 13.5GHz with 4kOe bias magnetic field applied perpendicular to the feed line. Furthermore, the tunable resonant frequency of 4 ~ 13.5GHz was obtained for the isolator with the tuning magnetic bias field 0.8kOe ~ 4kOe. 4 The non-reciprocal propagation behavior of magnetostatic surface wave in microwave ferrites such as YIG also provides the possibility of realizing such a nonreciprocal device. A new type of non-reciprocal C-band magnetic tunable bandpass filter with ultra-wideband isolation is presented. The BPF was designed with a 45 o rotated YIG slab loaded on an inverted-L shaped microstrip transducer pair. This filter shows an insertion loss of 1.6~2.3dB and an ultra-wideband isolation of more than 20dB, which was attributed to the magnetostatic surface wave. The demonstrated prototype with dual functionality of a tunable bandpass filter and an ultra-wideband isolator lead to compact and low-cost reconfigurable RF communication systems with significantly enhanced isolation between the transmitter and receiver. A novel distributed phase shifter design that is tunable, compact, wideband, low-loss and has high power handling will also be present. This phase shifter design consists of a meander microstrip line, a PET actuator, and a Cu film perturber, which has been designed, fabricated, and tested. This compact phase shifter with a meander line area of 18mm by 18mm has been demonstrated at S-band with a large phase shift of >360 o at 4 GHz with a maximum insertion loss of < 3 dB and a high power handling capability of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and compact phase shifter that operates between 1GHz to 6GHz was successfully demonstrated. Such phase shifter has great potential for applications in phased arrays and radars systems. 5 Table of Contents Acknowledgments ......................................................................................................................... 1 Abstract .......................................................................................................................................... 4 List of Figures .............................................................................................................................. 10 Chapter 1: Introduction .............................................................................................................. 17 1.1 Motivation .......................................................................................................................... 17 1.2 Background ....................................................................................................................... 18 1.3 Microwave magnetic material and its property ............................................................. 19 1.3.1 Microwave ferrites ..................................................................................................... 19 1.3.2 Permeability tensors .................................................................................................. 21 1.3.3 Demagnetizing Field .................................................................................................. 23 1.3.4 Remanence magnetization and the hysteresis loop ................................................. 25 1.4. Mechanism of Microwave ferrite device ........................................................................ 26 1.4.1 Non-reciprocity .......................................................................................................... 26 1.4.2 Tunability.................................................................................................................... 28 1.5 Dissertation overview........................................................................................................ 31 1.6 Reference ........................................................................................................................... 33 Chapter 2: Simulations and Experiment Setups ........................................................................ 36 2.1 Ferrite device modeling in HFSS ..................................................................................... 36 2.1.1 Saturation magnetization ( 2.1.2 Delta H ( ) and DC bias field ( ) in HFSS .................. 37 ) in HFSS ................................................................................................ 38 2.2 VNA for s-parameter and permeability measurement.................................................. 39 2.3 Electromagnet for applying DC bias field ...................................................................... 40 6 2.4 Reference ........................................................................................................................... 41 Chapter 3 Concept of magnetostatic surface wave .................................................................... 42 3.1 Motivation .......................................................................................................................... 42 3.2 Magnetostatic wave in tangential magnetized ferrite .................................................... 43 3.2.1 Magnetoquasistatic approximation .......................................................................... 43 3.2.2 Walker’s equation and magnetostatic modes .......................................................... 44 3.2.3 Magnetostatic surface wave in tangentially magnetized films (MSSW) ............... 45 3.2.4 Magnetostatic back volume wave in tangentially magnetized films ..................... 51 3.2.5 Summation of magnetostatic wave in tangentially magnetized films ................... 56 3.3 Magnetostatic wave in finite ferrite films ....................................................................... 58 3.3.1 Magnetostatic wave in ferrite films on metallic backed substrate ........................ 59 3.3.2 Magnetostatic wave in finite ferrite films (Straight Edge Resonator (SER)) ....... 61 3.4 Excitations of Magnetostatic wave .................................................................................. 65 3.5 Conclusion ......................................................................................................................... 70 3.6 Reference ........................................................................................................................... 70 Chapter 4 Bandpass Filters based on magnetostatic wave concepts......................................... 72 4.1 Motivation .......................................................................................................................... 72 4.2 Introduction of Previous BPF researches ....................................................................... 73 4.3 S-band magnetically and electrically tunable MSSW band pass filters ...................... 75 4.3.1 Filter design mechanism ............................................................................................ 76 4.3.2 Experimental and simulation verification ............................................................... 79 4.3.3 Magnetically and Electrically tunability.................................................................. 84 4.3.4 Conclusion and challenges ........................................................................................ 86 4.4. Reciprocal c-band Bandpass filters based on SER ....................................................... 88 7 4.4.1 Filter design mechanism ............................................................................................ 89 4.4.2 Simulations and Experimental verification ............................................................. 92 4.4.3 Magnetically tunability.............................................................................................. 96 4.4.4 Limitation of this design ............................................................................................ 99 4.5 Non-reciprocal c-band Bandpass filters based on rotated SER ................................... 99 4.5.1 The mechanism of the non-reflection boundary on a rotated YIG film ............. 100 4.5.2 Simulations and Experimental verification ........................................................... 104 4.5.3 Magnetically tunability............................................................................................ 106 4.5.4 Summary for C-band non-reciprocal filter ........................................................... 111 4.6 Integrated bandpass filter with spin spray materials .................................................. 112 4.7 Conclusion ....................................................................................................................... 115 4.8 References ........................................................................................................................ 116 Chapter 5: Tunable Planar Isolator with Serrated Microstrip Structure ............................... 120 5.1 Introduction of isolator based on ferrite ....................................................................... 121 5.1.1 Ferromagnetic resonance isolator .......................................................................... 122 5.1.2 Field displacement isolator...................................................................................... 126 5.2 Serrated Microstrip Isolator Design Mechanism......................................................... 128 5.2.1 Previous Researches on Planar approaches of isolator designs .......................... 128 5.3.2 Serrated Microstrip Structure and Circular polarization ................................... 129 5.2.3 Magnetic field distribution of Serrated Microstrip Structure ............................. 131 5.3 Simulation verification ................................................................................................... 134 5.3.1 Effect of Ferrite films location with Serrated Microstrip Structure ................... 134 5.3.2 Designed Serrated Microstrip isolator with thicker YIG slab ............................. 138 5.4 Measurement verification .............................................................................................. 139 8 5.4 Conclusion ....................................................................................................................... 142 5.5 Reference ......................................................................................................................... 142 Chapter 6 Phase Shifters with Piezoelectric Transducer Controlled Metallic Perturber ...... 144 6.1 Introduction of tunable phase shifter researches ......................................................... 145 6.2 Device construction ......................................................................................................... 148 6.2.1 Device Construction ................................................................................................. 148 6.2.2 Piezoelectric transducer (PET) - PI PICMA® PL140.10 ...................................... 151 6.3 Theoretical analysis ........................................................................................................ 153 6.3.1 Equivalent Circuit Model for Meander Line with variable copper perturber .. 153 6.3.2 The insertion Loss Analysis..................................................................................... 154 6.4 Simulation Results .......................................................................................................... 156 6.5 Measurement Results...................................................................................................... 160 6.6. Extended design for 1-6GHz ......................................................................................... 165 6.7. Comparison with previous approaches ........................................................................ 171 6.8 Conclusions ...................................................................................................................... 172 6.9 References ........................................................................................................................ 173 Chapter 7 Conclusion ............................................................................................................... 176 9 List of Figures Fig. 1. YIG elementary cell. Fe3+ in a-sites – empty circles, Fe3+ in d-sites –shaded circles, Y3+ ions – filled circles. The positions of the oxygen atoms are not shown [10, 11]..... 21 Fig. 1.2 Demagnetizing field of a magnetic plate with perpendicular external magnetic field ............................................................................................................................................... 24 Fig. 1.3 Demagnetizing field of a magnetic plate with tangential external magnetic field ... 24 Fig. 1.4 Hysteresis loops of magnetically YIG .......................................................................... 26 Fig 1.5, Spinning of electrons with right-handed polarization, with strong interaction with RHPL wave propagation [12] ............................................................................................ 27 Fig. 1.7 versus on TTI-390 at 5.5 GHz [21] .......................................................... 29 Fig. 1.8. Calculated and measured FMR frequency against the external magnetic bias field on YIG film ( ). ..................................................................................... 30 Fig. 2.1 The relation between magnetization moment and the Applied DC bias field H ..... 38 Fig.2.2 Vector network analyzer (Agilent PNA E8364A) ........................................................ 40 Fig.2.3 Current controlled Electromagnet................................................................................ 41 Fig. 3.1 Geometry for a tangential magnetized ferrite film. ................................................... 46 Fig. 3.2 Guided wave propagation in a tangential magnetized ferrite film. .......................... 46 Fig.3.3 Dispersion diagram for surface wave on infinite YIG slab (d=108um; H0=1500Oe, 4piMs=1750 Gauss) ............................................................................................................. 49 Fig.3.4 Potential profiles for surface wave on infinite YIG slab with forward ( backward ( - ) wave propagation at operating frequency ) and . with Dc bias field at z direction. ....................................................................................................... 50 Fig. 3.5 Surface wave propagation in a tangential magnetized ferrite film. .......................... 51 Fig.3.6 Potential profiles for back volume wave on infinite YIG slab ................................... 54 Fig.3.7 Dispersion relation for surface wave on infinite YIG slab (d=108um; H 0=1600Oe, 4piMs=1750 Gauss) ............................................................................................................. 55 Fig. 3.8 Comparison of dispersion relation between Magnetostatic surface wave (MSSW) and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um, 4piMs 1750Gauss).................................................................................................. 57 10 Fig. 3.9 Geometry for a tangential magnetized ferrite film with metallic backed substrate 58 Fig. 3.10 Compare the dispersion relation for a tangential magnetized ferrite film with/without metallic backed substrate ............................................................................ 60 Fig. 3.11 Geometry of straight edge resonator (SER)) ............................................................ 60 Fig. 3.12 MSSW propagation in straight edge resonator (SER)) .......................................... 61 Fig. 3.13. The dispersion relation for a YIG SER: Bias field applied .................................................... 63 Fig. 3.14 The s-parameter of a bandpass filter utilizing YIM films width and standing wave mode ; DC magnetic bias field 1500 Oe .................................................................. 64 Fig. 15. Transmission line model for magnetostatic wave excitation. ................................... 66 Fig. 3.16. Geometry of the transducers: Inverted L-shaped microstrip transducers with parallel YIG alignment; , . ........................................................... 68 Fig. 3.17. Radiation resistance for coupling of transducers to top and bottom surface of the YIG film. DC bias field is 1600 Oe. ................................................................................... 69 Fig. 3.18. Reciprocal excitations of microstrip transducer due to the reflection of the straight edge. ....................................................................................................................... 69 Fig. 4.1 bandpass filter using two microstrip line antennas, realized by exciting the magnetostatic surface waves (MSSW) reported by Srinivasan et. al: (a) schematic; (b) s-parameters ........................................................................................................................ 75 Fig. 4.2. Geometry of the transducers. (a) Parallel microstrip transducers as used in [16] and [7]. (b) L-shaped microstrip transducers as used in [14] and [15]. (c) T-shaped microstrip transducers were proposed in this paper. ...................................................... 76 Fig. 4.3. Geometry of a T-shaped microwave transducer (top view and side view). W1=1.18mm, W2=18.1mm, S1=9.0mm, S2=0.53mm, S4=1.2mm, H=1.28mm. ............ 78 Fig. 4.4. Schematic of the bandpass filter with single-sided YIG films ................................. 78 Fig. 4.5. Dispersion relation of Single crystal YIG film, which S3= 4mm and W3=10mm, DC bias field at 200 Oe, Applied perpendicular to the feed lines. standing wave modes indicates indicates the , as discussed in chapter 3. ............................................................................................................................................... 79 11 Fig. 4.5 S-parameters of the bandpass filter with 50-250 Gauss bias field ............................ 81 Fig. 4.6. 3-dB bandwidth versus magnetic bias field. S3=4mm, W3=10mm. ........................ 81 Fig. 4.7 Simulated and measured bandpass filter resonance frequency ................................ 83 Fig. 4.8. Simulated and measured bandpass filter 3-dB bandwidth. ..................................... 83 Fig. 4.9. Calculated and measured FMR frequency against the external magnetic bias field. ............................................................................................................................................... 84 Fig. 4.10. Measured electric field tunability of the bandpass filter ........................................ 85 Fig. 4.11 Transmission coefficient S21 of S-band bandpass filter utilizing single crystal YIG film, with DC bias magnetic field 200 Oe. ................................................................ 87 Fig. 4.12 Transmission coefficient S21 in terms of different S 3 (length of YIG film along the propagation axis ), with DC bias magnetic field 200 Oe ................................................. 88 Fig. 4.13 Geometry of the transducers: Inverted L-shaped microstrip transducers with parallel YIG alignment; , ...................................................................................... 91 Fig. 4.14. Dispersion relation of MSSW in a single crystal YIG film, which W4= 2mm and L2=3mm, DC bias field at 1.6 kOe, Applied perpendicular to the feed lines. the standing wave modes indicates indicates , as discussed in chapter 3, eq. (3.48). ............................................................................................................ 92 Table 4.2 The resonance frequency of width and standing wave mode with DC magnetic bias field 1600 Oe. ............................................................................................... 92 Fig. 4.15. Simulation result of bandpass filters based on YIG SER film, with DC magnetic bias field 1600 Oe ................................................................................................................ 93 Fig. 4.16. Experimental result of bandpass filters based on YIG SER film , with DC magnetic bias field 1600 Oe ................................................................................................ 94 Fig. 4.17. Resonance mode comparison between simulation and experimental data of the proposed c-band bandpass filter ....................................................................................... 96 Fig. 4.18 Transmission coefficient (S21) of proposed C-band tunable band pass filter on straight edge YIG film. The edge of the YIG film is parallel to the transducer and perpendicular to DC bias magnetic field .......................................................................... 97 12 Fig. 4.19 Transmission coefficient (S12) of proposed C-band tunable band pass filter on straight edge YIG film. The edge of the YIG film is parallel to the transducer and perpendicular to DC bias magnetic field .......................................................................... 98 Fig. 4.20 Comparison of transmission coefficient of proposed C-band tunable band pass filter on straight edge YIG film with the FMR frequency calculated from Kittel’s equation................................................................................................................................ 98 Fig. 4.21 MSSW propagation in a tapered YIG film. [16] .................................................... 101 Fig. 4.21 MSSW propagation in a YIG film with different bias condition at edges or an absorber. [12-15]. .............................................................................................................. 101 Fig. 4.22 MSSW propagation in a YIG film with a 45o inclined edge boundary at the YIGair boundary. ..................................................................................................................... 101 Fig. 4.23 Comparison of dispersion relation between Magnetostatic surface wave (MSSW) and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um, 4piMs 1750Gauss)................................................................................................ 103 Fig. 4.24 Non-reciprocal c-band BPF on a rotated YIG fim. ................................................ 103 Fig. 4.25 Simulated s-parameter of our bandpass filter with parallel/rotated YIG slab under DC bias field of 1.6 kOe......................................................................................... 105 Fig. 4.26 Measured s-parameter of our bandpass filter with parallel/rotated YIG slab under DC bias field of 1.6 kOe......................................................................................... 106 Fig. 4.27 Transmission coefficient (S21) of proposed C-band tunable band pass filter on rotated YIG film. ............................................................................................................... 107 Fig. 4.28 Transmission coefficient (S21) of proposed C-band tunable band pass filter on rotated YIG film. ............................................................................................................... 108 Fig. 4.29 Transmission coefficient (S11) of proposed C-band tunable band pass filter on rotated YIG film. ............................................................................................................... 108 Fig. 4.30 Transmission coefficient (S22) of proposed C-band tunable band pass filter on rotated YIG film. ............................................................................................................... 109 Fig. 4.31 Comparison of transmission coefficient of proposed C-band tunable band pass filter on rotated YIG film with the FMR frequency calculated from Kittel’s equation ............................................................................................................................................. 109 13 Fig. 4.32 The insertion loss of the forward pass bands and the isolation of the backward transmission. ...................................................................................................................... 110 Fig. 4.32 The 3-dB bandwidth of the forward pass bands for the fabricated c-band nonreciprocal bandpass filter. ................................................................................................ 111 Fig. 4.33 Geometry of integrated band pass filter with MSSW concept .............................. 113 Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape. ....... 114 Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape, with DC bias from 125Oe to 625 Oe ........................................................................................ 115 Fig. 5.1 Application of isolators in communication system. .................................................. 122 Fig. 5.2 Attenuation constants for circularly polarized plane waves in the ferrite medium ............................................................................................................................................. 124 Fig. 5.2 propagation constants for circularly polarized plane waves in the ferrite medium ............................................................................................................................................. 124 Fig. 5.3 Ferrite isolator with waveguide structure: (a) field distribution in waveguide; (b) Ferrite location in waveguide........................................................................................... 125 Fig. 5.4 Forward and reverse attenuation constants for the resonance isolator (a) Versus slab position. (b) Versus frequency.................................................................................. 125 Fig. 5.5 Field displacement isolator ......................................................................................... 127 Fig. 5.6. Geometry of the serrated microstrip isolator: , and . The dashed line indicates the current flowing on the substrate………………………………………………………………………………......130 Fig. 5.7. Microwave magnetic field distribution with the serrated structure ...................... 130 Fig. 5.8. The polarization of microwave magnetic field above and underneath the serrated structure: (a) Forward transmission; (b) Backward transmission .............................. 132 Fig. 5.9. The summarized polarization of microwave magnetic field above and underneath the serrated structure: (a) Forward transmission; (b) Backward transmission ......... 133 Fig. 5.11. Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG underneath serrated structure…………………………………………………………………………………..136 14 Fig. 5.13. Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe applied perpendicular to the feed line: YIG above serrated with taperededges .…..………………………………………………………………………...138 Fig. 5.14. Simulated s-parameter of serrated microstrip isolator. ..................................... 139 Fig. 5.15. Measured s-parameter of serrated microstrip isolator ...................................... 140 Fig. 5.16 Return Loss of tunable serrated microstrip isolator with 4kOe magnetic field bias. …..…………………………………………………………………………………….141 Fig. 5.17 Insertion loss and isolation of the tunable serrated microstrip isolator over operating frequency. ......................................................................................................... 141 Fig. 6.1 Phase shifter design with PET controlled dielectric perturber by Chang et al.[9] 147 Fig. 6.2. Phase shifter design with PET controlled magneto-dielectric perturber by Yang et al. ........................................................................................................................................ 148 Fig. 6.3. Schematic and photograph of the meander line phase shifter with PET controlled metallic perturber. ............................................................................................................ 149 Fig. 6.4. Design dimensions for the meander line phase shifter, the grayed area shows the size and position of the metallic perturber. .................................................................... 150 Fig. 6.5. Schematic and the equivalent circuit of piezoelectric transducer (PET) - PI PICMA® PL140.10 ........................................................................................................... 152 Fig. 6.6. Approximated gap dimension with applied voltage (0~50V). The original gap is 2 mm. ..................................................................................................................................... 153 Fig. 6.7 Equivalent circuit of meander line with piezoelectric bending actuator ............... 154 Fig. 6.8. Simulated S21 of the meander line with different distances between the metallic perturber and the substrate. ............................................................................................ 157 Fig. 6.9. Simulated S11 of the meander line with different distances between the metallic perturber and the substrate. ............................................................................................ 157 Fig. 6.10 Simulated relative phase shift of the phase shifter with different distances between the metallic perturber and the substrate ........................................................................ 159 Fig. 6.11. Measured S21 of the meander line with different voltage applied on the PET. . 160 Fig. 6.12. Measured S11 of the meander line with different voltage applied on the PET. . 161 15 Fig. 6.13. Measured and simulated relative phase shift of the meander line phase shifter with different voltage applied on the PET. The symbols indicate simulated results from HFSS. ........................................................................................................................ 164 Fig. 6.14. Measured insertion loss of the meander line phase shifter with different input power at 3 GHz.................................................................................................................. 165 Fig. 6. 15. Design dimensions for the extended meander line phase shifter. ....................... 166 Fig. 6.16. Measured relative phase shift of the extended meander line phase shifter with different voltage applied on the PET .............................................................................. 167 Fig. 6.17. Measured S12 of the extended meander line with different voltage applied on the PET. .................................................................................................................................... 170 Fig.6. 18. Measured S11 of the extended meander line with different voltage applied on the PET. .................................................................................................................................... 170 16 Chapter 1: Introduction 1.1 Motivation Modern ultra wideband communication systems and radars, and metrology systems all need reconfigurable subsystems. Multi-band and multi-mode radios are becoming prevalent and necessary in order to provide optimal data rates across a network with a diverse and spotty landscape of coverage areas. As the number of required bands and modes increases, the aggregate cost of discrete RF signal chains justifies the adoption of tunable solutions. More specifically, for example, the demand has been growing for bandpass filters with improved performance on tunable operating frequency, low insertion loss, bandwidth, linearity, size, weight, and power efficiency. Also, Compact tunable phase shifters with large phase shift, low loss and high power handling capability are desired for a variety of applications like phase array antennas. At the same time, tunable isolators with a large bandwidth are widely used in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. Conventional, these tunable and non-reciprocal microwave devices based on the non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide are usually bulky. This dissertation focuses on theoretical study, numerical evaluation and measurement verification of novel planar microstrip RF/microwave structures with 17 magnetic substrates and superstrates loading, demonstrating tunable and non-reciprocal characteristics, and insertion loss, size, weight and cost of systems can be reduced as well. 1.2 Background The key concept for everything in this dissertation is the well-known Maxwell’s equations, proposed by James Clark Maxwell in 1873, which are the foundation of electromagnetic wave propagation in a medium [1]-[4]. ⃑ (Gauss’s Law) ⃑ ⃑ (1.1) (Faraday’s Law) (1.2) ⃑ (Gauss’s Law for magnetism) ⃑ ⃑ (1.3) (Ampere’s Law) (1.4) where: is the electric displacement ( ) ρ is the charge density ( is the current density ( ) ) is the magnetic flux density ( ) H is the magnetic field intensity ( ) represents spatial location of any point in a 3-dimension space represents time This is the most general Maxwell’s equation. To describe the medium in which fields exist, the constitutive relationships are required [1]-[5]: ⃑ ⃑ 18 (1.5) ⃑ ⃑ ⃑ (1.6) ⃑ (1.7) where: ς is the conductivity (mhos/m) is the magnetization (amp/ ) is the permeability of free space (henrys/m), here π is the dielectric constant of free space (farads/m), here is the magnetic susceptibility; For an isotropic, homogenous and non-dispersive medium, and are constant. However, in reality many mediums are anisotropic, and dispersive. For example, the permeability of magnetic materials can be written as a tensor due to the induced magnetization: [ Each term of the ] (1.8) tensor may be frequency and spatial dependent if the material is dispersive and inhomogeneous. 1.3 Microwave magnetic material and its property 1.3.1 Microwave ferrites 19 Ferrimagnetic materials, or ferrites, are the most popular magnetic materials in RF and microwave application. In this dissertation, we are interested in two practical types of ferrites, which have cubic crystal structure: spinels and garnets [6]. Spinel ferrites exhibit a large static initial permeability, in the range of . However, its permeability at high frequencies drops down to one at around 2 GHz. Spinel ferrites are known as high relaxation loss materials, with typical ferrimagnetic loss ( ) in the order of 2-1000 Oe. Therefore, applications of spinel ferrites are usually limited to low frequencies (MHz frequency). The garnet ferrites have many applications in RF and microwave devices in past 20 years. G. Menzer first studied the cubic crystal structure of garnet ferrites in 1928. The most famous garnet ferrite, yttrium iron garnet (Y3Fe5O12, or YIG), was first prepared by F. Bertaut and F. Forrat [1]. YIG is an insulator with excellent high-frequency magnetic properties. It has the narrowest known ferromagnetic resonance line and the lowest spinwave damping. Besides, YIG is a very low loss material at high frequencies. The FMR linewidth, of a single crystal YIG was measured to be ~ 0.2 Oe at 3 GHz. Therefore, many commercial magnetic microwave devices are made of YIG substrates. The structure of YIG coincides with that of natural garnet [8, 9]. Its primitive elementary cell is a half of cube with lattice constant . This cell consist of 4 octants each containing 1 formula unit of Y3Fe5O12. The mutual positions of atoms are depicted on Fig. 1.1 [10, 11]. Atoms on the boundaries simultaneously belong to the neighboring octants. The lattice has body-centered cubic structure. Positions of all atoms 20 are listed in [9]. A typical YIG saturation magnetization linewidth of for single crystal and is around 1800 Gauss, with a for polycrystalline, which is very suitable for microwave device applications. Fig. 1. YIG elementary cell. Fe3+ in a-sites – empty circles, Fe3+ in d-sites –shaded circles, Y3+ ions – filled circles. The positions of the oxygen atoms are not shown [10, 11] 1.3.2 Permeability tensors At microwave frequencies, we are more interested in the net magnetization of ferrite, which is defined as magnetic dipole moment per unit volume in response to the external magnetic field. It can be written as: ̅ (1.9) 21 where ̅ is the magnetic susceptibility tensor of the medium. To make the problem simpler, first let us assume the external magnetic field is along z-axis. Since most applications in this dissertation is signals at microwave frequency with a DC bias field, the total magnetic field and total magnetization can be expressed as : where is the applied bias field, ̂ (1.10) ̂ (1.11) is the DC bias magnetization, and is the AC magnetic field and magnetization. The equation of motion of the magnetic dipole moments can be derived as [12]: [ where ] (1.12) is gyromagnetic ratio, which is 2.8MHz/Gauss. For the study of magnetostaic wave and magnetic resonance, we are primary interested in saturated single domain materials. So, the static magnetic field and magnetization will be parallel to each other in z-axis. Therefore, the first term of the right side of the equation zero. The fourth term is small enough to be neglected, due to the small signal analysis. saturation assumption. If the field can take the sinusoidal time dependent form for the , then the equation of the magnetization can be written as: [ ̂ ] [ ̂ ̂ [ 22 ] ] (1.13) where and . By writing the vector and and fully expanding the Eq. (1.13), we have the following matrix: [ ] [ [ ] ] ̅ ̅ ̅ (1.14) So we can write the permeability tensor as ̅ ̅ ̅ ] ̅ [ , and (1.15) 1.3.3 Demagnetizing Field In most microwave applications, external bias magnetic fields are applied on ferrite samples, in order to work in specific frequency bands. However, due to the magnetization inside the ferrite, the net magnetic field can be very different with that in the air. The demagnetizing field is a magnetic field due to the surface magnetic charges on the interface between the magnetic material and non-magnetic material. It tends to reduce the total magnetic moments inside the magnetic material and the internal magnetic field. Let’s consider a magnetic plate with external bias magnetic field either perpendicular or parallel to the plane, as shown in Fig. 1.2 and Fig. 1.3 . 23 Air M Magnetic material Air Fig. 1.2 Demagnetizing field of a magnetic plate with perpendicular external magnetic field Air Magnetic material Air Fig. 1.3 Demagnetizing field of a magnetic plate with tangential external magnetic field 24 To calculate demagnetizing field of a magnetic plate with perpendicular external magnetic field (Fig. 1.2), it is assumed that all the magnetic moment was aligned along the magnetization direction. Due to Gauss' theorem, normal component of is continuous on the surface. (1.16) (1.17) (1.18) (1.19) Where is the demagnetizing field of the magnetic plate is the applied field, is the magnetizing factor. M is the magnetization along the normal direction. To calculate demagnetizing field of a magnetic plate with tangential external magnetic field (Fig. 1.3), it is assumed that all the magnetic moment was aligned along the magnetization direction. The tangential component of is continuous on the surface. Therefore, we have: (1.20) For other directions, article [13] shows more detailed derivations. 1.3.4 Remanence magnetization and the hysteresis loop The remanence magnetization, , is the residue magnetization when the applied field is reduced to zero. The position of of YIG ferrite in a hysteresis loop is shown in Fig. 1.4 25 Fig. 1.4 Hysteresis loops of YIG 1.4. Mechanism of Microwave ferrite device Microwave magnetic devices have had a major impact on the development of microwave technology. As we discussed in the previous section, an electromagnetic wave propagating through the ferrite encounters strong interaction with the spinning electrons and give rise to desirable magnetic properties in ferrite. These properties have been utilized to develop many microwave devices like, filters, isolators, phase shifters and circulators. 1.4.1 Non-reciprocity The use of ferrites in a numbers of microwave devices is based on that propagation constants for different modes of an electromagnetic wave are different (typically left handed or right handed polarization). Under a proper external bias magnetic field, the ferrite encounters strong interaction with the spinning electrons if the wave is right handed 26 polarized, while have weak interaction for the left handed polarized wave, as shown in fig. 1.5. [12] The difference in the interaction between ferrite and the EM wave will result in different attenuation factor (magnitude) or Faraday rotation (polarization), Fig 1.6[12]. Also, the anisotropic permeability tensor of ferrites gives rise to different field or potential displacement in the medium. For example, with a perpendicular in plane DC bias field, the magnetostatic surface wave in ferrite will only propagate on one side of the ferrite surface, while staying on the other side if the propagation direction is opposite. [14] These two non-reciprocity properties can leads to a numbers of non-reciprocal devices like circulators, isolator, non-reciprocal phase-shifters and filters. Fig 1.5, Spinning of electrons with right-handed polarization, with strong interaction with RHPL wave propagation [12] 27 Fig. 1.6 Faraday rotation when wave propagate in a ferrite sample along external bias field [12] 1.4.2 Tunability Another important property of ferrites is that their propagation constant is highly depended by the external bias magnetic field. Therefore, one can tune the operating frequency, bandwidth, or even reciprocity by tuning the different bias condition. These tuning can be done the following method: (i) Mechanically: direction or magnitude of bias field; [15], (ii) Magnetically: electromagnet or hard magnet; [16]-[18], (iii) Magneto-electrically: the bias condition can be tuned via magneto-electric coupling on multiferroic structure with piezoelectric material bond to the ferrite film. The stress induced by applied voltage will result in magnetic bias changes, leading to tuning of FMR frequency [19]. (a) Tunable permeability 28 In many of the applications of ferrites in microwave devices the magnetic material is only partially magnetized. The performance of tunable devices will be significantly improved in unsaturated mode by allowing its operation in low-permeability (µr<1) range, as shown in Fig. 1.7. The mechanism is based on Schloemann’s theory partially magnetized ferrites [20], [21]. For the completely demagnetized state, the permeability in this case is given by [ ] (1.21) The permeability of partially magnetized ferrites is given by (1.22) The permeability then only depends on the operating frequency omega and magnetization . If omega is fixed for designed operating frequency, the permeability is only set by its magnetized state. Basically, the permeability can be tuned by the bias field applied, so is the operating frequencies, and phase delays of the microwave devices. Fig. 1.7 versus on TTI-390 at 5.5 GHz [21] 29 (b) Tunable ferromagnetic resonance frequency (FMR) The strong interaction between the Spinning of electrons and the RF signal usually happens when the magnetic material at ferromagnetic resonance. We can quickly estimate of the FMR frequency by using Kittel’s equation [22]-[24]. √ (1.23) where is the gyromagnetic constant of about 2.8 MHz/Oe, anisotropy field of the YIG film, and is the intrinsic in-plane is the external bias field. As expected, the measured resonance frequency of the bandpass filter matches excellently with equation (1), which is shown in Fig. 1.8. Fig. 1.8. Calculated and measured FMR frequency against the external magnetic bias field on YIG film ( ). 30 1.5 Dissertation overview Conventional, these tunable and non-reciprocal microwave devices based on the non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide are usually bulky. This dissertation will focus on theoretical study, numerical evaluation and measurement verification of novel planar microstrip RF/microwave structures with magnetic substrates and superstrates loading, demonstrating tunable and non-reciprocal characteristics, and insertion loss, size, weight and cost of systems can be reduced as well. In Chapter 2, we will briefly introduce the numerical modeling software and the experimental measurement setups for the microwave ferrite devices discussed in this dissertation. First, the modeling of ferrite material in Ansoft HFSS will be presented. Then the whole experimental environment will be introduced, including VNA for s-parameter measurement, Spin spray system for thin film deposition, electromagnet for applying DC bias field, and VSM system for in plane and out plane hysteresis loop measurement. In Chapter 3, we will provide a theoretical overview of electromagnetic wave propagation in ferrite medium. More specifically, the propagation characteristics of magnetostatic wave on a ferrite thin slab with an in-plane DC bias field will be investigated. Magnetostaic surface wave (MSSW) will be excited when the bias field is perpendicular to the wave propagation; Magnetostaic back volume wave (MSBVW) will be excited when the bias field is parallel to the wave propagation. The dispersion relation under these two bias conditions is also analyzed. Furthermore, the excitation structure of magnetostatic wave 31 for ferrites will be discussed. This chapter is introduced as the theoretical preparation for the following chapters on microwave ferrite devices. Chapter 4 will present my designs on tunable bandpass filters based on the coupling between magnetostatic wave and EM wave. Both experimental and simulation results of an s-band magnetically and electrically tunable bandpass filters (BPF) with yttrium iron garnet (YIG) will be introduced. The designed bandpass filters can be tuned by more than 50% of the central frequency with a magnetic bias field of 250 Oe. Then, a Cband low loss straight-edge resonator band pass filter will be presented based on a similar concept but with further discussion on the limitation on spurious resonance due to the standing wave mode and finite width modes. Also, Simulation and experimental verification will be presented for a new type of non-reciprocal C-band magnetic tunable bandpass filter with dual functionality of ultra-wideband isolation. Chapter 5 will present a novel planar tunable planar isolator with serrated microstrip structure based on ferromagnetic resonance (FMR) of microwave ferrites. A novel serrated microstrip structure will be presented to achieve circular polarization of magnetic field, in terms of DC bias field. Current and field distribution will be analyzed via HFSS simulations. The microwave ferrites experience LHCP (left-handed-handed circular polarization) RF excitation magnetic fields in backward propagation while RHCP (right-handed circular polarization) in forward propagation, leading to minimal absorption in backward propagation while strong FMR absorption in forward propagation. Simulation designs and experimental verification will be provided to understand the 32 mechanism behind this design. The non-reciprocal ferrite resonance absorption leads to over 19dB isolation and 3.5 insertion loss at 13.5GHz with 4kOe bias magnetic field applied perpendicular to the feed line. Chapter 6 will present a compact, low-loss, wideband and high power handling tunable phase shifters with piezoelectric transducer controlled metallic perturber. This phase shifter design consists of a meander microstrip line, a PET actuator, and a Cu film perturber, which has been designed, fabricated, and tested. This compact phase shifter with a meander line area of 18mm by 18mm has been demonstrated at S-band with a large phase shift of >360 o at 4 GHz with a maximum insertion loss of < 3 dB and a high power handling capability of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and compact phase shifter that operates between 1GHz to 6GHz was successfully demonstrated. Such phase shifter has great potential for applications in phased arrays and radars systems. Chapter 7 will be the conclusion for the dissertation. 1.6 Reference [1] C. Vittoria, Elements of microwave networks, World Scientific Publishing Co.,1998. [2] D. M. Pozar, Microwave engineering, 3rd edition, John Wiley, Hoboken, NJ, 2005. [3] R. F. Harrington, Time-harmonic electromagnetic field, Wiley-Interscience, NY, 2001. [4] C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley, Hoboken, NJ, 1989. [5] C. Vittoria, Microwave Properties of magnetic films, World Scientific Publishing Co., 33 1993. [6] B. Lax and K. J. Button, Microwave Ferrites and Ferrimagnetics (McGraw-Hill Book Company, Inc., 1962). [7] F. Bertaut, F. Forrat, Cornpt, A. Rend, Sci. Paris. 1956, vol. 242, 382-384. [8] Geller, S; Gilleo, MA. J. Phys. Chem. Solids., 1957, vol. 3, 30-36. [9] Huber, DL. In Landolt-Börnstein Group III Crystal and Solid State Physics; Hellwege, K.-H; Hellwege, AM; Ed; Numerical Data and Functional Relationships in Science and Technology Series; Springer- Verlag Berlin: New York, NY, 1970; vol. 4: Part a, 315367. [10] Plant, JS. J. Phys. C., 1977, vol. 10, 4805-4814. [11] David M. Pozar, Microwave Engineering, Second Edition (John Wiley & Sons, Inc., New York, 1998). [12] Carmine Vittoria, Magnetics, Dielectrics, and Wave Propagation with MATLAB® Codes (CRC Press, Taylor & Francis Group, Boca Raton, 2011). [13] Daniel D. Stancil, ―Theory of magnetostatic waves‖, Springer – Verlag, New York, 1993. [14] T. Y. Yun and K. Chang, ―Piezoelectric-Transducer-Controlled tunable microwave circuits,‖ IEEE Trans. Microw. Theory Tech. vol. 50, pp. 1303-1310, May 2002. [15] J. Uher and W. J. R. Hoefer, ―Tunable microwave and millimeter-wave band-pass filters,‖ IEEE Trans. Microw. Theory Tech. vol 39, pp. 643-653, Apr. 1991. [16] B. K. Kuamr, D. L. Marvin, T. M. Christensen, R. E. Camley, and Z. Celinski, ―Highfrequency magnetic microstrip local bandpass filters,‖ Appl. Phys. Lett. vol 87, 222506, Nov. 2005. 34 [17] N. Cramer, D. Lucic, R. E. Camley, and Z. Celinski, ―High attenuation tunable microwave notch filters utilizing ferromagnetic resonance,‖ J. Appl. Phys. vol 87, pp. 6911-6913, May 2000. [18] A. S. Tatarenko, V. Gheevarughese, and G. Srinivasan, ―Magnetoelectric microwave bandpass filter,‖ Electron. Lett. vol 42, pp. 540-541 , Apr. 2006. [19] Ernst Schlömann, ―Microwave Behavior of Partially Magnetized Ferrites,‖ J. Appl. Phys. 41, 204 (1970). [20] Jerome J. Green and Frank Sandy, ―Microwave Characterization of Partially Magnetized Ferrites,‖ IEEE Trans. Microw. Theory Tech. 22, 641 (1974). 35 Chapter 2: Simulations and Experiment Setups In Chapter 2, I will briefly introduce the numerical modeling software and the experimental measurement setups for the microwave ferrite devices discussed in this dissertation. First, the modeling of ferrite material in Ansoft HFSS will be presented. Then the whole experimental environment will be introduced, including VNA for s-parameter measurement, and electromagnet for applying DC bias field. 2.1 Ferrite device modeling in HFSS HFSS is a high-performance full-wave electromagnetic (EM) field simulator for arbitrary 3D volumetric passive device modeling that takes advantage of the familiar Microsoft Windows graphical user interface. HFSS employs the Finite Element Method (FEM), and can be used to calculate parameters such as S-Parameters, Resonant Frequency, and Fields. [1] The accuracy of HFSS simulation on non-ferrite device has been widely proved. In this dissertation, we are interested in ferrite devices, which relied on the B-H nonlinear material definition which model the interaction between a microwave signal and a ferrite material whose magnetic dipole moments are aligned with an applied bias field. The gyrotropic quality of the ferrite is evident in the permeability tensor which is Hermitian in the lossless case. The Hermitian tensor form leads to the non-reciprocal nature of the devices containing microwave ferrites. If the microwave signal is circularly polarized in the same direction as the precession of the magnetic dipole moments, the signal interacts 36 strongly with the material. When the signal is polarized in the opposite direction to the precession, the interaction will be weaker. Because the interaction between the signal and material depends on the direction of the rotation, the signal propagates through a ferrite material differently in different directions. There are three parameters we can monitor when we simulate a RF device with ferrite in HFSS: Saturation magnetization ( 2.1.1 Saturation magnetization ( ), Delta H ( ) and DC bias field ( ) and DC bias field ( ) ) in HFSS When a ferrite is placed in a uniform magnetic field, the magnetic dipole moments of the material begin to align with the field. In HFSS, the bias field is applied along z- axis by default. For different applications, the coordinate system should be rotated for align the expected bias direction to z-axis. As the strength of the applied bias field increases, more of the dipole moments align. The saturation magnetization , is a property which describes the point at which all of the magnetic dipole moments of the material become aligned. At this point, further increases in the applied bias field strength do not result in further saturation. The relationship between the magnetic moment , and the applied bias field , is shown in Fig. 2.1. Determined by the bias field, ferrites can work in two states: partially saturated or fully saturated. For example, the critical bias field for Yttrium iron garnet (YIG, Y3Fe5O12) is around 100~150 Oe. HFSS can only model the ferrite in the fully saturated state, where the permeability tensor can be expressed as: 37 [ ], (1.1) , and where , and , H0 is the DC bias field, and ω is the angular frequency. These models follow the wave propagation properties in ferrite, so the simulations are proved to have a good agreement with measurement verification in the following chapters. Fig. 2.1 The relation between magnetization moment and the Applied DC bias field H 2.1.2 Delta H ( ) in HFSS 38 Delta H is the full resonance line width at half-maximum, which is measured during a ferromagnetic resonance measurement. It relates to how rapidly a precessional mode in the biased ferrite will damp out when the excitation is removed. The factor doesn’t appear in the permeability tensor; instead, the factor α appears. The factor α is computed from: α The factor changes the applying and (1.2) terms in the permeability tensor from real to complex, by , which makes the tensor complex non-symmetric and leads to additional loss. 2.2 VNA for s-parameter and permeability measurement All measurements in this dissertation are carried out via a vector network analyzer (Agilent PNA E8364A). The photo of this Network analyzer is shown in Fig.2.2. The input and output are at 1mW power level and well calibrated from 45MHz to 20GHz. Sparameters can be measured and exported. 39 Fig.2.2 Vector network analyzer (Agilent PNA E8364A) 2.3 Electromagnet for applying DC bias field Measurement of RF devices with ferrite usually requires DC magnetic bias field. We use an electromagnet to vary the applied bias magnetic field, which can tuned either by the separation of the two magnets or the current in the coil. Here is the typical operation: first we mount the devices in between the magnets, then we adjust the separation to achieve a resonable magnetic tuning scales and finally tune the supplied current and checked with gauss meter for the desire bias field. 40 \ Fig.2.3 Current controlled Electromagnet 2.4 Reference [1] HFSS user manual 41 Chapter 3 Concept of magnetostatic surface wave 3.1 Motivation Modern ultra wideband communication systems and radars, and metrology systems all need reconfigurable subsystems such as tunable bandpass filters that are compact, lightweight, and power efficient [1]. At the same time, isolators with a large bandwidth are widely used in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. If a new class of non-reciprocal RF devices that combines the performance of a tunable bandpass filter and an ultra-wideband isolator is made available, new RF system designs can be enabled which lead to compact and low-cost reconfigurable RF communication systems with significantly enhanced isolation between the transmitter and receiver. The non-reciprocal propagation behavior of magnetostatic surface wave in microwave ferrites such as yttrium iron garnet (YIG) provides the possibility of realizing such a tunable and non-reciprocal device [2-3]. Magnetostatic waves are formed when electromagnetic waves couple to spin waves in magnetic materials. Under proper bias condition, these waves can exhibit properties such as dispersive propagation, nonreciprocity and frequency-selective nonlinearities. The goal of this chapter is to introduce the concept of magnetostatic waves, which will be further utilized in the filter designs. The study of this chapter can be divided in to three parts. First, an introduction will be presented to Maxwell equations with given permeability tensor of magnetic material. 42 Under magnetoquasistatic approximation, when the wavelength in the medium is much smaller than that of an ordinary electromagnetic wave at the same frequency, we can obtain Walker’s Equation [4], which is the basic equation for magnetostatic modes in homogeneous media. Second, boundary condition will be considered to deduce magnetostatic surface wave propagation modes inside a finite ferrite slab under tangential magnetization. Finally, the working excitation structure for magnetostatic wave in ferrite slab will be discussed, and microstrip transducers with be designed via Ansoft HFSS simulation. Non-reciprocity will be analyzed via radiation resistance equivalent model of the transducers for magnetostatic wave excitation. 3.2 Magnetostatic wave in tangential magnetized ferrite 3.2.1 Magnetoquasistatic approximation [4] First, let us consider uniform plane waves propagating in homogenous magnetic material neglecting exchanges and anisotropy. The magnetic fields and magnetization inside the material, ⃑ and ⃑⃑ can be expressed as following: ⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑ (3.1) ⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ (3.2) Which can be divided to DC static fields and time variable fields ⃑⃑⃑⃑⃑⃑⃑⃑ , ⃑⃑⃑⃑⃑⃑⃑⃑⃑ . , The Maxwell’s equation then can be written as : (3.3) (3.4) 43 By crossing into Eq. (3.3) and substituted Eq. (3.4) for , given (3.5) (3.6) Finally, since , (3.7) For certain frequencies, | | , vanished as | | for large | |. Then the wave propagation inside the homogeneous magnetic material can be described as: (3.8) (3.9) (3.10) (3.11) This equation set is the Maxwell’s equation under magnetoquasistatic approximation. Most cases discussed in this chapter will follow this limit. 3.2.2 Walker’s equation and magnetostatic modes [4] The permeability tensor without exchange and anisotropy can be written as : [ ], , and 44 (3.12) Where the bias field is supposed to lie along ̂ direction. where , and , H0 is the DC bias field, and ω is the angular frequency. Similar to the electric potential, since , we may define (3.13) where is the magnetostatic scalar potential. By substitute 3.12 and 3.13 to 3.9, we can write the Walker’s equation: ( ) ( (3.14) ) the Walker’s equation can be written as Eq. 3.15, when (3.15) . The solutions are called magnetostatic modes in homogeneous media. 3.2.3 Magnetostatic surface wave in tangentially magnetized films (MSSW) [4] Now let us consider a thin ferrite film with DC bias field, applied tangential to the its plane and normal to the propagation direction, as shown in fig. 3.1. In ferrite region (II), the static magnetic field . There are several boundary conditions we can use to take a trial solution. (1) The magnetostatic scalar potential will decay to 0 at infinite along ̂ direction; 45 (2) The magnetostatic scalar potential will be continuous at the interface of (3) The normal b will be continuous at the interface of ; ; will be uniform along ̂ direction if we excited the (4) The magnetostatic scalar potential spin wave to propagate in ̂ direction; y I. Air +d/2 II. Ferrite z x -d/2 III. Air Fig. 3.1 Geometry for a tangential magnetized ferrite film. HDC +d/2 + + -d/2 Fig. 3.2 Guided wave propagation in a tangential magnetized ferrite film. 46 Utilizing the above boundary conditions, we can analyze the guided wave in the film as shown in Fig. 3.2. The plane waves are bouncing back and forth from the upper and lower boundaries. The magnetostatic scalar potential can be written as: + (3.15) (3.16) + (3.17) Where v denotes the propagation direction, which is +1 for direction From the boundary condition (3), potential ̂ direction and -1 for ̂ will be uniform along ̂ direction if the fill is infinite. The Walker’s equation can be reduced as: ( ( ) ) So, Eq. 3.19 leads to the relation propagation in ̂ direction, (3.18) (3.19) . If we are looking for a solution of wave should be real and should be imaginary. Therefore, the potential in region II will not be oscillatory but contain growing and decaying exponentials. Eq. 3.16 can be modified as following: (3.20) + Here we can write | | , which is the propagation wave number along ̂ direction. 47 By applying boundary condition at for continuous , we have: + (3.21) + (3.22) Another boundary condition is that should be continuous at ( ) + ( : ( ) + ) + ( + (3.23) ) (3.24) By solving eq. 3.21~ eq.3.24, the following tensor equation can be written: [ ][ + ] (3.25) The dispersion relation between k and frequency can be expressed by letting the determinant of the coefficient matrix be 0 . Where the k-ω relation is + (3.25) , and 48 where , and , H0 is the DC bias field, and ω is the angular frequency. Based on eq. 3.25, Fig. 3.3 shows the dispersion diagram for magnetostaic wave on an infinite YIG slab with thickness d=108um, and saturation magnetization 1750 Gauss. The DC bias magnetic field 1500 Oe was applied in plane and perpendicular to the wave propagation. This dispersion relation is unchanged even if the wave propagation is reversed. There is only one mode in between 6.2GHz to 6.6GHz. However, the potential is not reciprocal . By substituting Eq. (3.25) to Eq. (3.15), Eq. (3.17), Eq. and (3.20). We have the potential distribution in all three regions. And they are not reciprocal. Frequency (GHz) 6.7 Infinite no Ground 6.6 6.5 6.4 6.3 6.2 0 2416 4832 7248 9664 12080 kd Fig.3.3 Dispersion diagram for surface wave on infinite YIG slab (d=108um; H0=1500Oe, 4piMs=1750 Gauss) 49 y axis (thickness (d)) 3 -z propagation +z propagation 2 1 +d/2 Backward -d/2 Forward 0 -1 Hdc -2 -3 0.0 0.2 0.4 0.6 0.8 Normalized Magnetic Potential 1.0 Fig.3.4 Potential profiles for surface wave on infinite YIG slab with forward ( backward ( ) wave propagation at operating frequency ) and . with Dc bias field at z direction. + (3.26) (3.27) + , (3.28) + + + + Figure 3.4 shows the normalized potential profiles for surface wave on infinite YIG slab with forward ( ) and reverse ( ) wave propagation. The wave amplitude decays exponentially from the interface of ferrite and the air. Therefore, we can imagine that the surface wave will shift from one side of a film to the other side if the direction of the propagation is reversed, given the same DC bias condition as shown in Fig. 3.5. 50 HDC +d/2 -d/2 Fig. 3.5 Surface wave propagation in a tangential magnetized ferrite film. 3.2.4 Magnetostatic back volume wave in tangentially magnetized films [4] In this section, we can consider the case with DC bias magnetic field applied tangential to its plane and parallel to the propagation direction. The geometry for a tangential magnetized ferrite film can be shown in Fig. 3.1. In ferrite region (II), the static magnetic field is . There are several boundary conditions we can use to take a trial solution. (1) The magnetostatic scalar potential will decay to 0 at infinite along ̂ direction; (2) The magnetostatic scalar potential will be continuous at the interface of (3) The normal will be continuous at the interface of (4) The magnetostatic scalar potential ; ; will be uniform along ̂ direction if we excited the spin wave to propagate in ̂ direction; 51 The wave will propagate along ̂ direction inside the ferrite, instead of ̂ direction. So the Walker’s equation can be written as: ( ( ) (3.29) ) (3.30) Then similar to the surface case, the scalar potential in all three regions can be written as: + (3.31) (3.32) + By Applying the boundary condition at By applying boundary condition at (3.33) , we have : for continuous , we have: (3.34) (3.35) Here, we can conclude , which is identified as odd mode. Another boundary condition is that should be continuous at : (3.36) 52 (3.37) These two equations are equivalent to the previous two. Substituting Eq. (3.36) to Eq. (3.34) gives the dispersion relation: ( ) (3.38) Substituting Eq. (3.29) give the dispersion relation for odd modes: ( ) + √ √ (3.39) For even modes, we can achieve it by a similar procedure: ( √ + ) √ (3.40) ( The even and odd mode then can be combined with identity ( √ + ) √ ) (3.41) Based on the dispersion relation above, the odd and even mode potential functions are given by : + (3.42) (3.43) ( ) + (3.44) + (3.45) (3.46) 53 ( ) + (3.47) Figure 3.6 shows the potential profiles on an infinite YIG slab with bias field applied parallel to wave propagation. The potentials amplitude is distributed sinusoidal through the volume of the film. There are fundamental modes like (for n=1) and (n=2) , and some other high order harmonics. Fig 3.7 shows that the dispersion relation of MSBVW is independent of the direction of propagation. On the other hand, all modes (n=1, 2, 3, 4, 5) have the same cut-off frequencies at √ , which can be calculated via . There is no frequency range that only one mode exists. Also, the group velocity seems to have opposite direction compared to the phase velocity. Therefore, it is also called backward volume waves. y axis (thickness (d)) 3 2 1 n=1 +d/2 n=2 0 -1 -d/2 -2 -3 -1.0 -0.5 0.0 0.5 Normalized Magnetic Potential 1.0 Fig.3.6 Potential profiles for back volume wave on infinite YIG slab 54 Frequency (GHz) 6.5 n=5 n=4 n=3 6.0 n=2 5.5 5.0 4.5 n=1 0 2 4 kd 6 8 10 Fig.3.7 Dispersion relation for surface wave on infinite YIG slab (d=108um; H0=1600Oe, 4piMs=1750 Gauss) 55 3.2.5 Summation of magnetostatic wave in tangentially magnetized films Table 3.1 comparison between magnetostatic surface wave and back volume wave Magnetostatic surface wave Wave Magnetostatic back volume wave Forward surface wave Backward volume wave In plane, perpendicular to wave In plane, parallel to wave propagation propagation Single mode Multi modes, with same cut-off characteristics Applied Bias field Modes frequencies reciprocity Non-reciprocal wave reciprocal wave propagation propagation with different independent of propagation potential distribution direction Magnitude Decays exponentially cross the Distributed sinusoidal cross the distribution film thickness, maximum volume of the film, including high locates at one side forward order harmonics propagation but the other side for reverse propagation Group/phase Same direction Opposite direction velocity 56 Frequency (GHz) 7.0 MSSW 6.5 FMR @ 6.485GHz n=4 6.0 n=3 MSBVW n=2 5.5 5.0 4.5 n=5 n=1 0 2 4 kd 6 8 10 Fig. 3.8 Comparison of dispersion relation between Magnetostatic surface wave (MSSW) and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um, 4piMs 1750Gauss) Table 3.1 shows the summation of magnetostatic wave in tangentially magnetized films for both MSSW and MSBVW. Figure 3.8 compares the dispersion relation for these two bias conditions. MSSW has a lower cut-off frequency above FMR and its wave propagation is with single mode. MSBVWs have an upper cut-off frequency below FMR and they are multi-modes. Therefore, there are always many modes existing at the same time. For practical device designs, the volume waves will suffer from ripples due to the 57 multi-resonance wave modes, while surface wave usually have a very smooth band. In this dissertation, we’ve focused on the surface wave for band pass filter designs. y I. Air II. Ferrite +d/2 x z III. Dielectric -d/2 t IV. Ground Fig. 3.9 Geometry for a tangential magnetized ferrite film with metallic backed substrate 3.3 Magnetostatic wave in finite ferrite films [5] In the previous section, we’ve discussed magnetostatic wave propagation in an infinite large ferrite film with tangential magnetic bias field. However, in practical there are finite boundary conditions which can change the wave propagation inside the ferrite film. 58 3.3.1 Magnetostatic wave in ferrite films on metallic backed substrate Let us consider a ferrite film mounted on top of a microstrip structure, as shown in Fig. 9. Compared with Fig. 1, region III is truncated by a metallic ground plane. The new boundary condition can be expressed as the following: (1) Continuous magnetic potential , (2) Magnetic potential (3) Magnetic potential (4) , will be uniform along ̂ direction if we excited the spin wave to propagate in ̂ direction; Previous researches have deduced the dispersion relation for wave propagation in a ferrite film placed with a metallic layer with a spatial separation : [5]. If goes to infinite, this equation will be reduced to the case that is discussed in previous sections. (3.48) Fig. 10 shows the comparison of the dispersion relation for a tangential magnetized ferrite film with/without metallic backed substrate when DC bias field is 1.5 kOe. The ground plane only affects the dispersion relation when k is small. For a large k solution, the difference between them is neglectable. 59 Frequency (GHz) 6.7 Unground Ground 6.6 6.5 6.4 6.3 6.2 0 2416 4832 7248 9664 12080 k Fig. 3.10 Compare the dispersion relation for a tangential magnetized ferrite film with/without metallic backed substrate L y +d/2 I. Air II. Ferrite x z III. Dielectric -d/2 t IV. Ground Fig. 3.11 Geometry of straight edge resonator (SER)) 60 Backward Straight Edge Standing Wave Straight Edge Forward Fig. 3.12 MSSW propagation in straight edge resonator (SER)) 3.3.2 Magnetostatic wave in finite ferrite films (Straight Edge Resonator (SER))[5] For a practical filter design, a rectangular YIG films with straight edges are used. Magnetostatic wave propagates in a finite medium, hits the edges, and reflected back. The wave is bouncing back and forward, which forms standing wave modes. Additionally, finite width of the films produces width mode resonance. Problems rise from the coupling to the width modes and standing wave modes. Figure 3.12 shows an example of magnetostatic surface wave propagating in a YIG film. The forward transmission happens on the bottom interface, which the backward transmission is on the top surface. Eventually, they overlap and form standing wave. It is similar to a cavity resonator, which resonate at different discrete frequencies. Suppose the YIG film has length L (x-axis) and width W (z- axis), as shown in Fig 11. The DC bias field is applied along z axis, which is perpendicular to the wave propagation in 61 x-axis, for surface waves. To find out the resonance frequency of the resonator, we can first have a rough guess on the solution in the ferrite film (region II). (3.49) where + is the solution found in the previous section (infinite case). A new term has been added to response to the finite width W in z-axis. So, The boundary condition can be expressed as following: (1) Y-axis similar to the previous cases. So leads to a same dispersion relation as infinite case. (2) Z-axis, at the edge ( ): (3) X-axis: standing wave condition: + Inside YIG + Outside YIG Applying this in (1), we get the dispersion relation: (3.49) m= 1, 2, 3, 4, 5, corresponding to width mode n= 1, 2 , 3, 4, 5, corresponding to standing wave resonance. For each of the primary resonance ( mode ), the high order width depends on the current distribution on the transducers. 62 represents transducers with an even current distribution. Figure 3.13 indicates the dispersion relation for all width , finite length represents odd modes. combos. Given the finite , corresponds to n=1, 2, 3, 4, 5. From the figure, we can read the resonance frequency of each mode , as indicated in Table 3.2. Frequency (GHz) 6.7 6.6 6.5 6.4 m=1 m=2 m=3 m=4 m=5 min 6.3 6.2 0 2416 4832 7248 9664 12080 k Fig. 3.13. The dispersion relation for a YIG SER: Bias field applied 63 Table 3.2 The resonance frequency of width and standing wave mode with DC magnetic bias field 1500 Oe. GHz 1 2 3 4 5 1 6.48 6.5 6.55 6.59 6.61 2 6.35 6.45 6.52 6.56 6.59 3 N/A 6.37 6.47 6.53 6.57 4 N/A N/A 6.41 6.49 6.54 5 N/A N/A 6.34 6.43 6.50 0 S12&S21(dB) -5 -10 -15 S21 S12 -20 -25 6.2 6.3 6.4 6.5 6.6 Frequency (GHz) Fig. 3.14 The s-parameter of a bandpass filter utilizing YIM films width and standing wave mode ; DC magnetic bias field 1500 Oe 64 Table 3.2 indicate the resonance frequency of width and standing wave mode around with DC magnetic bias field 1500 Oe. Here the FMR frequency is √ . The frequency band has been split by discrete resonant frequencies. When a bandpass filter is designed using the same YIG film resonator. The s-parameter response was shown in Fig 3.14. The splitting resonant frequency leads to many ripples in the pass band (both S21-forward and S12-backward transmission), which can be a huge drawback in the filter designs. More detailed design concerns and solutions will be presented in chapter 4. 3.4 Excitations of Magnetostatic wave [6] We’ve discussed the wave properties of the magnetostaic wave. Then, how can we excite? Experimentally it is easy to excite the magnetostatic waves in thin films. Placing a current carrying wire near the film will be enough to excite the spin wave. Most commonly, microstrip structures with short pins to the ground plane at the end of the strip line are utilized to achieve the excitation. Usually, the coupling between the current flowing on the microstrip transducer and the spin wave propagate in the ferrite film can be model as an equivalent lossy transmission line, are shown in Fig 3.14. As the incident wave propagates along the transducer, the energy is lost to the magnetostatic wave. 65 Fig.3.15. Transmission line model for magnetostatic wave excitation. There are plenty of previous researches on magnetostatic wave excitations. Adam et. al. [8] adopted parallel microstrip lines as the transducers. However, the minimum insertion loss of their bandpass filters is 10 dB, which is unsuitable for modern communication system. Most recently, a T-shaped microstrip coupling structure and YIG films were used to achieve a low-loss S-band tunable bandpass filter [9-10]. An L-shaped microstrip transducer was reported in [11] and [7], which could enhance the coupling to a minimum insertion loss of 5 dB . In order to improve the insertion loss and isolation, and achieve the non-reciprocal behavior at the same time, an inverted L-shaped transducer has been designed, are shown in Fig 3.15. The transducer is designed on a 0.381mm (15mil) thick Rogers TMM 10i substrate with width and . The length of the transducer is , with a spatial separation , . Single crystal YIG slab with thickness about 108µm was placed on top of the transducers. The saturation magnetization (4πMs) of the single crystal YIG slab is about 1750 Gauss and the FMR line width is less than1 Oe at X-band (~9.8 GHz). The bias magnetic field H is perpendicular to the feed line. The alignment of the YIG film is parallel to transducer, as well as the DC bias magnetic field H. The YIG film then forms a straight edge resonator with finite width modes and standing wave modes. The transducers will couple to these modes and deliver energy from one port to the other. 66 The radiation resistant per unit length for surface waves travelling in direction can be written as : [6] [ + + + ]| | (3.50) Where F indicates array factor for the microstrip transducer: . is the width mode wave number, function of zero order . usually it is around is the finite width of the YIG film. is the Bessel is the vertical spacing between the transducer and YIG film, . Because the surface wave exhibit field displacement non-reciprocity, as discussed in the previous section. Besides, the resistance is proportional to between transducer and the wave propagation surface. , where is the space The radiation resistance is different for the two directions of propagation. The excitation is much stronger for the mode localized at the surface near the transducer, while it is much weaker at the other side (by attenuation of , is thickness of YIG film). The radiation resistance (under bias field 1600 Oe) for our design is calculated as Fig 3.16. The resistance is close to 50 ohm, around 6.8GHz for bottom coupling, while close to 0dbm for the top surface coupling. Therefore, the energy coupled to the top surface is minimum, while that to bottom is maximum, which leads to non-reciprocity of wave propagation. These non-reciprocal coupling characteristics already suggest a potential use as an isolator. However, the non-reciprocity can be destroyed by the reflection from the straight edges. Suppose we have the forward wave propagation on the bottom surface of the ferrite 67 film, while backward wave on the top surface. As shown in Fig 3.17, although transducer 2 may have weak coupling to the top surface for the backward propagation, it can still excited the forward wave on the bottom surface and get reflected to the top surface for backward propagation. The surface wave can be bouncing forward and backward and form a standing wave in the film, which result in reciprocal transmission. On the next section, we will discuss the filter designs based on these microstrip transducers. Fig 3.16. Geometry of the transducers: Inverted L-shaped microstrip transducers with parallel YIG alignment; , . 68 Radiation resistance 70 60 50 40 30 20 10 0 TOP layer Bottom 6 7 8 9 Freq (GHz) 10 Fig 3.17. Radiation resistance for coupling of transducers to top and bottom surface of the YIG film. DC bias field is 1600 Oe. Backward wave Straight Edge Straight Edge Transducer 1 Transducer 2 Forward wave Fig 3.18. Reciprocal excitations of microstrip transducer due to the reflection of the straight edge. 69 3.5 Conclusion In this chapter we’ve presented permeability tensor and wave propagation properties of magnetic material under magnetoquasistatic approximation, when the wavelength in the medium is much smaller than that of an ordinary electromagnetic wave at the same frequency. Boundary conditions were considered to deduce magnetostatic surface wave propagation modes inside a finite ferrite slab under tangential magnetization. Also, the working excitation structure for magnetostatic wave in ferrite slab were discussed, and microstrip transducers were designed via Ansoft HFSS simulation. Non-reciprocity was analyzed via radiation resistance equivalent model of the transducers for magnetostatic wave excitation. 3.6 Reference [1] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microstrip Applications. New York: Wiley, 2001. [2] I. C. Hunter and J. D. Rhodes, ―Electronically tunable microwave bandpass filters,‖ IEEE Trans. Microw. Theory Tech., Vol. 30, pp. 1354-1360, Sept. 1982. [3] J. Uher and W. J. R. Hoefer, ―Tunable microwave and millimeter-wave band-pass filters,‖ IEEE Trans. Microw. Theory Tech., vol 39, pp. 643-653, Apr. 1991. [4] Daniel D. Stancil, ―Theory of magnetostatic waves‖, Springer-Verlag, 1993 [5] Kok Wai Chang and Waguih Ishak, "Magnetostatic surface wave straight-edge 70 resonators", Circuits, Systems, and Signal Processing, Vol 4, Numbers 1-2 (1985), pp 201-209 [6] P. R. Emtage, ―Interaction of magnetostatic waves with a current,‖ J. Appl. Phys., 49, p.4475 (1978) [7] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microstrip Applications. New York: Wiley, 2001. [8] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer, ―Ferrite Devices and Materials,‖ IEEE Trans. Microw. Theory Tech., vol. 50, pp. 721-737, Mar. 2002. [9] P. W. Wong and I. C. Hunter, ―Electronically Reconfigurable Microwave Bandpass Filter,‖ IEEE Trans. Microw. Theory Tech., vol. 57, pp. 3070-3079, Dec. 2009. [10] Y. Murakami and S. Itoh, ―A bandpass filter using YIG film grown by LPE,‖ in IEEE MTT-S Int. Microw. Symp. Dig., 1985, pp. 285-287. [11] Y. Murakami, T. Ohgihara, and T. Okamoto, ―A 0.5-4.0-GHz tunable bandpass filter using YIG film grown by LPE,‖ IEEE Trans. Microw. Theory Tech., vol 35, pp. 11921198, Dec. 1987. 71 Chapter 4 Bandpass Filters based on magnetostatic wave concepts 4.1 Motivation Modern ultra wideband communication systems and radars, and metrology systems all need reconfigurable subsystems such as tunable bandpass filters that are compact, lightweight, and power efficient [1]. At the same time, isolators with a large bandwidth are widely used in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. If a new class of non-reciprocal RF devices that combines the performance of a tunable bandpass filter and an ultra-wideband isolator is made available, new RF system designs can be enabled which lead to compact and low-cost reconfigurable RF communication systems with significantly enhanced isolation between the transmitter and receiver. As we’ve discussed in the previous chapter, the non-reciprocal propagation behavior of magnetostatic surface wave in microwave ferrites such as yttrium iron garnet (YIG) provides the possibility of realizing a non-reciprocal device [2-3]. Besides, the magnetostatic surface wave can only excited in certain frequency band, as shown in the dispersion relations from previous sections. The propagating frequency band is linearly proportional to the magnitude of DC bias field, following the Kittel’s equation [26]. Therefore, by applying DC bias field parallel to microstrip transducers and proper align the YIG film, one can achieve bandpass transmission performance with dual functionality of an isolator. 72 In this Chapter, bandpass filters based on Magnetostatic wave concept will be presented, with both reciprocal and non-reciprocal characteristics. The study of this chapter can be divided in to several parts. First, a literature review will be presented to introduce previous research on magnetostatic wave based filter. Second, an s-band magnetically and electrically tunable bandpass filters (BPF) with yttrium iron garnet (YIG) will be introduced. Both experimental and simulation results will be presented. Third, a Cband low loss straight-edge resonator band pass filter will be presented based on a similar concept as s-band filter. Then, Simulation and experimental verification will be presented for a new type of non-reciprocal C-band magnetic tunable bandpass filter with dual functionality of ultra-wideband isolation. Further parameter optimization will also been discussed. Finally, this verified concept is used to several further extended designs like Cband tunable circulator and integrated bandpass filter with spin spray NiCo ferrite. 4.2 Introduction of Previous BPF researches Recently, with the dramatic growth of wireless communication technologies, design and manufacturing of low cost microwave components are among the most critical issues in the communications systems [1]. As one of the basic components of transceivers, the use of low loss and small sized bandpass filters (BPF) has been continuously growing in modern communication systems. Generally speaking, the design of a BPF is subject to the size constraints of the whole circuit system. Also, a single filter with only one working band may not fulfill the requirements of multi-band systems. An ideal solution in such circumstance is a bandpass filters with compact size and low loss, which could also be tuned for different working 73 frequency. Basically, there are four different types tunable bandpass filters, including electronically tunable bandpass filters [2], magnetically tunable bandpass filters [3]-[5], mechanically tunable bandpass filters [6], and magnetoelectric (ME) interaction tunable bandpass filters [7]. Planar ferrite structures with straight edges have been applied in filters utilizing the magnetostatic wave theory (MSW) [4]-[10]. Most recently, Srinivasan et. al. [9], Fig 19, reported a bandpass filter using two microstrip line antennas, realized by exciting the magnetostatic surface waves (MSSW) which can be tuned by electric field. However, the designed bandpass filter has a large insertion loss of 5 dB, which may not be suitable for modern communication systems. (a) 74 Fig. 4.1 bandpass filter using two microstrip line antennas, realized by exciting the magnetostatic surface waves (MSSW) reported by Srinivasan et. al: (a) schematic; (b) sparameters 4.3 S-band magnetically and electrically tunable MSSW band pass filters In this section, we first present a design of magnetically and electrically tunable bandpass filter in S-band (2~4 GHz), based on the magnetostatic surface wave utilizing straight edge YIG films. A large resonant frequency shift of the primary resonant frequency of 840 MHz, or equivalent to 54% of the central frequency of the bandpass filter with bias fields of 50 ~ 250 Oe was obtained along with a low insertion loss of < 2dB. A maximum 3-dB bandwidth of 40 MHz was also achieved when the bias field of 250 Oe was applied perpendicular to the feed line. Also, limitations of this design will be discussed. In S-band (2~4 GHz), the high-order width mode and standing wave modes are clearly separated from the primary resonances, which leads to a series of high order spurious resonance, downgrading the filter’s band pass performance. 75 4.3.1 Filter design mechanism As a very important part in the design of a magnetostatic wave bandpass filter, a transducer with compact coupling structure is needed. In [16], parallel microstrips were adopted as the transducers, which are shown in Fig. 20 (a). However, the minimum insertion loss of such bandpass filter is -10 dB that is unsuitable for modern communication system. As shown in Fig. 20 (b), an L-shaped microstrip transducer was proposed in [14] and [15], which could enhance the coupling to a minimum insertion loss of -5 dB [15]. In order to improve the insertion loss problem in magnetostatic wave bandpass filters, a T-shaped microstrip transducer was proposed in this section and is shown in Fig. 4.2 (c). (a) (b) (c) Fig. 4.2. Geometry of the transducers. (a) Parallel microstrip transducers as used in [16] and [7]. (b) L-shaped microstrip transducers as used in [14] and [15]. (c) T-shaped microstrip transducers were proposed in this paper. The geometrical parameters of the T-shaped microstrip transducer include length and the width of the microstrip, the distance between the two transducers; the length, 76 width and thickness of the YIG film. This structure is realized by patterned copper cladding on the top surface of the underlying dielectric substrate. The width of the coupling microstrip is 0.53mm and the length is 18.1mm as we adopted Rogers R3010 as the substrate, which has a relative permittivity of 10.2 and a thickness of 1.28mm. All the parameters are listed in the caption of Fig. 21. Single-crystal YIG films that were grown on gadolinium gallium garnet (GGG) substrate were used. The thickness of the YIG films are 100 um and the thickness of the GGG substrate is 500 um. The single-crystal was cut along its (001) orientations to ensure strong coupling. The saturation magnetization (4πMs) of the YIG films is about 1750 Gauss, and the intrinsic anisotropy field is about 100 Oe. Due to its single-crystal nature, the FMR linewidth of the YIG film is only <1 Oe measured at X-band (~9.8 GHz) Single crystal YIG film was then introduced above the transducer, as indicated in Fig. 22, in which S3= 4mm and mm and W3=10mm. In order to get a magnetically tunable bandpass filter, the magnetic bias field (H) is applied perpendicular to the feed line from zero to 250 Oe. More specifically, if the DC bias field is 200 Oe, the dispersion relation of the MSSW in YIG can be plot as Fig 4.5, where the width modes ( seem to merge due to the small separation of resonance frequencies, while the standing wave modes (n=1, 2 ) seem to have large separations. For modes, . As a result, these modes can be distinguished from each other. 77 the primary Fig. 4.3. Geometry of a T-shaped microwave transducer (top view and side view). W1=1.18mm, W2=18.1mm, S1=9.0mm, S2=0.53mm, S4=1.2mm, H=1.28mm. Fig 4.4. Schematic of the bandpass filter with single-sided YIG films 78 Frequency (GHz) 2.8 2.71GHz 2.60GHz 2.6 2.41GHz 2.4 2.17GHz 2.2 m=5 m=4 m=3 m=2 m=1 2.0 1.8 0 1 2 n 3 4 5 Fig. 4.5. Dispersion relation of Single crystal YIG film, which S3= 4mm and W3=10mm, DC bias field at 200 Oe, Applied perpendicular to the feed lines. wave modes indicates indicates the standing , as discussed in chapter 3. 4.3.2 Experimental and simulation verification All the microwave measurements of the bandpass filter were done by a vector network analyzer (Agilent PNA E8364A) with the frequency scanning from 1 to 3GHz. The measured transmission coefficient (S21) and reflection coefficient (S11), as well as the 3-dB bandwidth of bandpass filter with different bias magnetic field were plotted and analyzed in Fig. 4.5 and Fig. 4.6. From Fig. 4.5 we can see that the central resonant frequency (primary mode of Fig.4.5) of the BPF with bias field of 50 Oe is about 1.561 GHz, the minimum insertion loss is about -2.63 dB and the 3-dB bandwidth is 10 MHz. When the bias field increases to 200 79 Oe, the central frequency shifts upward to 2.172 GHz, this indicates a frequency up shift of 620 MHz relative to the former bandpass filter, and the 3-dB bandwidth is 38 MHz. This agrees with the discussion for Fig 4.5 very well, where the primary resonance is 2.17GHz. When we continue to increase the bias field, the central frequency continues shift upward and the 3-dB bandwidth enhance as well. The central frequency is about 2.401 GHz and the 3-dB bandwidth is 40 MHz when the applied magnetic field is 250 Oe. In this case, the frequency shift is about 840 MHz, or is equivalent to 54% of the central frequency of the BPF with bias field of 50 Oe. The 3-dB bandwidth is greatly improved, which is almost four times than the BPF with 50 Oe. Clearly, a magnetic tunable bandpass filter can be achieved with single-crystal YIG film loaded over the T-shaped microstrip transducer under different bias field. As indicated in the Table I, the insertion loss was decreased with the increased magnetic bias field, a minimum insertion loss of -0.98 dB was obtained when the bias field is 150 Oe. After that the insertion loss increased with the increase of the bias field, which may due to the increased magnetic loss tangent after 150 Oe. 80 Fig 4.5 S-parameters of the bandpass filter with 50-250 Gauss bias field Fig 4.6. 3-dB bandwidth versus magnetic bias field. S3=4mm, W3=10mm. 81 TABLE 4.1 The Minimum insertion loss with different Magnetic Bias Field Magnetic field 50Oe 75Oe 100Oe 125Oe Insertion loss -2.63dB -2.24dB -1.69dB -1.44dB 150Oe 175Oe 200Oe 225Oe 250Oe -0.98dB -1.02dB -1.09dB -1.26dB -1.64dB In order to verify the measurement results on the magnetically tunable YIG band pass filter, simulations done by HFSS were also carried out, by using the exact geometric and physical parameters of the bandpass filter. Fig. 4.7 shows comparison of the resonance frequency of the bandpass filter between simulated and measured data under different bias magnetic field. Clearly, the simulated and measured resonance frequency of the bandpass filter showed an excellent match. Fig. 4.8 shows the 3-dB bandwidth comparison of the bandpass filter in measured and simulated data. Although there are some quite large difference at certain bias magnetic field (~20 MHz @ 200 Oe), which is likely due to the fact that the limited ability of HFSS in simulating magnetic materials, the overall trend of the data showed nice agreement between each other. 82 Fig. 4.7 Simulated and measured bandpass filter resonance frequency Fig. 4.8. simulated and measured bandpass filter 3-dB bandwidth. 83 4.3.3 Magnetically and Electrically tunability As a matter of fact, since the thickness of the YIG film is much smaller compare to its length and width, we can quickly estimate of the resonance frequency of such bandpass filter by using Kittel’s equation [17]-[19]. √ (4.1) where is the gyromagnetic constant of about 2.8 MHz/Oe, Hk is the intrinsic in-plane anisotropy field of the YIG film, and Hdc is the external bias field. As expected, the measured resonace requency of the bandpass filter matches excellently with equaiton (1), which is shown in Fig. 4.9. Fig. 4.9. Calculated and measured FMR frequency against the external magnetic bias field. 84 Fig. 4.10. Measured electric field tunability of the bandpass filter From Equ. 1, we can see that the resonate frequency of the YIG film can be changed by both DC bias magnetic field and magnetic anisotropy field. This provides us the opportunity to tune the bandpass filter without using bulky electromagnets. It has recently been shown that by using a mechanically coupled magnetoelectric composite that consisting both ferromagnetic and piezoelectric phases, the anisotropy of the ferromagnetic phase can be easily change [20, 21]. The magnetoelectric coupling can be easily applied to the YIG film by bonding it to a piezoelectric substrate. Although the magnetostriction constant for YIG films is very low, typically less than 1 ppm, with proper engineering, it is still possible to get considerable tunability. In our attempt, the PZN-PT single crystal was chosen as the piezoelectric substrate, and the YIG film was directly bonded to it by epoxy. Two very thin layers of 85 copper were pre-deposited on the surfaces of the PZN-PT as electrodes, which can introduce an in-plane strain in the YIG film by converse magnetoelectric coupling. Fig. 7 shows the preliminary results that demonstrate the electric field tunability of the bandpass filter. It is clear, by changing the electric field applied on the PZN-PT single crystal, the center frequency of the bandpass filter can be tuned by about 200 MHz with an 8 kV/cm of electric field. This corresponds to a change in the magnetic anisotropy of about 50 Oe according to Eq. 4.1. This is a relative small tunability that is mainly due to the small magnetostriction constant of YIG film. However, by properly choosing the magnetic material with higher magnetostriction constant, the electric field tunability of the bandpass filter can be dramatically improved. The detailed research will be presented in future papers. 4.3.4 Conclusion and challenges The designed bandpass filters can be tuned by more than 50% of the central frequency with a magnetic bias field of 250 Oe. It is also possible to tune the resonant frequency using electric fields by bonding the YIG film to piezoelectric substrate, and an electric field tunability of about 200 MHz was obtained. However, it does have some limitations in the applications due to the high-order spurious modes. As we discussed in Fig. 4.5, the high order modes for 200 Oe bias field is . The primary resonance is at 2.17GHz, which has been proved to have good tunability and bandwidth. Fig. 4.11 shows the s-parameter response, where additional resonances were found around 2.4GHz with insertion loss of 2dB, 2.6GHz with -10dB, 2.7GHz with -10dB, corresponding to different standing wave modes, which has a good agreement with the 86 dispersion relation in Fig. 4.5. The splitting due to finite width (m) seems have less impact. They are merge to the primary standing wave resonance around to . These high order modes can cause spurious resonances, which increased the rejection band of the band S-parameter(dB) pass filter. 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 1.5 S11 S21 2.0 2.5 Freq (GHz) 3.0 Fig. 4.11 Transmission coefficient S21 of S-band bandpass filter utilizing single crystal YIG film, with DC bias magnetic field 200 Oe. 87 0 S12(dB) -5 -10 -15 YIG_W 3 mm 5 mm 7 mm -20 -25 1.6 1.8 2.0 2.2 Freq (GHz) 2.4 Fig. 4.12 Transmission coefficient S21 in terms of different S3 (length of YIG film along the propagation axis ), with DC bias magnetic field 200 Oe In order to avoid these spurious resonances, further investigations have been done on the geometry of the YIG film. From Fig. 4.12, we can see that the primary central frequency shifted down and the resonant frequencies of different modes become closer when S3 increases from 3 mm to 8 mm. indicates the wave number in the propagation direction. Apparently, a decreased S3 will increase the separation between two resonance modes. 4.4. Reciprocal c-band Bandpass filters based on SER We then expand this concept to the design of magnetically tunable bandpass filter in C-band (4~8 GHz). A large resonant frequency shift of the primary resonant frequency from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a low 88 insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved when the bias field of 1.6kOe was applied perpendicular to the feed line. Also, challenges of this design will be discussed. Compared with the S-band design, the dimension of the YIG film is smaller ( for C-band compared to for S-band). Therefore, the high-order width modes ( ) have larger separation than that of S-band. As the example in Fig. 4.13, the pass band of this filter will be split by not only standing wave modes ( order width modes ( ), but also high- ), which leads to a series of spurious resonance (ripples in the pass band), downgrading the filter’s band pass performance. 4.4.1 Filter design mechanism In order to improve the insertion loss and isolation, an inverted L-shaped transducer has been designed, as shown in fig. 4.13. The transducer is designed on a 0.381mm (15mil) thick Rogers TMM 10i substrate with ε_r=9.8 and tanδ=0.002. The geometrical parameters of the inverted-L shaped microstrip transducer include length and the width of the microstrip, the distance between the two transducers; the length, width and thickness of the YIG film. This structure is realized by patterned copper cladding on the top surface of the underlying dielectric substrate. The width of the coupling microstrip is 0.32mm and the length is 4.5mm as we adopted Rogers tmm 10i as the substrate, which has a relative permittivity of 9.8 and a thickness of 0.381mm. All the parameters are listed in the caption of Fig. 4.13. 89 Single crystal YIG slab with thickness about 108µm was placed on top of the transducers, as shown in Fig. 1. The saturation magnetization (4πMs) of the single crystal YIG slab is about 1750 Gauss and the FMR linewidth is less than1 Oe at X-band (~9.8 GHz). The bias magnetic field H is at X- band (~9.8 GHz). The bias magnetic field H is applied perpendicular to the feed line. Single crystal YIG film was then introduced above the transducer, as indicated in Fig. 4.13, in which . In order to get a magnetically tunable bandpass filter in C-band (5GHz to 7GHz in this dissertation), the magnetic bias field ( ) is applied perpendicular to the feed line from 1.1 kOe to 1.6 kOe. More specifically, if the DC bias field is 1.6 kOe, the dispersion relation of the MSSW in YIG was plot as Fig. 4.14. indicates the standing wave modes eq. (3.48).The width modes ( indicates , as discussed in chapter 3, seem to have as large separation of resonance frequencies, as the standing wave modes (n=1, 2 ). So, the high order mode analysis is much more complicate than the S-band case, where the width modes can be neglected. For the primary modes, the resonance happens at . Other resonances with (n,m) combo can be found in Table 4.2. These modes are distinguished from each other, which leads to a pass band with many ripples. In other word, the pass band will be split by these discrete resonances and is no longer smooth. 90 Figure 4.13 Geometry of the transducers: Inverted L-shaped microstrip transducers with parallel YIG alignment; , Frequency (GHz) 7.0 m=4 6.88GHz m=3 6.86GHz m=2 6.8GHz m=1 6.9 6.8 6.7 6.67GHz 6.6 6.5 0 1 2 n 91 3 4 5 Fig. 4.14. Dispersion relation of MSSW in a single crystal YIG film, which W4= 2mm and L2=3mm, DC bias field at 1.6 kOe, Applied perpendicular to the feed lines. standing wave modes indicates indicates the , as discussed in chapter 3, eq. (3.48). Table 4.2 the resonance frequency of width and standing wave mode with DC magnetic bias field 1600 Oe. GHz 1 2 3 4 1 6.67 6.56 N/A N/A 2 6.8 6.75 6.67 N/A 3 6.86 6.83 6.73 6.73 4 6.88 6.88 6.83 6.80 4.4.2 Simulations and Experimental verification The proposed c-band bandpass filter was then simulated with Ansoft HFSS 12.1. DC magnetic bias field 1600 Oe applied perpendicular to the feed line. The transmission coefficient was calculated and shown in Fig. 4.15. We can see a very wide pass band with a central resonance 6.7GHz with -1.8dB insertion loss and 170MHz 3-dB band width. However, many discrete resonance modes can also be observed in the pass band: 6.56GHz with 6dB loss, 6.67GHz with 4dB loss, 6.7dB with 1.8dB loss, and 6.88GHz with 5.4dB loss, 92 along with many other high order ones. These resonances split the major pass band and cause the ripples. These observations match with the conclusion in figure 4.14 and table 4.2. S-parameter(dB) 0 6.70GHz , -1.8dB 6.80GHz -5.8dB 6.88GHz, -5.4dB 7GHz, -9dB 6.67GHz, -4dB 6.56GHz,-6dB -10 6.36GHz,-16dB -20 -30 6.0 S12 S21 6.4 6.8 7.2 Freq (GHz) 7.6 8.0 Fig. 4.15. Simulation result of bandpass filters based on YIG SER film, with DC magnetic bias field 1600 Oe 93 S-parameter(dB) 0 -10 -20 6.70GHz, -2.4dB 6.65GHz, -4.3dB 6.80GHz, -5.6dB 6.59GHz, -6.3dB 6.88GHz, -8.3dB S12 S21 7.0GHz, <-22dB 6.40GHz, -22dB -30 6.0 6.4 6.8 7.2 Freq (GHz) 7.6 8.0 Fig. 4.16. experimental result of bandpass filters based on YIG SER film , with DC magnetic bias field 1600 Oe Then the transmission coefficient was measured via network analyzer and shown in Fig 4.16. We can see a similar pass band as the simulation with a central resonance 6.7GHz with -2.4dB insertion loss and 160MHz 3-dB band width. The insertion loss increases from 1.6dB to 2.4dB, but the band becomes smoother, although it still contains lots of ripples, as shown in Fig. 4.16. The resonance modes from simulation and experiment were summarized in Table 4.3 and plotted in Fig. 4.17. The modes higher than the primary resonance (>6.7GHz) corresponds to the standing wave modes ( ) , while those lower than primary resonance (<6.7GHz) corresponds to the finite width modes ( ). In experiments, the edges of YIG film were cut via a diamond saw. The edges are not ideally 94 straight edge, which leads to more loss from the reflection. Therefore, these high order modes from experiment are proved to have higher insertion loss than those from the simulation results. Also, the insertion loss of the primary resonance increased from 1.6dB to 2.4dB, and the 3-dB band width decrease from 170MHz to 160MHz, because of other fabrication losses, like copper defects on transmission line and non-uniform thickness of YIG film. In one word, the simulation results match the experimental results very well on primary resonance. Table 4.3 Resonance mode comparison between simulation and experimental data of the proposed c-band bandpass filter Simulation Experiment 6.36GHz 6.56GHz 6.67GHz 6.7GHz 6.80GHz 6.88GHz 7.0GHz -16dB -4dB -1.6dB -5.8dB -5.4dB -9dB 6.40GHz 6.59GHz 6.65GHz 6.7GHz 6.80GHz 6.88GHz 7.0GHz -22dB -4.3dB -2.4dB -5.6dB -8.3dB -22dB -6dB -6.3dB 95 Insertion Loss(dB) 0 -5 -10 Simulation Experiemnt -15 -20 -25 6.5 6.6 6.7 6.8 6.9 Freq (GHz) 7.0 Fig. 4.17. Resonance mode comparison between simulation and experimental data of the proposed c-band bandpass filter 4.4.3 Magnetically tunability As a matter of fact, since the thickness of the YIG film is much smaller compare to its length and width, we can quickly estimate of the resonance frequency of such bandpass filter by using Kittel’s equation [17]-[19]. √ (4.2) where is the gyromagnetic constant of about 2.8 MHz/Oe, Hk is the intrinsic in-plane anisotropy field of the YIG film, and Hdc is the external bias field. Figure 4.18~4.20 shows the measured result of the fabricated C-band tunable band pass filter on straight edge YIG film. The DC bias magnetic field varies from 1.1k Oe to 96 1.6kOe. The central resonance frequencies were tuned from 5.1GHz to 6.7GHz. A tunability of 320MHz/100Oe bias shift has been observed. The high order modes under these bias conditions are similar to those with 1.6kOe bias, as we discussed in the previous section. Splitting resonances and ripples in the pass bands can be observed. Also, the pass bands in S12 are identical to those in S21, so this band pass filter is reciprocal. From Fig 4.20, we can see that the central frequencies of S12 and S21 are linearly proportional to the bias field. These central frequencies have 130MHz difference compared with the FMR frequencies calculated from the Kittel’s equation, which is the lower cut-off frequency of pass band. The central frequencies of these pass band match the primary resonances in the dispersion relation (Fig 4.14) very well. 0 -5 -10 S21(dB) -15 -20 -25 DC bias 1.1kOe 1.2kOe 1.3kOe 1.4kOe 1.5kOe 1.6kOe -30 -35 -40 4 6 8 Freq (GHz) Fig. 4.18 Transmission coefficient (S21) of proposed C-band tunable band pass filter on straight edge YIG film. The edge of the YIG film is parallel to the transducer and perpendicular to DC bias magnetic field 97 S12(dB) 0 -5 -10 -15 -20 -25 -30 -35 -40 DC bias 1.1kOe 1.2kOe 1.3kOe 1.4kOe 1.5kOe 1.6kOe 4 6 Freq (GHz) 8 Fig. 4.19 Transmission coefficient (S12) of proposed C-band tunable band pass filter on straight edge YIG film. The edge of the YIG film is parallel to the transducer and Resonance Freq. (GHz) perpendicular to DC bias magnetic field 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 S21 S12 FMR Frequency 1.1 1.2 1.3 1.4 1.5 1.6 Applied Bias field (Oe) Fig. 4.20 Comparison of transmission coefficient of proposed C-band tunable band pass filter on straight edge YIG film with the FMR frequency calculated from Kittel’s equation. 98 4.4.4 Limitation of this design All in all, we’ve investigate design of magnetically tunable bandpass filter in C-band (4~8 GHz) with YIG SER. A large resonant frequency shift of the primary resonant frequency from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a low insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved when the bias field of 1.6kOe was applied perpendicular to the feed line. However, this design has two major limitations that we might improve in the following sections: (1) Spurious resonances, or the high-order modes, split the major resonance to many ripples. The pass bands are not smooth. (2)The band pass transmission is reciprocal due to the reflection from the straight edges. 4.5 Non-reciprocal c-band Bandpass filters based on rotated SER In the previous section, MSSW based YIG devices have the unwanted reflected waves from the straight edges, which will induce spurious resonance [11] due to the standing wave modes, formed from the forward and backward wave. In this section, starting from the analysis and simulation of magnetostatic wave propagation in YIG slabs, a new method of suppressing the spurious resonance is proposed. The YIG slab was rotated by a proper angle to diminish standing wave modes in order to get a much smoother pass band. The designed C-band tunable bandpass filters show a central frequency shift from 5.2 GHz to 7.0 GHz under in-plane magnetic fields from 1.1 kOe to 1.6 kOe with a reasonable insertion loss < 2.3 dB. Furthermore, the oblique angle between the DC bias field and the propagation direction leads to non-reciprocal transmission characteristics of the forward and backward MSSW, which provide more 99 than 20 dB isolation across all measured frequency range. The proposed device prototype, which can perform simultaneously with the filtering and isolating functions, may be very useful in practical applications of the filter and RF system design. 4.5.1 The mechanism of the non-reflection boundary on a rotated YIG film The major spurious resonances are due to the unwanted reflected waves from the straight edges. One can diminish them by using a non-reflection edge. For example, several kinds of MSSW techniques have been reported to suppress the unwanted reflection by depositing a film or attaching an additional ferrite material on to the edges of YIG films to absorb the MSW [20]-[23]. Some simpler methods are: tapered the YIG film edges at an angle (≠90o) [24]; local low bias field at the edge of the film [22]. The schematic of a YIG resonator with a tapered edge is shown in Fig. 4.21. The reflection was diminished and no backward transmission was excited. The MSSW was restricted on the bottom interface of YIG film, which induces the non-reciprocal characteristics. However, in practical designs, the tapering process of YIG can cause some other issues like non-uniform thickness, cracks in YIG film due to damage, which make this approach not an ideal solution. Fig 4.22 shows the diminishing of unwanted reflection from edge by applying different DC bias condition , or applying a ferrite absorber around edge. These approaches, however, need extra effort to implement, which makes the design of band pass filter much more complicate. 100 Forward wave Fig. 4.21 MSSW propagation in a tapered YIG film. [16] Absorber Forward wave Fig. 4.21 MSSW propagation in a YIG film with different bias condition at edges or an absorber. [20-23]. Fig. 4.22 MSSW propagation in a YIG film with a 45o inclined edge boundary at the YIGair boundary. 101 A new method of suppressing the spurious resonance is proposed. Let us first consider a 45o edge boundary between YIG film and the air, as shown in fig. 4.22. The DC bias magnetic field is applied in plane and perpendicular to the incident magnetostatic surface wave (MSSW). After the reflection on the 45o edge boundary, the wave propagation is parallel to the bias field. So the wave profile follows the magnetostatic back volume wave (MSBVW), as discussed in chapter 3, (table 3.1). However, due to the different dispersion relations of these two wave profiles, the allowed frequency band for propagation modes are different, as shown in Fig 4.23. For example, suppose we applied HDC=1600Oe to a YIG film with thickness 108um, 4piMs 1750Gauss, the MSSW propagation is limited in 6.5GHz to 6.9GHz, where no propagation modes exist for MSBVW. So, the reflection like Fig4.22 won’t happen. Instead, the reflection will decay very fast and the energy dissipates fast along this path, because it is propagating in the stop band of MSBVW. In one word, the 45o rotated edge forms a non-reflection boundary for the MSSW, which is very useful for utilizing the non-reciprocal characteristics of MSSW and avoid the standing wave modes due to the reflection from the edges. By simply rotating the film by 45o, we do not need to apply either additional DC bias field and absorbers, or an additional complicate process to taper the edge. Therefore, Compared with other approaches, rotating a YIG film is much easier to be realized in a practical design. 102 Frequency (GHz) 7.0 MSSW 6.5 n=4 6.0 n=3 MSBVW n=2 5.5 5.0 4.5 n=5 n=1 0 2 4 kd 6 8 10 Fig. 4.23 Comparison of dispersion relation between Magnetostatic surface wave (MSSW) and back volume wave (MSBVW), with DC bias field 1.6kOe, on YIG (thickness 108um, 4piMs 1750Gauss) Fig. 4.24 Non-reciprocal c-band BPF on a rotated YIG film. 103 4.5.2 Simulations and Experimental verification Based on the non-reflection boundary discussion in section 4.5.1, and the previous reciprocal filter design in C-band, a non-reciprocal c-band BPF was proposed on a 45o rotated YIG film. The alignment of the YIG slab can be adjusted through rotating around its center, which can lead to a non-reciprocal s-parameter performance. This proposed C-band bandpass non-reciprocal filter was then simulated with Ansoft HFSS 12.1. More specifically, let us first investigate the DC magnetic bias field 1600 Oe applied perpendicular to the feed line. The transmission coefficient was calculated and shown in Fig 4.25. We can see a very wide pass band for S21 (forward transmission), with a central resonance 6.67GHz with -2dB insertion loss and 220MHz 3-dB band width. The pass band is clear and smoother that the un-rotated case, although some small ripples can be found, like 6.88GHz with 4dB insertion loss and 7GHz with -11dB insertion loss. On the other hand, the insertion loss S12 (backward transmission) was greater than 18dB over the band 6GHz to 8GHz. We can conclude that this filter has duel functionality of isolators. On the other word, it is a non-reciprocal band pass filter. Then another question is that if the backward transmission does not happen, where the energy goes. S22 is over 13dB, which means that very little energy was reflected back to the port 2. So, the missing energy dissipates in the YIG film. Then the transmission coefficient was measured via network analyzer and shown in Fig 4.26. We can see a similar pass band as the simulation with a central resonance 6.67GHz with -1.8dB insertion loss and 190MHz 3-dB band width. Compared with the 104 simulated results, the insertion loss decreases from 2dB to 1.8dB, and 3-dB bandwidth increases from 230MHz to 190MHz. Also, the band becomes smoother due to the suppression of the reflection through edges, although there is still a side lobe at 6.86GHz with -11dB insertion loss, which can be neglected. The measured S22 is -20dB at 6.62GHz, which confirms the analysis from the simulation that the energy dissipates in the medium instead of reflecting back to the port. It is notable this type of design has a relatively high Q of over 35 compared to other ferrite tunable bandpass filters. S-parameter(dB) 0 S21 S12 S22 -10 -20 -30 6.0 6.5 7.0 7.5 Frequency (GHz) 8.0 Fig. 4.25 Simulated s-parameter of our bandpass filter with parallel/rotated YIG slab under DC bias field of 1.6 kOe. 105 S-parameter(dB) 0 S21 S12 S22 -10 -20 -30 6.0 6.5 7.0 7.5 Frequency (GHz) 8.0 Fig. 4.26 Measured s-parameter of our bandpass filter with parallel/rotated YIG slab under DC bias field of 1.6 kOe. 4.5.3 Magnetically tunability (1) Resonance frequency vs bias field Figure 4.27~4.30 shows the measured result of the fabricated non-reciprocal C-band tunable band pass filter on rotated YIG film. The DC bias magnetic field varies from 1.3k Oe to 1.7kOe. The central resonance frequencies were tuned from 5.8GHz to 7.0GHz. A tunability of 300MHz/100Oe bias shift has been observed. The results indicated a wellshaped bandpass band with insertion loss between 1.8 ~ 3.0 dB, and bandwidth around 190MHz at 6.67GHz for 1.6 kOe bias field. The resonant frequencies follow the Kittel’s equation [27] and can be tuned by DC magnetic fields, as shown in fig 4.31 Furthermore, non-reciprocal performance was observed with isolation over 20dB between two 106 transmission directions, throughout the C-band 4GHz to 8GHz, and over15dB among 2GHz to 10GHz. From Fig 4.31, we can see that the central frequencies of S21 are linearly proportional to the bias field. These central frequencies have 200MHz difference compared with the FMR frequencies calculated from the Kittel’s equation, which is the lower cut-off frequency of pass band. The S11 (fig 4.29), and S22 (fig.4.30) shows little reflection back to the excitation ports, which means the missing energy dissipates in the YIG film. The central frequencies of these pass band match the primary resonances in the S21(dB) dispersion relation (Fig 4.14) very well. 0 -5 -10 -15 -20 -25 -30 -35 -40 DC bias H 1.3kOe 1.4kOe 1.5kOe 1.6kOe 1.7kOe 2 4 6 8 Freq (GHz) 10 Fig. 4.27 Transmission coefficient (S21) of proposed C-band tunable band pass filter on rotated YIG film. 107 S12(dB) 0 -5 -10 -15 -20 -25 -30 -35 -40 DC bias H 1.3kOe 1.4kOe 1.5kOe 1.6kOe 1.7kOe 2 4 6 8 Freq (GHz) 10 Fig. 4.28 Transmission coefficient (S21) of proposed C-band tunable band pass filter on rotated YIG film. 0 S11(dB) -5 -10 DC bias H 1.3kOe 1.4kOe 1.5kOe 1.6kOe 1.7kOe -15 -20 -25 -30 2 4 6 8 Freq (GHz) 10 Fig. 4.29 Transmission coefficient (S11) of proposed C-band tunable band pass filter on rotated YIG film. 108 0 S22(dB) -5 DC bias H 1.3kOe 1.4kOe 1.5kOe 1.6kOe 1.7kOe -10 -15 -20 2 4 6 8 Freq (GHz) 10 Fig. 4.30 Transmission coefficient (S22) of proposed C-band tunable band pass filter on Resonance frequency (GHz) rotated YIG film. 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 1.3 Measured central frequency Kittel's Equation 1.4 1.5 1.6 DC Bias field (k Oe) 1.7 Fig. 4.31 Comparison of transmission coefficient of proposed C-band tunable band pass filter on rotated YIG film with the FMR frequency calculated from Kittel’s equation 109 (2) Insertion Loss and isolation vs central frequency The insertion loss of the forward pass bands and the isolation of the backward transmission are then plotted in fig. 4.32 (a) and (b), respectively. The insertion loss increases from 1.8dB to 3dB, when the central resonance frequency increases. A possible reason for higher insertion loss in lower frequency is the impedance mismatch. From fig 4.29 and fig 4.30, we can see the return loss is 8dB at 5.7GHz (1.3kOe bias field), while is 18dB at 7GHz. Proper optimization on the transducer width may help fix this mismatch issue at whatever specific operating frequencies on a practical application. On the other -1.8 -2.0 -2.2 -2.4 -2.6 -2.8 -3.0 5.6 -18 Insertion Loss -19 isolation(dB) Insertion Loss (dB) hand, the isolation is over 20dB for the whole tunable band. 6.0 6.4 Freq (GHz) -20 -21 -22 -23 -24 5.6 6.8 Isolations 6.0 6.4 6.8 Freq (GHz) Fig. 4.32 The insertion loss of the forward pass bands and the isolation of the backward transmission. (3) Bandwidth vs central frequency The 3-dB bandwidth of the pass bands were plotted in terms of central resonant frequency, as shown in Fig. 4.33. The bandwidth is around 200MHz to 210MHz throughout the entire tuning range. So, the Q ( ) of the filter increases as the central frequency increases. 110 Bandwidth(MHz) 220 210 200 bandwidth(MHz) 190 180 5.6 6.0 6.4 6.8 Freq (GHz) Fig. 4.32 The 3-dB bandwidth of the forward pass bands for the fabricated c-band nonreciprocal bandpass filter. 4.5.4 Summary for C-band non-reciprocal filter In summary, a novel non-reciprocal C-band magnetic tunable bandpass filter (BPFs) with a YIG slab has been designed, fabricated and tested, which is based on an inverted Lcoupling structure loaded with a rotated single-crystal YIG slab. Magnetostatic surface wave propagation in the rotated YIG leads to non-reciprocal behavior. The tunable resonant frequency of 5.3 ~ 6.8GHz was obtained for the BPF with the magnetic bias field 1.1kOe ~ 1.6kOe, applied perpendicular to the feed line. At the same time, the BPF acts as an ultra-wideband isolator with more than 22dB isolation at the pass band with insertion loss of 1.6~3dB. The demonstrated nonreciprocal magnetically tunable bandpass filters with isolator duel functionality should be promising in C-band RF front and other microwave circuits. 111 4.6 Integrated bandpass filter with spin spray materials Nowadays, integrated components for communication system are highly demanded. The verified magnetostatic wave concept was then used to expand the filter designs to an integrated solution. The material we used is NiCo ferrite, which can be deposited via the spin spray thin film deposition process in our lab. 1 mm Top view 70um 400um 850 um Cross Section 15μm 5μm 15μm 2μm Cu Polyamide NiCo Ferrite Cu 1.5μm 6μm 2μm 112 Fig. 4.33 Geometry of integrated band pass filter with MSSW concept The geometrical parameters of the S-shaped co-planar wave transducer include length and the width of the microstrip, the distance between the two transducers, the length, width and thickness of the NiCo ferrite film are shown in fig.4.33. This structure is realized by patterned copper cladding on the top surface of the underlying dielectric substrate. The width of the coupling microstrip is 15μm and the length is 1 mm as we adopted polyamide as the substrate, which has a relative permittivity of 3.5 and a thickness of 6μm. The ends of the two transducers are connected to the ground, in order to achieve maximum current on the transducer. All the parameters are listed Fig. 4.33. The NiCo ferrite is deposited via spin spray thin film deposition. The thickness of the NiCo films is 2 um with parallelogram shape. The saturation magnetization (4πMs) of the NiCo films is about 4800 Gauss, and the intrinsic anisotropy field is about 165 Oe. The NiCo ferrite is then patterned underneath the transducer for magnetostatic wave, as indicated in Fig. 4.34. In order to get a magnetically tunable bandpass filter, the magnetic bias field (H) is applied perpendicular to the feed line from zero to 125 Oe to 625 Oe. More specifically, if the DC bias field is 500 Oe, the simulation transmission response was shown in Fig. 4.35. The central frequency is at 5.4GHz, with insertion Loss: 1.98dB and -3dB Bandwidth: 400MHz, or 7.4%. The return loss is over 23dB. Furthermore, the central resonant frequencies have been tuned from 3.7GHz to 5.9GHz with a varied DC bias 125 Oe to 625 Oe, which 440MHz/100Oe tunability. The transmission coefficient is reciprocal, due to the 113 small angle of the edges. This integrated design can lead to integrated bandpass filters for compact and low-cost reconfigurable RF communication systems S-parameter(dB) 0 -5 S12 S21 S11 S22 -10 -15 -20 -25 -30 1 2 3 4 5 6 Freq (GHz) 7 8 Fig. 4.34. Simulated results of integrated bandpass filter with parallelogram shape. 0 125 Oe 250Oe 375 Oe 500 Oe 625 Oe S12(dB) -5 -10 -15 -20 -25 -30 1 2 3 4 5 6 Freq (GHz) 114 7 8 Fig. 4.35. Simulated results of integrated bandpass filter with parallelogram shape, with DC bias from 125Oe to 625 Oe 4.7 Conclusion In this Chapter, bandpass filters based on Magnetostatic wave concept were presented, with both reciprocal and non-reciprocal characteristics. An s-band magnetically and electrically tunable bandpass filters (BPF) with yttrium iron garnet (YIG) will be introduced. A large resonant frequency shift of the primary resonant frequency of 840 MHz, or equivalent to 54% of the central frequency of the bandpass filter with bias fields of 50 ~ 250 Oe was obtained along with a low insertion loss of < 2dB. A maximum 3dB bandwidth of 40 MHz was also achieved when the bias field of 250 Oe was applied perpendicular to the feed line. A C-band low loss straight-edge resonator band pass filter was presented based on a similar concept as s-band filter. A large resonant frequency shift of the primary resonant frequency from 5GHz to 7GHz, with bias fields of 1.1 ~ 1.6 kOe was obtained along with a low insertion loss of < 1.5dB. A maximum 3-dB bandwidth of 230 MHz was also achieved when the bias field of 1.6kOe was applied perpendicular to the feed line. Then, Simulation and experimental verification will be presented for a new type of non-reciprocal C-band magnetic tunable bandpass filter with dual functionality of ultra-wideband isolation. The designed C-band tunable bandpass filters show a central frequency shift from 5.2 GHz to 7.0 GHz under in-plane magnetic fields from 1.1 kOe to 1.6 kOe with a reasonable insertion loss < 2.3 dB. Furthermore, the oblique angle between the DC bias field and the propagation direction leads to non-reciprocal transmission characteristics of 115 the forward and backward MSSW, which provide more than 20 dB isolation across all measured frequency range. The proposed device prototype, which can perform simultaneously with the filtering and isolating functions, may be very useful in practical applications of the filter and RF system design. 4.8 References [1] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microstrip Applications. New York: Wiley, 2001. [2] I. C. Hunter and J. D. Rhodes, ―Electronically tunable microwave bandpass filters,‖ IEEE Trans. Microw. Theory Tech., Vol. 30, pp. 1354-1360, Sept. 1982. [3] J. Uher and W. J. R. 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[19] C. Kittel, Introduction to Solid State Physics. New York: Wiley, 1996. [20] Y. Murakami, T. Ohgihara, and T. Okamoto, ―A 0.5-4.0-GHz tunable bandpass filter using YIG film grown by LPE,‖ IEEE Trans. Microw. Theory Tech., vol 35, pp. 11921198, Dec. 1987. [21] S. M. Hanna and S. Zeroug, ―Single and coupled MSW resonators for microwave channelizers,‖ IEEE Trans. Magn., Vol. 24, pp. 2808-2810, Nov. 1988. [22] W. S. Ishak and K. W. Chang, ―Tunable microwave resonators using magnetostatic wave in YIG films,‖ IEEE Trans. Microw. Theory Tech., vol 34, pp. 1383-1393, Dec. 1986. [23] J. D. Adam and S. N. Stitzer, ―MSW frequency selective limiters at UHF,‖ IEEE Trans. Magn., Vol. 40, No. 4, pp. 2844-2846, July 2004. [24] A. S. Tatarenko, V. Gheevarughese, and G. Srinivasan, ―Magnetoelectric microwave bandpass filter,‖ Electron. Lett., vol 42, pp. 540-541 , Apr. 2006. [25] G. M. Yang, J. Lou, G. Y. Wen, Y. Q. Jin and N. X. Sun, "Magnetically Tunable Bandpass Filters with YIG-GGG/ YIG-GGG-YIG Sandwich Structures", International Microwave Symposium (IMS) 2011, Baltimore, MD. [26] Kok-Wai Chang and W. S. Ishak, ―Magnetostatic surface wave straight-edge resonators,‖ Trans. Circuits, Syst., Signal Proc., vol. 4, no. 1-2, pp. 201-209, 1985. 118 [27] J. H. Collins, D. M. Hastie, J. M. Owens, and C. V. Smith, Jr., "Magnetostatic wave terminations," Appl. Phys., vol. 49, pp. 1800-1802, 1978 119 Chapter 5: Tunable Planar Isolator with Serrated Microstrip Structure Modern communication systems, radars, and metrology systems all need tunable components that are compact, lightweight, and power efficient. Tunable isolators are highly desired in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. The integration of passive devices using a ferrite, such as circulators and isolators, has become one focus of research for electronic applications in the microwave range. Isolators based on the non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide or on planar transmission lines have been widely used [17]. The microwave ferrites experience LHCP (left-handed-handed circular polarization) RF excitation magnetic fields in forward propagation while RHCP (right-handed circular polarization) in backward propagation, leading to minimal absorption in forward propagation while strong FMR absorption in backward propagation. Another class of isolators is based on field displacement. The energy from the backward travelling signal is absorbed in a resistive film [2]-[4]. However, the resist absorbers are usually very sensitive to the location of the ferrite, and they can hardly have tunability via magnetic field. In this Chapter, a tunable planar isolator with serrated microstrip structure based on ferromagnetic resonance (FMR) of microwave ferrites will be presented, with both 120 tunable and non-reciprocal characteristics. The study of this chapter can be divided in to several parts. First, a literature review will be presented to introduce previous researches on isolators. Second, a novel serrated microstrip structure will be presented to achieve circular polarization of magnetic field, in terms of DC bias field. Current and field distribution will be analyzed via HFSS simulations. Then, attenuation factor of wave propagation in magnetic material at the FMR frequency with serrated microstrip structure will be discussed. Finally, simulation designs and experimental verification will be provided for the proposed tunable planar isolator with serrated microstrip structure. 5.1 Introduction of isolator based on ferrite An isolator is a passive non-reciprocal 2-port device which permits RF energy to pass through it in one direction while absorbing energy in the reverse direction. Isolators are widely used for decoupling of circuit stages in cascade amplifier stages and suppress reflection between oscillators and multipliers, as shown in Fig. Tunable isolators are highly desired in communication systems for enhancing the isolation between the sensitive receiver and power transmitter. There are two types of ferrite isolators: (1) ferromagnetic resonance isolator, which is based on non-reciprocal ferromagnetic resonance (FMR) of microwave ferrites in waveguide or on planar transmission lines; (2) field displacement isolator, which is based on absorption in a resistive film for the backward travelling signal. 121 Fig. 5.1 Application of isolators in communication system. 5.1.1 Ferromagnetic resonance isolator To better understand the interaction between the circular polarized EM wave and the DC magnetic bias field, let us first introduce the effective permeability under circular polarization. The magnetic field then can be expressed as: RHCP: + + LHCP: ̂ ̂ (5.1) ̂ ̂ (5.2) where RHCP indicates right-handed circular polarization in terms of the DC bias magnetic field, LHCP in terms of left-handed circular polarization. By expressing the permeability as a tensor, as in Eq. (1.15) we can calculate the magnetization as: + + ̂ 122 ̂ (5.3) + + ̂ ̂ (5.4) So the permeability is then expressed as : + ( ) Suppose we have an infinite ferrite medium with saturation magnetization , linewidth field , permittivity , given a DC bias the propagation constant inside the ferrite is then calculated as : √ where , , which estimates the loss from the linewidth .A clear comparison between attenuation constant was plotted in Fig 5.2. The attenuation constant of LHCP is so small that we have times it by 1000 to compare with the RHCP. A stop band was found for RHCP at 12GHz to 16GHz, while the attenuation for LHCP is neglectable. Similarly, propagation constant 5.3. In the stop band (12GHz to 16GHz), + was plotted in Fig is close to zero, while is linearly proportional to the frequency. The difference of attenuation and propagation constant, regard of RH or LH circular polarization can lead to Ferromagnetic resonance isolator designs, as long as one can place the ferrite medium at the location where forward and backward transmission have different polarization. 123 Attenuation constant 1200 RHCP LHCP*1000 1000 800 600 Stop Band 400 200 0 4 8 12 16 Freq (GHz) 20 Fig. 5.2 Attenuation constants for circularly polarized plane waves in the ferrite medium Propagation constant 1600 RHCP LHCP 1200 800 400 0 4 8 12 16 Freq (GHz) 20 Fig. 5.2 propagation constants for circularly polarized plane waves in the ferrite medium 124 (a) (b) Fig. 5.3 Ferrite isolator with waveguide structure: (a) field distribution in waveguide; (b) Ferrite location in waveguide. Fig. 5.4 Forward and reverse attenuation constants for the resonance isolator (a) Versus slab position. (b) Versus frequency. 125 For example, a waveguide operating in mode has the magnetic field distribution like fig. 5.3(a). Suppose the wave is propagating along z –axis, the field component can be expressed as: (5.5) (5.6) If let / , we have . At the locations , a pure LHCP or RHCP wave are expected. From Fig. 5.4, we can see the difference of attenuation constant for forward and reverse transmission. The operating frequency of these isolators highly depends on the FMR frequency. So this type of isolator is called ferromagnetic resonance isolator. The basic characteristics are: (1) Bias field perpendicular to the propagation direction; (2) Ferrites are located at some location with circular polarization RHCP and LHCP (3) The operating frequency of these isolators can be tuned by the FMR frequency. (4)Narrow bandwidth due to the limit FMR band width 5.1.2 Field displacement isolator Another type of isolator is field displacement isolator. Consider a waveguide loaded with a ferrite film, the electric field distributions are different for the forward and backward transmission because of the loss characteristic of RHCP, as shown in Fig 5.5. As a result, if one place a lossy resistive film on the location of the ferrite, the forward transmission won’t be affected, while the reverse wave will be attenuated. 126 This type of isolator has the following characteristics: (1)Ferrite film is located at the center, so it is hard to dissipate heat. This approach is not good for high power application (2) Very sensitive to the location of the ferrite. (3) The operation frequency does not depend on FMR frequency, so only small bias field is required. On the other hand, the frequency cannot be tuned. (4)They have wider bandwidth, depending on the resistive film, not the FMR frequency. Fig. 5.5 Field displacement isolator 127 5.2 Serrated Microstrip Isolator Design Mechanism 5.2.1 Previous Researches on Planar approaches of isolator designs The conventional ferrite isolators on waveguides are usually bulky and not convenient to apply on modern communication systems. The combination of ferrite thin films and planar microwave structure constituted a major step in the miniaturization of such ferrites [5-8]. Wen [7] first realized a coplanar isolator with rods of magnetic material located in the slots between the coplanar waveguide. A transverse DC magnetic field applied parallel to the surface of the substrate is required to provide appropriate bias conditions. Low insertion losses < 2 dB and high isolation of 38 dB were achieved at 6 GHz for a line length of 2 cm. In this approach, high-k TiO2 rutile substrate with a dielectric constant of r=130 is required in order to produce the circularly polarized microwave magnetic field and furthermore the device is non-integrated due to the slot cut. Bayard [5] realized a coplanar isolator with ferrofluid between the conductors. An isolation of 13 dB and insertion losses of 10 dB were measured for a line length of 1 cm under a polarizing field of 340 kA/m. Capraro et al. [8] reported the transmission coefficients that showed a non-reciprocal effect, which reached 5.4 dB per cm of line length at 50 GHz for a 26.5μm thick BaM film. These approaches have large insertion loss of over 10 dB, which may not be suitable for modern communication systems. 128 5.3.2 Serrated Microstrip Structure and Circular polarization Ferrite resonance isolators are usually based on different attenuation constants for both directions of propagation, forward and backward. At the FMR frequency, EM waves with RHCP, in terms of the DC magnetic bias field or magnetization, will have strong coupling with the ferrite; while LHCP (left-handed-handed circular polarization) will have weak couplings. Figure 5.1 shows a new planar approach to generate RHCP and LHCP on microstrip lines. The microstrip line is cut via periodic slots, forming a serrated geometry with multiple fingers. The substrate we used is Rogers TMM 10i ( and ), with a thickness of 0.381mm. A polycrystalline Yttrium Iron Garnet (YIG) film was then placed covering the serrated part, with dimension 4 mm x 5 mm. The saturation magnetization (4πMs) of the YIG films is about 1750 Gauss with the FMR linewidth of the YIG film around 20 Oe measured at X-band (8 GHz). W2 W1 S2 H S1 129 Fig. 5.6. Geometry of the serrated microstrip isolator: , and . The dashed line indicates the current flowing on the substrate. Fig. 5.7. Microwave magnetic field distribution with the serrated structure For the original microstrip line, the current flows mainly on the edge along y axis as schematically shown in Fig. 5.6. Hx and Hz components dominate the magnetic field distribution. The disruption of the serrate structure forces the current flowing around the new edges, which generated rotating magnetic field with Hy and Hz components. When the DC bias field is applied along x- axis, the polarization of the magnetic field can either be RH or LH, in terms of the DC magnetic bias field or magnetization, as shown in fig. 5.7. When YIG films are placed either above or underneath the serrated 130 structure, opposite distributions of circular polarization can lead to different attenuation constants for both directions of propagation, forward and backward. The location, with the maximum attainable ratio of RHCP to LHCP, can be the optimal placement for YIG films to achieve best insertion/isolation performance. 5.2.3 Magnetic field distribution of Serrated Microstrip Structure Unlike the field distribution in waveguides, the analytical close form distribution equations for the serrated structure can be rather complicated. We used Ansoft HFSS full wave simulator to analyze the magnetic field distribution. Figure 5.8 shows the circular polarization of magnetic field above and underneath the serrated structure. For forward input, fig 5.9 (a), we found RHCP magnetic field above the serrated structure, with LHCP in the corner region of the YIG film, which is at the interconnection between serrated line and the feed line. The polarization is opposite underneath the serrated line: LHCP for major part and RHCP for interconnection part. Similarly, for backward input, fig 5.9 (b), we found LHCP magnetic field above the serrated structure, with RHCP in the corner region of the YIG film, which is at the interconnection between serrated line and the feed line. The polarization is opposite underneath the serrated line: RHCP for major part and LHCP for interconnection part. It is notable that the polarization at the interconnection between serrated part and the feed line are opposite to the serrated part, which may increase the insertion loss or add an additional isolation band. At the FMR frequency, YIG will have strong coupling with RHCP waves, while have weak coupling with LHCP. Different attenuation constants of 131 forward and backward propagation can lead to non-reciprocal characteristics and isolating behavior by properly load the ferrite film with the serrated microstrip line. Bias Field (a) Fig. 5.8. (b) The polarization of microwave magnetic field above and underneath the serrated structure: (a) Forward transmission; (b) Backward transmission 132 H YIG Fwd Input Port1 Sub (a) H YIG Bwd Input Port2 Sub (b) Fig. 5.9. The summarized polarization of microwave magnetic field above and underneath the serrated structure: (a) Forward transmission; (b) Backward transmission 133 5.3 Simulation verification 5.3.1 Effect of Ferrite films location with Serrated Microstrip Structure In order to verify the distribution of circular polarization, the isolator with different placements of YIG thin film (20μm) was analyzed via HFSS, and the simulation results were shown in Fig. 5.10~5.13. Four cases are investigated: (1) YIG above microstrip Figure 5.10 shows the S21 and S12 of the case when the YIG film was placed covering serrated structure. Insertion loss of 3.5dB at 14.5GHz for backward propagation (S12, LHCP) and isolation of 17.6dB for forward propagation (S21, RHCP) were observed. Besides, a side lobe can be observed at 15.1GHz with an opposite insertion/isolation characteristics (2.4dB and 9dB), due to the edge effect from the interconnection shown in Fig. 5.7. (2) YIG underneath microstrip In Fig. 5.11, YIG film was placed underneath serrated structure. Insertion loss of 5dB at 14.5GHz for forward propagation (S21, LHCP) and isolation of 13dB for backward propagation (S12, RHCP) were observed. Similarly, there is a side lobe with 2.5dB/8.5dB at 15.2GHz. (3) YIG both above and underneath microstrip 134 In Fig. 5.12, YIG film was placed both above and underneath. The isolator then becomes reciprocal, with isolation 23dB at 14.4GHz (main lobe) and 11dB at 15.4GHz (side lobe). (4) YIG above microstrip with tapered edge Figure 5.13 shows the S21 and S12 of the case when the YIG film was placed above serrated structure as untapped case. But, the straight edges of the YIG film at the interconnection were tapered to suppress the contribution from the unwanted opposite circular polarization. The insertion loss of backward wave (S12) at 15.4GHz (side lobe) was reduced from 9dB to 5dB. The insertion loss and isolation at 14.4GHz are similar to the untapped case. Clearly, YIG films placed either above or underneath can lead to non-reciprocal characteristics. YIG film with tapered edge above exhibits better suppression on edge effects, which is consistent with the circular polarized microwave magnetic field distribution. 135 S12 & S21(dB) 0 -5 S12 S21 -10 -15 -20 12 Fig.5.10. 13 14 15 16 Freq (GHz) 17 Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG above serrated structure. S12 & S21(dB) 0 -5 S12 S21 -10 -15 -20 12 Fig.5.11. 13 14 15 16 Freq (GHz) 17 Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG underneath serrated 136 S12 & S21(dB) 0 -5 -10 S12 S21 -15 -20 -25 12 structure. Fig.5.12. 13 14 15 16 Freq (GHz) 17 Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG placed both above and underneath the microstrip. 137 S12 & S21(dB) 0 -5 -10 S12 S21 -15 -20 12 Fig.5.13. 13 14 15 16 Freq (GHz) 17 Simulated s-parameter of the serrated isolator with different YIG placement with DC bias field 4.4kOe, applied perpendicular to the feed line: YIG above serrated with tapered edges 5.3.2 Designed Serrated Microstrip isolator with thicker YIG slab A 400μm thick YIG slab with tapered edge ( 90o) was then placed above the serrated part. DC magnetic bias field was applied perpendicular to the feed line, from 0 Oe to 4kOe. Figure 5.14 shows the simulated s-parameter results. With 4kOe bias, the insertion loss of the backward propagation is 5dB at 13.5GHz, while the isolation is 17.5dB for the forward propagation. 138 S12 & S21(dB) 0 -5 -10 S12-0.8kOe S12-1.6kOe S12-2.4kOe S12-3.2kOe S12-4.0kOe -15 -20 Fig.5.14. 2 4 6 S21-0.8kOe S21-1.6kOe S21-2.4kOe S21-3.2kOe S21-4.0kOe 8 10 12 14 Freq (GHz) Simulated s-parameter of serrated microstrip isolator. 5.4 Measurement verification The designed serrated microstrip isolator was then fabricated and measured via a vector network analyzer (Agilent PNA E8364A). A 400μm thick YIG slab with tapered edge ( 90o) was then placed above the serrated part. DC magnetic bias field was applied perpendicular to the feed line, from 0 Oe to 4kOe. Figure 15 shows the measured sparameter results. With 4kOe bias, the insertion loss of the backward propagation is 3.5dB at 13.5GHz, while the isolation is 19.3dB for the forward propagation, compared to the simulation result 5.2dB/17.5dB. Fig.16 shows that the return losses of both the forward (S11) and backward (S22 ) transmission with 4kOe magnetic field bias are greater than 10dB, which indicated that the missing energy was dissipated in the YIG slab instead of reflecting back to port 1. 139 Fig.17 shows the insertion loss and isolation of the tunable serrated microstrip isolator over operating frequency. The isolation increases from 5dB to 19.3dB, as the resonance frequency goes up, due to the increasing of electronic length, while the insertion loss remain low (2.5dB ~ 3.5 dB). Therefore, the proposed isolator may perform better in higher frequencies. The resonant frequencies of the serrated microstrip isolator can be tuned by changing the DC bias field and follow the Kittel’s equation [11]. S12 & S21(dB) 0 -5 -10 S12-0.8kOe S12-1.6kOe S12-2.4kOe S12-3.2kOe S12-4.0kOe -15 -20 2 Fig.5.15. 4 6 S21-0.8kOe S21-1.6kOe S21-2.4kOe S21-3.2kOe S21-4.0kOe 8 10 12 14 Freq (GHz) Measured s-parameter of serrated microstrip isolator 140 Return Loss(dB) S11 S22 0 -10 -20 -30 -40 2 Fig.5.16 4 6 8 10 12 14 Frequency (GHz) Return Loss of tunable serrated microstrip isolator with 4kOe magnetic Insertion & Isolation(dB) field bias. Fig.5.17 20 Meas. Insertion Meas. Isolation Sim. Insertion Sim. Isolation 16 12 8 4 0 2 4 6 8 10 12 Freq (GHz) 14 Insertion loss and isolation of the tunable serrated microstrip isolator over operating frequency. 141 5.4 Conclusion In summary, a novel serrated microstrip isolator has been presented. Microstrip lines with periodic serrated structure were shown to generate circularly polarized microwave magnetic field, allowing forward propagation LHCP, and strong ferromagnetic resonance absorption of the YIG slab at forward propagation. The non-reciprocal ferrite resonance absorption leads to over 19dB isolation and 3.5 insertion loss at 13.5GHz with 4kOe bias magnetic field applied perpendicular to the feed line. Furthermore, the tunable resonant frequency of 4 ~ 13.5GHz was obtained for the isolator with the tuning magnetic bias field 0.8kOe ~ 4kOe. The proposed serrated microstrip isolator prototype can have many applications in RF front and other microwave circuits. 5.5 Reference [1] D. M. Pozar, Microwave Engineering, Third edition, New York: J. Wiley & Sons, 2005 [2] J. J. Kostelnick, "Field displacement isolator," US Patent 3035235, 1962 [3] K. J. Button, "Theoretical Analysis of the Operation of the Field-Displacement Ferrite Isolator, " IEEE Trans. Microwave Theory & Tech., vol 6, pp. 303 -308, July 1958 [4] T. M. F. Elshafiey, J. T. Aberle, E. B. El-Sharawy, "Full wave analysis of edge-guided mode microstrip isolator," IEEE Trans. Microwave Theory & Tech., vol.44, no.12, pp.2661-2668, Dec 1996 142 [5] B. Bayard, D.Vincent, C. R. Simovski, and G. Noyel, ―Electromagnetic study of a ferrite coplanar isolator suitable for integration,‖ IEEE Trans. Microwave Theory & Tech., vol. 51, no. 7, pp. 1809–1814, Jul. 2003. [6] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stilzer, ―Ferrite devices and materials,‖ IEEE Trans. Microwave Theory & Tech., vol. 50, no. 3, pp. 721– 737, Mar. 2002. [7] C. P.Wen, ―Coplanar waveguide: A surface strip transmission line suitable for nonreciprocal gyromagnetic device applications,‖ IEEE Trans. Microw. Theory Tech., vol. MTT-17, no. 12, pp. 1087–1090, Dec. 1969. [8] Capraro, S.; Rouiller, T.; Le Berre, M.; Chatelon, J.-P.; Bayard, B.; Barbier, D.; Rousseau, J.J.; , "Feasibility of an Integrated Self Biased Coplanar Isolator With Barium Ferrite Films," IEEE Trans.Components and Packaging Technologies, vol.30, no.3, pp.411-415, Sept. 2007 [9] G. M. Yang, J. Lou, G. Y. Wen, Y. Q. Jin and N. X. Sun, "Magnetically Tunable Bandpass Filters with YIG-GGG/ YIG-GGG-YIG Sandwich Structures", International Microwave Symposium (IMS) 2011, Baltimore, MD. [10] Schlomann, E.; , "On the Theory of the Ferrite Resonance Isolator," IEEE Trans. Microwave Theory & Tech., vol.8, no.2, pp.199-206, March 1960 [11] C. Kittel, Introduction to Solid State Physics. New York: Wiley, 1996. 143 Chapter 6 Phase Shifters with Piezoelectric Transducer Controlled Metallic Perturber Phase shifters are essential microwave components that provide controllable phase shifts of microwave/RF signals. They are widely used for beam steering and beam forming for phased arrays, phase equalizers, and timing recovery circuits [1]. With thousands of phase shifters that are usually required for a phased-array antenna system, it is crucial to have phase shifters with small sizes, light weights and low costs. It is also important for phase shifter to have low loss, minimized power consumption and large power handling capability. In this chapter, we will present a novel distributed phase shifter design that is tunable, compact, wideband, low-loss and has high power handling. This phase shifter design consists of a meander microstrip line, a PET actuator, and a Cu film perturber, which has been designed, fabricated, and tested. This compact phase shifter with a meander line area of 18mm by 18mm has been demonstrated at S-band with a large phase shift of >360 o at 4 GHz with a maximum insertion loss of < 3 dB and a high power handling capability of >30dBm was demonstrated. In addition, an ultra-wideband low-loss and compact phase shifter that operates between 1GHz to 6GHz was successfully demonstrated. Such phase shifter has great potential for applications in phased arrays and radars systems. 144 6.1 Introduction of tunable phase shifter researches Phase shifters are used to change the transmission phase angle (phase of S21) of a network. Ideal phase shifters provide low insertion loss, and equal amplitude (or loss) in all phase states. While the loss of a phase shifter is often overcome using an amplifier stage, the less loss, the less power that is needed to overcome it. Most phase shifters are reciprocal networks, meaning that they work effectively on signals passing in either direction. Phase shifters can be controlled electrically, magnetically or mechanically. The applications of microwave phase shifters are numerous, perhaps the most important application is within a phased array antenna system (a.k.a. electrically steerable array, or ESA), in which the phase of a large number of radiating elements are controlled to force the electro-magnetic wave to add up at a particular angle to the array. The total phase variation of a phase shifter need only be 360 degrees to control an ESA of moderate bandwidth. Different techniques and approaches have been adopted for achieving phase shift in RF/microwave components, such as magnetic field tuned ferrite based phase shifters [2], ferroelectric varactors based phase shifters [3], p-i-n diodes [4], field-effect transistor (FET) switches [5], and RF micro-electro-mechanical systems (MEMS) switched line phase shifters [6]. Nevertheless, state of the art phase shifters listed above have their own limitations. Ferrite phase shifters have large power handling capability, but typically have limited bandwidth, large size, high power consumption and slow tuning. FET switches, p-i145 n diodes, and ferroelectric varactor based phase shifters typically have high insertion loss at W-band, and exhibit limited frequency range. RF MEMS phase shifters show good performance on bandwidth, insertion loss, size and power consumption [7-8]; however, they show limited power handling of < 1W (30dBm). These limitations prevent their applications in mission critical phased arrays, such as high power radars and electronic warfare. Chang et al. reported a new type of phase shifters with dielectric perturber controlled by piezoelectric transducers (PET) on a planar microstrip transmission line such has been reported [9]-[12], as shown in Fig. 6.1. With the introduction of the dielectric perturber that is closely placed above a microstrip transmission line, the characteristic impedance of the line is only slightly altered, while its effective dielectric constant can be changed significantly, which leads to phase shift. However, such phase shifters still have problems, such as limited phase shift, large size, and high insertion loss when the dielectric perturber is closely placed on the microstrip for achieving large phase shifter. For example, a phase shifter with the size of about 30 mm can only produce a controlled phase shift of less than 80°in S-band [9], which is far away from the typical requirement for a 360°phase shift. Most recently, we have reported a similar phase shifter design with PET controlled magneto-dielectric perturber,[2], as shown in Fig. 6.2, which leads to significantly enhanced phase change (> 2×) compared to PET controlled dielectric perturber approach due to the increased miniaturization factor, related to the high permeability of the magneto-dielectric 146 disturber. At the same time, the increased permeability of the magneto-dielectric disturber lead to better wave impedance match to the free space and therefore, much lower reflection due to the loading of the perturber and less insertion loss [2]. This leads to high phase shift per dB loss of >500/dB insertion loss. However, this approach has its own limited bandwidth of less than 3 GHz due to the increased loss tangent of the self-biased magnetodielectric perturber, and it still could not meet the need for ultra-wide band phased arrays, such as electronic warfare. Fig. 6.1 Phase shifter design with PET controlled dielectric perturber by Chang et al.[9] 147 Fig. 6.2 Phase shifter design with PET controlled magneto-dielectric perturber by Yang et al. [2] 6.2 Device construction 6.2.1Device Construction Similar to the previous PET phase shifter using dielectric perturber, the structure of the designed phase shifter is shown in Fig.6.3. The PET used in the design is a commercially available piezoelectric bending actuator (PI PICMA® PL140.10) which features a multilayer structure that reduces the voltage that needed for large deflection. The dimension of the PET is about 45 mm in length and 11 mm in width, and can be deflected up and down for a total range of 2 mm with a control voltage ranging from zero to 60V. 148 Fig. 6.3. Schematic and photograph of the meander line phase shifter with PET controlled metallic perturber. The meander line was designed to possess a characteristic impedance of 50 Ω, which has a conductor width of 0.356 mm. With each of the segments of the meander line being 10.8 mm and each of the corners being 0.71 mm, the total length of the meander line is about 4.5 inches within an area of 12.812.8 mm, as shown in Fig.6.4. Also shown in Fig. 4 is the dimension and position of the metallic perturber, which is a 12.8 mm 12.8 mm copper square that covers majority part of the meander line. Without the metallic perturber, the meander line structure is essentially a transmission line with a working frequency range of 0~4 GHz. The maximum insertion loss of the meander line is less than 1 dB at < 4 GHz. 149 Fig. 6.4. Design dimensions for the meander line phase shifter, the grayed area shows the size and position of the metallic perturber. For broadband true-time delay phase shifters (e.g. 1 ~ 6GHz), there is an important design trade-off between the highest and lowest operating frequencies. That is, the size of the phase shifter should be smaller than half wavelength at the highest frequency, e.g. 25 mm at 6GHz; and a large enough phase shifts should be achieved at the lowest frequency, say 90o. Clearly, we need to make the phase shifter small enough to fit size requirement, while achieve a moderate phase shift at lower frequencies at the same time. A substrate with relatively high K was used for the meander line design. Rogers TMM 10i has a 150 nominal dielectric constant of 9.8 and a thickness of 0.38 mm was chosen to accomplish both longer length of the meander line and higher power handling requirement. 6.2.2 Piezoelectric transducer (PET) - PI PICMA® PL140.10 PICMA®-series multilayer bender piezo actuators as shown in Fig 6.5, provide a deflection of up to 2 mm, forces up to 2 N (200 grams) and response times in the millisecond range. These multilayer piezoelectric components are manufactured from ceramic layers of only about 50 µm thickness. They feature internal silver-palladium electrodes and ceramic insulation applied in a cofiring process. The benders have two outer active areas and one central electrode network dividing the actuator in two segments of equal capacitance, similar to a classical parallel bimorph. The maximum travelling distance of the PET is 2 mm for 60V applied DC voltage. If we placed the meander line under PET with a gap separation – gap dimension with applied voltage using , we can approximate the (according to PL140 data sheet, Piezo University), where V is the voltage applied on the PET. For example, in our experiment, we have measured the original gap , then for 50V DC voltage, the gap is 0.13mm. The tuning of traveling distance is linear proportional as the applied voltage, as shown in Fig. 6.6. 151 Fig. 6.5. Schematic and the equivalent circuit of piezoelectric transducer (PET) - PI PICMA® PL140.10 152 gap separation (mm) 2.0 1.6 1.2 0.8 0.4 0.0 0 10 20 30 40 Applied DC voltage (V) 50 Fig. 6.6. Approximated gap dimension with applied voltage (0~50V). The original gap is 2 mm. 6.3 Theoretical analysis 6.3.1 Equivalent Circuit Model for Meander Line with variable copper perturber Microstrip meander line structure is widely used in phase shifter designs due to their broadband, low insertion loss, and ease of manufacturing. The characteristics impedance Z and phase velocity of a typical microstrip transmission line vph can be expresses as √ (6.1) √ where L and C indicates the equivalent capacitance and inductance. 153 (6.2) As a distributed transmission line, meander lines with piezoelectric bending actuator can be also modeled as an L-C circuit, as shown in Fig. 6.7. The variable distance from the copper perturber to the meander line leads to an equivalent variable capacitor. Therefore, the variable phase constant βvar caused by the perturbation can be calculated as: √ (6.3) The variable capacitance Cvar can be tuned electrically by applying variable voltage on the piezoelectric bending actuator. Hence, the phase shift can be estimated as: l 360o f L ( C Cmax C Cmin ) (6.4) where Cmax and Cmin denotes the capacitance variance. Fig. 6.7 Equivalent circuit of meander line with piezoelectric bending actuator 6.3.2The insertion Loss Analysis For microstrip meander lines, most losses are contributed by dielectric and conductor losses, given that the radiation loss is small. The dielectric loss d in dB/cm [13] caused by the finite conductivity of the dielectric layers is given by 154 d 8.686 * ( tan eff 1 r 1 )* , d r eff (6.5) where the substrate loss tangent tanδ=0.002; εr =9.8 denotes the dielectric constant of the substrate; εeff denotes the effective dielectric constant for the microstrip transmission line; λd denotes the wavelength in the substrate. The conductor loss c [14-16] can be obtained from c 8.686 RS Z cW (dB/cm) , Rs 2 (6.6) Where RS denotes the surface impedance; W denotes the width of the strip line; ζ denotes the conductivity; Zc denotes the characteristic impedance; w denotes the angular operating frequency. With a piezoelectric bending actuator, a variable capacitance leads to variable characteristics impedance. The return loss due to perturber perturber in dB/cm will increase due to the impedance mismatch to a standard 50 Ω port, which can be described as perturber 20 *log( 155 C Cmax C C Cmin C ) (6.7) The final form of the loss calculation is a function of loss metal thickness, strip width and conductivity, frequency and distance to the perturber. The insertion loss in unit of decibels for a perturbed length of the phase shifter is given by Insertion Loss = ( c + d + perturber ) * Δl (6.8) 6.4 Simulation Results Simulations of the device were carried out by HFSS before the meander line S-band transmission line was fabricated. To match the travelling distance of the PET of 2 mm, the maximum and minimum distances between the metallic perturber and the substrate were set to be 1.80 mm and 0.13 mm respectively. 156 Fig. 6.8. Simulated S21 of the meander line with different distances between the metallic perturber and the substrate. Fig. 6.9. Simulated S11 of the meander line with different distances between the metallic perturber and the substrate. Figure 6.8 shows the transmission coefficient (S21) of the meander line phase shifter with different distances between the metallic perturber and the substrate. Clearly when the metallic perturber is far away from the substrate (1.8 mm), the insertion loss of the phase shifter stays at a relatively low level of < 1 dB throughout the entire S-band. However, when the metallic perturber approaches the substrate, the insertion loss starts to increase due to the impedance mismatch introduced by the metallic perturber. Nevertheless, the 157 maximum insertion loss of the phase shifter is less than 2 dB at a 0.13 mm spacing between the metallic perturber and the meander line. Figure 6.9 shows the reflection coefficient (S11) of the phase shifter with different metallic perturber distances. As one may expect, when the distance between the perturber and the substrate is 1.8 mm, the return loss –is greater than 20 dB; while with the perturber getting closer to the substrate, the return loss eventually reaches a minimal level of about 8 dB for a 0.13 mm distance. The S11 and S21 spectra show clear ripples associated with the meander line structure, as shown in Figs. 4 and 5. The amplitude of the ripples increases with the approaching of the metallic perturber to the substrate, and their positions as well as their separations also vary. This is attributed to the change of the capacitance per unit length C of the transmission line due to the metallic perturber. This increased C leads to changes of the characteristic impedance of the meander line transmission line expressed by Z0 L / C , where L is the inductance per length of the meander transmission line, and therefore decreased return loss and increased insertion loss as shown in Figs. 4 and 5. At the same time, the increased C also decreases the phase velocity of the meander line, Vphase 1/ LC . As a result of such changes of the phase velocity of the microstrip line, the relative phase shift changes dramatically as a function of the distance between the metallic perturber and the substrate, as shown in Fig. 6.10. 158 Fig. 6.10 Simulated relative phase shift of the phase shifter with different distances between the metallic perturber and the substrate From Fig. 6.10, it is very clear that the phase shift of the meander line can be readily tuned by varying the distance between metallic perturber and the substrate, although it’s not a linear function of the distance. For example, the phase shift is only 28 o when the disturber-meander line gap is 1.12 mm at 4 GHz, and is 54o when the distance is 0.80 mm. However, the phase shift reaches a value of 266 o and 352 o at a gap of 0.20 mm and 0.13 mm, respectively. 159 Fig. 6.11. Measured S21 of the meander line with different voltage applied on the PET. 6.5 Measurement Results The meander line was fabricated by PCB fabrication technique and the phase shifter was assembled as schematically shown in Fig. 1. Measurement of the meander line phase shifter was done on an Agilent PNA series vector network analyzer. With a control voltage applied on the PET changing from zero to 50 V, the distance between the metallic perturber and the substrate can be tuned. It should be mentioned that due to the difficulty of accurately measuring the distance between the perturber and the meander line, the applied voltage should only be used for reference purpose to compare to the actual distance. 160 However, after careful calibration, these two values should be able to be preciously linked to each other. Figure 6.11 shows the transmission coefficient of the meander line phase shifter with different voltage applied on the PET. When the voltage is zero volts, which corresponds to the largest distance between the metallic perturber and the meander line, the insertion loss shows very flat response with the maximum loss being 1 dB, which matches well with simulated data shown in Fig. 6.9. With the increase of the voltage applied on the PET, the distance between the metallic perturber and the substrate was reduced, which led to degraded insertion loss. Fig. 6.12. Measured S11 of the meander line with different voltage applied on the PET. 161 Since the performance of the phase shifter is very sensitive to the distance between the perturber and the meander line, and waviness of the perturber surface may introduce additional loss in the device. As we can see from Fig. 6.12, compared to simulated results, the insertion loss of the device is slightly larger at higher voltage. Nevertheless, the overall insertion loss is still less than 2 dB over the entire S-Band. Similar to the simulated results, the measured reflection coefficient has the same trend, as shown in Fig. 12. For a control voltage of zero volt, the return loss stays at very low level of ~25 dB. For higher voltages however, a maximum return loss of 7 dB is observed for 50 V of control voltage, which is in close match with the simulated data. The maximum travelling distance of the PET is 2 mm for 60V applied DC voltage. Starting from a 1.8 mm gap with 0V, the PET bended down and the gap between the perturber and the meander can be approximated as (1.8 – 2*V/60) mm (PL140 Data sheet, Piezo University), where V is the applied voltage on the PET. For 50V DC voltage, the gap is 0.13mm, where the measured relative phase shift has a maximum phase shift of 362 o at 4 GHz as shown in Fig. 13. HFSS simulation showed 352o phase shift, indicating a decent match between measurement and simulation results. Also, compared to the published phase shifter based on dielectric perturber, this accounts for one order of magnitude enhancement [5]. Furthermore, it can be found that the relative phase shift is very sensitivity to the voltage change at higher control voltages as well. The phase shift from 40 to 50 volts contributes to almost 70% of the total phase shift range. This agrees well with the simulated results that the phase shift is particularly sensitive to the distance between the perturber and the substrate when the distance is small. This phenomenon leads to the conclusion that it is possible to use a much smaller tunable distance between the metallic 162 disturber and the meander line, which means that large phase shift can be achieved with a shorter PET and/or at a smaller voltage span in order to gain majority of the phase shift capability. As an alternative, one can start with a smaller distance between the perturber and the substrate as an initial reference state, and a much lower control voltage of 20V can lead to a phase shift of 300o. This will dramatically reduce the need for high control voltage and is needed to reduce the power consumption of the device. Compared to other phase shifter designs, this phase shifter design showed significantly enhanced phase shift and lower loss [9]. Unlike most semiconductor based planar phase shifters that can only handle very limited microwave input power of <30dBm [1-4], our phase shifter design with a PET controlled metallic disturber on meander line has the potential to handle a much larger range of input power since the phase shifter has just copper and dielectric substrates. As a result, power handling of such phase shifters will mainly be limited by Joule heating at large RF/microwave power level. We 163 Fig. 6.13. Measured and simulated relative phase shift of the meander line phase shifter with different voltage applied on the PET. The symbols indicate simulated results from HFSS. 164 Fig. 6.14. Measured insertion loss of the meander line phase shifter with different input power at 3 GHz. measured the insertion loss of our phase shifter at 3 GHz under different microwave input powers at 3GHz, with both zero and 50 V applied to the PET, as shown in Fig. 10. Clearly, the insertion losses of both cases stay nearly straight at different microwave input power level, with only negligible increase in the insertion loss at a control voltage of 50V and at 30 dBm. Maximum power level was only tested to up to 30dBm due to the limited power output level in our labs, while simple extrapolation of the two curves in Fig. 6.14 indicate that the phase shifter shows much higher power handling capability than 30dBm. The high microwave power handling capability of the meander line phase shifter is critical for high power phased array radars. 6.6. Extended design for 1-6GHz Some applications, such as satellite communication and radar system, require controllable phase shifts in wider band, 1GHz to 6GHz etc, which covers L band, S band, and part of C band. Hence, it is also important for phase shifters to have a wide working bandwidth and the properties of low profile, low loss, minimized power consumption and large power handling capability. Fig. 6.15 shows an extended meander line phase shifter working from 1GHz to 6GHz. The meander line was designed to have the conductor width of 14 mils. With each of the segments of the meander line being 5.58 mm and each of the corners being 0.508 mm, the total length of the meander line is about 223 mm within an 165 area of 18 18 mm. The same metallic perturber has been use to tune the capacitance through different heights. Fig. 6. 15. Design dimensions for the extended meander line phase shifter. It should be mentioned that the performance of the phase shifter is very sensitive to the distance between the perturber and the meander line. Besides, the bending actuator brings an inclined copper surface, which leads to additional insertion loss and non-linearity of phase shifts. These are more critical at closer distance. Therefore, in the extended meander line approach, the perturber was placed at the closest distance, and completely parallel to the meander line, when the voltage is 0 volts. Then, it would be bent up when higher voltages were applied. With the metallic perturber far away from the substrate, the phase shift due to the metallic surface will be neglected. So, we set the 25V applied voltage as the reference point for relative phase shift measurement. 166 Fig. 6.16. Measured relative phase shift of the extended meander line phase shifter with different voltage applied on the PET Table 6.1 Measured relative phase shift of the extended meander line phase shifter at 6GHz with different voltage applied on the PET Applied Phase IL RL Voltage (v) shifts (o) (dB) (dB) 0 806 3.8 11.6 3.5 520 2.9 19.4 8.0 343 2.8 21.2 12 192 2.5 24.0 15 100 2.9 27.3 167 25 0 3.0 31.9 Fig.6.16 shows the phase shifts of the meander line phase shifter with different voltage applied on the PET. It is very clear that the phase shift of the meander line can be readily tuned by varying the distance between metallic perturber and the substrate through variable voltage applied. The measured relative phase shift showed a maximum phase shift of 367 o at the center frequency 3.5 GHz with a control voltage of 0 V on the PET, 88 o at 1GHz and 807 o at 6GHz. With the increase of the voltage applied on the PET, the distance between the metallic perturber and the substrate was increased. Then, the reduced capacitance leads to smaller phase shifts. For example, if we set 6GHz as working frequency, we get the following phase shifts as Table 6.1. Fig. 6.17 show the transmission coefficient (S21) of the meander line phase shifter with different voltage applied on the metallic perturber. Clearly, with the higher voltage (25V), where the metallic perturber was far away from the substrate, the insertion loss of the phase shifter stays at a relatively low level of < 2 dB throughout the entire band of 16GHz. However, when the applied voltage was reduced, the metallic perturber approaches the substrate. The insertion loss starts to degrade to 3.8dB at 6GHz, which is the maximum insertion loss throughout the entire band. However, it should be mentioned that 360 o phase shift is sufficient for most applications. In our design, the phase shift exceeded the 360 o phase shift requirement in the frequency band of 3.5 - 6GHz, with the majority of bad insertion loss cases. A customized voltage set can be used to achieve the required phase shift while maintaining relatively low insertion loss. For example, at 6GHz, the tuning range of 8V to 25V can achieve 360 o phase shift, with the maximum insertion loss 2.85dB; 168 at 5GHz, the tuning range of 3.5V to 25V can achieve 360 o phase shift, with the maximum insertion loss 3.53dB. Fig. 6.18 shows the return loss (S11) of the meander line phase shifter with different voltage applied on the metallic perturber. A high S11 (6.5dB) was observed when the voltage is 0V, and the perturber was very close to the meander line. Once the voltage was increase, and the metallic perturber was far enough and had less impact on the meander line, S11 went beyond 10dB. Compared to the original design (working at 2-4GHz), the extended meander line shifter has a small insertion loss increase. Loss was then analyzed by applying equations (4) and (5). The estimated α of the meander line at 6GHz is 0.1035 dB/cm for conductivity loss and 0.0262dB/cm for dielectric loss. The total effective length of the meander line is 22.2976 cm. Therefore, the total loss can be estimated as 2.3dB for conductivity loss, 0.58dB for dielectric loss, 0.8dB for metallic perturber according to the measurement results in Table I, and the rest 0.12dB for impedance mismatching of original perfect conductor meander line. Apparently, the majority of the loss comes from finite conductivity of copper transmission line, which is also the bottleneck of meander-line phase shifter. However, it achieved much wider bandwidth (1-6GHz), which is very important for some application desired of wide operation frequency band. 169 Fig. 6.17. Measured S12 of the extended meander line with different voltage applied on the PET. Fig.6. 18. Measured S11 of the extended meander line with different voltage applied on the PET. 170 6.7. Comparison with previous approaches Table 6.2 Performance comparison of phase shifters with different device techniques. Reference Device Tech. Fre Compare Total IL Degree Size or DC power qG Freq. Phase (dB) /dB Area consumptio Hz (GHz) shifts loss (mm) n or DC voltage [4] SiGe 7~11 10 320 11 29 3.83.8 45mW Pin diodes [17] FET switches 4~8 6 360 5.7 63 1.720.81 0mW [18] RF MEMS 7~11 9.45 270 1.4 192 40 mm2 N/A [19] Ferroelectric 0~7 7 170 2.3 74 46 25V 1~5 5 40 0.5 80 2010 50V 1~6 6 75 1 75 70.432 40V 1~6 6 806 3.8 212 12.812.8 50V varactors [2] PET Magnetodielectric perturber [20] PET dielectric perturber Our work PET metallic 171 perturber Table 6.2 shows the performance comparison of the fabricated phase shifter in this work with the other reported phase shifters. The measured degree/dB low insertion loss of 212 are found to be better than those of the previously phase shifters. Also, the device size is the smallest among PET phase shifters, although larger than others. 6.8 Conclusions A novel type of phase shifter was proposed and demonstrated utilizing a piezoelectric transducer (PET) controlled metallic transducer on meander transmission line. Compared to phase shifters with PET controlled dielectric or magnetodielectric perturber, the phase shifter with PET controlled metallic perturber exhibited significantly enhanced phase shift (>10x) and bandwidth, reduced size and insertion loss. A compact SBand meander line phase shifter with metallic perturber controlled by a PET has been designed, fabricated and tested. The total dimension of the meander line is only 18 by 18 mm square. Compared to dielectric perturber that only exhibits very limited phase shift at S-Band, our design reached a phase shift of 360o with a low controlling voltage of 25 V at 3.5 GHz, along with a wide operating bandwidth from 1 GHz to 6GHz. In addition, there is no fundamental limit of the frequency range for such a phase shifter, as the frequency limit is mainly from the design of the meander line. While the meander line can be easily designed for frequencies of S-band was demonstrated in this work, similar phase shifter designs can be made for X-band, K-band, W-band and beyond from our simulations, and even extremely wideband phase shifter can be achieved with a straight transmission line 172 and a PET controlled metallic disturber. High power handling of 30dBm has been experimentally demonstrated in a compact S-band phase shifter, with an expected power handling limit of >50dBm. With the combined low insertion loss, large phase change, compacted size, high microwave power handling capability, and the extend abilities to other frequency bands, the new meander line phase shifter with PET controlled metallic perturber show great potential for different phased array systems. 6.9 References [1] B. York, A. Nagra, and J. Speck, ―Thin-film ferroelectrics: Deposition methods and applications,‖ in IEEE MTT-S Int. Microw. Symp., Boston, MA, Jun. 2000. [2] G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, ―Novel Compact and Low-Loss Phase Shifters with Magnetodielectric Disturber,‖ IEEE Microw. Wireless Compon. Lett, vol. 21, no. 5, May 2011 [3] J. B. L. Rao, D. P. Patel, and V. Krichevsky, ―Voltage-controlled ferroelectric lens phased arrays,‖ IEEE Trans. Antennas Propagat., vol. 47, pp. 458–468, Mar. 1999. [4] M. Teshiba, R. V.Leeuwen, G. Sakamoto, and T. Cisco, "A SiGe MMIC 6-Bit PIN Diode Phase Shifter" , IEEE Microw. wireless Comp. Lett., VOL. 12, NO. 12 Dec.2002 [5] A. S. Nagra, and R. A. York, ―Distributed analog phase shifters with low insertion loss,‖ IEEE Trans. Microw. Theory Tech., Vol. 47, pp. 1705-1711, Sep. 1999. [6] B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, C. Goldsmith, ―Ka-band RF MEMS phase shifters,‖ IEEE Microw. Guided wave Lett., vol 9, pp. 520-522, Dec. 1999. [7] N. S. Barker, G. M. Rebeiz, "Optimization of Distributed MEMS Transmission-Line Phase Shifters—U-Band and W-Band Designs", IEEE Trans. Microw. Theory Tech., 173 Vol. 48, NO. 11, Nov. 2000 [8] G.M. Rebeiz, G.L. Tan, J.S. Hayden, "RF MEMS Phase Shifters: Design and Application", Microwave Magazine, June 2002 [9] T. Y. Yun and K. Chang, ―Analysis and optimization of a phase shifter controlled by a piezoelectric transducer,‖ IEEE Trans. Microw. Theory Tech., Vol. 50, pp. 105-111, Jan. 2002. [10] T. Y. Yun and K. Chang, ―A low-cost 8 to 26.5 GHz phased array antenna using a piezoelectric transducer controlled phase shifter,‖ IEEE Trans. Antennas Propag., vol. 49, pp. 1290-1298, Sept. 2001. [11] T. Y. Yun and K. Chang, ―A low-loss time-delay phase shiter controlled by piezoelectric transducer to perturb microstrip line,‖ IEEE Microw. Guided wave Lett., vol 10, pp. 96-98, Mar. 2000. [12] J. M. Pond, S. W. Kirchoefer, H. S. Newman, W. J. Kim, W. Chang, and J. S. Horwitz, ―Ferroelectric thin films on ferrites for tunable microwave device applications,‖ Proceedings of the 2000 12th IEEE International Symposium on Applications of Ferroelectrics, 2000. [13] Jia-Sheng Hong, M. J. Lancaster, ―Microstrip filters for RF/Microwave Applications‖ Page 83. formula 4.18,4.19 [14] Brian C Wadell, ―Transmission Line Design Handbook‖ , Artech House 1991 [15] Harold A. Wheeler, Transmission-line properties of a strip on a dielectric sheet on a plane", IEEE Tran. Microwave Theory Tech., vol. MTT-25, pp. 631-647, Aug. 1977 [16] M. V. Schneider, "Microstrip lines for microwave integrated circuits," Bell Syst Tech. J., vol. 48, pp. 1422-1444, 1969. 174 [17] J.G. Yang; K. Yang, "Ka-Band 5-Bit MMIC Phase Shifter Using InGaAs PIN Switching Diodes," IEEE Microw. Wireless Compon. Lett, vol.21, no.3, pp.151-153, March 2011 [18] M. Hangai,M. Hieda, N. Yunoue,Y. Sasaki and M. Miyazaki, "S- and C-Band UltraCompact Phase Shifters Based on All-Pass Networks", IEEE Trans. Microw. Theory Tech., vol. 58, No. 1, pp. 44-47, Jan. 2010 [19] A. Malczewski, S. Eshelman, B. Pillans, J. Ehmke, and C. L. Goldsmith, "X-Band RF MEMS Phase Shifters for Phased Array Applications" IEEE Microw. Guided wave Lett., vol. 9, No. 12, pp. 517-519, Dec 1999 [20] S. Sheng, P. Wang, X. Chen, X.Y. Zhang, and C. K. Ong ―Two paralleled Ba0.25Sr0.75TiO3 ferroelectric varactors series connected coplanar waveguide microwave phase shifter‖, J. Appl. Phys. 105, 114509 , 2009 [21] S. G. Kim, T. Y. Yun, and K. Chang, "Time-Delay Phase Shifter Controlled by Piezoelectric Transducer on Coplanar Waveguide," IEEE Microw. Wireless Compon. Lett, vol.13, No. 1, pp. 19, Jan 2003 [22] C. Kim and K. Chang, ―A reflection-type phase shifter controlled by a piezoelectric transducer‖ Microwave and Optical Technology Letters, vol. 53, No. 4, pp. 938-940, April 2011 175 Chapter 7 Conclusion In this dissertation, I combine the ferrite thin films and planar microwave structure to realize tunable and non-reciprocal devices, including bandpass filters, isolators and phase shifters. A novel type of tunable isolator was presented, which was based on a polycrystalline yttrium iron garnet (YIG) slab loaded on a planar periodic serrated microstrip transmission line that generated circular rotating magnetic field. The non-reciprocal direction of circular polarization inside the YIG slab leads to over 19dB isolation and < 3.5dB insertion loss at 13.5GHz with 4kOe bias magnetic field applied perpendicular to the feed line. Furthermore, the tunable resonant frequency of 4 ~ 13.5GHz was obtained for the isolator with the tuning magnetic bias field 0.8kOe ~ 4kOe. The non-reciprocal propagation behavior of magnetostatic surface wave in microwave ferrites such as YIG also provides the possibility of realizing such a nonreciprocal device. A new type of non-reciprocal C-band magnetic tunable bandpass filter with ultra-wideband isolation is presented. The BPF was designed with a 45 o rotated YIG slab loaded on an inverted-L shaped microstrip transducer pair. This filter shows an insertion loss of 1.6~2.3dB and an ultra-wideband isolation of more than 20dB, which was attributed to the magnetostatic surface wave. The demonstrated prototype with dual functionality of a tunable bandpass filter and an ultra-wideband isolator lead to compact and low-cost reconfigurable RF communication systems with significantly enhanced isolation between the transmitter and receiver. 176

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