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UBC Theses and Dissertations

Design of efficient wireless power-transfer system and piezoelectric transducer for sonoporation-based… Ram Rakhyani, Anil 2010

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DESIGN OF EFFICIENT WIRELESS POWER-TRANSFER SYSTEM AND PIEZOELECTRIC TRANSDUCER FOR SONOPORATION-BASED DRUG-DELIVERY IMPLANTS by Anil Kumar Ram Rakhyani B.Tech., Indian Institute of Technology, Kanpur, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Electrical and Computer Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2010 c
 Anil Kumar RamRakhyani, 2010 Abstract Implantable devices are becoming popular in health and medical applications. In par- ticular, localized and controlled drug release systems have gained clinical relevance in the treatment of many diseases. The power requirement for sonoporation-based systems is com- paratively higher than that of other implantable devices. Ecient wireless power delivery and ecient small ultrasound transducer with low aspect ratio (G = length/thickness) is required to obtain high power transfer eciency for implantable sonoporation based system. To provide power wirelessly to implantable device, resonance-based wireless power de- livery system is considered. This system is modeled and optimized for given design con- straints. The prototype 4-coil system achieves at least 2  more eciency as compared to prior art inductive links operating with comparable size and operating range. With implanted coil of diameter 22 mm and at operating distance of 20 mm, power transfer eciency of 82% is achieved. The focus of the work is on power delivery in implantable devices. However, the method is general and can be applied to other applications that use wireless power transfer. Sono-Dynamic Therapy (SDT) uses ultrasonic cavitation to enhance the cytotoxicity of chemotherapeutic drugs. SDT requires ultrasound transducer to generate cavities. For implantable application, high electro-mechanical conversion eciency of transducer is re- quired to achieve high system eciency and low heat losses in tissues. In the present work, identication of key parameters for transducer selection for implantable sonotherapy ii Abstract systems are given. Eects of ultrasound transducer's aspect ratio reduction is analyzed and reduction in electro-acoustic conversion eciency is explained using mode coupling between resonance modes of transducer. Energy harvesting and driver circuit is presented to convert wirelessly received power to drive transducer to generate acoustic waves. This work demonstrates the rst prototype of a wirelessly powered sonoporation-based implantable system. Though only two blocks of the prototype are optimized, overall system eciency is measured as 2.04 % which is close to the theoretical value of 2.24 % of present design. By using an ecient power amplier (class-E amplier, eciency 80%), an overall system eciency of 22% can be achieved. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Wireless Power Delivery System . . . . . . . . . . . . . . . . . . . 2 1.2.2 Ultrasound Transducer/Stimulator . . . . . . . . . . . . . . . . . . 3 1.2.3 Energy Harvesting and Driving Circuit . . . . . . . . . . . . . . . . 4 1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Contributions of The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 6 iv Table of Contents 1.6 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Design and Optimization of Wireless Power Delivery System for Im- plantable Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Power Eciency in Resonance-Based Systems . . . . . . . . . . . . . . . . 11 2.2.1 Inductor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Parasitic Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.3 AC Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.4 Coil Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.5 Power Transfer Model . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.6 Analysis of 4-Coil Power-Transfer System . . . . . . . . . . . . . . 20 2.2.7 Design of High-Q Coils . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.8 Eect of Operating Frequency Variation . . . . . . . . . . . . . . . 31 2.2.9 Series versus Parallel Connection of Load Resistance . . . . . . . . 32 2.3 Design Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.1 Design Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 Initial Values and Range of Parameters . . . . . . . . . . . . . . . 35 2.3.3 Optimizing Design Parameters . . . . . . . . . . . . . . . . . . . . 39 2.4 Resonance-Based Power Transfer . . . . . . . . . . . . . . . . . . . . . . . 41 2.5 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.6 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.7 Comparison with Previous Work . . . . . . . . . . . . . . . . . . . . . . . 48 2.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3 Development of PZT based Sonotherapy System for Implantable Devices 50 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 v Table of Contents 3.2 Fabrication Technology and Mode of Operation . . . . . . . . . . . . . . . 51 3.2.1 Fabrication Technology . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2.2 Theory of Operation and Resonance Mode . . . . . . . . . . . . . . 52 3.2.3 Selected Parameters of PZT Material . . . . . . . . . . . . . . . . 53 3.3 Acoustic Wave Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Transmission Cocient and Matching Layers . . . . . . . . . . . . 56 3.4 Electrical Model of PZT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Acoustic Power and Eciency . . . . . . . . . . . . . . . . . . . . . . . . 62 3.6 Sample Preparation and Characterization . . . . . . . . . . . . . . . . . . 63 3.6.1 Selection of Acoustic Layers . . . . . . . . . . . . . . . . . . . . . . 64 3.6.2 Characterization of PZT . . . . . . . . . . . . . . . . . . . . . . . . 67 3.7 Aspect Ratio Reduction of PZT . . . . . . . . . . . . . . . . . . . . . . . 69 3.7.1 Eect on Electromechanical Coupling Factor . . . . . . . . . . . . 69 3.7.2 Eect on Input Impedance . . . . . . . . . . . . . . . . . . . . . . 70 3.7.3 Eects of Electrode Contact . . . . . . . . . . . . . . . . . . . . . . 70 3.8 Experiment and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.8.1 Instrument Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.8.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4 Development of Energy Harvesting and Driver Circuits for PZT . . . 80 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1 Rectier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.2 DC-DC Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.3 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 vi Table of Contents 4.2.4 Buer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2.5 Power Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3 Experiment Setup and Results . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.1 Characterization of Power Amplier . . . . . . . . . . . . . . . . . 85 4.3.2 Characterization of Oscillator and Buer . . . . . . . . . . . . . . 87 4.3.3 Characterization of DC-DC Converter . . . . . . . . . . . . . . . . 88 4.3.4 System Eciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5 Summary of Thesis and Future Research Topics . . . . . . . . . . . . . . 93 5.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2 Limitations and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.2.1 External Power Source for Constant Power Delivery . . . . . . . . 95 5.2.2 Current Limitation in Coil . . . . . . . . . . . . . . . . . . . . . . 95 5.2.3 Optimization of Transducer Size . . . . . . . . . . . . . . . . . . . 96 5.2.4 Low Power Circuit Design . . . . . . . . . . . . . . . . . . . . . . . 96 5.2.5 Implant Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Appendices A Eciency Maximization Distance in Eq.(2.31) . . . . . . . . . . . . . . . 105 B Optimization of Number of Turns Per Layer (Eq. 2.29) . . . . . . . . . 107 C Guidelines for High Q-factor Coil Preparation . . . . . . . . . . . . . . . 109 vii Table of Contents D Ultrasound Transducer Sample . . . . . . . . . . . . . . . . . . . . . . . . 111 E Acoustic Wave Transmission in Medium . . . . . . . . . . . . . . . . . . . 113 F Colpitts Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 G System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 H Driver Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 I Ultrasound Power Meter Setup . . . . . . . . . . . . . . . . . . . . . . . . 121 J DC-DC Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 viii List of Tables 2.1 Design constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Litz wire property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Coils physical specication . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Coils electrical specication . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5 Coils electrical specication (measured) . . . . . . . . . . . . . . . . . . . . 43 2.6 Comparsion with previous work . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1 Main parameters for selected material . . . . . . . . . . . . . . . . . . . . . 73 3.2 Acoustic property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.3 Samples mechanical parameters . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1 Design parameters of rectier . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.3 Buer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Power amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.5 PZT impedance at 4.4 MHz (PZT: sample3) . . . . . . . . . . . . . . . . . 88 ix List of Figures 1.1 System architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1  vs coil aspect ratio (b/t) . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Coil lumped model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 (a) Simplied schematic of the 4-coil system (b) electrical model of the power transfer circuit (for design example) . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Eciency versus Q factor (k12 = 0.58, k34 = 0.60, Q1 = 5, Q3 =100, Q4 = 0.15, k23 = 148.2  1 d2+320 1:2 (Equation 2.45) . . . . . . . . . . . . . . . . . 20 2.5 Sensitivity of eciency on Q1 ,Q4 (k12 = 0.58, k34 = 0.60, k23 = 0.05, Q2 =368, Q3 = 108) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 Q2:Q3 variation with number of strands . . . . . . . . . . . . . . . . . . . . 25 2.7 Optimum frequency of operation . . . . . . . . . . . . . . . . . . . . . . . 25 2.8 Optimum number of turns (Na = 12;DoutT = 60 mm, h = OD/2, f = 700 kHz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.9 Eect of Q factor(Q1) on maximum eciency distance (Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = coupling model Equation 2.45) 28 2.10 2 and 4 coil system eciency with respect to R1. For 2 coil (frequency = 700 kHz, Lp = 1.1 mH, Qs = 1.6,k = 0.055, RL = 100 ). For 4 coil (frequency = 700 kHz, L1 = 29.35 H;Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = 0.055, RL = 100  ) . . . . . . . . . . . . . . . . 29 x List of Figures 2.11 Sensivity of Q with frequency (DoutT = 60 mm, Nt = 11, h = OD/2) . . . 31 2.12 Eect of operating frequency variation on power-transfer eciency . . . . . 33 2.13 Series vs parallel connection of load resistance . . . . . . . . . . . . . . . . 34 2.14 Q2 vs number of layers, operating frequency . . . . . . . . . . . . . . . . . 38 2.15 Q3 vs number of layers, operating frequency . . . . . . . . . . . . . . . . . 39 2.16 Q4 vs number of layers, operating frequency . . . . . . . . . . . . . . . . . 39 2.17 Flow chart for coil dimension optimization . . . . . . . . . . . . . . . . . . 40 2.18 Mutual coupling (k23) versus distance . . . . . . . . . . . . . . . . . . . . . 42 2.19 Power transfer system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.20 Coil dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.21 Power transfer eciency (experiment, SPICE simulation, eciency Equa- tion 2.21, traditional two-coil model) . . . . . . . . . . . . . . . . . . . . . 46 2.22 Output voltage (simulation and measurement results) . . . . . . . . . . . . 46 2.23 Eciency with varied source resistance for 2 and 4 coils based system (mea- surement results) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1 Resonance modes in thin disk PZT transducer . . . . . . . . . . . . . . . . 53 3.2 Mason's electric model of PZT . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3 Simplied Mason's model for backing layer of acoustic impedance Zb . . . 59 3.4 Equivalent circuit of PZT at (a) anti-resonance frequency (b) resonance (series) frequency (c) near resonance frequency . . . . . . . . . . . . . . . . 61 3.5 Acoustic layers in sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.6 Mechanical setup of samples (a) cross sectional view (b) top view . . . . . 66 3.7 Impedance of air-backed PZT with water as acoustic load (size 5x5 mm) (Simulated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.8 Measurement of input impedance of transducer sample . . . . . . . . . . . 72 xi List of Figures 3.9 Measurement of electromechanical conversion eciency of transducer sample 73 3.10 Simulated and measured amplitude of input impedance of air-backed PZT (sample 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.11 Simulated and measured input impedance of air-backed PZT (sample 1) . 75 3.12 Output power of air-backed PZT (sample 1) (simulated and measured) . . 76 3.13 Electro-acoustic conversion eciency of sample 1 (simulated and measured) 76 3.14 Measured amplitude of input impedance of air-backed PZT (sample 2 and sample 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.15 Measured phase of input impedance for air-backed PZT (sample 2 and sam- ple 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.16 Measured electro-acoustic conversion eciency of sample 2 and sample 3 . 79 4.1 Full wave bridge rectier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Colpitts oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3 Common drain buer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.4 Class-A power amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.5 Power amplier input voltage (transistor's base voltage) . . . . . . . . . . . 89 4.6 Power amplier output voltage (input voltage of PZT) . . . . . . . . . . . 90 4.7 Output waveform of colpitts oscillator . . . . . . . . . . . . . . . . . . . . . 91 4.8 Input voltage at wireless power delivery system (driver coil's input) and at sense resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 C.1 Coil cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 D.1 Piezo-electric sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 E.1 Transmission of acoustic wave through dierent medium . . . . . . . . . . 114 E.2 Equivalent acoustic impedance for multilayer system . . . . . . . . . . . . 115 xii List of Figures E.3 Equivalent electric model of acoustic layer . . . . . . . . . . . . . . . . . . 116 F.1 Oscillator block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 G.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 H.1 Energy harvesting and driver circuit . . . . . . . . . . . . . . . . . . . . . . 120 I.1 Ultrasound power meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 J.1 TI-TPS61045EVM board (DC-DC boost converter) . . . . . . . . . . . . . 122 xiii List of Abbreviations  Wireless power transfer eciency em Electromechanical conversion eciency z specic (characteristics) acoustic impedance AWG American Wire Gauge Cself Self capacitance of coil CMUT Capacitive Micromachined Ultrasonic Transducer DoutT Transmitter outer diameter ESR Eective Series Resistance fm Minimum impedance (resonance) frequency fn Maximum impedance (anti-resonance) frequency fp Parallel resonance frequency fs Series resonance frequency FDTD Finite-Dierence Time-Domain FEA Finite-Element Analysis HIFU High Intensity Focus Ultrasound JFET Junction Field-Eet Transistor kt Thickness mode electromechanical coupling factor Leff Eective Inductance of coil as Equation 2.16 Lself Self Inductance of coil mA milli Ampere xiv List of Abbreviations MEMS Micro-Electro-Mechanical Systems MUT Micro Ultrasonic Transducer mW milli Watt Na Number of layers in coil Ns Number of strands per bundle of Litz wire Nt Number of turns per layer NPN Bipolar junction transistor pMUT piezo Micromachined Ultrasonic Transducer PZT Lead zirconate titanate (Transducer) Qm Mechanical quality factor Q-factor Quality factor Rayl Unit of acoustic impedance, 1 Rayl = 1 N.s.m3 RFID Radio Frequency Identication SDT Sonodynamic Therapy TTF Transmission Transfer Function WPT Wirless Power Transfer xv Notations Ni=af(i) sum of function f(i) for i from a to N Ni=af(i) Product of function f(i) for i from a to NR y =x f() Denite integration of function f() for  from x to y f 0(d) First derivative of function f(d) with respect to d xvi Acknowledgments First of all, I would like to express my sincere gratitude to my supervisor, Prof. Shahriar Mirabbasi and co-supervisor Prof. Mu Chiao for their whole{hearted support during the past two years. Not only they greatly helped me with the technical contributions of this thesis, but also constantly encouraged and directed me toward the right direction in my research. Their friendly and understanding attitude provided the perfect environment for me to achieve my research goals. Also, I greatly thank Prof. Rob Rohling and Prof. Boris Stoeber for their invaluable comments. My deep appreciation goes as well to Dr. Roberto Rosales for his technical assistance and support for the measurements. I would like to thank students in MEMS lab; Ms Nazly Primoradi, Reza Rashidi, Hadi Mansoor, Colin Chen, Kaan Williams and other friends who accompanied and encouraged me during my Masters program. I thank my family from the bottom of my heart for their love and inspiration and their understanding for my decision to pursue higher studies. I would like to dedicate my thesis to my father Mr. Girdhari Lal and my mother Mrs. Kavita Devi. I would like to thank my sister Ms. Kanta, Ms. Geetanjali and my best friend Yu (Vivian) Li. It was their support which gave me encouragement to overcome many challenges. This work is supported in part by research funding from the Natural Sciences and Engi- neeing Council of Canada (NSERC) and the Canada Research Chair (CRC) Program, and infrastructure funding from Canada Foundation of Innovation (CFI) and British Columbia Knowledge Development Fund (BCKDF). xvii Chapter 1 Introduction 1.1 Motivation Localized and controlled drug release systems have gained clinical relevance in the treat- ment of many diseases over the past decade. To avoid the systemic toxicity issues associated with intravenous routes of drug management systems, a localized and controlled drug de- livery system is especially relevant to administering antiproliferative drugs which have high levels of toxicity. For example, prolonged systemic use of rst line disease modifying drugs for rheumatoid arthritis (RA) and cancer is impossible due to cumulative cardiac toxicity. State-of-the-art polymeric-based drug delivery systems, for localized drug delivery, can be injected locally to provide localized treatment but they do not provide exact dose and temporal control. With advances in Micro-electro-mechanical systems (MEMS), MEMS based drug reser- voirs provide better control over drug release and are becoming among popular methods for drug delivery. To increase the drug intake eciency, sonoporation-based drug delivery has attracted attention in the past decade. Ultrasound waves are used to create temporary bubbles that, upon collapse, send out shock waves that open temporary pores in the cell membrane. The drug in the surrounding area may then diuse into the cells before the pores are closed. Sonodynamic enhancement of doxorubicin cytotoxicity was investigated using micro-ultrasonic transducers (MUTs) in combination with cancer drug in [1]. Using 4 MHz ultrasound transducer with 60 seconds of toned burst operation at acoustic intensity 1 Chapter 1. Introduction of 40 Watt/cm2, cytotoxicity of doxorubicin treatment increased from 27 to 91%. Power requirement of sonoporation-based systems is comparatively higher than that of other implantable devices. Using ultrasound transducer of area 1 mm2 (dimension 1 mm  1 mm  0.5 mm), the system requires 400 mW of power to stimulate the trans- ducer, which is much higher compared to most of reported biomedical implants [2{4]. To realize localized drug delivery and implantable sonoporation-based systems, high power- transfer eciency from external source to ultrasound device is required (to reduce excessive losses in power transfer link). This chapter introduces the motivation of the present work. Section 1.2 presents the block diagram of the system. Literature review is done in Section 1.3, and key contributions of the present work are described in Section 1.5. Section 1.6 presents the organization of this thesis. 1.2 System Architecture The focus of this work is on wireless power transfer from external power source to im- plantable device and use the received energy to generate signal for ultrasound transducer. Figure 1.1 shows the block diagram of the overall system as well as the energy 
ow between the blocks. The system can be divided into three main sub-system, namely, wireless power delivery, ultrasound transducer and driver circuit. 1.2.1 Wireless Power Delivery System Providing required power to implanted devices in a reliable manner is of paramount impor- tance. Some implants use (rechargeable) batteries, however, their applications are limited due to the size and/or longevity of the batteries. Wireless power transfer schemes are of- ten used in implantable devices not only to avoid transcutaneous wiring, but also to either 2 Chapter 1. Introduction Figure 1.1: System architecture recharge or replace the device battery. Due to high power requirement, the focus of this work is to design an ecient wireless power-delivery systems. Design requirements of the present application are taken as example and a generalized approach is developed to achieve a high-eciency wireless power-transfer system. Similar design steps can be applied for dierent applications or with dierent design constraints. Generally implantable electron- ics are of low voltage and consume high current based on power requirement. Hence in general low load resistance are used to design wireless power-delivery system (200  [5] and 500  [6]). In the present work, wireless power delivery block is optimized for a resistive load of 100 . 1.2.2 Ultrasound Transducer/Stimulator Size of the implantable device is an important design criteria. In general, for implantable devices a small size stimulator is preered. In applications where high power density 3 Chapter 1. Introduction is required [1], smaller size reduces the total power requirement to achieve high power density. As size of the device increases, the required power also increases propotionally to the surface area of the device. Design and characterization of the miniturized transducer is an important step to identify design parameters for driver block. Reduction in aspect ratio of transducer can cause secondary eects on electro-mechanical energy conversion. The focus of this work is to characterize small size transducer to obtain optimum operating conditions and its limitations. 1.2.3 Energy Harvesting and Driving Circuit Functionality of this module is to recieve energy over wireless link and eciently convert it to generate driving signal for the ultrasonic transducer. This module can be subdivided into multiple circuit modules based on functionality. Dierent approaches can be applied to convert incoming energy into driving signal. In present system, input power is rectied to generate DC (direct current) voltage which is further boosted to high-voltage and is used along with a power amplier (PA) to generate high voltage sinusoidal driving signal for the ultrasound transducer. Due to the dependance of the design parameters of this block over wireless power delivery module and transducer parameters, specications of submodules of this block are dened after design and characterization of wireless power delivery block and ultrasound transducer. 1.3 Literature Review A popular technique for wireless power transfer, particularly in biomedical implants, is inductive coupling which was rst used to power an articial heart [7, 8] and since then has commonly been used in implantable devices [2{5,9{14]. An inductively coupled power- transfer system consists of two coils that are generally referred to as primary and secondary 4 Chapter 1. Introduction coils. In such systems, power transfer eciency is a strong function of the quality factor (Q) of the coils as well as the coupling between the two coils. Hence, the eciency depends on the size, structure, physical spacing, relative location and the properties of the envi- ronment surrounding the coils. The coupling between the coils decreases sharply as the distance between the coils increases and causes the overall power transfer eciency to de- crease monotonically. Inductive power transfer in a (co-centric) 2-coil system is extensively analyzed in the literature [2, 13, 15,16]. Resonant-based power delivery is an alternative wireless power transfer technique that typically uses four coils, namely, driver, primary, secondary and load coils which will be discussed later. Coupled-mode theory [17] has been used to explain this phenomenon [18{20]. Initially, this method was focused on high power transfer and hence requiring big coils. In [21], this technique is used for implantable and wearable devices, though a system with a large transmitter coil (radius of 176 mm) around the waist and several receivers is advocated. Similar independent work has been presented in [22] using very big external coils (radius of 150 mm) and small load coils (radius 6.5 mm). This system uses inductive coupling between driver and primary coil as well as between secondary and load coil. Sonotherapy is a novel emerging technique and is becoming popular because of its min- imally invasive and non-invasive therapy. It uses ultrasound waves, propagated through tissue media, as carriers of energy [23{25]. To understand transducer behaviour, electrical model of transducers are studied in [26{28]. For composite ultrasound transducer theoret- ical study was done to formulate electromechanical coupling factor as function of aspect ratio [29, 30]. As per our knowledge, for single crystal PZT, eect analysis of aspect ratio reduction of PZT on its parameters has not been done. Resonance frequency of a transducer depends on its dimensions and is generally dif- fernt from wireless power delivery link frequency. Energy from external power source is a 5 Chapter 1. Introduction transferred form of magnetic 
ux and hence input energy to implantable device is in form of alternative current(AC) signal. In practice, induced voltage at receiving coil's terminal is very small compare to required signal to derive transducer so an AC-AC boost converter can be used to drive the transducer. Design of the AC-AC boost converter can be done in two parts and hence subdivided into AC-DC and DC-AC converter. AC-DC module can be realized using a full-wave rectier circuit. Due to low voltage gain of DC-AC boost in- verter [31], [32], and complexity of design [33], present work uses high voltage gain DC-DC boost converter in combination with power amplier. As per our knowledge, no previous design of implantable ultrasonic transducer based sonoporation system is done. 1.4 Research Objectives Based on requirements to implement implantable sonoporation-based drug-delivery system, the following research objectives can be deduced: 1. Design a highly ecient wireless power transfer system for implantable devices, in perticular to sonoporation-based drug-delivery system. 2. Design and characterization of ultrasound transducer to obtain optimum operating frequency. 3. Design energy harvesting and driver circuit to convert received power using im- plantable coil and transfer it to ultrasound transducer to generate acoustic power. 1.5 Contributions of The Thesis This work is done in three steps. Each step is kept modular and generalized. Target application, [1] is taken as a design example. For each step design guidelines are given and 6 Chapter 1. Introduction based on change in application or design target, new design parameters can be calculated without loss of generality. First step presents state-of-art ecient wireless power delivery system for implantable devices. Electrical model of wireless power delivery system is developed as part of this work. Detailed analysis of design parameters is done and a 
owchart to design and optimize coil dimensions and parameters is presented. Due to generalized approach, presented wireless power delivey system can be optimized for new design constraints or for dierent applications. In this work, detailed analysis of ultrasound transducer is done. Idetication of im- portant parameters is done along with guidelines to select transducer material for given application. Electric model of transducer is used to identify eects of electrode size on electromechanical conversion ecieny. Eect of aspect ratio of transducer on its behaviour is analyzed using experimental data. A prototype circuit is built showing the conversion of received power (by implantable device) to driving signal to transducer. O-the-self discrete components are used for present design which can be implemented in a single integrated ciruit in future work. All of the three modules are designed and characterized separately and integrated to transmit and receive power wirelessly and to generate acoustic power using ultrasound transducer. 1.6 Organization of Thesis This work is presented in three main chapter. Each chapter corresponds to individual mod- ule presented in block diagram of system. Chapter 2 provides electric model of resonance- based wireless power-delivery system. Detailed analysis of design parameters is done and the eects of each parameter on wireless power-transfer link ecieny is presented. Chapter 7 Chapter 1. Introduction 3, presents key parameters to achieve high electro-mechanical conversion eciency. Electri- cal model of transducer is presented and experiments are done to verify the model. Eects of transducer aspect ratio is analyzed using experimental data with dierent size transduc- ers and are explained using transducer vibration theory. Chapter 4, provides prototype circuit to receive energy wirelessly from external coil and deliver energy to dierent sub- modules and to drive transducer. Chapter 5, summerizes the work along with guidelines for future work. 8 Chapter 2 Design and Optimization of Wireless Power Delivery System for Implantable Devices 2.1 Introduction Implantable devices are becoming more and more popular in health and medical appli- cations due to their ability to locally stimulate internal organs and/or monitor and com- municate the internal vital signs (signals) to the outer world. The power requirement of biomedical implants depends on their specic application and typically ranges from a few W [9{12] to a few tens of milliwatts [2{4,13]. Some implants use (rechargeable) batteries, however, their applications are limited due to the size and/or longevity of the batteries. Wireless power transfer schemes are often used in implantable devices not only to avoid transcutaneous wiring, but also to either recharge or replace the device battery. Wireless power transfer is also used in other application domains where remote powering is required, for example, contactless battery charging [34] and radio-frequency identication (RFID) tags [15]. The power transfer eciency, , versus normalized distance, R, i.e., the ratio of the separation between the coils (d) and the geometric mean of the primary and the secondary 9 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices coil radii (rm = p rprs), is a commonly used performance metric for comparing dierent designs. Because of the low Q-factor (due to the source and load resistances) and low coupling of the coils in the two-coil system, two-coil-based power transfer systems suer from a relatively low power transfer eciency, typically,   40% for d  rm [2, 3, 35] and generally  drops geometrically with distance (/ 1/d3) for d  rm. In implantable devices, the size of the implanted coil is constrained by the implant site. Typically external coil can be made big enough to improve power transfer range. As coupling between coils depends on amount of magnetic 
ux linkage between primary and secondary coils, for a given operating range and small size of the implanted (secondary) coil, coupling reduces as dierence between external(primary) coil radius and secondary coil radius increases. Increasing external coil dimension, however, increases the inductance of the coil and hence improves its Q-factor. Thus, there exist an optimum dimension of external coil for which eect of coupling and Q-factor (k Qp) is maximum. For implants with high power requirement, a more ecient power transfer mechanism, e.g., with  of 60 to 90 % for a distance of 20 mm or more, is desired. To provide high power at a low eciency, a strong alternating magnetic eld is required. High eddy currents due to strong magnetic eld could result in an excessive heat in the tissues and in turn violate the safety requirements of the federal regulations. For example, sonodynamic therapy (SDT), a drug delivery approach that uses ultrasonic cavitation to enhance the cytotoxicity of chemotherapeutic drugs requires comparatively large power for stimulation and hence a high link eciency is desired. Sonodynamic enhancement of doxorubicin cytotoxicity was investigated using micro ultrasonic transducers (MUTs) in combination with cancer drug in [1]. Using ultrasound transducer of area 1 mm2 (dimension 1 mm  1 mm  0.5 mm), the system requires 400 mW of power to stimulate the transducer. It should be noted that most of reported biomedical implants consume less than 100 mW of power [2{4]. 10 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Resonant-based power delivery, an alternative wireless power transfer technique, is recently used for high power transfer eciently [18{20]. We have analyzed resonant-based power delivery for implantable devices and provided a simple electrical model for it [36]. In this work, we present a more comprehensive circuit-based model for the system and analyze the eect of each design parameter. Furthermore, given the system requirements, we propose and analyze a step-by-step design procedure to optimize the system. Example application of the technique for biomedical implants, in particular, implants that require relatively large power such as [1] is provided and design constraints are applied to nd the optimum design to achieve maximum eciency. Our focus is on the eciency of the power transfer link itself and peripheral circuits such as power amplier in the transmitter and rectier and/or dc-dc converter in the receiver are outside the scope of this module. This chapter is organized as follows: Section 2.2 formulates the power transfer eciency of resonant-based systems. Section 2.3 describes the design steps. Section 2.4 provides the optimized system parameters. Section 2.5 presents the experimental setup. Results and analysis are provided in Section 2.6. Comparsion with previous works is done in Section 2.6 and concluding remarks are provided in Section 2.8. 2.2 Power Eciency in Resonance-Based Systems This section presents the individal models for inductance, capacitance and resistance of coils. Analytical models of each component are presented and is followed by detailed analysis of resonance power transfer system. The models are based on a multi-layer helical coil that uses Litz wire. However, the presented design steps are general. In case other types of coil are used, the respective inductance, capacitance and resistance model of coil can be adjusted accordingly and rest of the design steps and guidelines will remain the same 11 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 2.2.1 Inductor Model Self inductance is a measure of magnetic 
ux through the area (cross section) enclosed by a current carrying coil. The self inductance of a coil with loop radius a and wire radius R (assuming R a  1) can be approximated as [37,38]: L(a;R) = oa  ln  8a R   2  (2.1) Mutual inductance is a measure of the extent of magnetic linkage between current carrying coils. Mutual inductance of two parallel single turn coils with loop radius a and b can be approximated using equation (2.2) where d and  are relative distance and lateral misalignment, respectively, between the two coils [37, 38]. The mutual inductance is a strong function of coil geometries and separation between them. M(a; b; ; d) = o p ab Z 1 0 J1  x r a b  J1  x r b a ! J0  x p ab  exp  x dp ab  dx (2.2) where J0 and J1 are zeroth and rst-order Bessel functions . For perfectly aligned loops ( = 0), the mutual inductance between the coils can be calculated as: M(a; b;  = 0; d) = 0 p ab  2 k  k  K(k) 2 k E(k)  (2.3) where k =  4ab (a+ b)2 + d2  1 2 (2.4) 12 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices and K(k) and E(k) are the complete elleptic integrals of the rst and second kind, respec- tively [37{39]. Coils with dierent geometries have been used and modelled in the literature. Planar spiral coil are modeled in [5,37,38]. For a sprial coil with Na co-centric circular loops with dierent radii ai(i = 1; 2; _:::; Na) and wire radius R, self-inductance can be calculated as: La = NaX i=1 L(ai; R) + NaX i=1 NaX j=1 M(ai; aj;  = 0; d = 0)(1 ij) (2.5) where ij = 1 for i = j and ij = 0 otherwise. Printed spiral coils are implemented and optimized in [6]. It provides low self-inductance and constrains maximum achievable Q-factor. To achieve large self-inductance, multilayer helical coils can be used. For a helical coil with Nt turns per layer and Na coaxial layers, total self-inductance can be modeled as: La = Nt NaX i=1 L(ai; R) + NaX i=1 NaX j=1 NtX k=1 NtX l=1 M(aik; ajl;  = 0; d = dljk  lj) (1 ij)(1 kl) (2.6) where ij (or kl) = 1 for i = j (or k = l) and ij (or kl) = 0 otherwise. dl is minimum distance between two consecutive turns. 2.2.2 Parasitic Capacitance In general inductors suer from stray capacitance between turns. Stray capacitance causes self-resonance and limits the operating frequency of the inductor. Stray capacitance of a single-layer air-cored inductors is modelled analytically in [40, 41] and using numerical 13 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices methods in [42]. For a multilayer solenoid with Na layers and Nt turns per layer, stray capacitance is approximated as [43]: Cself = 1 N2 " Cb(Nt  1)Na + Cm NtX i=1 (2i 1)2(Na  1) # (2.7) where N is total turns, Cb is parasitic capacitance between two nearby turns in the same layer and Cm is parasitic capacitance between dierent layers. For a tightly wound coil, parasitic capacitance between two nearby turns is Cb = 0r Z  4 0 Diro & + rro(1 cos) d (2.8) Cm = 0r Z  4 0 Diro & + rro(1 cos) + 0:5rh d (2.9) where Di; r0; &; r; h are average diameter of coil, wire radius, thickeness and relative per- mittivity of strand insulation and separation between two layers respectively [43]. 2.2.3 AC Resistance To achieve high quality factors, inductors with low eective series resistance (ESR) are required. At high frequencies, skin and proximity eect increases the ESR. To reduce the AC resistance, multi-strand Litz wires are commonly used [9, 43]. Finite-dierence time- domain (FDTD) techniques are used to model AC resistance numerically [44]. Analytical models of winding losses in Litz wires are presented in [45,46]. Semi-empirical formulation using nite element analysis (FEA) is presentd in [47]. The AC resistance of coils made of multi-strand Litz wires including skin and proximity eect can be approximated as [43]: Rac = Rdc  1 + f 2 f 2h  (2.10) 14 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices where fh is the frequency at which power dissipation is twice the DC power dissipation and is given by fh = 2 p 2 r2s0 p NNsa (2.11) where Rdc, rs, Ns, 0;  are DC resistance of the coil, radius of each single strand, number of strands per bunch, permeability of free space and the area eciency of the bunch, respectively. a is area eciency of coil with width b and thickness t and can be determined using gure 2.1 cited in [43]. 10−2 10−1 100 101 102 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ratio of b/t (width over thickness) Ar ea  E ffi cie nc y Figure 2.1:  vs coil aspect ratio (b/t) DC resistance of the coil with Na coaxial layers and diameter Di can be calculated 15 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices using equation Rdc = NaX i=1  NtDi A = NaX i=1 NtDiRul (2.12) where Rul is DC resistance of the unit-length Litz wire with A, Rs, NB, NC , Ns as wire cross-section area, maximum DC resistance of each individual strand, number of bunching operation, number of cabling operation [48] and number of individual strands respectively [49]. Rul = Rs(1:015) NB(1:025)NC ANs (2.13) 2.2.4 Coil Model Considering the eect of the stray capacitance and the AC resistance of an inductor, the total impedance of a coil can be written as [50] Ze = (j!Lself +Rac)k 1 j!Cself (2.14) Figure 2.2: Coil lumped model The coil can be modelled as an inductor with a self-inductance Leff and eective series resistance given by: 16 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices ESR = Rac (1 !2LselfCself )2 (2.15) Leff = Lself (1 !2LselfCself ) (2.16) As operating frequency of coil approaches fself , ESR increases drastically. From Equa- tion 2.16, for frequency more than fself coil behave as capacitor and hence it can not be used as inductor after its resonance frequency. The Q-factor of an unloaded inductor can be written as: Qunloaded = !Leff ESR = 2fLself  1 f2 f2self  Rdc  1 + f 2 f2h  (2.17) 2.2.5 Power Transfer Model 2-Coil System Conventionally, two coils are used in inductively coupled power transfer systems and power is transferred from one coil to another coil. Power transfer eciency is a strong function of Q-factor of primary coil (Qp) and secondary coil (Qs). Mutual coupling (k) between the coils is function of alignment and distance between the coils. Eciency of a 2-coil-based power-transfer system is given by [3,15,36]:  = k2QpQs 1 + k2QpQs : (2.18) 17 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 4-Coil System Couple-mode theory [17] has been originally used to describe resonance-based coupling [18, 19]. A simple circuit-based model for such systems is presented in [36]. The eect of the low Q-factor and the low-coupling between the source and load coils can be compensated using intermediate high-Q-factor coils. To realize ecient power transfer, the system consists of 4 coils referred to as driver, primary, secondary and load coil (also denoted as coils 1 to 4). Figure 2.3 shows the simplied schematic and electrical model of the 4-coil system. Figure 2.3: (a) Simplied schematic of the 4-coil system (b) electrical model of the power transfer circuit (for design example) By applying circuit theory to this system, the relationship between current through 18 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices each coil and the voltage applied to the driver coil can be captured in the following matrix form: 266666664 I1 I2 I3 I4 377777775 = 266666664 Z11 Z12 Z13 Z14 Z21 Z22 Z23 Z24 Z31 Z32 Z33 Z34 Z41 Z42 Z43 Z44 377777775 1 266666664 E 0 0 0 377777775 ; (2.19) where Zmn = Rn + j!Ln + 1 j!Cn for m = n = j!Mmn for m 6= n; E is amplitude of voltage source applied to the driver coil, and Rn, Ln, Cn are the eective resistance, inductance and capacitance of the coil n. Mmn is the mutual inductance between coil m and n. Mmn = kmn p LmLn where kmn is coupling factor between coil m and coil n. Tuning all coils to same resonance frequency and operating it at their resonance fre- quency, Zmn = Rn (for m = n and n 2 f1; 2; 3; 4g). For small driver and load coil inductance and relatively large distances between coils 1 and 4, coils 1 and 3, and coils 2 and 4, coupling coecients k14; k13 and k24 would be neglected. From Equation 2.19, at resonance, current in load coil can be calculated as: I4 = k12k23k34 p Q1Q2 p Q2Q3 p Q3Q4p R1R4[(1 + k212Q1Q2)(1 + k 2 34Q3Q4) + k 2 23Q2Q3] E (2.20) 19 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices where Qn is loaded quality factor of coil n at frequency of operation. The power-transfer eciency can be computed as  = (k212Q1Q2)(k 2 23Q2Q3)(k 2 34Q3Q4) [(1 + k212Q1Q2)(1 + k 2 34Q3Q4) + k 2 23Q2Q3][1 + k 2 23Q2Q3 + k 2 34Q3Q4] (2.21) 2.2.6 Analysis of 4-Coil Power-Transfer System To optimize the design to achieve high eciency, the eects of dierent parameters on the power transfer eciency will be analyzed here. High-Q Requirement From Equation 2.21, low coupling between coils 2 and 3 can be compensated for by high-Q factor of these coils. Eciency is computed and plotted in Figure 2.4 with varying Q-factor of coil 2 (primary coil), Q2, and distance between coils 2 and 3,(d). Note that respective, k23, the coupling coecient between primary and secondary coils corresponding to distance decays geomatrically with increasing distance between them. 0 200 400 600 01020 304050 0 10 20 30 40 50 60 70 80 Q2Coil Distance (d) in mm Po w er  tr an sf er  e ffi cie nc y (% ) Figure 2.4: Eciency versus Q factor (k12 = 0.58, k34 = 0.60, Q1 = 5, Q3 =100, Q4 = 0.15, k23 = 148.2  1 d2+320 1:2 (Equation 2.45) 20 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Figure 2.4 shows the eect of Q-factor on power transfer eciency (Equation 2.21). It can be deduced that for given coupling between primary and secondary coils, as the Q-factor of the coils increases, power transfer eciency increases. To achieve a high power transfer eciency (e.g., 80% or beyond) for high operating range, high Q-factor coils are required. Using moderate coupling between driver and primary coils (k12) and secondary and load coils (k34) along with a high Q-factor primary (Q2) and secondary (Q3) coils, the following approximation can be derived: (1 + k212Q1Q2)(1 + k 2 34Q3Q4)  (k212Q1Q2)(k234Q3Q4) (2.22) (k212Q1Q2)(k 2 34Q3Q4) k223Q2Q3 ) (1+k212Q1Q2)(1 + k 2 34Q3Q4) + k 2 23Q2Q3  (k212Q1Q2)(k234Q3Q4)(2.23) (1 + k223Q2Q3) k234Q3Q4 ) (1 + k234Q3Q4 + k 2 23Q2Q3)  (1 + k223Q2Q3) (2.24) Applying above assumptions, the eciency expression (Equation 2.21) can be simplied to:  = k 2 23Q2Q3 1 + k223Q2Q3 (2.25) This approximate model is similar to the model for 2-coil systems. Since in the 4- coil system, Q2 and Q3 are independent of the source and load resistances, high quality 21 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices factors for primary and secondary coils can be achieved. Power transfer eciency increases monotonically as k223Q2Q3 increases. Note that for Equation 2.25 to be a valid approximation, Q4 has to be within a certain range as explained below. For approximation in Equation 2.22 to be reasonable, (1 + k234Q3Q4) 1) (k234Q3Q4) > 10) Q4 > 10 Q3k234 (2.26) For Equation 2.24 to be reasonable approximation, we should have, (k223Q2Q3) > 10k234Q3Q4 ) Q4 6 k223Q2 10k234 (2.27) From Equation 2.26 and Equation 2.27, range of Q4 can be shown as: 10 Q3k234 6 Q4 6 k223Q2 10k234 (2.28) Eect of Q1 and Q4 on Eciency Driver coil's Q-factor is limited by the source series resistance and load coil's Q-factor is limited by the load resistance as well as implant size limitation. Due to high load resistance (s 100 ) and small size of inner coil Q4 is typically limited to small value. However, moderate Q-factor of 5 to 20 can be achieved for driver coil. Figure 2.5 plots the eciency of a 4-coil system as a function of Q1 and Q4. Note that, for the four-coil-based power-transfer system, eciency does not vary much with respect to driver coil's Q factor and it has a maxima for low load coil's Q-factor (refer 22 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 5 10 15 20 00.2 0.40.6 0.81 68 70 72 74 76 78 80 82 Q1Q4 Po w er  tr an sf er  e ffi cie nc y (% ) Figure 2.5: Sensitivity of eciency on Q1 ,Q4 (k12 = 0.58, k34 = 0.60, k23 = 0.05, Q2 =368, Q3 = 108) to Figure 2.5). As mentioned above, it is common for the load coil to have a low Q-factor. 2.2.7 Design of High-Q Coils To achieve high Q factor for primary and secondary coils, Litz wire which provides low AC resistance can be used. Based on operating frequency, the gauge of the single strand in the Litz wire is chosen. The number of strands in one bunch is used as a design parameter. Wire Property Litz wires are commonly used to reduce the AC resistance of wire and hence improve Q- factor of coils. To dene the link operating frequency the following considerations are taken into account. First, for the frequency range of 100 kHz to 4 MHz band, no biological eects have been reported, in contrast to the extreme-low-frequency band and the microwave band [51]. Second, tissues have lower absorption for low-frequency RF signals as compared to high-frequency signals. Third, due to small size of the implanted coil, it has a small inductance and small parasitic capacitance. For lower frequency of operation, coil need to 23 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices be tuned by using an high value external resonating capacitor. Furthermore, by using large tuning capacitance, parasitic capacitances due to wire winding and variation in capacitance due to tissues would be negligible. Hence resonating frequency of implanted coil will not be aected by proximity of tissue. Fourth, if operating frequency is close to the self-resonant frequency of coil, ESR of the coil increases drastically (Equation 2.15) thus for a moderate self-resonant-frequency coil, by operating at lower frequency, high quality factor can be achieved (Equation 2.17). Based on above points, Litz wire with single strand wire gauge of AWG44 (AWG: American Wire Gauge) is chosen. AWG44 provides Rac=Rdc = 1 for frequency range of 350 kHz to 850 kHz [49]. For applications where operating frequency is xed, respective wire gauge can be chosen to keep Rac close to Rdc. Rdc reduces as Ns increases. Due to proximity eect, fh reduces as Ns increases (fh/ 1/ p Ns) and causes high AC resistance (Equation 2.11). The diameter of the Litz wire increases as the number of enclosed strands is increased. For a given thickness of coils, the optimum number of strands that improves Q2 and Q3 can be calculated. Figure 2.6 shows the product of Q2 and Q3 for a given dimension of primary and secondary coils with varying number of strands. Figure 2.7 shows the frequency at which this product (Q2:Q3) is maximum. Based on gures 2.6 and 2.7, 40 strands Litz wire of strand gauge AWG 44 is chosen for this work. Similar calculation can be done based on design constraints to calculate the number of strands and single strand wire gauge. Number of Turns To analyze the eect of number of turns per layer on Q-factor of the coils, using equations 2.6, 2.7, 2.10 and 2.17, one can derive an expression for the Q-factor and it can be max- imized with respect to number of turns per layer (Nt) for a given number of layers (for Na  1) as follows (a full derivation is provided in Appendix B): 24 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 50 100 150 200 250 300 350 400 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 104 # of strands Q 2 * Q 3 Figure 2.6: Q2:Q3 variation with number of strands 0 50 100 150 200 250 300 350 400 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 # of strands Ap pr ox im at e op er at in g Fr eq en cy  (x  10 5 ) Hz Figure 2.7: Optimum frequency of operation (dQ=dNt = 0)) 1 4 ! 2 !2self  3 ! 2 !2self !2 !2h = 0 (2.29) where !self = 1p LselfCself , ! = 2f and !h = 2fh. Lself , Cself and !h are fucntion of Nt (Equation 2.6, 2.7 and 2.11). 25 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Typically operating frequency is kept limited to 2  fh as AC resistance increases geomatrically with operating freqency (Equation 2.11). For !  2!h, !2!2h  4. From Equation 2.29 and !  2!h, (dQ=dNt  0)) 1 16 ! 2 !2self  0 (2.30) As number of turns increases, Lself increases and self resonating frequency (fself ) de- creases. With Nt for which !  14!self , Q-factor increases monotonically with increment of Nt (dQ=dNt  0, Equation 2.30). Nt(opti) can be dened as Nt for which ! = 14!self . 0 5 10 15 20 80 100 120 140 160 180 200 220 240 260 280 # of turns per layer Q fa cto r Figure 2.8: Optimum number of turns (Na = 12;DoutT = 60 mm, h = OD/2, f = 700 kHz) As an example, Figure 2.8 shows the graph of Q-factor for a coil with a xed number of layers and xed width. h is distance between two layers and OD is diameter of wire. As can be seen from the gure, Q-factor of the coil increases monotonically when the number of turns is less than 10. 26 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Optimum Operating Distance and Eect of Q1 In typical case, relative position and dimension of driver coil and primary coil (and of secondary and load coil) is xed and hence in normal operating mode Q2, Q3, Q4, k12, k34 are xed. For given operating distance (respective k23), only Q1 can be varied using changing source resistance and hence eect of Q1 on power transfer eciency is shown here. Power transfer eciency is a strong function of coupling between coils 2 and 3 (k23). By maximizing eciency () with respect to the coupling coecient, the optimum distance of operation can be achieved. From eciency equation (refer Equation 2.21), we have: @=@k23 = 0) k23(opt) =  p k212Q1Q2[1 + k 2 34Q3Q4] Q2Q3 ! 1 2 (2.31) @2=@k223 < 0 for k23 = k23(opt) (2.32) An expression for eciency at k23(opt) is given by (appendix A):  =  k34 k23 2 (k12 p Q1Q2) 3 (1 + k12 p Q1Q2)2 Q4 Q2 (2.33) To achieve maximum eciency at any given distance (which is equivalent to a given k23), Q1 can be varied by controlling the source resistance. Figure 2.9 shows that for a given system parameters for each value of Q1, there exists a corresponding distance for which eciency is maximum. Equation 2.31 shows the depen- dence of optimum value of k23 on design parameter Q1 so by changing the Q-factor of the 27 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 10 20 30 40 50 10 20 30 40 50 60 70 80 90 Coil distance (mm) Po w er  tr an sf er  e ffi cie nc y (% )   Q1=1 Q1=5 Q1=10 Q1=15 Figure 2.9: Eect of Q factor(Q1) on maximum eciency distance (Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = coupling model Equation 2.45) driver coil (Q1) optimum operating distance changes. Sensitivity of Eciency () to Source Series Resistance To compare the eect of source resistance in 2-coil-based systems and 4-coil-based systems, we derive an expression for the slope of eciency with respect to source series resistance (R1). @ @R1 = @ @Q1 @Q1 @R1 (2.34) For a 2-coil system, the rate of change of eciency is (from Equation 2.18, 2.34) and Q1 = !L1=R1 @ @R1 = !L1 R21 k2Q2 (1 + k2Q1Q2) 2 for Q1  1; @ @R1   1 !L1 (k2Q2) (2.35) 28 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices For 4-coil system, using equations 2.21 and 2.34, an (approximate) analytical expression for the change in eciency with respect to R1 can be derived (Equation 2.36). @ @R1   k 2 23 !L1k212k 2 34Q4 (2.36) For xed design parameters, both equations (Equation 2.35 and 2.36) show that e- ciency decreases linearly as source resistance increases. To validate the accuracy of Equa- tion 2.35, eciency is calculated using Equation 2.18 for dierent values of R1 and plotted in gure 2.10. A linear regression model is used to nd the slope of changes in eciency with respect to R1. From linear regression model of eciency for varying source resistance, slope = -0.00768 1 and from Equation 2.35 slope = -0.01069 1. 2 4 6 8 10 12 14 16 18 20 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Source Resistance(in ohm) Po w er  tr an sf er  e ffi cie nc y   4−coil system regression model 2−coil system regression model Figure 2.10: 2 and 4 coil system eciency with respect to R1. For 2 coil (frequency = 700 kHz, Lp = 1.1 mH, Qs = 1.6,k = 0.055, RL = 100 ). For 4 coil (frequency = 700 kHz, L1 = 29.35 H;Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = 0.055, RL = 100  ) Similarly to validate the accuracy of Equation 2.36, with the same system parameters, eciency is calculated using Equation 2.21 with varying R1 and plotted in gure 2.10. From linear regression model of eciency for varying source resistance, slope = -0.00130 29 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  1 and from Equation 2.36, slope = -0.001431 1 (approximated model). This example provides the validity of Equation 2.35 and Equation 2.36. For given example, by comparing the slope of eciency for 2-coil-based and 4-coil-based systems, the eciency of the latter decreases  10 times slower as compared to that of the former. Slope for 2-coil-based systerm is inversely propotional to k2 (equivalent to k23) and hence have high value compare to 4-coil based system in which slope is propotional to k223 (note that k23  1). In typical case, an increase in value of R1 has much more severe eect in 2-coil-based systems as compared to 4-coil-based systems and hence 4-coil based system shows better robustness to source resistance variation. Sensitivity of Q to Frequency The Q factor of an inductor is a function of frequency: Q(f) = 2fL (1 (f=fself )2 Rdc(1 + (f=fh)2) (2.37) At low frequencies, Q(f) increases with frequency and for f > fh, due to the dominance of proximity eect on AC resistance [43], the Q-factor decreases. To utilize the coil for dierent operating frequency, it is desirable to have a Q-factor that is not too sensitive to frequency. The bandwidth of Q is mainly dened by fh. To reduce sensitivity to operating frequency, fh should be kept suciently high so that AC resistance stays small (Equation 2.10). Figure 2.11 shows the Q-factor variation with respect to operating frequency for coils with dierent number of layers. As number of layer increases, fh decreases (Equation 2.11) and self resonating frequency (fself ) decreases due to the increase in both stray capacitance and inductance. As it can be seen from Figure 2.11 that variations of Q factor around its maxima (with respect to frequency) are smaller for the coils with lower number of layers. 30 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 2 4 6 8 10 12 14 16 x 105 50 100 150 200 250 300 350 400 Frequency (in Hz) Q− fa cto r   l=12 l=16 l=20 l=24 Figure 2.11: Sensivity of Q with frequency (DoutT = 60 mm, Nt = 11, h = OD/2) Thus to be robust to frequency changes, the number of layers in the each coil should be kept as small as possible. To reduce frequency eects on Q factor of coils and to achieve good operating range using same coils, number of layers should be kept less. 2.2.8 Eect of Operating Frequency Variation A 4-coil-based system provides a better immunity to operating frequency variation as compared to its corresponding 2-coil-based system. For 4-coil system, by itself driver coil has a low Q-factor due to low inductance and hence has high bandwidth of operation. Driver coil and high-Q primary coil are closely coupled and mutual inductance seen by driver coil due to primary coil is high. This increases the in
uence of frequency variation on driver coil. When the distance between the secondary coil and the primary coil decreases, the current in the secondary coil opposes the current in the primary coil which in turn reduces the eect of primary coil's on driver coil (reduced I2). Hence, the closer the secondary coil to the primary coil, the lower the eective Q factor of the driver coil. For the 2-coil-based system, with comparable primary coil size and same source resistance as 31 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices of 4-coil system, the Q-factor of primary coil is higher than that of driver coil in the 4-coil system. Therefore the 2-coil system is narrower band and thus more sensitive to operating frequency. Figures 2.12(a) and 2.12(b) show that for a 4-coil-based power-transfer system as the coil separation between primary and secondary coils decreases, the frequency range over which the 4-coil system has a higher eciency is wider as compared to the corresponding 2-coil based system. (Note that for comparison, same size primary coil and secondary coils are used for 2-coil and 4-coil based system.) 2.2.9 Series versus Parallel Connection of Load Resistance To improve the Q-factor of the load coil, the load resistance can be either attached in series or parallel to a resonating capacitor (Cp, refer to Figure 2.13). For parallel connection of the load resistance as shown in Figure 2.13(a), we have: Reff = RLk  !L Rs 2 Rs = RLk(!L) 2 Rs (2.38) Qp = RL!L RsRL + (!L)2 (2.39) For series connection of the load resistance as shown in Figure 2.13(b), we have: Qs = !Leff ESR +RL (2.40) for f  fself ; 1 f2=f2self  1 Qs = !L Rs +RL (2.41) To compare the Q factor of the coils with series and parallel load connection and to nd which connection improves the Q factor, the sign of the dierence between the parallel- 32 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 20 40 60 24 68 1012 x 105 −80 −60 −40 −20 0 Coil Distance (mm) f (operating frequency) Po w er  T ra ns fe r g ai n (dB ) (a) Eciency with frequency, coil separation(4-coil based system) 0 20 40 60 24 68 1012 x 105 −80 −60 −40 −20 0 Coil Distance (mm) f (operating frequency) Po w er  T ra ns fe r g ai n (dB ) (b) Eciency with frequency, coil separation(2-coil based system) Figure 2.12: Eect of operating frequency variation on power-transfer eciency 33 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Figure 2.13: Series vs parallel connection of load resistance and series-connected Q factors can be calculated as: Qp Qs = !LR 2 L[1 (!L=RL)2] (Rs +RL)(RsRL + (!L)2)) (2.42) Note that for !L RL < 1 the parallel connection of load resistance will improve the Q factor. 34 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 2.3 Design Steps In this section, design steps for resonance-based (4-coil) power delivery systems are pre- sented. These steps are presented in the context of a design example that requires relatively high power to be transferred to the implantable device. 2.3.1 Design Constraints The rst step is to identify the design constrains. The specic application requirements constrain the design parameters (particularly in terms of size and source and load resis- tances) of the implantable device. For example, Table 2.1 shows the design constrains dictated by the specic application of [1]. Table 2.1: Design constraints Parameter symbol Design Value Transmitter Outer diameter DoutT  80mm Transmitter Coil Thickness hT 5.5 mm Implanted outer diameter DoutR 22 mm Implanted Coil Thickness hR 2.5 mm Minimum Coil inner diameter DinR 8 mm Coil relative distance d 20 mm Source resistance R1 5.6  Load resistance RL 100  2.3.2 Initial Values and Range of Parameters The initial design parameters are chosen as follows: 35 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices External Coil Radius In a single-turn circular coil with radius r, magnetic eld strength, H, at distance x along the axis can be written as [6] H(x; r) = I:r2 2 p (r2 + x2)3 (2.43) For r = x p 2, H will be maximized and, therefore, a good choice of diameter for external coil is DoutT = 2 p 2d. For d = 20 mm, DoutT can be chosen as 60 mm. Wire Property Single strand copper wire has high AC resistance for high frequency operation. Using multistrand Litz wire and using them in their operating frequency range, AC resistance can be kept very close to their DC resistance. For implantable coils Litz wire is commonly used [9, 43]. Based on analysis done in Section 2.2.7 for properties of the Litz wire with dierent number of strands (Figure 2.6), to improve the Q-factor, one can choose a specic Litz wire. In our example application, a 40-strand Litz wire with gauge 44 is chosen. Table 2.2 shows the properties of this particular Litz wire [49]. Table 2.2: Litz wire property Parameter symbol Value Strand gauge - AWG 44 Number of Strands Ns 40 Insulation thickness  3 m Strand radius rs 25 m Operating Frequecny - 350-850 kHz Outer Diameter OD 0.48 mm Max. DC resistance RDC 2.873/feet Unit length DC resistance Rul 0.0758/feet Filling factor  0.4784 36 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Q-Factor As for the Q-factor of the 4 coils that are used in the system, we have: Q1 As shown in gure 2.5, for high values of Q2 and Q3, eect of Q1 on eciency is not considerable. For constrained system dimensions, driver coil is made of single layer (Nt = 1) to keep enough room for primary coil winding. It is kept in the outermost layer to obtain considerable inductance as compared to the case when driver coil is wrapped in the innermost layer of primary coil. Its number of turns are maximum permissible given by the design constraints. As power amplier have output impedance on the order of 5 to 6  , a source resistance of 5.6  is chosen as sense resistance to mimic the source impedance. Q2 For small number of turns per layer, increasing the number of turns improvesQ-factor. Number of turns in coil 2 is constrained by design requirements. In our example, hT of 5.5 mm implies Nt = 11 with OD = 0.48 mm. Figure 2.14 shows the variation of Q2 with changing number of layers and operating frequency. Increasing primary coil size increases the parasitic capacitance between its turns. To obtain high Q-factor at low frequency, inductance of primary coil should be of large value. It results in signicant eect of parasitic capacitance on its self-resonanting frequency. To reduce the parasitic capacitance between coil turns, low dielectic insulating material is inserted between layers. As a rule of thumb thickness of dielectric layer should be varied till self resonating frequency (SRF) is 3-4 times higher than the operating frequency so that eect of SRF can be reduced in Q-factor (Equation 2.17). In present design example,insulating layer of dielectric constant similar to that of strand insulation (r = 5) and thickness 0.3 mm is taken. 37 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 5 10 15 20 0 2 4 6 8 10 x 105 0 100 200 300 400 500 f (operating frequency) in Hzl (number of layers) Q 4  (Q ua lity  fa cto r) Figure 2.14: Q2 vs number of layers, operating frequency Q3 With the constraint of hR = 2.5 mm, 5 turns per layer can be accommodated and Figure 2.15 shows the variation of Q3 for dierent number of layers and operating frequen- cies. Due to bigger size of the external coil (and correspondingly larger self-inductance and parasitic capacitance), the self resonance frequency (SRF) of the external coil is lower than that of implantable coil. Typically at operating frequency, the Q factor of implantable coil is not much eected by its SRF. In present design, self resonance frequency of secondary coil, without dielectric between layers is high enough compared to operating frequency range so no dielectric layer is used. Q4 Given the load resistance, e.g., 100 , and single turn per layer, Figure 2.16 shows the variation of Q4 for dierent number of layers and operating frequencies. To approximate 4-coil power-transfer model with a 2-coil equivalent, equations 2.26 and 2.27 can be used to nd the desired Q4 from the graph. 38 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 5 10 15 0 2 4 6 8 10 x 105 0 20 40 60 80 100 120 140 160 180 f (operating frequency) in Hzl (number of layers) Q 4  (Q ua lity  fa cto r) Figure 2.15: Q3 vs number of layers, operating frequency 1 2 3 4 5 0 2 4 6 8 10 x 105 0 0.2 0.4 0.6 0.8 1 f (operating frequency) in Hzl (number of layers) Q 4  (Q ua lity  fa cto r) Figure 2.16: Q4 vs number of layers, operating frequency 2.3.3 Optimizing Design Parameters To implement coils, the driver and primary coils are made co-centric (and coaxial), and the number of turns per layer in driver (Nt(1)) and primary (Nt(2)) coil are equal and kept close to Nt(opti). Due to small size of secondary coil, self resonanting frequency is high compared to operating frequency so number of turns are mainly limited by design constraints. The number of turns per layer in secondary coil (Nt(3)) and load coil (Nt(4)) are also chosen as 39 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices equal. Figure 2.17: Flow chart for coil dimension optimization Figure 2.17 shows the design steps to obtain system parameters (Nt(i) and Na(i) for i 2 f1; 2; 3; 4g) to achieve the optimum eciency at a given distance. The range for number of layers in coil and turns per layer depend on the design constraints and may vary as per the application requirement. 40 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 2.4 Resonance-Based Power Transfer Previous sections provide the models of dierent design parameters of 4-coil-based power- transfer system. Section 2.3 (Design steps) helps selecting the design parameters based on design constraints (Table 2.1). Based of the design constraints, the power transfer eciency can be maximized with respect to design parameters (e.g., number of turns and layers of each coil and operating frequency) for a targeted operating distance (e.g., d = 20 mm) and operating frequency can be calculated for which the design provides the maximum eciency. Table 2.3 shows the mechanical specications of the optimized design by following the design 
ow chart (gure 2.17). Table 2.3: Coils physical specication Type Coil Outer Dia. Inner Dia. Turns layers Number (mm) (mm) /layer Driver Coil 1 64 62 11 1 Primary Coil 2 60 39.5 11 12 Secondary Coil 3 20 10.5 5 9 Load coil 4 22 20 5 2 Based on simulation by following the design 
ow chart (Figure 2.17) operating frequency of 700 kHz is chosen. Depending on the application and the design constraints, the optimum design parameters can be calculated based on the design 
ow chart in Figure 2.17. Table 2.4 shows simulated electric parameters for the optimized coil dimensions to obtain high power transfer eciency. Source series resistance of R1(= 5.6 ) is used to emulate the nominal output impedance of power amplier for driver coil. Load resistance of RL (= 100 ) are used which is realistic load for targeted application. Coupling between coil 1 and coil 2 (k12) can be calculated using the coil dimensions and parameters. From simulation k12 = 0.6335, k34 = 0.601 and k23 = 0.058 for d = 20 mm. For coaxial primary and secondary coil with physical dimensions as per Table 2.3, 41 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Table 2.4: Coils electrical specication Coil Inductance DC fself fh Q (loaded) (Number) (H) Resistance MHz (MHz) (@700kHz) ( ) 1 15.90 0.5211 41.0 2.6 11.42 2 1131 5.34 3.75 0.490 295 3 33.25 0.538 24.7 0.844 160 4 3.629 0.159 44 1.84 0.1593 0 5 10 15 20 25 30 35 40 45 50 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Coil Distance (mm) Co up lin g k 2 3   Coupling vs. distance Regression model Figure 2.18: Mutual coupling (k23) versus distance Fig. 2.18 shows the coupling coecient k23 along with the tted curve based on regression model (95 % condence). The curve is modeled as: k23 = 148:2  1 d2 + r2m 1:2  0:0002857 (2.44) rm = p rprs = p 32  11 where d is the edge-to-edge minimum distance between the coils. rp and rs are the radius of the primary (coil 2) and the secondary coil (coil 3), respectively. For other applica- tions based on design constrains and dimension of coils (calculated based on 
ow chart), 42 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices coecients of coupling model will change. Table 2.5: Coils electrical specication (measured) Coil Inductance Self fself fh Q (loaded) (Number) (H) Resistance MHz (MHz) (@700 kHz) ( ) 1 15.58 0.55 40.7 2.58 11.06 2 1099 5.1 2.21 0.512 330.3 3 29.35 0.493 18.7 0.798 148 4 3.564 0.225 19.4 1.36 0.1563 2.5 Experimental Setup To demonstrate the validity of the presented modelling techniques and the design 
ow, a prototype 4-coil wireless power transfer system is designed and implemented. Table 2.3 shows the optimized dimension of the coils based on the design constraints. Multi- strand Litz wire (Ns = 40) of strand AWG 44 is used to implement the coils. HP4194A impedance/gain-phase analyzer is used to measure the electrical parameters of the coils which are reported in Table 2.5. The Q-factor of each coil is limited due to the high AC resistance for operating frequencies above fh (Equation 2.10) and the increase in eective resistance due to low self-resonant frequency (SRF) [43]. k12 and k34 are measured to be 0.56 and 0.59, respectively, which are close to simulated coupling factors. k12 and k34 do not change during the operation of the system (since coils 1 and 2 and coils 3 and 4 do not move with respect to each other). A 50  sinusoidal source is used to generate a signal with a 10-V amplitude (maximum limit of the generator) at 700 kHz. Resistance of 5.6  is used in series with the driver coil to measure the current of this coil. As most of energy is dissipated at internal source resistance of 50  , a supply with a lower impedance should be used to improve the eciency of the system. In this set up, the eciency is calculated 43 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices from the output terminal of the signal source and the eect of realistic power amplier source resistance is taken into account by using 5.6  sense resistance. Figure 2.19: Power transfer system For this system, primary coil is wound over plastic tube of height 5.5 mm with side walls. After making the primary coil, driver coil is wrapped over primary coil to obtain a high coupling between these coils (k12). Similarly, secondary coil is made on a smaller tube and load coil is wrapped over secondary coil (Fig. 2.19). Figure 2.20 shows the relative dimensions of the coils. As plastic does not aect the magnetic eld, the eect of tube on the operation of the system can be neglected. In our experiment, all coils are centred around the same axis and the horizontal distance between the primary and the secondary coils is varied to change their coupling factor (k23). 44 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Figure 2.20: Coil dimensions 2.6 Results and Analysis Distance between the primary and secondary coils is varied from 6 mm to 52 mm in steps of 2 mm. Measured eciency of the power transfer system (Figure 2.19) is illustrated in Fig. 2.21 and shows that even with a relatively large distance between the coils of d > 20 mm (equivalent rm = 1.07), a high power transfer eciency is achieved. The measured 45 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Coil distance d(mm) Po w er  T ra ns fe r E ffi cie nc y   Spice Simulation Effi−formula Experiment Effi−2coil Figure 2.21: Power transfer eciency (experiment, SPICE simulation, eciency Equation 2.21, traditional two-coil model) 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 distance d(mm) O ut pu t v ol ta ge (V )   Spice Simulation Experiment Figure 2.22: Output voltage (simulation and measurement results) 46 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Coil distance d(mm) Po w er  T ra ns fe r E ffi cie nc y (% )   2−Sim−50ohm 2−Sim−5.6ohm 2−Sim−100ohm 4−Exp−50ohm 4−Exp−5.6ohm 4−Exp−100ohm 4−Sim−50ohm 4−Sim−5.6ohm 4−Sim−100ohm Figure 2.23: Eciency with varied source resistance for 2 and 4 coils based system (mea- surement results) results match very well with the SPICE simulations and the analytical equations derived to calculate power transfer eciency. The four-coil-based power transfer system provides stable power transfer eciency over long operating range. When the primary coil and the secondary coils are close ( 5-10 mm) experimental results are slightly dierent from the approximated analytical model derived for power transfer model (equation (2.21)). This slight descripancy is due to the assumption of low k14, k24 and k13 to derive Equation 2.21. When coils are close then these parameters can not be neglected. For SPICE simulations, the eect of k14, k24 and k13 are taken into account and hence closer matches are obtained with respect to measured data. In the traditional two-coil inductively coupled power-transfer system [15] the decrease in  with respect to distance is more pronounced (see Fig. 2.21). This is because the coupling coecient of the two coils drops rapidly with the distance (/ 1/d3) and the coils 47 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices have small Q-factor (in this case, the loaded Q-factor for the external coil is  236 and for the implanted coil which is loaded by a 100  load is 1.28). The results conrm that using the presented four-coil power-transfer system, high-power-transfer eciency can be achieved and can be optimized for relatively longer operating range as compared to that of conventional 2-coil systems. Measured Q1, Q2, Q3, Q4, k12 and k34 are used for simulation. Power transfer eciency is obtained as 82% for coil separation of 20 mm (with k23  0.05) between primary and secondary coils. The output voltage at 100  load resistance of the four-coil system is measured and plotted in Fig. 2.22. Measured values closely matches with the simulated values. Figure 2.23 shows the eect of source resistance on power transfer eciency. For a low value of source series resistance, a high eciency can be obtained. Q-factor of the driver coil changes the optimum eciency point and shifts with the distance as shown by simulation (gure 2.9). For the same series resistance 2-coil power transfer system has much more severe eects as shown in Figure 2.23. 2.7 Comparison with Previous Work The design based on the proposed technique is compared with previously reported power- transfer methods applied for implanted devices. Table 2.6 summarizes the results. To make a fair comparison with dierent designs eciency at normalized distance (d=rm) is presented. rm is geometric mean of rp and rs where rp, rs are radius of primary and secondary coils. Table 2.6 shows that 4-coil system achieves better eciency as compared to prior art inductive links operating with comparable size and operating range. 48 Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Table 2.6: Comparsion with previous work Ref. Dimension Freq. Eciency Distance (rp, rs)(mm) (MHz) (d(mm), d=rm) [9] (15, 15) 4.5 54% (10, 0.67) [2] (8.5, 6) 1 30% (7, 0.98) [3] (30, 10) 0.7 36% (30, 1.73) [5] (26, 5) 6.78 22% (15, 1.31) [38] (12, 12) 2 40% (12, 1) [6] (35, 10) 5 30% (20, 1.07) This Work (32, 11) 0.7 82% (20, 1.07) This Work (32, 11) 0.7 72% (32, 1.73) 2.8 Concluding Remarks In this work, the design and optimization steps for resonance-based four-coil wireless power delivery systems are described. The focus of the work is on power delivery in implantable devices. However, the method is general and can be applied to other applications that use wireless power transfer [34], [15]. Experimental results show that signicant improvements in terms of power-transfer eciency are achieved (as compared to traditional inductively coupled 2-coil systems). Measured results are in good agreement with the theoretical models and match well with the simulation results. Eciency is enhanced using high-Q factor coils ( 300) and high coupling between driver and primary coils (k12  0.56 ) and secondary and load coils (k34  0.59). The prototype 4-coil system achieves at least 2  more eciency as compared to prior art inductive links operating with comparable size and operating range. With external and implantable coils of diameters 64 mm and 22 mm, respectively, and at operating distance of 20 mm, power transfer eciency of 82% is achieved. For operating distance of 32 mm, eciency slightly drops to 72%, which conrms the robustness of 4-coil based power transfer system when operating at long range. 49 Chapter 3 Development of PZT based Sonotherapy System for Implantable Devices 3.1 Introduction Ultrasound transducer is one of the most important component for any ultrasonic imaging system [52{55]. It is also a key component for applications such as high intensity focused ultrasound therapy [23, 24], high voltage transformers [56], energy harvesting devices [57], ultrasound sensors and actuators [58], thermosonic welding [59], biotelemetry [60], low noise oscillators design [61]. In all these applications, ultrasound transducers convert electrical energy into mechanical energy and conversely, convert mechanical energy to electric energy. Ultrasound therapy is becoming popular for minimally invasive and non-invasive ther- apy. High Intensity Focused Ultrasound (HIFU) and Sono-Dynamic Therapy (SDT) are two promising techniques that are used for cancer Therapy and local drug delivery re- spectively. HIFU is a novel emerging therapy that uses ultrasound waves, propagated through tissue media, as carriers of energy [23{25]. This method has great advantage of targeted drug/gene delivery, tumor ablation, hemostasis and thrombolysis [24]. SDT is a drug delivery approach that uses ultrasonic cavitation to enhance the cytotoxicity of 50 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices chemotherapeutic drugs. Sonodynamic enhancement of doxorubicin cytotoxicity was inves- tigated using micro ultrasonic transducers (MUTs) in combination with cancer drug in [1]. Using 60 seconds of toned burst ultrasound at 40 Watt/cm2, cytotoxicity of doxorubicin treatment increased from 27 to 91%. In case of implantable devices used for application shown in [1], size of ultrasound trans- ducer plays an important role to generate high power density acoustic waves (40 Watt/cm2) with a limited input power and hence should be kept small. This chapter investigates the eect of aspect ratio reduction of transducer on its physical parameters. Electrical models of transducer are used to estimate the performance of transducer. Dierent size ultrasound transducer samples are made and experimental results are used to explain eects of aspect ratio reduction of transducer on electro-mechanical conversion eciency. This chapter is organised as follows: Section 3.2 provides overview of fabrication tech- nology and operation mode and guidelines to select transducer type and material. Section 3.3 introduces basic theory of acoustic waves followed by electrical model of transducer presented in Section 3.4. Formulation of electrical to acoustic power transfer eciency is formulated in Section 3.5. Section 3.6 gives guidelines for transducer sample preparations and characterization steps. Section 3.7 analyze the eect of minituraization of transducer on its properties. Section 3.8 presents the experimental results of samples and chapter is concluded in Section 3.9. 3.2 Fabrication Technology and Mode of Operation Strain and stress are the two commonly used terms in mechanical system. In the context of transducer, strain S = =t, where  and t are thickness deformation and transducer thickness, respectively. Stress T = F=A, where F is the applied force over transducer of area A. 51 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 3.2.1 Fabrication Technology Piezoelectric materials, mainly lead zinconate titanate (PZT) is a commonly used ceramic for ultrasound transducer. In micromachined technology, capacitive-micromachined ul- trasound transducers (CMUTs) [23, 62] and piezo-micromachined ultrasound transducers (pMUT) [63] are becoming the two popular technology to design new ultrasound trans- ducers. Dierent fabrication [58, 64] and composite materials [65{68] are used to design and optimize the transducer paramaters to improve the performance. CMUTs oer better acoustic matching to the propagation medium, resulting in broader fractional bandwidth and thus CMUTs provide advantages for ultrasound imaging [69]. For sonotherapy appli- cation where single frequency is used, high bandwidth is not required. Furthermore due to high electro-mechanical conversion eciency compare to CMUT (or pMUT), PZT is considered for present application. 3.2.2 Theory of Operation and Resonance Mode The microscopic origin of piezoelectric eect is the displacement of ionic charges within the crystal structure. When an external electric eld is applied, the charges are displaced and a net strain is generated and vice-versa. Based on direction of generated strain, dierent vibration modes are dened [65, 70, 71]. Mode theory has been used to analyze resonant modes of vibration of composite transducer [72]. In general for thin disk PZT, two vibration modes are studied namely planar (radial) and thickness (longitudinal) modes. The planar (radial) mode of vibration involves mechanical motion perpendicular to the length of a PZT element. The thickness mode resonance of a PZT element is of greatest importance as it transmits and receives the longitudinal waves (waves in direction of applied electric eld). Figure 3.1 shows the thickness and radial mode vibrations in thin disk PZT transducer. 52 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Figure 3.1: Resonance modes in thin disk PZT transducer 3.2.3 Selected Parameters of PZT Material This section provides information about main parameters that need to be used to compare dierent PZT materials while selecting for particular application. More detailed denitions of each parameter can be found in [73]. Piezoelectric charge constant (symbol: d, unit: C/N) It is the polarization generated per unit of mechanical stress (T ) applied to a piezoelectric material or, alternatively, is the mechanical strain (S) experienced by a piezoelectric mate- rial per unit of electric eld applied. It is an important indicator of a material's suitability for strain-dependent (stimulator/actuator) applications. Piezoelectric Voltage Constant (symbol: g, unit: Vm/N) It is the electric eld generated by a piezoelectric material per unit of mechanical stress applied or, alternatively, is the mechanical strain experienced by a piezoelectric material per unit of electric displacement applied. Higher value of g corresponds to generation of higher electric eld across PZT for given mechanical stress. g is important for assessing a material's suitability for sensing (sensor) applications. 53 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Electromechanical Coupling Factor (symbol: k, unitless) The electromechanical coupling factor, k, is an indicator of the eectiveness with which a piezoelectric material converts electrical energy into mechanical energy, or converts me- chanical energy into electrical energy. A high k usually is desirable for ecient energy conversion, but k does not account for dielectric losses or mechanical losses, nor for recov- ery of unconverted energy. The accurate measure of eciency is the ratio of converted, useable energy delivered by the piezoelectric element to the total energy taken up by the element. By this measure, piezoelectric ceramic elements in well designed systems can exhibit eciencies that exceed 90 %. Based on resonance mode dierent Electromechanical Coupling Factor can be dened based on mode of operation. k33 : factor for electric eld in direction 3 (parallel to direction in which ceramic element is polarized) and longitudinal vibrations in direction 3 (ceramic rod, length  10  diameter) kt : factor for electric eld in direction 3 and vibrations in direction 3 (thin disc, surface dimensions large relative to thickness; kt < k33) k31 : factor for electric eld in direction 3 (parallel to direction in which ceramic element is polarized) and longitudinal vibrations in direction 1 (perpendicular to direction in which ceramic element is polarized) (ceramic rod) kp : factor for electric eld in direction 3 (parallel to direction in which ceramic element is polarized) and radial vibrations in direction 1 and direction 2 (both perpendicular to direction in which ceramic element is polarized) (thin disc) 54 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Thickness mode Frequency Constant (symbol: NT , unit: Hz-m) The thickness mode frequency constant, NT , is related to the thickness of the ceramic element, t, by NT = fst, where fs is series resonance frequency. This is used to calculate the frequency of operation. Mechanical Quality factor (symbol: Qm, unitless) This corresponds to selectiveness of PZT with applied electric eld frequency. Many empir- ical model suggested that ecieny is function of mechanical quality factor. This should be kept high while selecting PZT material. In general, in datasheet given value corresponds to Qm in air. Dielectric Dissipation Factor (symbol: tan, unitless) It corresponds to dielectic loss in PZT and should be kept low to reduce heat loss in PZT for implant applications. 3.3 Acoustic Wave Theory The specic acoustic impedance(z) is a ratio of acoustic pressure to specic 
ow, or 
ow per unit area, or 
ow velocity v. For sound intensity, I, particle velocity, v, and 
ow cross section area, A, z = p v = I v2 = p2 I (3.1) The characteristic impedance (Z0) of a medium, such as air, PZT or water is a material property, Z0 = c. where  is the density of the medium and c is the longitudinal wave speed 55 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices or sound speed. Specic acoustic impedance is sometimes also called the characteristic acoustic impedance of a medium (z = c). For acoustic intensity, I and for surface force, F at PZT surface with cross section area (A), acoustic power output will be Pout = IA = p2 z A = F 2 zA = F 2 cA (3.2) Acoustic parameters, p, z, v, I, are equivalent to voltage (V ), impedance (R), current (i) and power(P ) of electrical system respectively. In other matrix to equate acoustic output power (= IA) to electric power in terms of unit, for transducer of acoustic port area, A, electric parameters V , R and i are equivalent to surface force (F = pA), acoustic impedance (Z = zA) and particle velocity (v) respectively. Appendix E gives the formulation to calculate acoustic force and equivalent acoustic impedance of multilayer system. 3.3.1 Transmission Cocient and Matching Layers Impedance matching is a design practise of setting the input impedance (ZL) of an electri- cal/acoustic load equal to the xed output impedance (ZS) of the signal source to which it is connected, usually in order to maximize the power transfer and minimize re
ections from the load. Matching is obtained when ZS = Z  L where (where * indicates complex conjugates). In acoustic systems involving acoustic transmission lines, such as matching layers (glue, epoxy), where the length of the line is large compared to the wavelength of the signal, line should be matched to the transmission line's characteristic impedance, Z0 to prevent re
ections of the signal at the ends of the line from causing echoes. At the boundary, the two waves on the source side of the boundary (with impedance Z1) will be equal to the waves on the load side (with impedance Z2). The derivatives will also be equal. Using that equality and solving the wave equation, getting a transmission 56 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices cocient(T ) and re
ection coecient () :  = Z1  Z2Z1 + Z2 2 (3.3) T = 1  (3.4) Air has acoustic impedance of 400 Rayl which is very small compared to tissue acoustic impedance (ztissue  1.514 MRayl). The gel used in medical ultrasonography (zgel  1.54 MRayl) helps transfer of acoustic energy from the transducer to the body and back again. Without the gel, the impedance mismatch in the transducer-to-air and the air-to-body discontinuity re
ects almost all the energy, leaving very little to go into the body. For medical ultrasound imaging, wide bandwidth and good sensitivity is required as wide band pulse are sent to tissue and re
ected wave is captured to nd the time of transit. As the characteristic impedance of the PZT (zPZT  36 MRayl) is greater than that of water/tissue (zwater  1.5 MRayl), the transducer must be matched to tissue to transmit wideband pulse and recieve low amplitude echo of pulse. Eciency of power transfer is not a concern here and generally 50% power can be transmit from source to tissue. For sonotherapy, however single frequency acoustic waves are transmitted to tissue and wide-bandwidth power transmission is not required. Based on operating frequency, a respective PZT can be chosen with resonance frequency equal (or close) to frequency of operation. For present work, matching layers are not required. 3.4 Electrical Model of PZT To dene the electromechnical property and conversion of electric energy to acoustic energy and vice-versa, many electric models of PZT were proposed in litrature. The eectiveness 57 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices of these approaches is to predict the frequency-dependent electrical impedance and the transmitted and received acoustic waveforms for the transducer. Redwood [28], Mason [26], Krimholtz, Leedom, and Matthaei (KLM model) [27], Rhyne' model [74] are commonly accepted model for analysis and design of system for ultrasound imaging and sonotherapy. To simulate PZT performance, many publications were focused on PSPICE implementation of Mason and KLM model [75]. Comparison between Mason and KLM models is done in [76] and basic limitations of each model is provided. To include the eect of lossy dielectric, model were created based on Mason and KLM models [75, 77]. This section uses the Mason model to present an equivalent circuit that separates the piezoelectric material into an electrical port and two acoustic ports through the use of an ideal electromechanical transformer [26, 78{80]. Mason equivalent circuit for thickness mode PZT is shown in Figure 3.2. The element values are given as: Figure 3.2: Mason's electric model of PZT 58 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices C0 = KS0lw t (3.5) Z0 = clw !0 = 2f0 = c t 
 = f f0 N = r !0C0Z0k2t  Xa = Z0 sin Xb = Z0tan(
=2) where C0, K S, l, w are capacitance, dielectric constant of PZT under constant stress, length and width of PZT respectively. , c, t, kt are density, sound velocity in PZT, thickness and electromechanical coupling factor of PZT. For sonotherapy, one side of PZT (an acoustic port) is in proximity of tissue to transfer acoustic waves. Based on specic application dierent materials (with dierent acoustic impedance) can be as backing layer. Figure 3.2 shows the front and back acoustic port with current 
ow of I1 and I2. For back layer acoustic load of Zb, Mason model can be simplied as Figure 3.3 Figure 3.3: Simplied Mason's model for backing layer of acoustic impedance Zb 59 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Simplifying the mason model using network theory following equations can be derived as [78]:  A  = 1 NH 264 1 jN2=!C0 j!C0 0 375 A0  (3.6) H = cos
  1 + jz1sin
 (3.7) for z1 = Zb=Z0 A 0  = 264 cos
 + jz1sin
 Z0(z1cos
 + jsin
) jsin
=Z0 2(cos
  1) + jz1sin 375 (3.8) For n acoustic layer in front port of PZT, using Equation E.5 equivalent acoustic impedance seen by PZT for front layer and can be presented as Zf . The transfer matrix for PZT with input voltage V and input current I is, 264 V I 375 =  A  264 F1 v1 375 (3.9) where 264 F1 v1 375 = nY i=1 264 cos
i jZisin
i jsin
i=Zi cos
i 375 264 Fload vload 375 (3.10) Zf = F1=u1 From Equation E.5 and Equation 3.9, for PZT with equivalent back acoustic impedance of Zb and front acoustic impedance of Zf , input electric impedance can be calculated as, Zin = V I = 1 j!C0  1 k 2 t  (z1 + z2)sin
 + j2(1 cos
) (z1 + z2)cos
 + j(1 + z1z2)sin  (3.11) 60 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices where z1 = Zb=Z0 and z2 = Zf=Z0 for ! = !0, 
 =  and hence for anti-resonance frequency (!0) Zin = 1 j!0C0 + 4k2tZ0 !0C0(Zb + Zf ) (3.12) At anti-resonance frequency, PZT can be represented as series connection of capacitor of C0 and resistance Ra = 4k2tZ0 !0C0(Zb + Zf ) (3.13) as shown in Figure 3.4. Figure 3.4: Equivalent circuit of PZT at (a) anti-resonance frequency (b) resonance (series) frequency (c) near resonance frequency Similarly for resonance(series) frequency (for which Zin is minimum). PZT with match- 61 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices ing layer can be represented as parallel connection of C0 and resistance of Rs = (Zb + Zf ) 4k2t!sC0Z0 (3.14) and presented in Figure 3.4. In medium like water, impedance (Rs) increases (as Zf (orZwater) > Zair) and hence mechanical Q-factor (Qm) drops. Near resonance frequency, piezoelectric element can be modeled as commonly referred Van Dyke's model. For Van dyke's model, CR = k2t 1k2t C0 and LR = 1=! 2 sCR. Van Dyke's model is recommendated by the IEEE Standard on Piezoelectricity [81] to reduce the system complexity. For accurate analysis of transducer for dierent operating frequency, Mason or KLM models are recommended. 3.5 Acoustic Power and Eciency An important parameter studied in these calculations was the eciency of acoustic trans- mission. According to the 3 port system, the Transmission Transfer Function (TTF) is dened as TTF = FL=V , where FL is the force across the front load (e.g. water), and V is the AC voltage applied to the transducer [82]. The electromechanical conversion eciency, em, is dened as em = Po=Pi, where Po is output acoustic power and Pi is input electric power. Po = jFL(rms)j2 ZL (3.15) 62 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Pi = Vrms _I  rms = jVrmsj2cosh(Zin + Zg)i Zin + Zg (3.16) em = Po Pi = 1 ZL jFL(rms)j2 jVrmsj2 Zin + Zg cosh(Zin + Zg)i = jTTFrmsj2 ZL Zin + Zg cosh(Zin + Zg)i (3.17) and h(Zin + Zg)i = tan1  Imag(Zin + Zg) Real(Zin + Zg)  where Zin is electrical impedance seen by voltage source (Equation 3.11) and Zg is source internal resistance. Many emperical formulations have been presented to calcualte the electro-acoustic converstion eciency based on spring-mass model of PZT [57, 83, 84], which shows the eect of electromechanical coupling factor (kt) and mechanical quaity factor (Qm) over eciency. Higher value of (kt) and Qm are required to convert electric power to acoustic output ecienctly. 3.6 Sample Preparation and Characterization Appendix D provides the step-by-step process to create ultrasound transducer samples. This section provides the guidelines to select acoustic layers for transducer and shows methods to characterize transducers. Tissue has similar acoustic impedance as water (ztissue = 1.514 MRayl, zwater = 1.5 MRayl [85]), for experiment samples are tested in proximity 63 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices of water. 3.6.1 Selection of Acoustic Layers This section presents methods to select front and back layer for PZT based on acoustic impedance and mechanical stability of transducer sample. Selection of Backing Layer The front surface of a PZT is in contact with acoustic load (e.g. tissue). To transmit full acoustic power from front surface, it is desired to have a perfect re
ection of acoustic waves from back surface. As air has the least characteristic acoustic impedance (Z0 = 400 Rayl) so for sonotherapy applications, air-backed PZT is chosen. For medical ultrasound imaging applications where high sensitivity of transducers is desired and hence re
ection from the back surface is not recommended. Instead, characteristic acoustic impedance close to transducer (PZT) acoustic impedance (ideally Zb = ZPZT ) is desirable to have no re
ection from back surface (Equation 3.4). Selection of Front layer For sonotherapy, if a PZT transducer is operated at its resonant frequency, low electrical impedance (Rs) can be seen by the source and a matching layer is not required. To have electrical connection with PZT electrode from front side, aluminium(Al) foil with a 25 m thickness is chosen. While testing PZT sample using water exposed to the front layer, Al provides impermeable layer and stops water to ll in the back layer of PZT (as air- backed PZT is desired). Aluminium is electrically conductive, water impermeable and has moderate characteristic acoustic impedance (ZAl = 17.1 MRayl [85]) and hence it is a good choice for front layer. To provide stable contact between front layer aluminium and 64 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices PZT front surface, conductive silver epoxy is used which has low characteristic acoustic impedance (ZAg = 5.1 MRayl [85],  = 2.38 kg/m 3 [86]). To reduce eect of Al and silve epoxy layer on input impedance, thickness of these layers should be kept very small compared to wavelength (at operating frequency) of acoustic wave in respective layer. Ideally, thickness of silver epoxy layer should be kept very small (less than 50m). Figure 3.5: Acoustic layers in sample Figure 3.5 shows the conguration of each layer and Figure 3.6 shows the cross section and top view of sample device. Connection with Electrodes To access the front electrode of PZT, thin layer of conductive silver epoxy and aluminium is used. However if the bonding layer is thin enough compared to acoustic wavelength, the bonding layer does not need to be conductive and for reasonable values for the dielectric constant cheaper material than conductive epoxy can be used [87]. Back electrode of PZT is accessed directly using probe. The contact area of probe changes the backing layer 65 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Figure 3.6: Mechanical setup of samples (a) cross sectional view (b) top view acoustic impedance seen by PZT. To keep the backing layer property close to air, probe with small contact area should be used. Eect of probe size will be discussed in section 3.7. Figure 3.6 shows the electode connection method used for sample device. 66 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 3.6.2 Characterization of PZT Input Impedance PZT can be treated as 3-port network with one electric port and two acoustic ports. For PZT samples with measured layer thickness, Mason's model of PZT and electric model of acoustic layers (Equation 3.11) can be used to calculate theoretical input impedance of a sample. Figure 3.7 shows the real and imaginary part of input impedance for a sample PZT. While designing driver circuit for PZT, based on operating frequency corresponding impedance can be calculated using 3.11. To measure the input impedance of PZT with varying operating frequency, HP4294A (Agilent Technologies) impedance analyzer is used. Determining Resonant Frequency When exposed to an AC electric eld, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the eld. The frequency at which the ceramic element vibrates most readily, and causes minimum impedance, is the resonance frequency (fm). It is also known as series resonance frequency (fs). The composition of the ceramic material and the shape and volume of the element determine the resonance frequency. Generally, a thicker element has a lower resonance frequency than a thinner element of the same shape. As the cycling frequency is further increased, impedance increases to a maximum (minimum admittance). The maximum impedance frequency, fn , approximates the parallel resonance frequency, fp , the frequency at which parallel resistance in the equivalent electrical circuit is innite if resistance caused by mechanical losses is ignored. The maximum impedance frequency also is the anti-resonance frequency, fa. Maximum response from the element will be at a point between fm and fn. Values for minimum impedance frequency, fm , and maximum impedance frequency, fn , can be determined by measurement as shown in Figure 3.7. Figure 3.7 shows the typical impedance seen by source in connection with 67 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices PZT. 3 3.5 4 4.5 5 5.5 x 106 −150 −100 −50 0 50 100 150 Frequency Im pe da nc e   Zin Real(Zin) Imag(Zin) f m f n Figure 3.7: Impedance of air-backed PZT with water as acoustic load (size 5x5 mm) (Simulated) Measuring Electromechanical Coupling Factor General methods to characterize PZT are described in [88]. Based on experimentally evaluated series resonance frequency (fm) and parallel resonance frequency (fn), to estimate the electro-mechanical coupling factor(kt), emperical formulation were presented [73]. Coupling Factor for Discs: kp kp = p [(2:51(fn  fm)=fn) ((fn  fm)=fn)2] (3.18) 68 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Coupling Factor for Rods: k33 k33 = p (=2)(fn=fm)tan [(=2)((fn  fm)=fn)] (3.19) A resonance method for measurement of the electromechanical coupling factor k33 was proposed that is based on phase characteristics [89]. 3.7 Aspect Ratio Reduction of PZT 3.7.1 Eect on Electromechanical Coupling Factor The coupling between the thickness and planar(radial) modes is detrimental to perfor- mance at the frequency of the thickness mode. To reduce eect of mode coupling between dierent resonance while using PZT in thickness mode, ideally length (l) (and width (w)) of PZT should be 10  larger than thickness of PZT. For composite PZT (1-3 piezocom- posites), eect of lateral resonance was analyzed [68]. Similarly, [70] provides analysis of the resonance modes of PZT/Epoxy 1-3 Composite Rings. For 1-3 piezocomposites, as the transverse resonance modes couple with the thickness mode, the thickness mode electro- mechanical coupling factor (kt), decreases from the value for pure thickness mode [90]. Based on mode coupling theory and denition of the electromechanical coupling coe- cient, formula for eective electromechanical coupling coecient (keff ) of PMN-30%PT crystal is derived for arbitrary aspect ratio (G = l=t). Based on mode interaction analysis done for other transducer congurations (composite or partially crystal), reduction in kt can be expected for PZT ceramic as well for reduce aspect ratio (G < 10). For APCI material type 844 [73], planar (radial)-mode frequency constant (Nr = 2250 Hz-m) is close to thickness mode frequency constant (Nt = 2050 Hz-m). For aspect ra- tio (G) of 10, planar-mode fundamental resonance frequency will be quite smaller than 69 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices thickness-mode resonance frequency and hence these two modes will not couple eectively. For G = 10, reported value of kt (s 0.48, [73]) can be expected. For small PZT (G 10) the planar-mode low order harmonics comes close to thickness- mode resonance frequency and strong coupling occurs between the two resonance mode and causes reduction in thickness mode coupling factor (kt). Reduction in kt cause lower electromechnical energy conversion eciency. Intutively this phenomenon can be thought as leakage of energy from thickness mode operation to radial mode. Since acoustic load (e.g., tissue) is connected to front port of transducer, only thickness-mode vibration energy can be transferred. 3.7.2 Eect on Input Impedance Capacitance C0 of PZT is linearly propotional to its area (l  w) (as C0 = KS0lwt ). As the size of PZT reduces, capacitance also reduces propotionally. For small sized PZT (G < 10), with the reduction of the electromechanical coupling factor (kt), resonance series resistance Rs increases (Equation 3.14). While for small size PZT transducer , resonance parallel (anti-resonance) resistance (Ra) decreases with reduction in kt. Increase in Ra due to reduction is C0 is higher compared to reduction (of Ra) due to k 2 t . In general, Ra increases with reduction in PZT size. 3.7.3 Eects of Electrode Contact For a perfect re
ection from the back layer, acoustic impedance of back layer (Zb) should be very small so that all acoustic power will be transferred through front surface (connected to tissue). For this reason, air (zair = 400 Rayl) is used as backing layer of PZT (zPZT = 36  106 Rayl). To drive a PZT, the electrode with contact area Aelec ( Aelec = area in contact with back layer of PZT) is connected to the back layer of PZT (area = A). Input 70 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices impedance of PZT transducer is inversely propotional to its area (Equation 3.11), thus eective input impedance of electrode connected PZT transducer can be calculated by parallel impedance of two PZT transducers as electrode backed PZT (area = Aelec) and air backed transducer (area = A Aelec). For A Aelec, eect of electrode contact on input impedance will be small and hence can be ignored. For small sized PZT, the eect of electrode size can not be ignored. For the same electrode area, input impedance increases as PZT shrinks in size. Part of the input power goes through back layer and hence reduces the power going to front layer of PZT. This eect causes reduction in the electromechanical conversion eciency (em). 3.8 Experiment and Results 3.8.1 Instrument Setup Figure 3.8 shows the setup of PZT impedance measurement. Samples are partially im- mersed in the water bath so that one acoustic port (front port) will be in contact with water and second acoustic port (back part) will be in contact with air. Positive and nega- tive electrodes are connected to back layer and front layer of PZT sample, respectively, as shown in Figure 3.8. An impedance analyzer, HP4294A, is used to measure the amplitude and phase of input impedance of PZT. As for the present design, the resonance frequency is in the range of 4 MHz to 5 MHz, frequency is sweeped from 2 MHz to 6 MHz to capture impedance data. A copper wire of 0.25 mm radius is used as back electrode. Figure 3.9 shows the setup of electromechanical (or electroacoustic) conversion e- ciency measurement. Samples are partially immersed in water bath of ultrasound power meter (UPM-DT-1AV, Ohmic Instruments Co.). PZT samples are centered over the cone- shaped ultrasound power sensor shown in Figure 3.9. PZT samples are driven using signal 71 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Figure 3.8: Measurement of input impedance of transducer sample generator with varied frequencies. The voltage at the signal generator's output and the sense resistor (Rsense = 22 ) pin is recorded using an oscilloscope. Using this data, volt- age and current across the PZT can be calcualted. For present design, electric impedance matching is not done between source and PZT sample and hence input power will have both real and reactive part at operating frequency. Overall input power is calculated using power formula (jSj = jVrmsj:jIrmsj). Generated acoustic power can be noted down directly from display of ultrasound power meter. Basic properties of a PZT APCI material type 844 ( [73]) are shown in table 3.1. Table 3.2 gives the acoustic property of materials that are used to make the samples. [85], [91]. Samples are made with structure showed in Figure 3.6 and the dimensions of each layer are listed in Table 3.3. Design steps to construct samples are provided in Appendix D. 72 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Figure 3.9: Measurement of electromechanical conversion eciency of transducer sample Table 3.1: Main parameters for selected material Symbol denition value tan  Dielectric Dissipation Factor 0.4 kt Electromechanical Coupling Factor 0.48 d33 Piezoelectric Charge Constant 300 pC/N NT Thickness frequency Constant 2050 Hz-m Np Planar frequency Constant 2250 Hz-m Qm Mechanical Quality Factor 1500 3.8.2 Results and Analysis Sample 1 Sample 1 is made using a 5 mm x 5 mm-PZT sample and has an aspect ratio (G = l=t) of approximately 10, hence the principal radial mode resonance frequency will be order of 0.4 MHz (= Np=l). In the operating range of the PZT (4 MHz to 5 MHz), only high order harmonics (10th order frequency = 4 MHz) will couple with principal resonance frequency of thickness mode vibration. As eect of higher order harmonics is small so 73 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices Table 3.2: Acoustic property Material Acoustic impedance density Mrayl (= 106Rayl) x103kg=m3 PZT 36.72 7.7 Epoxy 5.1 2.38 Aluminium 17.1 2.7 Copper 41.61 8.93 Steel 56.7 7.67 Air 0.0004 0.001 Table 3.3: Samples mechanical parameters Sample l w Thickness (mm) number (mm) (mm) PZT Aluminium Foil Epoxy Ni/Ag -Electrode 1 5 5 0.5 0.025 0.033 0.006 2 2.5 2.15 0.5 0.025 0.027 0.006 3 2.5 2 0.5 0.025 0.038 0.006 no coupling between radial and thickness mode vibration is seen in impedance curve of sample 1 (Figure 3.10). Figure 3.10 and 3.11 show the amplitude and phase of the input impedance for sample 1, respectively. 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 0 50 100 150 200 250 300 Operating Frequency (Hz) Im pe da nc e (Z in  in  o hm )   Simulated Experiment Figure 3.10: Simulated and measured amplitude of input impedance of air-backed PZT (sample 1) 74 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 −100 −50 0 50 Operating Frequency (Hz) Ph as e (Z in  in  d eg re e)   Simulated Experiment Figure 3.11: Simulated and measured input impedance of air-backed PZT (sample 1) The acoustic power is measured using an ultrasound power meter as shown in Figure 3.9. For an input sinusoidal voltage of amplitude of 9.05 V, output acoustic power is measured and plotted in Figure 3.12. For applied input voltage, front port force (FL) can be calculated by solving Equation 3.11. Using the simulated acoustic force that is FL, generated acoustic output power is determined by Equation 3.15 and plotted along with experimental data. Input power is calculated using product of voltage across PZT and current through it (formula 3.16). As voltage is measure from output port of signal generator so source impedance can be taken as zero (Zg = 0). Eciency is calculated based on equation 3.17. Figure 3.13 shows the calculated and measured electromechanical (electroacoustic) conversion eciency of sample 1. 75 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 0 0.02 0.04 0.06 0.08 0.1 0.12 Operating Frequency (Hz) Ac ou st ic  O ut pu t P ow er  (W att )   Simulated Experiment Figure 3.12: Output power of air-backed PZT (sample 1) (simulated and measured) 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Operating Frequency (Hz) El ec tro −A co us tic  c on ve rs io n Ef fic ie nc y   Simulated Experiment Figure 3.13: Electro-acoustic conversion eciency of sample 1 (simulated and measured) Sample 2 and Sample 3 Sample 2 is made using a 2.5 mm x 2.15 mm PZT and has an aspect ratio (G = l=t) of approximately 5, hence the principal radial mode resonance frequency will be on the order 76 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices of 0.9 MHz (= Np=l). In the operating frequency of PZT (2 MHz to 5 MHz), the third order harmonics (2.7 MHz) and fourth order harmonics (3.6 MHz) of radial resonance mode will couple with principal resonance frequency of thickness mode vibration. This eect can be seen in the highlighted section of Figure 3.14. The principal resonace frequency of thickness mode vibration is shifted to high frequency due to mode coupling. Figure 3.15 shows the measured phase of sample 2 input impedance. Sample 3 is made using a 2.5 mm x 2 mm PZT and has an aspect ratio (G = w=t and G = l=t ) of order 4 (w/t = 4) and 5 (l/t = 5). Principal radial mode resonance frequency in width direction will be order of 1.125 MHz (= Np=w) and in length direction is 0.9 MHz (= Np=l). In operating frequency range of PZT (2 MHz to 5 MHz), second and third order harmonics ( 2.25 MHz and 3.375 MHz) of radial vibration in width direction and third and fourth order harmonics ( 2.7 MHz and 3.6 MHz) of radial resonance in length direction will couple with principal resonance frequency of thickness mode vibration. This eect can be seen in the highlighted section of Figure 3.14. The principal resonace frequency of thickness mode vibration is shifted to high frequency due to mode coupling. Figure 3.15 shows the measured phase of sample 3 input impedance. From Figure 3.16, it can be seen that due to mode coupling, electro-acoustic conversion eciency drops to around 60 %. Part of input energy goes as radial vibration which can not be utilized in thickness mode operation. Due to lack of accurate analytical model of transducer to analyze its performance under mode coupling conditions, simulation results for low aspect ratio transducers are not shown. 3.9 Conclusions As size of transducer reduces, the mode coupling causes leakage of input power in radial vi- bration energy and hence reductions in electro-acoustic conversion eciency. To reduce the 77 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 100 200 300 400 500 600 700 800 900 Operating Frequency (Hz) Im pe da nc e (Z in  in  o hm )   Sample 2 Sample 3 Higher Harmonics Sample 3 Higher Harmonics Sample 2 Figure 3.14: Measured amplitude of input impedance of air-backed PZT (sample 2 and sample 3) 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 Operating Frequency (Hz) Ph as e (Z in  in  d eg re e)   Sample 2 Sample 3 Figure 3.15: Measured phase of input impedance for air-backed PZT (sample 2 and sample 3) eect of mode coupling, thickness mode resonance frequency should be kept far from lower order harmonics (principal or third) of radial mode vibrations. In present work, eects 78 Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices 2 2.5 3 3.5 4 4.5 5 5.5 6 x 106 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Operating Frequency (Hz) El ec tro −A co us tic  c on ve rs io n Ef fic ie nc y   Sample 2 Sample 3 Figure 3.16: Measured electro-acoustic conversion eciency of sample 2 and sample 3 of aspect ratio reduction of PZT is analyzed and reduction in electro-acoustic conversion eciency is explained using mode coupling between dierent resonance modes. Eect of electrode area on transducer eciency is explained. Sample 3 is used as ultrasound transducer to make the overall system to generate ultrasound acoustic wave. 79 Chapter 4 Development of Energy Harvesting and Driver Circuits for PZT 4.1 Introduction To harvest the energy from resonance coupled wireless power delivery system, presented in Chapter 2, and to drive PZT, a set of circuits are used. Figure 1.1 (in Chapter 1) shows the block diagram of overall system showing the energy 
ow among wireless power- transfer (WPT) block, energy harvesting and driver block and the device (PZT sample-3). Chapter 2 and Chapter 3 provide the design and optimization steps of wireless power delivery system and characterization of transducer sample (to actuate the tissue cells), respectively. In this chapter we design a prototype energy harvesting system and driver circuit. This is a proof-of-concept design to demonstrate the funtionality of overall system. Not all the blocks are optimized but most of design steps are valid. 4.2 Circuit Design To reduce dependance of dierent design blocks, wireless power transfer block is optimized independently for xed load condition. Based on design constrains (small size requirement: 2 mm 2 mm), PZT samples are made and characterized for optimum operating frequency. Due to change in operating conditions of device based on application, design of driver circuit 80 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT should be done in the last step. Following blocks are identied as part of energy harvesting and driver circuit. 4.2.1 Rectier WPT block provides alternating current (AC) signal across load. As this energy can not be used directly to drive the device, a transformation from AC signal to direct current (DC) signal is required. Diode-based full-wave bridge rectier is one of most commonly used techniques to convert an AC signal to DC with good eciency. For ideal diodes, eciency of this block is 81.2 % [92]. Figure 4.1 shows the circuit diagram of full wave bridge rectier. For this bridge, diodes with low built-in voltage (Vf = 0.4 V) and high reverse-breakdown voltage (Vb = 20 V) are needed. The bridge is followed by a DC-DC converter which acts as load resistance (Rload). Crect acts as input lter capacitor of DC-DC converter. Figure 4.1: Full wave bridge rectier 4.2.2 DC-DC Boost Converter For wireless power transfer of operating range 1-3 cm, rectier output voltage is of the order of 4 to 8 volts (in practical design). To provide targeted power of order 400 mW 81 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT to small size PZT, (impedance  1 k ) requires high voltage of order 25 V. Therefore DC-DC boost converter is required for present design. O-the-self DC-DC boost converter will be used for present design. Specication of DC-DC converter depends on the power requirement of transducer and characteristics of device used. This section provides the guidelines to choose the voltage and current specications of DC-DC converter. PZT sample should be characterize for two main parameters, 1) electromechanical conversion eciency versus frequency 2) impedance versus frequency. While operating the sample at their most ecient frequency, corresponding impedance value can be used to calcualte operating voltage of PZT for given power requirement. As induced voltage across rectier input changes with variation in operating distance of power transfer coils, hence DC-DC converter input voltage range should be kept wide enough. Output voltage of power amplier (class-A) should be biased at Vdd=2 (Vdd = DC- DC output voltage) to achieve high output voltage swing. With the power amplier DC load resistance of Rin, DC current can be calculated as Idc = Vdd 2Rin and hence DC power consumption will be V 2dd 2Rin . For voltage swing of amplitude Vdd/2 and load reistance of Rin, AC power consumption can be formualted as V 2dd 8Rin . For optimum operating frequency of fopt with electromechanical conversion eciency (em) (or PZT ) and PZT's input impedance of Rin, to generate the acoustic power of Pout, the following formulation can be derived: Pin = Pout PZT = V 2dd 2Rin (DC) + V 2dd 8Rin (AC) Vdd = Vdcdc = r 8 5 PinRin (4.1) Idcdc = Vdcdc=2Rin (4.2) 82 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Equation 4.2 is valid assuming the full conversion of DC-DC input power to PZT stimulting signal power. It provides the minimum value of Vdcdc and Idcdc. Eciency of DC-DC converter is maximum near its full load condition. Chosing the current specication of DC-DC converter, full load current can be chosen close to Idcdc. Based on above calculation to transfer 400 mW power to PZT sample with input impedance of  1 k , 12.6 mA current will be drawn from DC-DC converter. Due to unavailabilty of DC-DC converter with above specications, DC-DC converter (TPS61045, Texas Instruments) of voltage  17:8 V and current capacity of 10 mA is chosen which can provide input power of approximately 180 mW. Appendix J provides the schematics of selected DC-DC converter evaluation board. 4.2.3 Oscillator To generate the periodic (sinusoidal) waveform to drive PZT, a Colpitts-based oscillator is used [92]. This oscillator circuit uses a combination of an inductance (L) with a capacitor (C) for frequency determination. Thus it is an LC oscillator. One of the key features of this type of oscillator is its simplicity (needs only a single transistor) and robustness. Figure 4.2 shows the circuit diagram of oscillator used. In general, oscillator gain is limited by selection of RE and RC (Figure 4.2). Loading PZT directly to oscillator output will change its operating frequency. Hence to drive PZT, oscillator output need to be buered and amplied using high voltage power amplier. 4.2.4 Buer To reduce the loading eect of power amplier on oscillator circuit, a buer stage is needed between oscillator output and power amplier input. For present design common drain- amplier, which has approximately a gain of 1, is used. Figure 4.3 shows the circuit 83 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.2: Colpitts oscillator diagram of buer. 4.2.5 Power Amplier For present design, class-A power amplier (PA) is used. Maximum eciency of class-A power amplier is 25 %. Figure 4.4 shows the circuit diagram of class-A amplier. To improve the eciency of overall system, higher eciency power ampliers, such as class- E PAs can be used in the future design. To achieve high voltage swing at the power amplier output, high amplitude input voltage is used to get switching characteristics at power amplier output. It generates square type wave at PA's output. As PZT generates acoustic power eectively at its resonant frequency only and hence other harmonics power can not be utilized to generate acoustic waves. 84 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.3: Common drain buer 4.3 Experiment Setup and Results Each block of system is made as explained in Section 4.2. Components and their values for each block are listed as follows in Tables 4.1, 4.2, 4.3, 4.4. Table 4.1: Design parameters of rectier Symbol Parameter Value Unit D1/D2/D3/D4 Vf 0.5 V (MUR115) Vb -150 V 4.3.1 Characterization of Power Amplier Load resistance of power amplier is kept close to PZT impedance for maximum power transfer (by impedance matching). Circuit is built as shown in Figure 4.4. Due to impedance matching power transfer eciency (PT ) of 50 % can be achieved. Theoretical 85 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.4: Class-A power amplier maximum eciency of power amplier circuit with PZT as load is calcualted as follows: PA = 0:25 PZT = 0:53 PT = 0:5 d(driver circuit) = PA:PZT :PT = 6:66% (4.3) With power supply voltage of 17.5 V and driving PZT at 4.4 MHz with bias voltage of 0.81 V and oscillator amplitude of 1.47 V (peak-to-peak), output swing of 8 V is achieved at PZT output. Power amplier draws 8 mA from the power supply. It results in input power of 140 mW. Using ultrasound power meter acoustic power is recorded and found 86 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Table 4.2: Oscillator Symbol parameter value unit RC R 5.1 k  RE R 2 k  L1 L 10 H (murata) 18r103c C1 C 220 pF C2 C 302 pF C3 C 560 pF Q1 JFET 2N5484 - Table 4.3: Buer Symbol parameter value unit R1 R 180 k  R2 R 18 k  RE R 1 k  Cac C 470 pF Q1 JFET 2N5484 - to be around 8 mW. It corresponds to power amplier eciency of 5.7% which is close to theoretical maximum value. Figures 4.5 and 4.6 show the base and output voltage of PA respectively. 4.3.2 Characterization of Oscillator and Buer Colpitts oscillator is used to generate a 4.4 MHz sinusoidal signal. Circuit diagram is shown in Figure 4.2. Oscillator generates output swing of 1.6 V at its drain terminal. As oscillator can not drive the input of power amplier directly, hence a unity gain buer (Figure 4.3) is used as interface between the oscillator and the power amplier. With supply voltage of 17.5 V, oscillator consumes 0.6 mA current (10 mW of power consumption). Figure 4.7 shows the oscillator output waveform. Output signal of oscillator is connected to input terminal of buer. With supply voltage of 17.5 V, buer draws approximately 2 mA of current from the supply (resulting in 35 mW of power consumption). The output waveform 87 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Table 4.4: Power amplier Symbol parameter value unit R1 R 51 k  R2 R 4.6 k  RC R 1 k  RE R 20  RB R 10  C1 C 470 pF Cac C 470 pF Q1 NPN MRF544 - Table 4.5: PZT impedance at 4.4 MHz (PZT: sample3) Symbol parameter value unit PZT Zin 500  phase -20 degree PZT 0.53 - of buer has an peak-to-peak voltage of 1.47 V and is shown in Figure 4.5. 4.3.3 Characterization of DC-DC Converter DC-DC converter has a non-linear input impedance based on its input voltage. For given output voltage and current of dc-dc converter, the higher the input voltage the higher the impedance seen by power source. For a xed load and output voltage, DC-DC converter can be considered as constant power source. For a given output power requirement and xed input voltage, eective input impedance of DC-DC converter depends on its input voltage, output power and the eciency of DC-DC converter. From simple energy conversion method, Rin(dcdc) = dcdc:V 2in(dcdc)=Pout, where dcdc, Vin(dcdc) and Pout are eciency of DC-DC converter at given load, DC-DC input voltage and output power, respectively. 88 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.5: Power amplier input voltage (transistor's base voltage) 4.3.4 System Eciency All the blocks are connected as shown Figure 1.1. Using design setups in chapter 2, for resistive load of 100 , wireless power transfer system is optimized for 1 to 3 cm operating distance and it has resonance frequency of 700 kHz. Signal generator is used to generate 160 mV (peak-to-peak) sinusoidal signal with frequency of 700 kHz and amplied using power amplier (Model 240L, 50 dB gain, Bell Electronics, Nw. Inc.) to feed the driver coil of wireless power delivery system. For coil distance of 1.5 cm, with load coil and energy harvesting and driver circuit in place, DC-DC converter shows a load impedance of 300  at the load coil terminals and voltage at input of DC-DC converter is measured as 8 V. High load resistance causes the reduction in eciency of wireless power transfer (WPT ) to 60 %. Power consumption of oscillator and buer is independant of output power requirement. Using lower power oscillator and buer circuit (typically oscillator 89 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.6: Power amplier output voltage (input voltage of PZT) power of 2 mW and buer circuit power of 4 mW using 3 V supply), eect of oscillator and buer circuit will be very small on overall power transfer eciency. Hence to calculate the system eciency, power consumption of oscillator and buer can be omitted. For driver circuit with eciency 5.7 %, d and with rectier eciency of 80% and DC-DC converter eciency of 82%, theoretical maximum eciency of present system will be approximately 2.24 %( = rect:dcdc:WPT :d). Figure 4.8 shows the input voltage of the external coil. The signal generator output of 160 mV (peak-to-peak) at 700 kHz is fed to power amplier (Model 240L, 50 dB gain, Bell Electronics, NW Inc.) and output is connected to the driver coil of wireless power delivery system. Output acoustic power of 8 mW is recorded using ultrasound power meter. Figure 4.8 shows the input voltage of driver coil and voltage across the 5.6  sense resis- tor. Input power of 0.53 W is fed to the driver coil and 190 mW of power is received after 90 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.7: Output waveform of colpitts oscillator the DC-DC converter. This includes the power transfer eciency of the wireless power de- livery block, the rectier and the DC-DC converter and 35.8 % eciency (rect:dcdc:WPT ) is achieved which is close to theoretical eciency of 38.4 %. Excluding the eect of os- cillator and buer power, system eciency is measured as 2.04 % which is close to the theoretical maximum eciency of 2.24 %. Appendeix G, Figure H and Figure I shows the overall system, circuit and ultrasound power meter setup. 4.4 Conclusions Presented energy harvesting and driver circuit is designed to convert received energy (from external coil) and drive the implanted device (PZT) to generate the acoustic waves. Each block of circuit is designed invidually and interfaced to realize overall system showing energy 
ow from external coil to PZT device and generation of acoustic power. The 91 Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT Figure 4.8: Input voltage at wireless power delivery system (driver coil's input) and at sense resistor eciency of the overall system measured as 2.04 % which is close to the theoretical value of 2.24 %. By designing circuit to re
ect resistive load of 100  at load coil terminals, it results wireless power transfer eciency of 80 % for 1-2 cm operating distance. In present design, power amplier restricts the overall eciency of ciruit which can be boosted to 80% by using class-E power amplier. By using class-E amplier, system eciency can be boost to 20 % (WPT = 0:8; rect = 0:81; DCDC = 0:8; PA = 0:8; em = 0:53). Similarly low power oscillator can be made to reduce eect of its power consumption on system eciency. Even though eciency overall system is small but key component of design, wireless power delivery system and PZT are optimized. 92 Chapter 5 Summary of Thesis and Future Research Topics In this chapter, we summarize the main results obtained in this thesis and propose ideas for future related research. 5.1 Summary of Results Microultrasonic transducers (MUTs) for therapeutic applications in combination with a cancer drug for sonodynamic enhancement have previously been investigated in vitro using human prostate cancer cells in [1]. The main goal of this thesis is to design an implantable wireless power delivery system in combination with minituarized ultrasound transducer to generate acoustic shock waves for sonoporation. Due to the high power requirement by ultrasound transducer to achieve acoustic output power density of 40 Watt/cm2, the focus of this work is to design an ecient power transfer system from an external power source to transducers. Chapter 1 outlines the advancement of localized drug delivery using MEMS based im- plantable devices and sets requirement of power ecient system design for sonoporation based drug delivery system. Block diagram of overall system is proposed and design con- straints for each block is set. Chapter 1 shows the key contributions of present work. Chapter 2 provides design and optimization of the state-of-art ecient wireless power 93 Chapter 5. Summary of Thesis and Future Research Topics transfer system for implantable device. Based on system design constraints dened in table 2.1, wireless power transfer eciency of 80 % is achieved. By use of high quality (Q) factor power transfer coils compared to traditional designs for implantable devices, high power transfer eciency is achieved. Results are compared with previous wireless power delivery systems for implantable devices and more than 2  eciency improvement is reported. Analytical model and generalized design steps are presented. For change in design require- ments, system can be optimized to provide maximum power transfer eciency with new design constraints. Chapter 3 provides the theoretical background of ultrasound transducer and electrical model for transducer in thickness-mode vibration. In this chapter, key parameters for material selection are described to achieve high electro-mechanical conversion eciency. Eects of transducer aspect ratio are presented. Transducer samples of size 5 mm x 5 mm, 2.5 mm x 2.15 mm and 2.5 mm x 2 mm are made and eect of resonance mode coupling between radial and thickness mode is shown experimentally. Sample 3 (Table 3.3) is used for design of driver circuit which shows electromechanical conversion eciency (em) of 53 % at 4.4 MHz operating frequency. Chapter 4 gives the combined structure of system using wireless power delivery block, ultrasound transducer device and interface circuit between them. For proof-of-concept, discrete components are used to build rectier, oscillator, buer and power amplier. O- the-shelf, DC-DC boost converter is used. Driver circuit was designed for prototype purpose and low power circuit design techniques are not part of present work. By driving current from DC-DC converter (output voltage of 17.5 V), oscillator and buer consume 10 mW and 35 mW of power respectively. Power amplier generates the output swing of 8 V at transducer input. Due to generalized approach to design ecient wireless power delivery system and 94 Chapter 5. Summary of Thesis and Future Research Topics guidelines on aspect ratio reduction of transducer, present design blocks can be used in other applications as well. Due to use of discrete component and non-optimized circuits, present system eciency is limited to 2 .04 % which can be further improved upto 22 % using low power circuit design and energy ecieny power amplier. 5.2 Limitations and Future Work 5.2.1 External Power Source for Constant Power Delivery Proposed wireless power delivery system for implantable device can provide stable eciency in long operating range (10 mm to 30 mm) and hence can be considered as constant e- ciency system with respect to operating distance. Based on the distance between primary and secondary coils, input power of power delivery system changes and hence constant power can not be achieved at load with distance variation. To achieve constant power, input voltage should be varied to compensate change in impedance of driver coil due to change in mutual coupling between coils. A feedback control system can be implemented to control input voltage of external coil. 5.2.2 Current Limitation in Coil Current design uses AWG28 Litz wire type to make the power delivery coils which can carry upto 1.4 A current [93]. In the present design, output power at implanted device was not taken as design constraint. As power requirement of present design is order of 400 mW so large current will not be generated in coils. For high power applications, using design and optimization steps of wireless power delivery system, calculation of current in each coil can be done based on coils' electric porperties. Based on simulation, optimum wire gauge can be recommended or dierent wire gauge can be used for simulation for further 95 Chapter 5. Summary of Thesis and Future Research Topics calculation. 5.2.3 Optimization of Transducer Size Mode coupling between dierent resonance modes causes major eect on electromechanical conversion eciency. Diernt material types (or technologies) for transducer need to be characterized to reduce mode coupling for small size transducer. Using a higher frequency transducer, the thickness of the transducer will be small and a moderate aspect ratio can be achieved for similar length and width of the transducer. 5.2.4 Low Power Circuit Design For prototype, low power circuit design techniques for energy harvesting and driver block can be done. Low drop diode (with high breakdown voltage) should be used for rectier circuit to reduce power consumption by rectier. Low power oscillator can be used to generate the reference signal for device. JFET or MOSFET based power amplier can be used to reduce the input current or power amplier stage. Class-E or advanced power amplier can be used to increase the ecieny of power amplier. Unity gain buer can be optimized for low DC current and low load current of power amplier. 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Oxford Universtiy Press, 2004. [93] MTI corporation, \American wire gauge table and awg electrical current load limits." [Online]. Available: http://www.mtixtl.com/knowledgeofamericanwiregauge.aspx [94] R. Hill and S. M. A. El-Dardiry, \A theory for optimization in the use of acoustic emission transducers," The Journal of the Acoustical Society of America, vol. 67, no. 2, pp. 673{682, 1980. 104 Appendix A Eciency Maximization Distance in Eq.(2.31) Ecient of 4-coil based wireless power delivery system can be expressed as (Equation A.1):  = (k212Q1Q2)(k 2 23Q2Q3)(k 2 34Q3Q4) [(1 + k212Q1Q2)(1 + k 2 34Q3Q4) + k 2 23Q2Q3][1 + k 2 23Q2Q3 + k 2 34Q3Q4] (A.1) For ease of derivation, abbrivated letter are used to replace the terms by C1 = (k 2 12Q1Q2)(k 2 34Q3Q4) (A.2) C2 = (k 2 12Q1Q2) (A.3) C3 = 1 + k 2 34Q3Q4 (A.4) f(d) = k223 (A.5) C4 = C1 + C2 + C3 (A.6) Taking rst order derivative of Equation 2.21 with respect to d and equate to zero will provide: @ @d = 0 105 Appendix A. Eciency Maximization Distance in Eq.(2.31) ) [C4 + f(d)Q2Q3][C3 + f(d)Q2Q3]C1Q2Q3f 0(d) C1f(d)Q2Q3[C4f 0(d)Q2Q3 + C3f 0(d)Q2Q3 + 2f 0(d)f(d)(Q2Q3)2] = 0 ) [C3C4 + (f(d)Q2Q3)2 + (C3 + C4)f(d)Q3Q3]C1Q2Q3f 0(d) C1Q2Q3f(d)[(C3 + C4)f 0(d)Q2Q3 + 2f 0(d)f(d)(Q2Q3)2] = 0 ) C3C4  (f(d)Q2Q3)2 = 0 (A.7) replacing values of C3, C4 and f(d) to A.7, expression A.7 can be rewritten as: [1 + k223Q3Q4] 2[1 + k212Q1Q2] = (f(d)Q2Q3) 2 k23(max) =  Q1 Q2  1 4  k12(1 + k 2 34Q3Q4) Q3  1 2 (A.8) placing k23(max) in eciency Equation 2.21: max =  k12 p Q1Q2 1 + k12 p Q1Q2 2  k234Q3Q4 1 + k234Q3Q4  (A.9) 106 Appendix B Optimization of Number of Turns Per Layer (Eq. 2.29) Self capacitance of Multilayer-helical coil, is expressed as [43]: Cself = 1 N2 " Cb(Nt  1)Na + Cm NtX i=1 (2i 1)2(Na  1) # (B.1) where N is total turns, Cb is parasitic capacitance between two nearby turns in the same layer and Cm is parasitic capacitance between dierent layers. Na is number of layers and Nt is number of turns per layer. for large value of layers Na  1 and Cb  Cm, Cself = Cm 1 N2 " NtNa + NtX i=1 4i2(Na  1) # (B.2) as Pk i=1 i 2 = 1 6 k(k + 1)(2k + 1), Cself can be rewritten as Cself = CmNaNt N2  1 + 4Nt(Nt + 1)(2Nt + 1) 6  Cself  4 3 CmNt Na as N = NtNa and Nt  1 (B.3) Cself = K1Nt Na where K1 = 4Cm 3 (B.4) Self inductance of coil can be approximated by Lself = K2N 2 = K2N 2 t N 2 a , where K2 107 Appendix B. Optimization of Number of Turns Per Layer (Eq. 2.29) is constant which depends of coil dimensions and is independent of number of turns and number of layers. Based of Cself and Lself , self resonating frequency can be calculated as fself = 1 2 1p LselfCself !self = 2fself = 1p K1K2Na 1 N 3=2 t (B.5) DC resistance of coils is propotional to coil wire length and hence depends on total number of turns. It can be written as Rdc = K3NaNt where K3 is a positive constant independent of Na and Nt. Similarily fh can be written in terms of Na and Nt. From eqution 2.11, fh = K4p NtNa where K4 is a constant. As per the Equation 2.17, Q(Quality)-factor of a coil is function of Lself , fself , Rdc and fh. Based on previous analysis and express as function of Na and Nt: Q(!) = !K2N 2 t N 2 a (1 !2(K1K2Na)N3t ) K3NtNa  1 + ! 2NtNa K4  = K5Nt (1K6N3t ) K3 (1 +K7Nt) where K5 = !K2Na, K6 = ! 2K1K2Na and K7 = !2Na K4 and are independant of Nt. Taking derivative of Q as function of Nt will give, @Q @Nt = 0) K3K5  1 4K6N3t  3K6K7N4t  = 0 (B.6) Placing values of K6 and K7 values to Equation B.6 will give: @Q @Nt = 0) K3K5  1 4! 2 !2s  3! 2 !2s !2 !2h  = 0 (B.7) 108 Appendix C Guidelines for High Q-factor Coil Preparation Chapter 2 provides the design parameters of high Q-factor coils to obtain high wireless power transfer eciency. In present design multilayer helical coil is used. Cross section of coil is shown in gure C.1 which shows the winding order of wire. Figure C.1: Coil cross section To make coils following steps need to be followed: 1. Prepare mechanical base with radius and height obtained using optimization which 109 Appendix C. Guidelines for High Q-factor Coil Preparation has thin sidewall to keep the wire in dened height. 2. On the mechanical base wrap the alternative layers of wire from left to right and right to left respetively as shown in gure C.1. 3. Dielectric layer is used to keep the self capacitance of coil small. It will be desired for big external coil to obtain high self resonating frequency. For implant coil as size of coil is small so dielectric layer is not required. 4. After making the primary and secondary (in this design implant) coil on their mechanical structure, driver coil and load coil should be wrapped over primary coil and secondary coil respectively by taking them as base. 5. Distance between turns in same layer should be keep minimum. 6. In present design 40 strands Litz wire is used which changes is resistive property while squeezing hardly. Wire should be wrapped gently. 110 Appendix D Ultrasound Transducer Sample Following steps need to be followed to make transducer sample for experiment: 1. Cut hollow aluminium/copper (conductive) tube in a piece with size of required dimensions. Diameter should be kept bigger than size of tranducer sample. 2. Cut the PZT transducer of desired size using diamond cutter. Extra precaution need to be taken at this step as PZT is very brittle. 3. Cut aluminium foil (thickness  25  m) in small piece. 4. Measure thickness of PZT transducer and aluminimum foil. 5. Use silver conductive epoxy (MG chemicals [86]) to glue PZT transducer to alu- minium foil. Very small amount of epoxy need to be used to realize the epxy thickness of 30  m or lesser. 6. Heat treat the glued sample at 100o C for 15 minutes to make good bondage between aluminium and PZT. 7. Measure the tickness of overall sample including PZT, aluminium and epoxy. Cal- culate the nal thickness of silver epoxy. 8. Attach the aluminium tube to aluminium foil using conductive glue keeping the sample in inner part of tube. Heat treat the glued sample again at 100o C for 15 minutes to make good bondage between aluminium tube and aluminium foil. 9. Wrap the extra aluminium foil over tube and glue it with tube to make sure other side of transducer should be dry and should be in the air while sample is partially dipped in water. Figure D.1 shows the nal construction of sample. 111 Appendix D. Ultrasound Transducer Sample 10. Use ultrasound power meter (UPM-DT-1AV, Ohmic Instruments Co.) or impedance analyzer (HP4294A, Agilent Technologies) to measure acoustic power or impadance char- acteristics of sample repectively. Figure D.1: Piezo-electric sample 112 Appendix E Acoustic Wave Transmission in Medium To explain the transmission of acoustic wave through series of layers, a multilayer system dened in gure E.1 can be taken. A plane unattenuated longitudinal sound wave is travelling from left to right (the positive x direction) through a series of n layers of material with dierent specic acoustic (characteristic) impedance zi. The incident wave travels through medium i, undergoes a series of re
ections and transmissions in the subsequent layers until a transmitted wave emerges into medium n, which is assumed to be of innite thickness. The incident wave has pressure pi and particle velocity vi, a re
ected wave has pressure pr and particle velocity vr, and the transmitted wave has pressure pt and particle velocity vt. Each layer has thickness ln where n is the subscipt for the appropriate layer number [94]. Based on the analysis presented in [94], The following assumptions are made concerning the transmission of waves through a multilayer system: (i) The layers are assumed to be of innite extent in the y and z directions to have acoustic plane waves in medium. (ii) Due to long propogation length of medium n compared to acoustic wavelength, the re
ected wave in medium n is assumed to be nonexistent. (iii) Even though the bounded media would produce multiple re
ections and transmissions at the boundaries surrounding them, it is sucient to suppose that there is only one wave in each direction. Provided that the boundary conditions are satised, these waves will include all the individual components. 113 Appendix E. Acoustic Wave Transmission in Medium Figure E.1: Transmission of acoustic wave through dierent medium (iv) During the transmission process, the piezoelectric material in general extract some energy from the acoustic wave and convert it to an electrical one. In present analysis it is neglected. Based on analysis presented in [94] by satisfying the boundary conditions for each layer following relation between acoustic pressure and particle velocity at medium boundaries can be derived. 264 pii1 vii1 375 = 264 Ai Bi Di Ci 375 264 pi+1i vi+1i 375 (E.1) where pii1 and v i i1 are acoustic pressure and particle velocity respectively in medium i1 at medium boundary of i 1 and i. For specic acoustic impedance of zi for medium i and 
i = !li ci (!, li and ci are frequency of acoustic wave, medium thickness and speed of sound in medium i, respectively), each acoustic layer can be dened as, 114 Appendix E. Acoustic Wave Transmission in Medium 264 Ai Bi Di Ci 375 = 264 cos
i jzisin
i j zi sin
i cos
i 375 (E.2) Assuming plane wave propogation in medium, for layers of cross section area A, acoustic force Fi at each layer will be product of area and acoustic pressure of waves (Fi = A:pi). For multilayer transmission of acoustic waves through n layers, 264 F1 v1 375 = 264 An Bn Dn Cn 375 264 Fn vn 375 (E.3) where Zi = zi:A264 An Bn Dn Cn 375 = nY i=1 264 cos
i jziAsin
i j ziA sin
i cos
i 375 = nY i=1 264 cos
i jZisin
i j Zi sin
i cos
i 375 (E.4) Figure E.2: Equivalent acoustic impedance for multilayer system 115 Appendix E. Acoustic Wave Transmission in Medium Acoustic impedance is dened as ratio of Acoustic force (F ) over cross section Area A. Figure E.2 shows the equivalent acoustic impedance and can be calculated by Zeq = F1 v1 . Using simple network theory for multiple acoustic layers Zeq = F1 v1 = AnFn +Bnvn DnFn + Cnvn = An(Fn=vn) +Bn Dn(Fn=vn) + Cn = AnZn +Bn DnZn + Cn (E.5) Each acoustic layer can be represented as transmission line with conguration as per gure E.3. Using network theory, it can be represented as Equation E.6 264 Ai Bi Di Ci 375 = 264 cos
i jZisin
i j Zi sin
i cos
i 375 (E.6) Figure E.3: Equivalent electric model of acoustic layer 116 Appendix F Colpitts Oscillator Present section provides analysis to calculate oscillation frequency of Colpitts oscillator shown in gure 4.2. Figure F.1 shows the block diagram of oscillator consists of amplier (gain A) and passive components L, C1, C2 and C3. Impedance of inductor and capacitor is shown in laplace equivalent (s = j!). Figure F.1: Oscillator block diagram i = i1 + i2 (KCL at Node1) (F.1) Ls+ 1 C1s  i1 = 1 C2s i2 (KV L in loop2) (F.2) 117 Appendix F. Colpitts Oscillator From above equations, i =  1 + C2 C1 + LC2s 2  i1 (F.3) Applying KVL in loop 1, shown in gure F.1: Vout  1 C3s i 1 C1s i1 = Vin (F.4) replacing i, in terms of i1, Equation F.4 can be re-written as: Vout   1 C3s  1 + C2 C1 + LC2s 2  + 1 C1s  i1 = Vin (F.5) asVin = Lsi1 (KV L in loop2) Vout Vin = 1 + 1 Ls  1 C3s  1 + C2 C1 + LC2s 2  + 1 C1s  (F.6) rearranging Equation F.6 and replacing Vout Vin = A (gain of amplier), A 1 C2 C3 = 1 Ls  1 C3s  1 + C2 C1  + 1 C1s  (F.7) Equation F.7 can be used to calculate the oscillation frequency of colpitt oscillator. It shows that for sustain oscillation, gain of amplier should be less than 1 + C2 C3 . A+ 1 + C2 C3 can be replaced by term G. Equation F.7 can be simplied to, s2 =  1 GLCeq ) ! = 1p GLCeq (F.8) where; Ceq = C1C3 C1 + C2 + C3 (F.9) 118 Appendix G System Setup Figure G.1: Experimental setup 119 Appendix H Driver Circuit Figure H.1: Energy harvesting and driver circuit 120 Appendix I Ultrasound Power Meter Setup Figure I.1: Ultrasound power meter 121 Appendix J DC-DC Boost Converter Figure J.1: TI-TPS61045EVM board (DC-DC boost converter) 122

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