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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 particular, localized and controlled drug release systems have gained clinical relevance in the treatment of many diseases. The power requirement for sonoporation-based systems is comparatively higher than that of other implantable devices. Efficient wireless power delivery and efficient small ultrasound transducer with low aspect ratio (G = length/thickness) is required to obtain high power transfer efficiency for implantable sonoporation based system. To provide power wirelessly to implantable device, resonance-based wireless power delivery system is considered. This system is modeled and optimized for given design constraints. The prototype 4-coil system achieves at least 2 × more efficiency 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 efficiency 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 efficiency of transducer is required to achieve high system efficiency and low heat losses in tissues. In the present work, identification of key parameters for transducer selection for implantable sonotherapy ii  Abstract systems are given. Effects of ultrasound transducer’s aspect ratio reduction is analyzed and reduction in electro-acoustic conversion efficiency 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 first prototype of a wirelessly powered sonoporation-based implantable system. Though only two blocks of the prototype are optimized, overall system efficiency is measured as 2.04 % which is close to the theoretical value of 2.24 % of present design. By using an efficient power amplifier (class-E amplifier, efficiency 80%), an overall system efficiency 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  1.2 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2  1.1 Motivation  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  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6  1.5 Contributions of The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . .  6  1.4 Research Objectives  iv  Table of Contents 1.6 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7  2 Design and Optimization of Wireless Power Delivery System for Implantable Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9  2.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9  2.2 Power Efficiency 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  Effect 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 Cofficient and Matching Layers  . . . . . . . . . . . .  56  3.4 Electrical Model of PZT . . . . . . . . . . . . . . . . . . . . . . . . . . . .  57  3.5 Acoustic Power and Efficiency  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  . . . . . . . . . . . . . . . . . . . . . . .  3.7.1  Effect on Electromechanical Coupling Factor  3.7.2  Effect on Input Impedance  3.7.3  69  . . . . . . . . . . . .  69  . . . . . . . . . . . . . . . . . . . . . .  70  Effects 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  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80  4.2.1  Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  81  4.2.2  DC-DC Boost Converter . . . . . . . . . . . . . . . . . . . . . . . .  81  4.2.3  Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83  4.1 Introduction 4.2 Circuit Design  vi  Table of Contents 4.2.4  Buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83  4.2.5  Power Amplifier  84  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4.3 Experiment Setup and Results  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  85  4.3.1  Characterization of Power Amplifier  85  4.3.2  Characterization of Oscillator and Buffer  . . . . . . . . . . . . . .  87  4.3.3  Characterization of DC-DC Converter . . . . . . . . . . . . . . . .  88  4.3.4  System Efficiency  . . . . . . . . . . . . . . . . . . . . . . . . . . .  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 Efficiency 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  J DC-DC Boost Converter  . . . . . . . . . . . . . . . . . . . . . . . . 121  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122  viii  List of Tables 2.1 Design constraints  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  35  2.2 Litz wire property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36  2.3 Coils physical specification . . . . . . . . . . . . . . . . . . . . . . . . . . .  41  2.4 Coils electrical specification . . . . . . . . . . . . . . . . . . . . . . . . . .  42  2.5 Coils electrical specification (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 rectifier . . . . . . . . . . . . . . . . . . . . . . . . .  85  4.2 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  87  4.3 Buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  87  4.4 Power amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  88  4.5 PZT impedance at 4.4 MHz (PZT: sample3) . . . . . . . . . . . . . . . . .  88  ix  List of Figures 1.1 System architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3  2.1 η vs coil aspect ratio (b/t) . . . . . . . . . . . . . . . . . . . . . . . . . . .  15  2.2 Coil lumped model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  2.3 (a) Simplified schematic of the 4-coil system (b) electrical model of the power transfer circuit (for design example) . . . . . . . . . . . . . . . . . . . . . .  18  2.4 Efficiency versus Q factor (k12 = 0.58, k34 = 0.60, Q1 = 5, Q3 =100, Q4 = ( 1 )1.2 (Equation 2.45) . . . . . . . . . . . . . . . . . 0.15, k23 = 148.2 d2 +320  20  2.5 Sensitivity of efficiency 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 Effect of Q factor(Q1 ) on maximum efficiency 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 efficiency with respect to R1 . For 2 coil (f requency = 700 kHz, Lp = 1.1 mH, Qs = 1.6,k = 0.055, RL = 100 Ω). For 4 coil (f requency = 700 kHz, L1 = 29.35 µH,Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = 0.055, RL = 100 Ω ) . . . . . . . . . . . . . . . .  29  x  List of Figures 2.11 Sensivity of Q with frequency (DoutT = 60 mm, Nt = 11, h = OD/2) . . .  31  2.12 Effect of operating frequency variation on power-transfer efficiency . . . . .  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 efficiency (experiment, SPICE simulation, efficiency Equation 2.21, traditional two-coil model) . . . . . . . . . . . . . . . . . . . . .  46  2.22 Output voltage (simulation and measurement results) . . . . . . . . . . . .  46  2.23 Efficiency with varied source resistance for 2 and 4 coils based system (measurement results) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  47  3.1 Resonance modes in thin disk PZT transducer . . . . . . . . . . . . . . . .  53  3.2 Mason’s electric model of PZT . . . . . . . . . . . . . . . . . . . . . . . . .  58  3.3 Simplified 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 efficiency of transducer sample 73 3.10 Simulated and measured amplitude of input impedance of air-backed PZT (sample 1)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3.11 Simulated and measured input impedance of air-backed PZT (sample 1)  74  .  75  3.12 Output power of air-backed PZT (sample 1) (simulated and measured) . .  76  3.13 Electro-acoustic conversion efficiency 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 sample 3)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  78  3.16 Measured electro-acoustic conversion efficiency of sample 2 and sample 3 .  79  4.1 Full wave bridge rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . .  81  4.2 Colpitts oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  84  4.3 Common drain buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  85  4.4 Class-A power amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . .  86  4.5 Power amplifier input voltage (transistor’s base voltage) . . . . . . . . . . .  89  4.6 Power amplifier 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 different 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 η  Wireless power transfer efficiency  ηem  Electromechanical conversion efficiency  z  specific (characteristics) acoustic impedance  AWG  American Wire Gauge  Cself  Self capacitance of coil  CMUT  Capacitive Micromachined Ultrasonic Transducer  DoutT  Transmitter outer diameter  ESR  Effective Series Resistance  fm  Minimum impedance (resonance) frequency  fn  Maximum impedance (anti-resonance) frequency  fp  Parallel resonance frequency  fs  Series resonance frequency  FDTD  Finite-Difference Time-Domain  FEA  Finite-Element Analysis  HIFU  High Intensity Focus Ultrasound  JFET  Junction Field-Effet Transistor  kt  Thickness mode electromechanical coupling factor  Lef f  Effective 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.m−3  RFID  Radio Frequency Identification  SDT  Sonodynamic Therapy  TTF  Transmission Transfer Function  WPT  Wirless Power Transfer  xv  Notations ΣN i=a f (i)  sum of function f (i) for i from a to N  ΠN i=a f (i) ∫y f (θ) θ=x  Product of function f (i) for i from a to N  ′  f (d)  Definite integration of function f(θ) for θ from x to y 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 Engineeing 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 treatment 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 delivery system is especially relevant to administering antiproliferative drugs which have high levels of toxicity. For example, prolonged systemic use of first 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 reservoirs provide better control over drug release and are becoming among popular methods for drug delivery. To increase the drug intake efficiency, 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 diffuse 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 transducer, which is much higher compared to most of reported biomedical implants [2–4]. To realize localized drug delivery and implantable sonoporation-based systems, high powertransfer efficiency 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 implantable 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 flow 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 importance. 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 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 efficient wireless power-delivery systems. Design requirements of the present application are taken as example and a generalized approach is developed to achieve a high-efficiency wireless power-transfer system. Similar design steps can be applied for different applications or with different design constraints. Generally implantable electronics 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 Ω [5] and 500 Ω [6]). In the present work, wireless power delivery block is optimized for a resistive load of 100 Ω.  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 preffered. 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 effects 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 efficiently convert it to generate driving signal for the ultrasonic transducer. This module can be subdivided into multiple circuit modules based on functionality. Different approaches can be applied to convert incoming energy into driving signal. In present system, input power is rectified to generate DC (direct current) voltage which is further boosted to high-voltage and is used along with a power amplifier (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, specifications of submodules of this block are defined 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 first used to power an artificial heart [7, 8] and since then has commonly been used in implantable devices [2–5,9–14]. An inductively coupled powertransfer system consists of two coils that are generally referred to as primary and secondary 4  Chapter 1. Introduction coils. In such systems, power transfer efficiency is a strong function of the quality factor (Q) of the coils as well as the coupling between the two coils. Hence, the efficiency depends on the size, structure, physical spacing, relative location and the properties of the environment surrounding the coils. The coupling between the coils decreases sharply as the distance between the coils increases and causes the overall power transfer efficiency to decrease 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 minimally 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 theoretical study was done to formulate electromechanical coupling factor as function of aspect ratio [29, 30]. As per our knowledge, for single crystal PZT, effect 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 differnt from wireless power delivery link frequency. Energy from external power source is a  5  Chapter 1. Introduction transferred form of magnetic flux 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 rectifier circuit. Due to low voltage gain of DC-AC boost inverter [31], [32], and complexity of design [33], present work uses high voltage gain DC-DC boost converter in combination with power amplifier. 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 efficient 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 implantable 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 efficient 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 flowchart 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 different applications. In this work, detailed analysis of ultrasound transducer is done. Idetification of important parameters is done along with guidelines to select transducer material for given application. Electric model of transducer is used to identify effects of electrode size on electromechanical conversion efficieny. Effect 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. Off-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 module presented in block diagram of system. Chapter 2 provides electric model of resonancebased wireless power-delivery system. Detailed analysis of design parameters is done and the effects of each parameter on wireless power-transfer link efficieny is presented. Chapter 7  Chapter 1. Introduction 3, presents key parameters to achieve high electro-mechanical conversion efficiency. Electrical model of transducer is presented and experiments are done to verify the model. Effects of transducer aspect ratio is analyzed using experimental data with different size transducers and are explained using transducer vibration theory. Chapter 4, provides prototype circuit to receive energy wirelessly from external coil and deliver energy to different submodules 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 applications due to their ability to locally stimulate internal organs and/or monitor and communicate the internal vital signs (signals) to the outer world. The power requirement of biomedical implants depends on their specific application and typically ranges from a few µW [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 identification (RFID) tags [15]. The power transfer efficiency, η, 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 =  √  rp rs ), is a commonly used performance metric for comparing different  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 suffer from a relatively low power transfer efficiency, typically, η ≤ 40% for d ≥ rm [2, 3, 35] and generally η 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 flux linkage between primary and secondary coils, for a given operating range and small size of the implanted (secondary) coil, coupling reduces as difference 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 effect of coupling and Q-factor (k × Qp ) is maximum. For implants with high power requirement, a more efficient power transfer mechanism, e.g., with η of 60 to 90 % for a distance of 20 mm or more, is desired. To provide high power at a low efficiency, a strong alternating magnetic field is required. High eddy currents due to strong magnetic field 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 efficiency 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 efficiently [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 effect 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 find the optimum design to achieve maximum efficiency. Our focus is on the efficiency of the power transfer link itself and peripheral circuits such as power amplifier in the transmitter and rectifier 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 efficiency 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 Efficiency 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 flux 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]: [ ( ) ] 8a L(a, R) = µo a ln −2 R  (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 ρ 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. ( √ ) ( √ ) a b J1 x J1 x M (a, b, ρ, d) = πµo ab b a 0 ( ) ( ) ρ d ×J0 x √ exp −x √ dx ab ab ∫  √  ∞  (2.2)  where J0 and J1 are zeroth and first-order Bessel functions . For perfectly aligned loops (ρ = 0), the mutual inductance between the coils can be calculated as: √  M (a, b, ρ = 0, d) = µ0 ab  [(  ) ] 2 2 − k K(k) − E(k) k k  (2.3)  where ( k=  4ab (a + b)2 + d2  ) 12 (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 first and second kind, respectively [37–39]. Coils with different 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 different radii ai (i = 1, 2, ..., ˙ Na ) and wire radius R, self-inductance can be calculated as:  La =  Na ∑  L(ai , R) +  i=1  Na ∑ Na ∑  M (ai , aj , ρ = 0, d = 0)(1 − δij )  (2.5)  i=1 j=1  where δij = 1 for i = j and δij = 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  Na ∑  L(ai , R)  i=1  +  Nt Na ∑ Na ∑ Nt ∑ ∑  M (aik , ajl , ρ = 0, d = dl |k − l|)  i=1 j=1 k=1 l=1  ×(1 − δij )(1 − δkl )  (2.6)  where δij (or δkl ) = 1 for i = j (or k = l) and δij (or δkl ) = 0 otherwise. dl is minimum distance between two consecutive turns.  2.2.2  Parasitic Capacitance  In general inductors suffer 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  [ ] Nt ∑ 1 = 2 Cb (Nt − 1)Na + Cm (2i − 1)2 (Na − 1) N i=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 different layers. For a tightly wound coil, parasitic capacitance between two nearby turns is ∫  π 4  πDi ro dθ 0 ς + ϵr ro (1 − cosθ) πDi ro dθ ς + ϵr ro (1 − cosθ) + 0.5ϵr h  Cb = ϵ0 ϵr ∫ π 4  Cm = ϵ0 ϵr 0  (2.8) (2.9)  where Di , r0 , ς, ϵr , h are average diameter of coil, wire radius, thickeness and relative permittivity of strand insulation and separation between two layers respectively [43].  2.2.3  AC Resistance  To achieve high quality factors, inductors with low effective series resistance (ESR) are required. At high frequencies, skin and proximity effect increases the ESR. To reduce the AC resistance, multi-strand Litz wires are commonly used [9, 43]. Finite-difference timedomain (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 finite element analysis (FEA) is presentd in [47]. The AC resistance of coils made of multi-strand Litz wires including skin and proximity effect can be approximated as [43]: ( Rac = Rdc  f2 1+ 2 fh  ) (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 √ 2 2 √ fh = 2 πrs µ0 σ N Ns ηa β  (2.11)  where Rdc , rs , Ns , µ0 , β are DC resistance of the coil, radius of each single strand, number of strands per bunch, permeability of free space and the area efficiency of the bunch, respectively. ηa is area efficiency of coil with width b and thickness t and can be determined using figure 2.1 cited in [43].  1 0.9  Area Efficiency  0.8 0.7 0.6 0.5 0.4 0.3 0.2 −2 10  −1  10  0  10  1  10  2  10  Ratio of b/t (width over thickness) Figure 2.1: η 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 Na Na ∑ Nt πDi ∑ Rdc = ρ = πNt Di Rul A i=1 i=1  (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 =  2.2.4  ρRs (1.015)NB (1.025)NC ANs  (2.13)  Coil Model  Considering the effect of the stray capacitance and the AC resistance of an inductor, the total impedance of a coil can be written as [50]  Ze = (jωLself + Rac )∥  1 jωCself  (2.14)  Figure 2.2: Coil lumped model The coil can be modelled as an inductor with a self-inductance Lef f and effective series resistance given by:  16  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  ESR =  Lef f =  (1 −  Rac 2 ω Lself Cself )2  (2.15)  (1 −  Lself 2 ω Lself Cself )  (2.16)  As operating frequency of coil approaches fself , ESR increases drastically. From Equation 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  ) ( f2 2πf L 1 − 2 self fself ωLef f ( ) = = 2 ESR Rdc 1 + ff 2  (2.17)  h  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 efficiency 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. Efficiency of a 2-coil-based power-transfer system is given by [3, 15, 36]:  η=  k 2 Qp Qs . 1 + k 2 Qp Qs  (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 effect 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 efficient 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 simplified schematic and electrical model of the 4-coil system.  Figure 2.3: (a) Simplified 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:       −1    I1   Z11     I2   Z21     =     I3   Z31    Z41 I4  Z12 Z13 Z14 Z22 Z23 Z24 Z32 Z33 Z34           Z42 Z43 Z44    E      0    ,     0    0  (2.19)  where  Zmn = Rn + jωLn + = jωMmn  1 jωCn  f or m = n  f or m ̸= n,  E is amplitude of voltage source applied to the driver coil, and Rn , Ln , Cn are the effective resistance, inductance and capacitance of the coil n. Mmn is the mutual inductance between coil m and n.  Mmn = kmn  √ Lm Ln  where kmn is coupling factor between coil m and coil n. Tuning all coils to same resonance frequency and operating it at their resonance frequency, Zmn = Rn (for m = n and n ∈ {1, 2, 3, 4}). 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 coefficients k14 , k13 and k24 would be neglected. From Equation 2.19, at resonance, current in load coil can be calculated as: √ √ √ k12 k23 k34 Q1 Q2 Q2 Q3 Q3 Q4 I4 = √ E 2 2 2 R1 R4 [(1 + k12 Q1 Q2 )(1 + k34 Q3 Q4 ) + k23 Q2 Q3 ]  (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 efficiency can be computed as  η=  2.2.6  2 2 2 (k12 Q1 Q2 )(k23 Q2 Q3 )(k34 Q3 Q4 ) 2 2 2 2 Q Q + k2 Q Q ] [(1 + k12 Q1 Q2 )(1 + k34 Q3 Q4 ) + k23 Q2 Q3 ][1 + k23 2 3 34 3 4  (2.21)  Analysis of 4-Coil Power-Transfer System  To optimize the design to achieve high efficiency, the effects of different parameters on the power transfer efficiency 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. Efficiency 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 coefficient between primary and secondary coils corresponding to distance decays geomatrically with increasing distance between them.  Power transfer efficiency (%)  80 70 60 50 40 30 20 10 0 50  600 40  400 30  20  Coil Distance (d) in mm  10  200 0  0  Q2  Figure 2.4: Efficiency versus Q factor (k12 = 0.58, k34 = 0.60, Q1 = 5, Q3 =100, Q4 = ( 1 )1.2 (Equation 2.45) 0.15, k23 = 148.2 d2 +320  20  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Figure 2.4 shows the effect of Q-factor on power transfer efficiency (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 efficiency increases. To achieve a high power transfer efficiency (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:  2 2 2 2 (1 + k12 Q1 Q2 )(1 + k34 Q3 Q4 ) ≈ (k12 Q1 Q2 )(k34 Q3 Q4 )  (2.22)  2 2 2 (k12 Q1 Q2 )(k34 Q3 Q4 ) ≫ k23 Q2 Q3 ⇒ 2 2 2 2 (1+k212 Q1 Q2 )(1 + k34 Q3 Q4 ) + k23 Q2 Q3 ≈ (k12 Q1 Q2 )(k34 Q3 Q4 )(2.23) 2 2 (1 + k23 Q2 Q3 ) ≫ k34 Q3 Q4 ⇒ 2 2 2 (1 + k34 Q3 Q4 + k23 Q2 Q3 ) ≈ (1 + k23 Q2 Q3 )  (2.24)  Applying above assumptions, the efficiency expression (Equation 2.21) can be simplified to: η∼ =  2 Q2 Q3 k23 2 1 + k23 Q2 Q3  (2.25)  This approximate model is similar to the model for 2-coil systems. Since in the 4coil 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 efficiency increases 2 Q2 Q3 increases. monotonically as k23  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,  2 2 (1 + k34 Q3 Q4 ) ≫ 1 ⇒ (k34 Q3 Q4 )  10 ⇒ Q4  10 2 Q3 k34  (2.26)  For Equation 2.24 to be reasonable approximation, we should have,  2 (k23 Q2 Q3 )  2 10k34 Q3 Q4 ⇒ Q4  2 k23 Q2 2 10k34  (2.27)  From Equation 2.26 and Equation 2.27, range of Q4 can be shown as:  10 2 Q3 k34  Q4  2 k23 Q2 2 10k34  (2.28)  Effect of Q1 and Q4 on Efficiency 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 (∼ 100Ω) 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 efficiency of a 4-coil system as a function of Q1 and Q4 . Note that, for the four-coil-based power-transfer system, efficiency 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  Power transfer efficiency (%)  82 80 78 76 74 72 70 68 1  20 15 0.8  10 0.6  0.4  Q  4  5 0.2  0  0  Q1  Figure 2.5: Sensitivity of efficiency 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 Qfactor of coils. To define 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 effects 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 affected 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 fixed, respective wire gauge can be chosen to keep Rac close to Rdc . Rdc reduces as Ns √ increases. Due to proximity effect, fh reduces as Ns increases (fh ∝ 1/ N s) 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 figures 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 effect 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 maximized 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 4  5  x 10  4.5 4 3.5  Q2*Q3  3 2.5 2 1.5 1 0.5 0  0  50  100  150  200  250  300  350  400  # of strands  Figure 2.6: Q2 .Q3 variation with number of strands  4.5  5  Approximate operating Freqency (x 10 ) Hz  5  4 3.5 3 2.5 2 1.5 1 0.5  0  50  100  150  200  250  300  350  400  # of strands  Figure 2.7: Optimum frequency of operation  (dQ/dNt = 0) ⇒ 1 − 4 where ωself = √  1 , Lself Cself  ω2 ω2 ω2 − 3 =0 2 2 ωself ωself ωh2  (2.29)  ω = 2πf and ωh = 2πfh . Lself , Cself and ωh 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 ω ≤ 2ωh ,  ω2 2 ωh  ≤ 4. From  Equation 2.29 and ω ≤ 2ωh , (dQ/dNt ≥ 0) ⇒ 1 − 16  ω2 ≥0 2 ωself  (2.30)  As number of turns increases, Lself increases and self resonating frequency (fself ) decreases. With Nt for which ω ≤ 41 ωself , Q-factor increases monotonically with increment of Nt (dQ/dNt ≥ 0, Equation 2.30). Nt(opti) can be defined as Nt for which ω = 14 ωself . 280 260 240  Q factor  220 200 180 160 140 120 100 80  0  5  10  15  20  # of turns per layer  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 fixed number of layers and fixed width. h is distance between two layers and OD is diameter of wire. As can be seen from the figure, 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 Effect of Q1 In typical case, relative position and dimension of driver coil and primary coil (and of secondary and load coil) is fixed and hence in normal operating mode Q2 , Q3 , Q4 , k12 , k34 are fixed. For given operating distance (respective k23 ), only Q1 can be varied using changing source resistance and hence effect of Q1 on power transfer efficiency is shown here. Power transfer efficiency is a strong function of coupling between coils 2 and 3 (k23 ). By maximizing efficiency (η) with respect to the coupling coefficient, the optimum distance of operation can be achieved. From efficiency equation (refer Equation 2.21), we have:  ∂η/∂k23 = 0 ⇒ k23(opt)  (√ ) 12 2 2 k12 Q1 Q2 [1 + k34 Q3 Q4 ] = Q2 Q3  2 ∂ 2 η/∂k23 <0  f or  k23 = k23(opt)  (2.31)  (2.32)  An expression for efficiency at k23(opt) is given by (appendix A):  ( η=  k34 k23  )2  √ (k12 Q1 Q2 )3 Q4 √ (1 + k12 Q1 Q2 )2 Q2  (2.33)  To achieve maximum efficiency 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 efficiency is maximum. Equation 2.31 shows the dependence 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  90 Q1=1 Q1=5  Power transfer efficiency (%)  80  Q1=10 Q1=15  70 60 50 40 30 20 10  0  10  20  30  40  50  Coil distance (mm)  Figure 2.9: Effect of Q factor(Q1 ) on maximum efficiency 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 Efficiency (η) to Source Series Resistance To compare the effect of source resistance in 2-coil-based systems and 4-coil-based systems, we derive an expression for the slope of efficiency with respect to source series resistance (R1 ).  ∂η ∂η ∂Q1 = ∂R1 ∂Q1 ∂R1  (2.34)  For a 2-coil system, the rate of change of efficiency is (from Equation 2.18, 2.34) and Q1 = ωL1 /R1  f or  ∂η ωL1 k 2 Q2 =− 2 ∂R1 R1 (1 + k 2 Q1 Q2 )2 ∂η 1 Q1 ≫ 1, ≈− ∂R1 ωL1 (k 2 Q2 )  (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 efficiency with respect to R1 can be derived (Equation 2.36). 2 k23 ∂η ≈− 2 2 ∂R1 ωL1 k12 k34 Q4  (2.36)  For fixed design parameters, both equations (Equation 2.35 and 2.36) show that efficiency decreases linearly as source resistance increases. To validate the accuracy of Equation 2.35, efficiency is calculated using Equation 2.18 for different values of R1 and plotted in figure 2.10. A linear regression model is used to find the slope of changes in efficiency with respect to R1 . From linear regression model of efficiency for varying source resistance, slope = -0.00768 Ω−1 and from Equation 2.35 slope = -0.01069 Ω−1 . 0.8  Power transfer efficiency  0.75 4−coil system regression model 2−coil system regression model  0.7  0.65  0.6  0.55  0.5  0.45 2  4  6  8  10  12  14  16  18  20  Source Resistance(in ohm)  Figure 2.10: 2 and 4 coil system efficiency with respect to R1 . For 2 coil (f requency = 700 kHz, Lp = 1.1 mH, Qs = 1.6,k = 0.055, RL = 100 Ω). For 4 coil (f requency = 700 kHz, L1 = 29.35 µH,Q2 = 368, Q3 = 108, Q4 = 0.15, k12 = 0.56, k34 = 0.59, k23 = 0.055, RL = 100 Ω ) Similarly to validate the accuracy of Equation 2.36, with the same system parameters, efficiency is calculated using Equation 2.21 with varying R1 and plotted in figure 2.10. From linear regression model of efficiency for varying source resistance, slope = -0.00130 29  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices Ω−1 and from Equation 2.36, slope = -0.001431 Ω−1 (approximated model). This example provides the validity of Equation 2.35 and Equation 2.36. For given example, by comparing the slope of efficiency for 2-coil-based and 4-coil-based systems, the efficiency of the latter decreases ≈ 10 times slower as compared to that of the former. Slope for 2-coil-based systerm is inversely propotional to k 2 (equivalent to k23 ) and hence 2 have high value compare to 4-coil based system in which slope is propotional to k23 (note  that k23 ≪ 1). In typical case, an increase in value of R1 has much more severe effect 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 ) = 2πf L  (1 − (f /fself )2 Rdc (1 + (f /fh )2 )  At low frequencies, Q(f ) increases with frequency and for f  (2.37)  fh , due to the dominance  of proximity effect on AC resistance [43], the Q-factor decreases. To utilize the coil for different operating frequency, it is desirable to have a Q-factor that is not too sensitive to frequency. The bandwidth of Q is mainly defined by fh . To reduce sensitivity to operating frequency, fh should be kept sufficiently 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 different 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  400 l=12 l=16 l=20 l=24  350  Q−factor  300  250  200  150  100  50  0  2  4  6  8  10  Frequency (in Hz)  12  14  16 5  x 10  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 effects on Q factor of coils and to achieve good operating range using same coils, number of layers should be kept less.  2.2.8  Effect 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 influence 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 effect of primary coil’s on driver coil (reduced I2 ). Hence, the closer the secondary coil to the primary coil, the lower the effective 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 efficiency 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: ( Ref f = RL ∥  )2  (ωL)2 Rs RL ωL Qp = Rs RL + (ωL)2  ωL Rs  Rs = RL ∥  (2.38) (2.39)  For series connection of the load resistance as shown in Figure 2.13(b), we have:  Qs = f or  f ≪ fself ,  ωLef f ESR + RL  (2.40)  2 1 − f 2 /fself ≈1  Qs =  ωL Rs + RL  (2.41)  To compare the Q factor of the coils with series and parallel load connection and to find which connection improves the Q factor, the sign of the difference between the parallel-  32  Power Transfer gain (dB)  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  0  −20  −40  60  −60 40 −80 12  10  20 8  5  x 10  6  4  f (operating frequency)  2  0  Coil Distance (mm)  Power Transfer gain (dB)  (a) Efficiency with frequency, coil separation(4-coil based system)  0  −20  −40 60  −60 40 −80 12  10 5  x 10  20 8  6  f (operating frequency)  4  2  0  Coil Distance (mm)  (b) Efficiency with frequency, coil separation(2-coil based system)  Figure 2.12: Effect of operating frequency variation on power-transfer efficiency  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 =  Note that for  ωL RL  ωLRL2 [1 − (ωL/RL )2 ] (Rs + RL )(Rs RL + (ωL)2 ))  (2.42)  < 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 presented. 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 first step is to identify the design constrains. The specific application requirements constrain the design parameters (particularly in terms of size and source and load resistances) of the implantable device. For example, Table 2.1 shows the design constrains dictated by the specific application of [1]. Table 2.1: Design constraints Parameter Transmitter Outer diameter Transmitter Coil Thickness Implanted outer diameter Implanted Coil Thickness Minimum Coil inner diameter Coil relative distance Source resistance Load resistance  2.3.2  symbol DoutT hT DoutR hR DinR d R1 RL  Design Value ≤ 80mm 5.5 mm 22 mm 2.5 mm 8 mm 20 mm 5.6 Ω 100 Ω  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 field strength, H, at distance x along the axis can be written as [6] I.r2 H(x, r) = √ 2 (r2 + x2 )3  (2.43)  √ For r = x 2, H will be maximized and, therefore, a good choice of diameter for external √ coil is DoutT = 2 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 different number of strands (Figure 2.6), to improve the Q-factor, one can choose a specific 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 Strand gauge Number of Strands Insulation thickness Strand radius Operating Frequecny Outer Diameter Max. DC resistance Unit length DC resistance Filling factor  symbol Value AWG 44 Ns 40 ζ 3 µm rs 25 µm 350-850 kHz OD 0.48 mm RDC 2.873/feet Rul 0.0758/feet β 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 figure 2.5, for high values of Q2 and Q3 , effect of Q1 on efficiency 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 amplifier have output impedance on the order of 5 to 6 Ω, a source resistance of 5.6 Ω is chosen as sense resistance to mimic the source impedance.  Q2  For small number of turns per layer, increasing the number of turns improves Q-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 significant effect 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 effect 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 (ϵr = 5) and thickness 0.3 mm is taken.  37  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  500  300  200  4  Q (Quality factor)  400  100  0 0 5 10 15 20  l (number of layers)  0  2  4  6  8  10 5  x 10  f (operating frequency) in Hz  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 different number of layers and operating frequencies. 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 effected 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 Ω, and single turn per layer, Figure 2.16 shows the  variation of Q4 for different 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 find the desired Q4 from the graph.  38  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  180 160  Q4 (Quality factor)  140 120 100 80 60 40 20 0 0 5 10 15  0  2  4  6  8  10 5  x 10  f (operating frequency) in Hz  l (number of layers)  Figure 2.15: Q3 vs number of layers, operating frequency  4  Q (Quality factor)  1 0.8 0.6 0.4 0.2 0 1 2 3 4 5  l (number of layers)  0  2  4  6  8  10 5  x 10  f (operating frequency) in Hz  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 ∈ {1, 2, 3, 4}) to achieve the optimum efficiency 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 different design parameters of 4-coil-based powertransfer 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 efficiency 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 efficiency. Table 2.3 shows the mechanical specifications of the optimized design by following the design flow chart (figure 2.17). Table 2.3: Coils physical specification Type  Coil Outer Dia. Inner Dia. Number (mm) (mm) Driver Coil 1 64 62 Primary Coil 2 60 39.5 Secondary Coil 3 20 10.5 Load coil 4 22 20  Turns /layer 11 11 5 5  layers 1 12 9 2  Based on simulation by following the design flow 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 flow chart in Figure 2.17. Table 2.4 shows simulated electric parameters for the optimized coil dimensions to obtain high power transfer efficiency. Source series resistance of R1 (= 5.6 Ω) is used to emulate the nominal output impedance of power amplifier for driver coil. Load resistance of RL (= 100 Ω) 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 specification Coil (Number) 1 2 3 4  Inductance DC (µH) Resistance (Ω) 15.90 0.5211 1131 5.34 33.25 0.538 3.629 0.159  fself MHz  fh (MHz)  Q (loaded) (@700kHz)  41.0 3.75 24.7 44  2.6 0.490 0.844 1.84  11.42 295 160 0.1593  Coupling vs. distance Regression model  0.14 0.12  Coupling k  23  0.1 0.08 0.06 0.04 0.02 0  5  10  15  20  25  30  35  40  45  50  Coil Distance (mm)  Figure 2.18: Mutual coupling (k23 ) versus distance Fig. 2.18 shows the coupling coefficient k23 along with the fitted curve based on regression model (95 % confidence). The curve is modeled as: ( k23 = 148.2  )1.2 1 − 0.0002857 2 d2 + rm √ √ rm = rp rs = 32 ∗ 11  (2.44)  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 applications based on design constrains and dimension of coils (calculated based on flow chart),  42  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices coefficients of coupling model will change. Table 2.5: Coils electrical specification (measured) Coil (Number) 1 2 3 4  2.5  Inductance Self (µH) Resistance (Ω) 15.58 0.55 1099 5.1 29.35 0.493 3.564 0.225  fself MHz  fh (MHz)  Q (loaded) (@700 kHz)  40.7 2.21 18.7 19.4  2.58 0.512 0.798 1.36  11.06 330.3 148 0.1563  Experimental Setup  To demonstrate the validity of the presented modelling techniques and the design flow, 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. Multistrand 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 effective 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 Ω 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 Ω 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 Ω , a supply with a lower impedance should be used to improve the efficiency of the system. In this set up, the efficiency 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 effect of realistic power amplifier source resistance is taken into account by using 5.6 Ω 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 affect the magnetic field, the effect 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 efficiency 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 efficiency is achieved. The measured 45  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  90 Spice Simulation Effi−formula Experiment Effi−2coil  Power Transfer Efficiency  80 70 60 50 40 30 20 10 0  0  10  20  30  40  50  60  Coil distance d(mm)  Figure 2.21: Power transfer efficiency (experiment, SPICE simulation, efficiency Equation 2.21, traditional two-coil model) 7 Spice Simulation Experiment 6  Output voltage(V)  5  4  3  2  1  0  0  10  20  30  40  50  60  distance d(mm)  Figure 2.22: Output voltage (simulation and measurement results)  46  Chapter 2. Design and Optimization of Wireless Power Delivery System for Implantable Devices  90 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  Power Transfer Efficiency (%)  80 70 60 50 40 30 20 10 0  0  10  20  30 40 Coil distance d(mm)  50  60  Figure 2.23: Efficiency with varied source resistance for 2 and 4 coils based system (measurement results) results match very well with the SPICE simulations and the analytical equations derived to calculate power transfer efficiency. The four-coil-based power transfer system provides stable power transfer efficiency over long operating range. When the primary coil and the secondary coils are close (≈ 5-10 mm) experimental results are slightly different 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 effect 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 η with respect to distance is more pronounced (see Fig. 2.21). This is because the coupling coefficient 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 Ω load is 1.28). The results confirm that using the presented four-coil power-transfer system, high-power-transfer efficiency 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 efficiency is obtained as 82% for coil separation of 20 mm (with k23 ≈ 0.05) between primary and secondary coils. The output voltage at 100 Ω 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 effect of source resistance on power transfer efficiency. For a low value of source series resistance, a high efficiency can be obtained. Q-factor of the driver coil changes the optimum efficiency point and shifts with the distance as shown by simulation (figure 2.9). For the same series resistance 2-coil power transfer system has much more severe effects as shown in Figure 2.23.  2.7  Comparison with Previous Work  The design based on the proposed technique is compared with previously reported powertransfer methods applied for implanted devices. Table 2.6 summarizes the results. To make a fair comparison with different designs efficiency 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 efficiency 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 (rp , rs )(mm) [9] (15, 15) [2] (8.5, 6) [3] (30, 10) [5] (26, 5) [38] (12, 12) [6] (35, 10) This Work (32, 11) This Work (32, 11)  2.8  Freq. Efficiency (MHz) 4.5 54% 1 30% 0.7 36% 6.78 22% 2 40% 5 30% 0.7 82% 0.7 72%  Distance (d(mm), d/rm ) (10, 0.67) (7, 0.98) (30, 1.73) (15, 1.31) (12, 1) (20, 1.07) (20, 1.07) (32, 1.73)  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 significant improvements in terms of power-transfer efficiency 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. Efficiency 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 efficiency 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 efficiency of 82% is achieved. For operating distance of 32 mm, efficiency slightly drops to 72%, which confirms 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 therapy. High Intensity Focused Ultrasound (HIFU) and Sono-Dynamic Therapy (SDT) are two promising techniques that are used for cancer Therapy and local drug delivery respectively. 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 investigated 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 transducer 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 effect of aspect ratio reduction of transducer on its physical parameters. Electrical models of transducer are used to estimate the performance of transducer. Different size ultrasound transducer samples are made and experimental results are used to explain effects of aspect ratio reduction of transducer on electro-mechanical conversion efficiency. This chapter is organised as follows: Section 3.2 provides overview of fabrication technology 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 efficiency is formulated in Section 3.5. Section 3.6 gives guidelines for transducer sample preparations and characterization steps. Section 3.7 analyze the effect 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 = ξ/t, where ξ 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 ultrasound transducers (CMUTs) [23, 62] and piezo-micromachined ultrasound transducers (pMUT) [63] are becoming the two popular technology to design new ultrasound transducers. Different fabrication [58, 64] and composite materials [65–68] are used to design and optimize the transducer paramaters to improve the performance. CMUTs offer better acoustic matching to the propagation medium, resulting in broader fractional bandwidth and thus CMUTs provide advantages for ultrasound imaging [69]. For sonotherapy application where single frequency is used, high bandwidth is not required. Furthermore due to high electro-mechanical conversion efficiency 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 effect is the displacement of ionic charges within the crystal structure. When an external electric field is applied, the charges are displaced and a net strain is generated and vice-versa. Based on direction of generated strain, different vibration modes are defined [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 field). 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 different PZT materials while selecting for particular application. More detailed definitions 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 material per unit of electric field 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 field 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 field 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 effectiveness with which a piezoelectric material converts electrical energy into mechanical energy, or converts mechanical energy into electrical energy. A high k usually is desirable for efficient energy conversion, but k does not account for dielectric losses or mechanical losses, nor for recovery of unconverted energy. The accurate measure of efficiency 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 efficiencies that exceed 90 %. Based on resonance mode different Electromechanical Coupling Factor can be defined based on mode of operation.  k33  : factor for electric field 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 field in direction 3 and vibrations in direction 3 (thin disc, surface  dimensions large relative to thickness; kt < k33 ) k31  : factor for electric field 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 field 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 = fs t, 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 field frequency. Many empirical model suggested that efficieny 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: tanδ, 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 specific acoustic impedance(z) is a ratio of acoustic pressure to specific flow, or flow per unit area, or flow velocity v. For sound intensity, I, particle velocity, v, and flow cross section area, A,  z =  I p2 p = 2 = v v I  (3.1)  The characteristic impedance (Z0 ) of a medium, such as air, PZT or water is a material property, Z0 = ρc. where ρ 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. Specific acoustic impedance is sometimes also called the characteristic acoustic impedance of a medium (z = ρc). 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 F2 F2 A= = z zA ρcA  (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 Cofficient and Matching Layers  Impedance matching is a design practise of setting the input impedance (ZL ) of an electrical/acoustic load equal to the fixed output impedance (ZS ) of the signal source to which it is connected, usually in order to maximize the power transfer and minimize reflections from the load. Matching is obtained when ZS = ZL∗ 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 reflections 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 cofficient(T ) and reflection coefficient (Γ) :  Γ =  Z1 − Z2 Z1 + Z2  2  T = 1−Γ  (3.3) (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 reflects 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 reflected wave is captured to find the time of transit. As the characteristic impedance of the PZT (zP ZT ≈ 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. Efficiency 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 define the electromechnical property and conversion of electric energy to acoustic energy and vice-versa, many electric models of PZT were proposed in litrature. The effectiveness  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 effect 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 =  K S ϵ0 lw t  (3.5)  Z0 = ρclw ω0 = 2πf0 =  πc t  πf f √0 ω0 C0 Z0 kt2 N = π −Z0 Xa = sinγ γ =  Xb = Z0 tan(γ/2)  where C0 , K S , l, w are capacitance, dielectric constant of PZT under constant stress, length and width of PZT respectively. ρ, 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 specific application different materials (with different acoustic impedance) can be as backing layer. Figure 3.2 shows the front and back acoustic port with current flow of I1 and I2 . For back layer acoustic load of Zb , Mason model can be simplified as Figure 3.3  Figure 3.3: Simplified 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     2  jN /ωC0  1  1 =   N H jωC 0 0  [  ] A  ′  (3.6)  H = cosγ − 1 + jz1 sinγ  (3.7)  f or  z1 = Zb /Z0   [ ]  cosγ + jz1 sinγ Z0 (z1 cosγ + jsinγ)  ′ =   A jsinγ/Z0 2(cosγ − 1) + jz1 sinγ  (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,      V    = I  [  ] A       F1    v1  (3.9)  where      F1    = v1   n ∏     i=1   cosγi jsinγi /Zi    jZi sinγi   Fload    cosγi vload  (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, [ ] 1 kt2 (z1 + z2 )sinγ + j2(1 − cosγ) V = 1− Zin = I jωC0 γ (z1 + z2 )cosγ + j(1 + z1 z2 )sinγ  (3.11)  60  Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices where  z1 = Zb /Z0 and  z2 = Zf /Z0  for ω = ω0 , γ = π and hence for anti-resonance frequency (ω0 )  Zin =  4kt2 Z0 1 + jω0 C0 πω0 C0 (Zb + Zf )  (3.12)  At anti-resonance frequency, PZT can be represented as series connection of capacitor of C0 and resistance  Ra =  4kt2 Z0 πω0 C0 (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 match61  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 =  π(Zb + Zf ) 4kt2 ωs C0 Z0  (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 =  kt2 C 1−kt2 0  and LR = 1/ωs2 CR . Van Dyke’s  model is recommendated by the IEEE Standard on Piezoelectricity [81] to reduce the system complexity. For accurate analysis of transducer for different operating frequency, Mason or KLM models are recommended.  3.5  Acoustic Power and Efficiency  An important parameter studied in these calculations was the efficiency of acoustic transmission. According to the 3 port system, the Transmission Transfer Function (TTF) is defined as T T F = 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 efficiency, ηem , is defined as ηem = Po /Pi , where Po is output acoustic power and Pi is input electric power.  Po =  |FL(rms) |2 ZL  (3.15)  62  Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices  |Vrms |2 cos⟨(Zin + Zg )⟩ ∗ Pi = Vrms I˙rms = Zin + Zg  (3.16)  Po 1 |FL(rms) |2 Zin + Zg = 2 Pi ZL |Vrms | cos⟨(Zin + Zg )⟩ |T T Frms |2 Zin + Zg = ZL cos⟨(Zin + Zg )⟩  ηem =  (3.17)  and ( ⟨(Zin + Zg )⟩ = tan  −1  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 efficiency based on spring-mass model of PZT [57, 83, 84], which shows the effect of electromechanical coupling factor (kt ) and mechanical quaity factor (Qm ) over efficiency. Higher value of (kt ) and Qm are required to convert electric power to acoustic output efficienctly.  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 reflection 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 reflection from the back surface is not recommended. Instead, characteristic acoustic impedance close to transducer (PZT) acoustic impedance (ideally Zb = ZP ZT ) is desirable to have no reflection 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 µm thickness is chosen. While testing PZT sample using water exposed to the front layer, Al provides impermeable layer and stops water to fill in the back layer of PZT (as airbacked 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], ρ = 2.38 kg/m3 [86]). To reduce effect 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 50µm).  Figure 3.5: Acoustic layers in sample Figure 3.5 shows the configuration 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. Effect 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 field, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the field. 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 infinite 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.  150  f  Zin  n  Real(Zin) Imag(Zin)  fm  100  Impedance  50  0  −50  −100  −150  3  3.5  4  4.5  5  Frequency  5.5 6  x 10  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 ∼ =  √ [(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 =  √  (π/2)(fn /fm )tan [(π/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 3.7.1  Aspect Ratio Reduction of PZT Effect on Electromechanical Coupling Factor  The coupling between the thickness and planar(radial) modes is detrimental to performance at the frequency of the thickness mode. To reduce effect of mode coupling between different 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 piezocomposites), effect 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 electromechanical coupling factor (kt ), decreases from the value for pure thickness mode [90]. Based on mode coupling theory and definition of the electromechanical coupling coefficient, formula for effective electromechanical coupling coefficient (kef f ) of PMN-30%PT crystal is derived for arbitrary aspect ratio (G = l/t). Based on mode interaction analysis done for other transducer configurations (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 ratio (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 effectively. For G = 10, reported value of kt (∼ 0.48, [73]) can be expected. For small PZT (G 10) the planar-mode low order harmonics comes close to thicknessmode 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 efficiency. 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  Effect on Input Impedance  Capacitance C0 of PZT is linearly propotional to its area (l × w) (as C0 =  K S ϵ0 lw ). t  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 kt2 . In general, Ra increases with reduction in PZT size.  3.7.3  Effects of Electrode Contact  For a perfect reflection 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 (zP ZT = 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 effective 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 , effect of electrode contact on input impedance will be small and hence can be ignored. For small sized PZT, the effect 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 effect causes reduction in the electromechanical conversion efficiency (ηem ).  3.8 3.8.1  Experiment and Results Instrument Setup  Figure 3.8 shows the setup of PZT impedance measurement. Samples are partially immersed 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 negative 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 efficiency measurement. Samples are partially immersed in water bath of ultrasound power meter (UPM-DT-1AV, Ohmic Instruments Co.). PZT samples are centered over the coneshaped 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 Ω) pin is recorded using an oscilloscope. Using this data, voltage 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 (|S| = |Vrms |.|Irms |). 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 efficiency of transducer sample Table 3.1: Main parameters for selected material Symbol definition value tan δ 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 effect 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 6 Mrayl (= 10 Rayl) x103 kg/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. 300 Simulated Experiment  200  in  Impedance (Z in ohm)  250  150  100  50  0  2  2.5  3  3.5  4  4.5  Operating Frequency (Hz)  5  5.5  6 6  x 10  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  50  Phase (Zin in degree)  Simulated Experiment  0  −50  −100  2  2.5  3  3.5  4  4.5  Operating Frequency (Hz)  5  5.5  6 6  x 10  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). Efficiency is calculated based on equation 3.17. Figure 3.13 shows the calculated and measured electromechanical (electroacoustic) conversion efficiency of sample 1.  75  Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices  0.12 Simulated Experiment  Acoustic Output Power (Watt)  0.1  0.08  0.06  0.04  0.02  0  2  2.5  3  3.5  4  4.5  5  5.5  Operating Frequency (Hz)  6 6  x 10  Figure 3.12: Output power of air-backed PZT (sample 1) (simulated and measured)  Electro−Acoustic conversion Efficiency  1 Simulated Experiment  0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0  2  2.5  3  3.5  4  4.5  Operating Frequency (Hz)  5  5.5  6 6  x 10  Figure 3.13: Electro-acoustic conversion efficiency 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 effect 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 effect 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 efficiency 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 vibration energy and hence reductions in electro-acoustic conversion efficiency. To reduce the 77  Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices  900  700 600  in  Impedance (Z in ohm)  Sample 2 Sample 3  Higher Harmonics Sample 2  800  500 400 300 200  Higher Harmonics Sample 3 100  2  2.5  3  3.5  4  4.5  5  5.5  Operating Frequency (Hz)  6 6  x 10  Figure 3.14: Measured amplitude of input impedance of air-backed PZT (sample 2 and sample 3) 10 Sample 2 Sample 3  0  Phase (Zin in degree)  −10 −20 −30 −40 −50 −60 −70 −80 −90  2  2.5  3  3.5  4  4.5  Operating Frequency (Hz)  5  5.5  6 6  x 10  Figure 3.15: Measured phase of input impedance for air-backed PZT (sample 2 and sample 3) effect 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, effects  78  Chapter 3. Development of PZT based Sonotherapy System for Implantable Devices  Electro−Acoustic conversion Efficiency  0.7 Sample 2 Sample 3 0.6  0.5  0.4  0.3  0.2  0.1  0  2  2.5  3  3.5  4  4.5  Operating Frequency (Hz)  5  5.5  6 6  x 10  Figure 3.16: Measured electro-acoustic conversion efficiency of sample 2 and sample 3 of aspect ratio reduction of PZT is analyzed and reduction in electro-acoustic conversion efficiency is explained using mode coupling between different resonance modes. Effect of electrode area on transducer efficiency 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 flow among wireless powertransfer (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 different design blocks, wireless power transfer block is optimized independently for fixed 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 identified as part of energy harvesting and driver circuit.  4.2.1  Rectifier  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 rectifier is one of most commonly used techniques to convert an AC signal to DC with good efficiency. For ideal diodes, efficiency of this block is 81.2 % [92]. Figure 4.1 shows the circuit diagram of full wave bridge rectifier. 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 filter capacitor of DC-DC converter.  Figure 4.1: Full wave bridge rectifier  4.2.2  DC-DC Boost Converter  For wireless power transfer of operating range 1-3 cm, rectifier 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 Ω) requires high voltage of order 25 V. Therefore DC-DC boost converter is required for present design. Off-the-self DC-DC boost converter will be used for present design. Specification 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 specifications of DC-DC converter. PZT sample should be characterize for two main parameters, 1) electromechanical conversion efficiency versus frequency 2) impedance versus frequency. While operating the sample at their most efficient frequency, corresponding impedance value can be used to calcualte operating voltage of PZT for given power requirement. As induced voltage across rectifier 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 amplifier (class-A) should be biased at Vdd /2 (Vdd = DCDC output voltage) to achieve high output voltage swing. With the power amplifier DC load resistance of Rin , DC current can be calculated as Idc = consumption will be  2 Vdd  2Rin  Vdd 2Rin  and hence DC power  . For voltage swing of amplitude Vdd /2 and load reistance of Rin ,  AC power consumption can be formualted as  2 Vdd . 8Rin  For optimum operating frequency of fopt  with electromechanical conversion efficiency (ηem ) (or ηP ZT ) and PZT’s input impedance of Rin , to generate the acoustic power of Pout , the following formulation can be derived:  Pout ηP ZT 2 2 Vdd Vdd = (DC) + (AC) 2Rin 8Rin √ 8 = Vdc−dc = Pin Rin 5  Pin =  Vdd  Idc−dc = Vdc−dc /2Rin  (4.1) (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 Vdc−dc and Idc−dc . Efficiency of DC-DC converter is maximum near its full load condition. Chosing the current specification of DC-DC converter, full load current can be chosen close to Idc−dc . Based on above calculation to transfer 400 mW power to PZT sample with input impedance of ≈ 1 kΩ, 12.6 mA current will be drawn from DC-DC converter. Due to unavailabilty of DC-DC converter with above specifications, 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 buffered and amplified using high voltage power amplifier.  4.2.4  Buffer  To reduce the loading effect of power amplifier on oscillator circuit, a buffer stage is needed between oscillator output and power amplifier input. For present design common drainamplifier, 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 buffer.  4.2.5  Power Amplifier  For present design, class-A power amplifier (PA) is used. Maximum efficiency of class-A power amplifier is 25 %. Figure 4.4 shows the circuit diagram of class-A amplifier. To improve the efficiency of overall system, higher efficiency power amplifiers, such as classE PAs can be used in the future design. To achieve high voltage swing at the power amplifier output, high amplitude input voltage is used to get switching characteristics at power amplifier output. It generates square type wave at PA’s output. As PZT generates acoustic power effectively 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 buffer  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 rectifier Symbol Parameter Value Unit D1/D2/D3/D4 Vf 0.5 V (MUR115) Vb -150 V  4.3.1  Characterization of Power Amplifier  Load resistance of power amplifier 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 efficiency (ηP T ) of 50 % can be achieved. Theoretical 85  Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT  Figure 4.4: Class-A power amplifier maximum efficiency of power amplifier circuit with PZT as load is calcualted as follows:  ηP A = 0.25 ηP ZT = 0.53 ηP T = 0.5 ηd (driver  circuit) = ηP A .ηP ZT .ηP T = 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 amplifier 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  Symbol RC RE L1 C1 C2 C3 Q1  Symbol R1 R2 RE Cac Q1  Table 4.2: Oscillator parameter value unit R 5.1 kΩ R 2 kΩ L 10 µH (murata) 18r103c C 220 pF C 302 pF C 560 pF JFET 2N5484 Table 4.3: Buffer parameter value R 180 R 18 R 1 C 470 JFET 2N5484  unit kΩ kΩ kΩ pF -  to be around 8 mW. It corresponds to power amplifier efficiency 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 Buffer  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 amplifier directly, hence a unity gain buffer (Figure 4.3) is used as interface between the oscillator and the power amplifier. 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 buffer. With supply voltage of 17.5 V, buffer 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 amplifier Symbol parameter value R1 R 51 R2 R 4.6 RC R 1 RE R 20 R 10 RB C1 C 470 Cac C 470 Q1 NPN MRF544  unit kΩ kΩ kΩ Ω Ω pF pF -  Table 4.5: PZT impedance at 4.4 MHz (PZT: sample3) Symbol parameter value unit PZT Zin 500 Ω phase -20 degree ηP ZT 0.53 of buffer 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 fixed load and output voltage, DC-DC converter can be considered as constant power source. For a given output power requirement and fixed input voltage, effective input impedance of DC-DC converter depends on its input voltage, output power and the efficiency of DC-DC converter. From simple energy conversion 2 method, Rin(dc−dc) = ηdc−dc .Vin(dc−dc) /Pout , where ηdc−dc , Vin(dc−dc) and Pout are efficiency 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 amplifier input voltage (transistor’s base voltage)  4.3.4  System Efficiency  All the blocks are connected as shown Figure 1.1. Using design setups in chapter 2, for resistive load of 100 Ω, 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 amplified using power amplifier (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 Ω 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 efficiency of wireless power transfer (ηW P T ) to 60 %. Power consumption of oscillator and buffer is independant of output power requirement. Using lower power oscillator and buffer circuit (typically oscillator  89  Chapter 4. Development of Energy Harvesting and Driver Circuits for PZT  Figure 4.6: Power amplifier output voltage (input voltage of PZT) power of 2 mW and buffer circuit power of 4 mW using 3 V supply), effect of oscillator and buffer circuit will be very small on overall power transfer efficiency. Hence to calculate the system efficiency, power consumption of oscillator and buffer can be omitted. For driver circuit with efficiency 5.7 %, ηd and with rectifier efficiency of 80% and DC-DC converter efficiency of 82%, theoretical maximum efficiency of present system will be approximately 2.24 %(η = ηrect .ηdc−dc .ηW P T .ηd ). 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 amplifier (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 Ω sense resistor. 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 efficiency of the wireless power delivery block, the rectifier and the DC-DC converter and 35.8 % efficiency (ηrect .ηdc−dc .ηW P T ) is achieved which is close to theoretical efficiency of 38.4 %. Excluding the effect of oscillator and buffer power, system efficiency is measured as 2.04 % which is close to the theoretical maximum efficiency 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 flow 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 efficiency of the overall system measured as 2.04 % which is close to the theoretical value of 2.24 %. By designing circuit to reflect resistive load of 100 Ω at load coil terminals, it results wireless power transfer efficiency of 80 % for 1-2 cm operating distance. In present design, power amplifier restricts the overall efficiency of ciruit which can be boosted to 80% by using class-E power amplifier. By using class-E amplifier, system efficiency can be boost to 20 % (ηW P T = 0.8, ηrect = 0.81, ηDC−DC = 0.8, ηP A = 0.8, ηem = 0.53). Similarly low power oscillator can be made to reduce effect of its power consumption on system efficiency. Even though efficiency 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 efficient power transfer system from an external power source to transducers. Chapter 1 outlines the advancement of localized drug delivery using MEMS based implantable devices and sets requirement of power efficient system design for sonoporation based drug delivery system. Block diagram of overall system is proposed and design constraints 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 efficient wireless power 93  Chapter 5. Summary of Thesis and Future Research Topics transfer system for implantable device. Based on system design constraints defined in table 2.1, wireless power transfer efficiency of 80 % is achieved. By use of high quality (Q) factor power transfer coils compared to traditional designs for implantable devices, high power transfer efficiency is achieved. Results are compared with previous wireless power delivery systems for implantable devices and more than 2 × efficiency improvement is reported. Analytical model and generalized design steps are presented. For change in design requirements, system can be optimized to provide maximum power transfer efficiency 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 efficiency. Effects 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 effect 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 efficiency (ηem ) 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 rectifier, oscillator, buffer and power amplifier. Offthe-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 buffer consume 10 mW and 35 mW of power respectively. Power amplifier generates the output swing of 8 V at transducer input. Due to generalized approach to design efficient 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 efficiency is limited to 2 .04 % which can be further improved upto 22 % using low power circuit design and energy efficieny power amplifier.  5.2 5.2.1  Limitations and Future Work External Power Source for Constant Power Delivery  Proposed wireless power delivery system for implantable device can provide stable efficiency in long operating range (10 mm to 30 mm) and hence can be considered as constant efficiency 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 different 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 different resonance modes causes major effect on electromechanical conversion efficiency. Differnt 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 rectifier circuit to reduce power consumption by rectifier. Low power oscillator can be used to generate the reference signal for device. JFET or MOSFET based power amplifier can be used to reduce the input current or power amplifier stage. 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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 Efficiency Maximization Distance in Eq.(2.31) Efficient of 4-coil based wireless power delivery system can be expressed as (Equation A.1):  η=  2 2 2 (k12 Q1 Q2 )(k23 Q2 Q3 )(k34 Q3 Q4 ) 2 2 2 2 2 [(1 + k12 Q1 Q2 )(1 + k34 Q3 Q4 ) + k23 Q2 Q3 ][1 + k23 Q2 Q3 + k34 Q3 Q4 ]  (A.1)  For ease of derivation, abbrivated letter are used to replace the terms by  2 2 C1 = (k12 Q1 Q2 )(k34 Q3 Q4 )  (A.2)  2 C2 = (k12 Q1 Q2 )  (A.3)  2 C3 = 1 + k34 Q3 Q4  (A.4)  2 f (d) = k23  C4 = C1 + C2 + C3  (A.5) (A.6)  Taking first order derivative of Equation 2.21 with respect to d and equate to zero will provide:  ∂η =0 ∂d  105  Appendix A. Efficiency Maximization Distance in Eq.(2.31)  ′  ⇒ [C4 + f (d)Q2 Q3 ][C3 + f (d)Q2 Q3 ]C1 Q2 Q3 f (d) ′  ′  ′  −C1 f (d)Q2 Q3 [C4 f (d)Q2 Q3 + C3 f (d)Q2 Q3 + 2f (d)f (d)(Q2 Q3 )2 ] = 0  ′  ⇒ [C3 C4 + (f (d)Q2 Q3 )2 + (C3 + C4 )f (d)Q3 Q3 ]C1 Q2 Q3 f (d) ′  ′  −C1 Q2 Q3 f (d)[(C3 + C4 )f (d)Q2 Q3 + 2f (d)f (d)(Q2 Q3 )2 ] = 0 ⇒ C3 C4 − (f (d)Q2 Q3 )2 = 0  (A.7)  replacing values of C3 , C4 and f (d) to A.7, expression A.7 can be rewritten as: 2 2 [1 + k23 Q3 Q4 ]2 [1 + k12 Q1 Q2 ] = (f (d)Q2 Q3 )2 ]1 ( ) 41 [ 2 Q1 k12 (1 + k34 Q3 Q4 ) 2 k23(max) = Q2 Q3  (A.8)  placing k23(max) in efficiency Equation 2.21: √ ]2 [ 2 ] k12 Q1 Q2 k34 Q3 Q4 √ = 2 1 + k34 Q3 Q4 1 + k12 Q1 Q2 [  ηmax  (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  [ ] Nt ∑ 1 = 2 Cb (Nt − 1)Na + Cm (2i − 1)2 (Na − 1) N i=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 different 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 as  ∑k i=1  [ ] Nt ∑ 1 = Cm 2 Nt Na + 4i2 (Na − 1) N i=1  (B.2)  i2 = 16 k(k + 1)(2k + 1), Cself can be rewritten as [ ] Cm Na Nt 4Nt (Nt + 1)(2Nt + 1) 1+ Cself = N2 6 4 Cm Nt Cself ≈ as N = Nt Na and Nt ≫ 1 3 Na K1 Nt 4Cm Cself = where K1 = Na 3  (B.3) (B.4)  Self inductance of coil can be approximated by Lself = K2 N 2 = K2 Nt2 Na2 , 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 1 √ 2π Lself Cself  ωself = 2πfself = √  1 1 K1 K2 Na Nt3/2  (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 = K3 Na Nt 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 =  √ K4 Nt Na  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(ω) = ωK2 Nt2 Na2  (1 − ω 2 (K1 K2 Na )Nt3 ) (1 − K6 Nt3 ) ( ) = K5 N t 2 K3 (1 + K7 Nt ) t Na K3 Nt Na 1 + ω N K4  where K5 = ωK2 Na , K6 = ω 2 K1 K2 Na and K7 =  ω 2 Na K4  and are independant of Nt .  Taking derivative of Q as function of Nt will give, [ ] ∂Q = 0 ⇒ K3 K5 1 − 4K6 Nt3 − 3K6 K7 Nt4 = 0 ∂Nt  (B.6)  Placing values of K6 and K7 values to Equation B.6 will give:  [ ] ∂Q ω2 ω2 ω2 = 0 ⇒ K3 K5 1 − 4 2 − 3 2 2 = 0 ∂Nt ωs ωs ωh  (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 efficiency. In present design multilayer helical coil is used. Cross section of coil is shown in figure 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 defined height. 2. On the mechanical base wrap the alternative layers of wire from left to right and right to left respetively as shown in figure 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 µ 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 aluminium foil. Very small amount of epoxy need to be used to realize the epxy thickness of 30 µ 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. Calculate the final 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 final 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 characteristics 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 defined in figure 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 different specific acoustic (characteristic) impedance zi . The incident wave travels through medium i, undergoes a series of reflections and transmissions in the subsequent layers until a transmitted wave emerges into medium n, which is assumed to be of infinite thickness. The incident wave has pressure pi and particle velocity vi , a reflected 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 infinite 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 reflected wave in medium n is assumed to be nonexistent. (iii) Even though the bounded media would produce multiple reflections and transmissions at the boundaries surrounding them, it is sufficient to suppose that there is only one wave in each direction. Provided that the boundary conditions are satisfied, these waves will include all the individual components. 113  Appendix E. Acoustic Wave Transmission in Medium  Figure E.1: Transmission of acoustic wave through different 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.           i+1 i  pi−1   Ai Bi   pi  =      i vi−1 Di Ci vii+1  (E.1)  i where pii−1 and vi−1 are acoustic pressure and particle velocity respectively in medium i − 1  at medium boundary of i − 1 and i. For specific acoustic impedance of zi for medium i and γi =  ωli ci  (ω, li and ci are frequency  of acoustic wave, medium thickness and speed of sound in medium i, respectively), each acoustic layer can be defined as,  114  Appendix E. Acoustic Wave Transmission in Medium           Ai Bi   cosγi jzi sinγi     =  j sinγ cosγ Di Ci i i zi  (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,             F1   An Bn   Fn    =    v1 Dn Cn vn  (E.3)  where Zi = zi .A      An Bn    = Dn Cn     n ∏ i=1     cosγi j sinγi zi A  jzi Asinγi  = cosγi      n ∏   cosγi jZi sinγi    (E.4) j sinγ cosγ i=1 i i Zi  Figure E.2: Equivalent acoustic impedance for multilayer system 115  Appendix E. Acoustic Wave Transmission in Medium Acoustic impedance is defined 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 F1 A n Fn + B n v n = v1 Dn Fn + Cn vn An (Fn /vn ) + Bn = Dn (Fn /vn ) + Cn An Zn + Bn = Dn Zn + Cn  Zeq =  (E.5)  Each acoustic layer can be represented as transmission line with configuration as per figure E.3. Using network theory, it can be represented as Equation E.6           Ai Bi   cosγi jZi sinγi    =   j Di Ci sinγ cosγ i i Zi  (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 figure 4.2. Figure F.1 shows the block diagram of oscillator consists of amplifier (gain A) and passive components L, C1 , C2 and C3 . Impedance of inductor and capacitor is shown in laplace equivalent (s = jω).  Figure F.1: Oscillator block diagram  i = i1 + i2 (KCL at N ode1) [ ] 1 1 Ls + i2 (KV L in loop2) i1 = C1 s C2 s  (F.1) (F.2)  117  Appendix F. Colpitts Oscillator From above equations, [ ] C2 2 i= 1+ + LC2 s i1 C1  (F.3)  Applying KVL in loop 1, shown in figure F.1:  Vout −  1 1 i− i1 = Vin C3 s C1 s  (F.4)  replacing i, in terms of i1 , Equation F.4 can be re-written as: ( Vout −  Vout Vin  [ ) ] 1 C2 1 2 1+ + LC2 s + i1 = Vin C3 s C1 C1 s  (F.5)  asVin = Lsi1 (KV L in loop2) ( [ ] ) 1 1 C2 1 2 =1+ 1+ + LC2 s + Ls C3 s C1 C1 s  rearranging Equation F.6 and replacing 1 C2 = A−1− C3 Ls  (  Vout Vin  (F.6)  = A (gain of amplifier),  [ ] ) 1 C2 1 1+ + C3 s C1 C1 s  (F.7)  Equation F.7 can be used to calculate the oscillation frequency of colpitt oscillator. It shows that for sustain oscillation, gain of amplifier should be less than 1 + −A + 1 +  C2 C3  C2 . C3  can be replaced by term G. Equation F.7 can be simplified to,  1 1 ⇒ω= √ GLCeq GLCeq C1 C3 where, Ceq = C1 + C2 + C3  s2 = −  (F.8) (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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