WIRELESS IMPLANTS FOR INCREASED SIGNAL SENSITIVITY OF NUCLEAR MAGNETIC RESONANCE MONITORING OF A BIO ARTIFICIAL PANCREAS By WALKER JOSEPH TURNER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2015
Â© 2015 Walker Joseph Turner
To my family
4 ACKNOWLEDGMENTS First and foremost, I would like to thank God who was a major source of strength throughout this process and that in all things work for good and His glory. I would like to thank Dr. Rizwan Bashirullah for his help and guidance throughout this process and the opportunity to work on this research . I would like to thank my family, especially my mom, d ad, and s ister , for their unwavering support through out the years and the confidence in me to finish this body of work. I would like to thank the members of my Ph.D. committee for their input and support on this research including Dr. Thomas Mareci, Dr. Robert Fox, and Dr. Toshikazu Nishida. I would like to thank all of the members of the Integrated Circuits Research Labo ratory for their technical help and discussions throughout the years, incl uding Hong Yu, Yan Hu, Jikai Chen, Zhiming Xiao, Lin Xue, Chun Ming Tang, Tanuj Aggarwal , Christopher Dougherty , Edgar Garay, and Quizhong Wu. I would also like to thank the scientists and engineers at the McKnight Brain Institute for their insight and ass istance on this collaboration project including Barbara Beck, Garrett Astary, Luis Colon Perez, Kelly Jenkins, and Malathy Elumalai. I would like to thank the research scientists and engineers at the U.S. Army Research Laboratory for their help and support in developing the wireless power analytical models , specifically Sarah Bedair, Christopher Meyer, and Nathan Lazarus. I would like to thank Dr. Andr Ã© Luiz Aita for the insight and technical discussions he provided during the initial design stages of the t ransimpedance amplifier. I would also like to thank Kelly Jones for her undying love and support in the finishing of this project. This body of work would not have been possible without all of these people.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 8 LIST OF FIGURES ................................ ................................ ................................ ......................... 9 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 14 ABSTRACT ................................ ................................ ................................ ................................ ... 16 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 18 1.1 Motivation ................................ ................................ ................................ ......................... 18 1.2 Research Goals ................................ ................................ ................................ ................. 18 1.3 Thesis Organization ................................ ................................ ................................ .......... 19 2 RESEARCH MOTIVATION ................................ ................................ ................................ . 22 2.1 Research Motivation ................................ ................................ ................................ ......... 22 2.1.1 Diabetes Mellitus ................................ ................................ ................................ .... 22 2.1.2 Treatments for Diabetes Mellitus ................................ ................................ ........... 23 2.2 Nuclear Magnetic Resonance Imaging and Spectroscopy ................................ ................ 26 2.3 Implantable NMR Coils ................................ ................................ ................................ .... 32 2 .4 Magnetic Compliance ................................ ................................ ................................ ....... 33 2.4.1 Diamagnetism ................................ ................................ ................................ ......... 35 2.4.2 Paramagnetism ................................ ................................ ................................ ....... 35 2.4.3 Ferromagnetism ................................ ................................ ................................ ...... 36 2.4.4 Superparamagnetism ................................ ................................ .............................. 36 2.4.5 Magnetic Compliance for an Implantable Device ................................ .................. 37 3 STAGGERED STRONGLY COUPLED MAGNETIC RESONANT WIRELESS SYSTEM FOR UNIFORM WIRELESS POWER TRANSFER TO A BIOMEDICAL IMPLANT ................................ ................................ ................................ ............................... 38 3.1 Introduction ................................ ................................ ................................ ....................... 38 3.2 Wireless Power Transfer Overview ................................ ................................ .................. 39 3.1.1 Near Field Inductive Coupling ................................ ................................ ............... 39 3.1.2 Strongly Coupled Magnetic Resonant Wireless Power Transfer ........................... 40 3.1.3 Magnetic Resonance for Increased Wireless Power Transmission ........................ 42 3.2 Transmitter and Receiver Coil Design ................................ ................................ ............. 43 3.2.1 Magnetic Field Link Analysis ................................ ................................ ................ 43 3.3.2 Receiver Co il Geometry Analysis ................................ ................................ .......... 45
6 3.3.3 Transmitter and Strongly Coupled Magnetic Resonant Coil Design ..................... 47 3.3 Wireless Power Transfer Anal ysis ................................ ................................ .................... 48 3.3.1 Mutual Inductance Modeling ................................ ................................ ................. 49 3.3.2 Wireless System Network Theory ................................ ................................ .......... 52 188.8.131.52 Two coil wireless system: 1 TX coil and 1 RX coil ................................ .. 52 184.108.40.206 Three coil wireless system: 1 TX coil, 1 SCMR coil, and 1 RX coil ........ 55 220.127.116.11 Four coil wireless system: 1 TX coil, 2 SCMR coils, and 1 RX coil ........ 57 3.3.3 Wireless Power Transfer Metrics ................................ ................................ ........... 60 3.4 Experimental Results ................................ ................................ ................................ ........ 63 3.4.1 Strongly Coupled Magnetic Resonant Effect on Equivalent Input Impedance ...... 63 3.4.2 Wireless Power Transfer Characteristics of 2 Coil and 4 Coil Systems ................ 64 3.5 Conclusion ................................ ................................ ................................ ........................ 66 4 A WIRELESSLY PROGRAMMAB LE IMPLANT FOR INCREASED SIGNAL SENSITIVITY OF NUCLEAR MAGNETIC RESONANCE MEASUREMENTS ............. 68 4.1 Introduction ................................ ................................ ................................ ....................... 68 4.2 Motivation and Background ................................ ................................ ............................. 68 4.3 NMR Acquisition with the Implanted Probe ................................ ................................ .... 69 4.4 Circuit Implementation ................................ ................................ ................................ ..... 73 4.4.1 Multi Resonant NMR Detection Coil ................................ ............................. 73 4.4.2 Receiver ................................ ................................ ................................ ........... 78 4.4.3 Power Management Unit ................................ ................................ ................. 81 4.5 Implant Assembly and Encapsulation ................................ ................................ .............. 85 4.6 Experimental Results ................................ ................................ ................................ ........ 87 4 .6.1 Preliminary D Cap NMR Results ................................ ................................ ... 87 4.6.2 Oscillator Performance ................................ ................................ .................... 89 4.6.3 Device Wireless Performance ................................ ................................ ......... 91 4.6.4 Tissue Equivalent Phantom NMR Measurements ................................ .......... 94 4.6.5 Bio Artificial Pancreas In Vivo NMR Measurements ................................ .... 95 4.7 Conclusion ................................ ................................ ................................ ........................ 97 5 AN IMPLANTABLE NMR ACQUISITION COIL FOR INCREASED SIGNAL DETECTION OF NUCLEAR MAGNETIC RESONANCE MEASUREMENTS ............... 99 5.1 Introduction ................................ ................................ ................................ ....................... 99 5.2 Wireless NMR Acquisition Coil System Overview ................................ ....................... 100 5.3 Circuit Design ................................ ................................ ................................ ................. 104 5.3.1 Transimpedance Amplifier ................................ ................................ ............ 104 18.104.22.168 Closed loop transimpedance amplifier design ................................ . 105 22.214.171.124 Noise performance considerations ................................ ................... 109 126.96.36.199 Operational amplifier offset voltage ................................ ................. 114 188.8.131.52 Transimpedance amplifier implementation ................................ ...... 115 5.3.2 Voltage Amplifier ................................ ................................ ......................... 118 5.3.3 IQ Demodulation Stage ................................ ................................ ................. 121 184.108.40.206 IQ channel demodulation ................................ ................................ . 121 220.127.116.11 Chopper demodulation switches ................................ ...................... 123
7 18.104.22.168 Sine to square wave IQ signal generator ................................ ......... 124 5.3.4 Differential to Single Ended Conversion ................................ ...................... 125 5.4 Experimental Resul ts ................................ ................................ ................................ ...... 127 5.4.1 Transfer Function Characterization ................................ ............................... 129 5.4.2 Current to Voltage Amplification and Demodulation Measurements .......... 130 5.4.3 Current to Voltage Gain Measurements ................................ ....................... 132 22.214.171.124 Continuous wave signal amplification ................................ ............. 132 126.96.36.199 Amplitude modulated signal amplification ................................ ...... 133 188.8.131.52 Amplitude modulated signal amplification and demodulation ........ 134 5.4.4 Noise Characterization Measurements ................................ .......................... 135 5.5 Conclusion ................................ ................................ ................................ ...................... 136 6 SUMMARY AND FUTURE WORK ................................ ................................ .................. 137 6.1 Summary ................................ ................................ ................................ ......................... 137 6.2 Future Work ................................ ................................ ................................ .................... 138 APPENDIX A CIRCUIT NETWORK THEO RY ................................ ................................ ........................ 140 B PDMS ENCAPSULATION PROCESS ................................ ................................ ............... 142 C COMMON MODE REJECTION RATIO MEASUREMENT SET UP ............................. 144 LIST OF REFERENCES ................................ ................................ ................................ ............. 147 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 156
8 LIST OF TABLES Table page 2 1 Summary of the classifications of material magnetism. ................................ .................... 35 3 1 Summary of the receiver coil structures. ................................ ................................ ........... 45 3 2 Measured average mouse dimensions of four mice. ................................ .......................... 4 8 4 1 Signal to noise ratio (SNR) summary for 1 H NMR images on the tissue equivalent gel phantom and small animal studies in 4.7T and 11.1T magnetic fields. ....................... 97 5 1 Summary of the noise sources within a closed loop amplifier ................................ ........ 113 5 2 Transimpedance amplifi er transistor summary. ................................ ............................... 117 5 3 Voltage amplifier transistor summary. ................................ ................................ ............ 121 5 4 Differencing amplifier transistor summary. ................................ ................................ ..... 127 5 5 Measured transfer function summary. ................................ ................................ ............. 130
9 LIST OF FIGURES Figure page 2 1 Di agrams of a (a) Nuclear spin in the excitation state and (b) 2 dimensional NMR image. ................................ ................................ ................................ ................................ . 28 2 2 NMR spin echo imaging pulse sequence. ................................ ................................ .......... 30 3 1 Diagram of wireless power transfer via inductive coupling. ................................ ............. 39 3 2 Current and magnetic field distribution diagrams and |S11| simulation of two closely coupled resonant coils. ................................ ................................ ................................ ....... 41 3 3 Diagrams of wireless power transfer via strongly coupled magnetic resonant (SCMR) coils (a) oriented at the TX and RX coil locations and (b) located equidistant from the TX coil (d SCMR ) for a RX coil located at an arbitrary distance ......... 42 3 4 Magnetic field link analysis diagram. ................................ ................................ ................ 44 3 5 Layout diagrams of the receiver coil structure for a (a) PCB planar coil, (b) PCB solenoid coil, and (c) Litz wire wrapped coil. ................................ ................................ ... 46 3 6 Simulated TX coil Ampere Turns versus transmission distance for various TX co il radii using the (a) PCB planar coil, (b) PCB solenoid coil, and Litz wire wrapped coils with overall wire diameters of (c) 710Âµm and (d) 180Âµm. ................................ ....... 47 3 7 Photographs of the PCB (a) Receiver coil and (b) External bore coil. .............................. 48 3 8 Mutual inductance modeling diagrams for (a) Two external circular coils and (b) An external circular coil and the PCB solenoid RX coil. ................................ ........................ 49 3 9 Modeled and measured mutual inductances between two coils as a function of coil separation for (a) Two external circular coils and (b) An external circular coil and the PCB solenoid RX coil. ................................ ................................ ................................ ....... 52 3 10 Schematic of a 2 coil wireless system. ................................ ................................ .............. 53 3 11 Measured (solid) and modeled (dashed) metrics of a 2 coil system: (a) TX coi l input impedance magnitude and phase and (b) V oltage gain for d RX = 0cm and R L ...... 55 3 12 Schematic of a 3 coil resonant based wireless system. ................................ ..................... 56 3 13 Measured (solid) and modeled (dashed) metrics o f a 3 coil system: (a) TX coil input impedance magnitude and phase and (b) V oltage gain for d RX = 0cm and R L ...... 57 3 14 Schematic of a 4 coil resonant based wireless system. ................................ ..................... 58
10 3 15 Measured (solid) and modeled (dashed) metrics of a 4 coil system: (a) TX coil input impedance magnitude and phase and (b) V oltage gain for d RX = 0cm and R L ...... 60 3 16 Power transfer diagram for a device under test (DUT) with input and output matching networks. ................................ ................................ ................................ ............ 61 3 17 Impedance matched TX coil and SCMR coil induct ive link (a) Schematic, (b) Photograph, and (c) |S11| measurements across coil spacing. ................................ ........... 64 3 18 Wireless power transfer experimental set up for the (a) 2 coil and (b) 4 coil systems. .... 65 3 19 V ), and maximum power gain (G MAX ) versus receiver coil placement for the (a) 2 coil system and 4 coil system with TX to SCMR c oil spacings of (b) 3cm, (c), 4cm, and (d) 5cm. .................... 66 3 20 gain (A V ), and (c) maximum power gain (G MAX ) versus r eceiver coil placement. ............ 66 4 1 System diagram for NMR acquisition through an inductive link between a NMR surface coil and the wirelessly powered implant. ................................ .............................. 70 4 2 Diagram of the experimental set up for acquisition of in vivo NMR measurements using the wirelessly powered implanted device. ................................ ................................ 71 4 3 System diagram of t he implantable device consisting of a power management unit (PMU), envelope detector (Env.), clock/data recovery (CDR) circuitry with reference oscillator (osc), finite state machine (FSM), and digitally programmable capacitor. ....... 72 4 4 Resonant frequency ( ) versus output capacitance of a LC tank consisting of a 20nH inductor and variable capacitor. ................................ ................................ ............... 74 4 5 (a) Schematic of a digitally controlled capacitor (D Cap) array and (b) Q degradatio n associated with D R ) and discrete frequency step f ). ........... 75 4 6 Contour plots for the D Cap (a) maximum capacitance (C max ) and degradation in resonant tank quality f actor (Q R /Q tank ) at (b) 190MHz and (c) 470MHz for swept values of unit sized capacitance (C u ) versus transistor switch ON resistance (R ON ). ........ 77 4 7 Schematics of the (a) digital capacitor (D Cap) array used for selective L NMR resonance and (b) unit size capacitive bank. ................................ ................................ ..... 78 4 8 Schematic of the a) Envelope detector front end and b) Low power hysteretic comparator. ................................ ................................ ................................ ........................ 79 4 9 System diagram and schematic of the a) All digital clock/data recovery circuitry and b) Rail to rail 2.4MHz reference oscillator. ................................ ................................ ...... 80 4 10 Schematic of the power management unit. ................................ ................................ ........ 82
11 4 11 Schematics of a RF DC converter (a) Single stage and (b) Charge transfer model. ......... 82 4 12 (a) Assembled implant device, (b) Die micrograph, and (c) Cross section diagram of the PDMS coated implant device. ................................ ................................ ...................... 86 4 13 Die micrograph of the digital capacitor (D Cap) a rray. ................................ ..................... 87 4 14 Coronal plane NMR images of a tissue equivalent gel phantom at 470MHz (11.1Tesla) using a NMR surface coil (a) only and (b) with the PDMS coated copper sheet coil connected to the hard wired D Cap. ................................ ...................... 89 4 15 Measured oscillator (a) Output spectrum, (b) Jitter performance, (c) Phase noise, and (d) Frequency and current dissipation of 17 samples. ................................ ....................... 90 4 16 Measured transient waveforms of the V RX and V CAP supply voltages during the (a) charge, program, and low power phases and (b) charging phase start up conditions. (c) Measured current dissipation before a nd after programming the device. .................... 93 4 17 Measured resonances of the device L NMR when wirelessly powered and programmed to selectively resonate at the (a) 11.1T NMR frequencies and (b) full f requency range. ................................ ................................ ................................ ................................ .. 93 4 18 1 H NMR images acquired on a tissue equivalent gel phantom using a surface coil alone and surface coil inductively coupled to the wirelessly programmed implant device within (a, b) 4.7T and (d, e) 11.1T magnetic field strengths respectively. ............ 94 4 19 Photograph of the a) PDMS coated device with bio artificial pancreas and (b) experimental set up for in viv o NMR acquisition. ................................ ............................. 95 4 20 Acquired NMR images of the in vivo artificial pancreas with the wirelessly programmed implant at 470MHz (11.1Tesla) for the (a) coronal, (b) sagittal, and (c) axia l planes. ................................ ................................ ................................ ........................ 96 4 21 1 H NMR images acquired on a bio artificial pancreas using the implanted device for image resolutions of 128x128, 256x256, and 512x512 in (a c) 4.7T and (d f) 11.1T magn etic field strengths. ................................ ................................ ......................... 97 5 1 System diagram for NMR acquisition using the implanted wireless NMR acquisition coil. ................................ ................................ ................................ ................................ ... 100 5 2 S ystem diagram of the wireless NMR acquisition coil. ................................ ................... 101 5 3 System diagram of the (a) Integrated NMR acquisition chain and the (b) Intermediate frequency to baseband (IF to BB) circuit. ................................ ................. 102 5 4 Schematic of a basic single ended transimpedance amplifier. ................................ ........ 105
12 5 5 (a) Schematic and (b) |A OL | and |1/ | transfer functions of a basic transimpedance amplifier and (c) Schematic and (d) |A OL | and |1/ | transfer functions of a transimpedance amplifier with capacitive compensation. ................................ ............... 107 5 6 ( a) Differential MOSFET pair equivalent noise model and (b) MOSFET noise spectral density. ................................ ................................ ................................ ................ 111 5 7 (a) Input referred noise model for an open loop amplifier and (b) DC offset model of a close d loop amplifier. ................................ ................................ ................................ ... 112 5 8 Noise model for a multi stage op amp with resistive feedback. ................................ ...... 114 5 9 Schematic of the (a) Transim pedance amplifier and (b) Transistor level op amp. ......... 116 5 10 Schematic of the (a) Voltage amplifier and (b) Transistor level op amp. ....................... 119 5 11 Differential chopper switch (a) Symbol and (b) Schematic. ................................ ............ 124 5 12 (a) Block diagram of the sine to square wave IQ generator and (b) Timing diagram. ... 125 5 13 Schematic of the (a) Differencing amplifier and (b) Transistor level op amp. ............... 126 5 14 (a) Die micrograph and (b) Diagram of the experimenta l set up. ................................ .... 128 5 15 Simulated and measured transfer functions of the (a) Transimpedance amplifier and (b) Voltage amplifier. ................................ ................................ ................................ ....... 129 5 16 Simulated and measured transfer function of the complete system with chopper demodulation disabled. ................................ ................................ ................................ .... 130 5 17 Measured frequency spectrum of the output voltage ( ) for a 100pA amplitude c m = 500Hz, 100% modulation index) and 1.2V p p CM = 600mV) wi th chopper demodulation . .............. 131 5 18 Measured outp ut amplitude at 500Hz versus phase mismatch between the c m = 500Hz, 100% modulation index) and sinusoidal drive signal (1.075V p p c = 13kHz, V CM = 537.5mV). ................................ .................. 132 5 19 Measured output voltage ( ) versus input current amplitude ( ) for a 13kHz continuous wave sinusoidal input signal. ................................ ................................ ......... 133 5 20 Measured output voltage ( ) versus input current amplitude ( ) at 12.5kHz, c m = 500Hz, 100% modulation index). ................................ ................................ ................................ . 133 5 21 Measured output voltage ( ) versus input current amplitude ( ) at 500Hz for c m = 500Hz, 100% modulation index) and 1.2V p p CM = 600mV). ................................ ......... 134
13 5 22 Measured (a) Input referre d noise spectrum and (b) Input referred noise power spectral density versus source resistance (R S ) at 13kHz. ................................ ................. 135 B 1 (a) Cross section of the PDMS encapsulated implant and (b) 3D printed mol d. ............ 142 B 2 PDMS encapsulation process: (a) Placement of uncured PDMS gel, (b) Vacuum chamber degassing, (c) Cured PDMS layers after release from the sample and trimming of excess PDMS, (d) P lacement of a thin layer of uncured PDMS gel. .......... 143 C 1 Common mode gain measurement set up. ................................ ................................ ...... 145
14 LIST OF ABBREVIATIONS ADC Analog to Digital Converter AIM Automatic Impedance Matching AM Amplitude Modulation B 0 Static Magnetic Field B field Magnetic Field CDR Clock and Data Recovery D Cap Digital Capacitor DSA Dynamic Signal Analyzer DUT Device Under Test ESR Effective Series Resistance FOM Figure of Merit FSM Finite State Machine G X Frequency Encoded Gradient G Y Phase Encoded Gradient IF to BB Intermediate Frequency to Baseband MLCC Multi Layer Ceramic Chip NMR Nuclear Magnetic Resonance NRZ Non Return to Zero OOK On Off Keying PCB Printed Circuit Board PDMS Polydimethylsiloxane
15 PMU Power Management Unit POR Power On Reset PZT Lead Zirconate Titanate Q Quality Factor RF DC Radio Frequency to Direct Current RF to IF Radio Frequency to Intermediate Frequency ROI Region of Interest RX Receiver SCMR Strongly Coupled Magnetic Resonance SNR Signal to Noise Ratio TE Echo Time TIA Transimpedance Amplifier TX Transmitter
16 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy WIRELESS IMPLANTS FOR INCREASED SIGNAL SENSITIVITY OF NUCLEAR MAGNETIC RESONANCE MONITORING OF A BIO ARTIFICIAL PANCREAS By Walker Joseph Turner May 2015 Chair: Rizwan Bashirullah M ajor: Electrical and Computer Engineering The non invasive monitoring of bio engineered organs using nuclear magnetic resonance (NMR) imaging and spectroscopy is crucial in the development of a bio artificial pancreas capable of providing physiological b lood glucose regulation for the treatment of type 1 diabetes. Current monitoring techniques are limited in providing sufficient NMR signal sensitivity at multiple frequencies, which hinders the ability to fully characterize the tissue construct functionali ty post implantation. This work investigates the design of implantable electronics capable of increasing NMR signal sensitivity over a 190MHz 470MHz frequency range through complete wireless control to enable detailed visualization and characterization o f an implanted bio artificial pancreas . A highly integrated implantable device is developed to selectively resonate a NMR detection coil across a frequency range spanning important metabolic nuclei including 1 Hydrogen, 19 Flourine, and 31 Phosphourus . Devic e functionality was validated through 1 H NMR images acquired within tissue equivalent gel phantom and small animal studies, which increased the acquired signal sensitivity by 140% (7.7dB) and 80% (5.3dB) within 4 magn etic fields respectively and provided signal enhancement of high resolution images up to 73% (4.8dB ) . Untethered operation of t he implant is enab l ed through a staggere d resonant based wireless transmission scheme that
17 provides uniform energy transfer acro ss a range of possible implant locations while increasing the maximum transmission distance up to a factor of two. Analytical models an d experimental measurements of the energy transfer characteristics of the wireless topology are compared with a typical n ear field inductive link. A wireless implantable NMR acquisition coil is also proposed to increase NMR signal sensitivity through the amplification and transmission of the NMR response to an external base station. A test chip is designed and experimentall y validated as part of the implantable system for the amplification and demodulation of pA to nA differential currents with 179.9dB (1nA/V) current to voltage gain, 16.2kHz bandwidth, and 177.5fA/Hz Â½ input referred current noise.
18 CHAPTER 1 INTRODUCTION 1 .1 Motivation Type 1 diabetes is a disease that results from the autoimmune destruction of the insulin producing cells within the pancreas and results in the inability to regulate blood glucose levels. Implantable bio artificial pancreatic tissue construc ts, consisting of insulin producing ÃŸ cells encapsulated in a porous membrane, have been shown to provide physiological blood glucose regulation without the need for immunosuppressive medication. Techniques using nuclear magnetic resonance (NMR) imaging an d spectroscopy are essential in non invasively monitoring bio artificial organs post implantation to aid in the development of the construct efficacy and functional lifetime. The most direct and sensitive method to isolate the NMR signal response is to imp lant an electrically resonant coil around the region of interest to increase the acquired signal to noise ratio through the inductive link formed with the external NMR acquisition coil. Current implementations of implantable NMR coils rely on passive compo nents to achieve resonance, which limits the ability to acquire increased signal sensitivity at multiple frequencies and restricts the metabolic characterization to a single nucleus . Thus, there is a need to develop an implantable coil capable of increasin g the acquired NMR signal sensitivity at multiple frequencies to aid in the development of bio artificial tissue constructs by providing increased visualization and characterization not readily available with current techniques. 1.2 Research Goals The ove rall goal of this work is to design and implement a n implantable device capable of increasing the acquired signal sensitivity of NMR measurements at multiple frequencies. Since the device will be operated within high magnetic field environments, wireless power delivery to the implant removes the need to use primary and secondary batteries, which contain
19 magnetic materials that can introduce artifacts into the NMR measurements. One of the goals of this research is to design a wireless transmission scheme ca pable of providing uniform energy transfer over a wide range of distances due to untethered operation of the implanted device. The design of the wireless system is essen tial in providing power and data to the implant to ensure reliable device functionality throughout NMR acquisition. S ufficient isolation between the wireless power transmissions and the NMR acquisition coil is necessary to prevent interference with the acquisition of the NMR response . The main objective of this research is the design and im plementation of an implantable device capable of providing selective resonance of a NMR detection coil over a range spanning multiple NMR frequencies in an 11.1T magnetic field strength including 1 Hydrogen (470MHz), 19 Flourine (442MHz), and 31 Phosphourous (190MH z). The implant requires a high level of system integration as implantation restricts the overall device dimensions to a 15x20x5mm 3 volume . Operation within a high magnetic field environment constrains the materials and components used in assembling the device to ensure magnetic compliance. Additionally, wireless powering of the device requires low power circuit techniques in the design of the implant electronics to reduce the device input sensitivity. Another goal of this research is to quantify t he increase in NMR signal sensitivity provided by the implanted device. NMR experiments should be performed at multiple frequenc ies using tissue equivalent gel phantoms and small animal studies to characterize the device performance and validate in vivo op eration. Control experiments should be conducted using an external NMR coil alone to quantify the increase in NMR signal sensitivity provided by the device. 1.3 Thesis Organization Chapter 2 discusses the motivation and background for the development of a wirelessly controlled implant to increase the signal sensitivity of NMR measurements. An overview of
20 diabetes mellitus is provided along with a description of treatments that are currently used to regulate blood glucose levels. An explanation of the NMR p henomenon and the acquisition of NMR measurements are described along with a review of previous implantable NMR detection coils. The characteristics of material magnetism are discussed and how it pertains to the challenges of designing electronic implants for use in high magnetic field environments. Chapter 3 discusses the design and modeling of a wireless power transmission system to provide power and data to the implant during NMR acquisition. A brief overview of wireless power transfer is provided, whic h includes descriptions of near fi e ld inductive links and resonant based s ystems. A staggered strongly coupled magnetic resonant wireless coil topology is experimentally validated to provide uniform energy transfer to an arbitrarily placed implant while in creasing the maximum transmission distance for a specified receiver input sensitivity. Analytical models along with experimental measurements are presented to characterize and compare the energy transfer characteristics of the wire less system with a standa rd two coil approach. Chapter 4 discusses the design and implementation of a wireless implant to increase NMR signal sensitivity through a wirelessly programmable NMR detection coil. A system overview details the implant functionality and the external NMR system used to interface with the implant ed device. The design and assembly of the implant able electronics are presented along with measurements to characterize the wireless performance. The increase in acquired NMR signal sensitivity provided by the devi ce is experimentally validated through acquisition of 1 H NMR images within 4.7T (200MHz) and 11.1T ( 470MHz) magnetic field strengths within tissue equivalent gel phantom and small animal studies.
21 A n implantable wireless NMR acquisition coil is proposed in Chapter 5 to increase NMR signal sensitivity through the amplification and transmission of the NMR response to an external base station. A system overview is provided that details the implant functionality and the NMR acquisition chain . The analysis and d esign of a current to voltage amplifier with back end demodulation is presented for use in the implant able NMR acquisition coil. Experimental measurements are provided to characterize the circuit gain and noise characteristics.
22 CHAPTER 2 RESEARCH MOTIVAT ION 2.1 Research Motivation This C hapter discusses the motivation for the development of a wireless implant capable of increas ing the signal sensitivity of nuclear magnetic resonance (NMR) measurements of an implanted bio artificial pancreas. A descriptio n of diabetes mellitus and current treatments for the disease are provided . The acquisition of NMR measurements is discussed in conjunction with previously developed implant coils used to increase NMR measurement signal sensitivity. An overview of material magnetic susceptibility is provided for consideration when operating electronic components within a high magnetic field environment. 2.1 . 1 Diabetes Mellitus Diabetes mellitus is a group of diseases marked by the inability of the body to produce or proper ly utilize the insulin hormone. I t is estimated that 9.3 % of children and adults have diabetes mellitus in the United States alone  , which accounts for approximately 14% of healthcare expenditures  and co ntributed to over 230,000 deaths in 2007  . Insulin is a hormone produced by the endocrine tissue within the pancreas and is crucial to the metabolic process by assisting in the absorption of glucose into the muscle, fat, and liver cells for energy while removing exces s glucose from the blood stream. Glucose is a simple sugar that is a byproduct from the breakdown of carbohydrates during the digestion process and is a major source of c ellular energy within the body. However, u nregulated blood glucose levels can result i n health complications with symptoms ranging from increased tiredness to organ failure . The three types of diabetes mellitus a re characterized as t ype 1, t y pe 2, and gestational diabetes. Type 1 diabetes, known as insulin dependent diabetes, is marked by cells within the pancreas, resulting in the
23 inability to produce the insulin hormo ne. It is estimated that 5% 10% of peopl e diagnosed with diabetes worldwide have t ype 1 diabetes  . Type 2 diabetes , also known as non insulin dependent diabetes, is an adult onset disease where the cells within the body becom e insulin resistant as a result of constant exposure to increased insulin production due to consistently high levels of glucose within the blood stream. Type 2 diabetes can bring about a gradual decline in the number of cells within the pancreas, eventually rendering the body unable to produce insulin  . Type 2 diabetes is the most common form of diabetes mellitus with approximately 24% of people going undiagnosed  . Gestational diabetes is marked by high blood sugar levels that arise during pregnancy and is typically temporary  . If left untreated, consistently high blood glucose levels can lead to diabetes complications , which include limb amputation, limited joint mobility [7 ] , bone loss  , increased risk of heart attack resulting from coronary heart disease, stroke, kidney failure, nerve damage, and blindness as a result of retina damage  . Even with proper treatment, diabetes mellitus affects the overall health, quality of life, and work productivity of the patient  . 2.1 . 2 Treatments for Diabetes Mellitus Treatment s for diabetes mellitus involve the regulation of blood glucose, blood pressure, and blood lipids  in conjunction with constant m onitoring of blood glucose levels to ensure a normoglycemic state. Treatment of t ype 1 diabetes involves daily insulin administration to provid e the necessary basal and bolus insulin requirements. Treatment of t ype 2 diabetes includes oral medication to de crease liver glucose production , regulation of sugar intake through modification of patient diet, and weight loss to reduce insulin resistance. In some cases, insulin administration and regulation is also required as a result of the degradation in the insu lin producing cells  .
24 The most common form of insulin administration consists of multiple daily subcutaneous injections of short acting (bolus) and long acting (basal) insulin in conjunction with blood glucose measurements four to seven times daily  . This requires constant monitoring of bloo d glucose levels to ensure insulin is administered as needed, where the delayed reaction of the injected insulin can lead to large fluctuations in blood glucose levels throughout the day. While these methods provide the patient with a near normal lifestyle , this form of insulin administration therapy places the responsibility of maintaining healthy blood glucose levels solely on the patient in addition to being a time consuming and potentially painful process. A more autonomous method of insulin therapy is the use of external insulin pum ps that are worn 24 hours a day , which have been shown to provide more consistent blood glucose profiles in comparison to manual injections  . Insulin pumps are electromechanical devices that provide continuous insulin infusion through a syringe inserted within the body and can be triggered to provide additional bolus doses of insulin before a meal. While this allows for increased flexibi lity when t iming meals, the external device can be cumbersome to the patient as it must be worn constantly throughout the day. In addition to affecting the patient quality of life, external insulin pumps increase the cost of treatment, have potential risks of hardware failure and infection of the surgical site, and do not provide ful l autonomous insulin regulation  . Personalized non linear predictive algorithms have been developed for the external insulin pumps to provide automatic insulin administration by taking into account glucose measurements, insulin infusion rates, and carbohydrate intake [13 15] . These closed loop insulin pump s have varied results in accurately predicting the delay ed absorpt ion of the basal rate insulin when determining the required bolus rate before a meal  .
25 Implantable insulin pumps , capable of implant ation within the subcutaneous pocket of the lower abdomen , have been developed to provide manual insulin therapy through remote control  . Insulin is stored in a reservoir within the implanted device, which must be refilled every one to two months via needle injection. W hil e the implantable insulin pumps provide insulin regulation with a near normal lifestyle, biocompatibility complications require device replacement approximately every three years. An alternative to manual insulin therapy is the transplantation of pancreati c tissue from a donor, which has been shown to provide sustained insulin independence within diabetic patients [3, 18, 19] . This procedure runs a high risk of organ rejection even in the presence of continuous admi nistration of immunosuppressive medication. Additionally, complications arise for large scale application as donor tissue is limited since the transplant requires a match in both the blood and tissue types of the patient and donor. Bio artificial pancreati c tissue constructs show promise as a viable treatment for insulin dependency without the need for immunosuppressive medication [20 27] . T he tissue constructs consist of insulin prod cells, harvested from the pancreas of a healthy patient, that are encapsulated in a semi permeable alginate based membrane [28, 29] . The external membrane acts as a protective layer from the immune system w hile allowing diffusion of nutrients and insulin in to and out of the membrane. Once implanted, the micro encapsulated cells provide physiological blood glucose regulation through the active release of insul in in response to increased glucose levels within the blood stream . In recent studies, bio artificial tissue constructs have successfully restored normal glycemic states over extended periods using diabetic animal models in quadruped animals [20, 24, 30 33] and non human primates [30, 34, 35] , and have reduced regression of diabetes complications in
26 some studies [32, 33] . While l imited human trials show promise in the ability to t reat diabetic patients [36, 37] , further long term studies and development to the tissue construct structure are required to increase the efficacy and durability of the cells  . One of the key issues in the development of bio art ificial organ substitutes is the ability to non invasively monitor the construct s post implantation  . Techniques using NMR imaging and spectroscopy have been specif ically developed to assess bio artificial pancreatic tissue constructs through visualization and metabolic characterization of the insulin producing cells [38, 39] . These non invasive techniques provide information pertaining to construct functionality, viable cell number  , membrane integrity, metabolic activity , cell organization , and cell growth patterns  . Additionally, peri odic monitoring is required to verify tissue construct functionality and predict construct failure to ensure continual administration of insulin. 2.2 Nuclear Magnetic Resonance Imaging and Spectroscopy Nuclear magnetic resonance (NMR) is a physical phenom enon associated with the magnetic moment vectors within the nuclei of specific atoms. Certain n uclei continually rotate about an arbitrary axis where the angular momentum of the nucleus is r eferred to as the nuclear spin. The resulting nuclear magnetic mom ent vector produces magnetic interactions with the surrounding environment and has both positive and negative poles similar to a dipole magnet  . NMR imaging and spectroscopy are non invasive techniques used to measure the magnetic response of the nuclear sp ins within a region of interest (ROI) . Images and molecular spectra can be extracted from the acquired NMR signal to provide visualization and intracellular metabolism of deep tissue implants. NMR measurements are performed through the manipulation of the magnetic moment vectors within a sample by applying static and time varying magnetic fields to force the nuclear magnetic moment vectors into a state of excitation. The application of a static and uniform magnetic field (B 0 ) causes the magnetic moment vect ors of the nuclei to align in
27 parallel or anti parallel with the applied B 0 . This creates an overall macroscopic magnetism within the sample due to the resulting equilibrium charge state. NMR excitation is performed by transmitting specific RF pulse seque nces using e xternal RF coils to generate time varying magnetic fields, known as excitation fields, perpendicular to the applied static B 0 . The excitation fields create Lorentz forces on the magnetic moment vectors of the nuclei within the ROI, where the re sulting differential force ( ) is equivalent to: (2 1 ) where is the magnetic field strength of the excita tion field and is the product of the charge and velocity of the rotating nuclear spins. T he cross product within equation (2 1) denotes that the resulting forces are perpendicular to the applied excitation field. Thus, generating excitation fields perpendicular to the static B 0 causes the aligned magnetic moment vectors of the nuclei to rotate away from the static field vector. The degree to which the magnetic moment vectors rotate, known as the tip angle, is dependent upon the strength, shape, frequency, and duration of the transmitted RF pulses. The rotated nuclear spins result in a state of excitation where the nuclear magnetic moment vectors begin to precess around the static magnetic field as a result of the Lorentz forces generated between the propagating magnetic moment vectors and B 0 , as shown in Figure 2 1(a). The speed at which the ma gnetic moment vectors precess about B 0 is dependen t upon the applied static magnetic field strength and the properties of the nuclei, where the frequency of rotation ( ) can be expressed by the Larmor equation: (2 2 ) where is a nucleus specific constant known as the gyromagnetic ratio that is dependent upon the magnetism of the nuclei itself. The precession of the nuclear m agnetic moment vectors
28 generate a time varying magnetic field known as the free induction magnetic field, which can be coupled to an external receiver coil for processing and analysis of the signal generated by the resonating nuclei. In the presence of a u niform static magneti c field, the magnetic moment vectors of identical isotopes (i.e. 1 Hydrogen) will resonate at the same freq uency as denoted by equation (2 2). Thus, the magnitude and frequency response of the received signal directly correlates to conc entration of specific nuclei within the ROI. (a) (b) Figure 2 1 . Diagram s of a (a) N uclear spin in the excitation state and (b) 2 dimensional NMR image. A gradient magnetic field, with field strength that is a function of distance in a specific direction, can be superimposed on top of the static B 0 to generate a spatially dependent net magnetic field. After excitation, a shift in the precession frequency of the resonating magnetic moment vectors occurs, where the shift i n frequency correlates to the physical location of the nuclei along the spatially dependent gradient field. Thus, Fourier transformation of the received free induction signal can be used to construct a 1 dimensional image since the signal strength at each shifted frequency corresponds to the nuclei concentration at a specific location. 2 dimensional images can be acquired through the application of gradient magnetic fields along orthogonal ax es to create spatial dependency on both the frequency and phase o f the
29 resonating magnetic moment vectors. A magnetic field gradient is applied along the X direction (G X ) with field strength that is a function of location t o generate spatial dependency on the pr ecession frequencies along the X axis. A secondary magnetic fi eld gradient is applied in the Y direction (G Y ) for a brief period of time to create a momentar y spatial dependency along the Y axis. This produces a temporary increase or decrea se in the precession frequency that results in a change in the phase of the resonating magnetic moment vectors after G Y is turned off. The frequency encoded gradient (G X ) is applied throughout NMR signal acquisition to obtain information on the precession frequencies in real time. The phase encoded gradient (G Y ) is applie d for a specific Y coordinate and is incremented in magnitude within a series of subsequent pulse sequences to obtain the phase information along the full Y axis. The resolution of the constructed image is dictated by the number of frequency (n r ) and phase (n p ) e ncodings as shown in Figure 2 1(b). In standard NMR imaging, measurements are acquired on the 1 Hydrogen isotope to construct images based on the spatial distribution of water within the ROI. A typical spin echo NMR pulse sequence is shown in Figure 2 2 wh ere frequency encoded, phase encoded, and slice select gradients are incrementall y applied in the presence of the excitation RF pulses. The spin echo sequence consists of excitation and refocusing RF pulses (DAQ) . The excitation pulse rotates the nuclear magnetic moment vectors by 90 with respect to the static B 0 to maximize the free induction magnetic field strength. In homogenei ties within the static magnetic field cause the NMR signal amplitude to decay over time as a result of de alignment of the spin phases  . A refocusing RF pulse is transmitted with twice the signal amplitude to invert the phases of the nuclear spins by 180 . As the spins continue to precess about B 0 , the
30 phases realign to temporarily increase the free induction magnetic field amplitude for signal acquisition. Figure 2 2 . NMR spin echo imaging pulse sequence. After excitation, the resonating magnetic moment vectors gradually return to equilibrium and realign with the static B 0 . The times associated with the decay of the longitudinal spin to lattice magnetization and the transversal spin to spin magnetization are referred to as the T 1 and T 2 relaxation times respectively. The acquired image contrast can be altered through modification of the timing between the excitation and refocusing pulses , which changes the weighting of the T 1 and T 2 relaxation times. While the refocusing RF pulse increases the NMR signal as a result of temporary phase alignment, significant signal losses can occur as a result of the T 2 decay rate before signa l acquisition can be performed. Gradient echo NMR pulse sequence s are an alternative excitation metho d that uses a 90 RF excitation pulse followed by the application of frequency specific gradients to perform the phase inversion necessary for spin realignment. While gradient echo sequences can be performed faster , since an additional refocusing RF pulse is not required, the technique is more susceptible to signal losses that result from static field in homogeneities and increased T 2 decay rates.
31 NMR spectroscopy consists of the transmission of RF pulse sequenc es in the absence of a magnetic field gradient to determine th e overall concentration of specific chemical compounds, where t he simplest pulse sequence consists of a hard 90 RF pulse. The magnetic shielding associated with the electron cloud varies from compound to compound, which results in a slight shift in the magnetic moment vector resonant frequency. When the free induction signal is acquired after spectroscopy excitati on, Fourier transformation provides a frequency spectrum where the spectral amplitudes at specific frequencies represent the concentration of different chemical compounds as it relates to the chemical shift in resonance. The acquired NMR signal sensitivit y is characterized by the ratio of the received NMR signal amplitude to the ambient noise levels that couple to the acquisition coil. The signal to noise ratio (SNR) is dictated by the applied static magnetic field strength, measurement resolution, nuclei concentration within the ROI, and penetration depth of the acquisition coil. Increased NMR sensitivity can be achieved with higher static magnetic field strengths as a result of an increased number of nuclear magnetic moment vectors aligning with the stati c B 0  . The acquired SNR can be calculated using the Henkelman method  , which relates the measured mean signal level within the ROI ( ) and the sta ndard deviation of the ambient noise ( ) : (2 3 ) where is equivalent to: (2 4 ) where and are the variances of the measured noise and mean signal level respectively.
32 2.3 Implantable NMR Coils The ability to isolate the NMR response within the ROI is limited by the low sensitivity of NMR acquisition methods  , small cell densities associated with the bio artificial pancreas micro encapsulation approach  , and deep tissue implantation sites , wher e adequate signal sensitivity is achieved through increased cell diameters that are not physiologically relevant for in vivo implementation [39, 45] . The received signal sensitivity is also dictated by the coil des ign used for acquisition of the free induction magnetic field as it relates to the coil shape, size, geometry, proximity to the ROI, tissue loading, and electrical impedance matching. Various types of excitation and acquisition coil configurations are used within NMR measurements, which include configurations ranging from planar and curved single channel surface coils, quadrature surface coils, phased array coils, and volume coils such as birdcage resonators. The most straightforward coil configuration is t he use of a single turn planar surface coil for both NMR excitation and acquisition. Since NMR signal sensitivity is inherently limited within deep tissue applications, methods of increasing the acquired NMR response are necessary t o improve the efficacy o f NMR characterization of an implanted bio artificial tissue construct . Implantation of the NMR excitation/ acquisition coil is a method used to increas e the acquired NMR signal by decreasing the physical spacing between the coil and the RO I [46 48] . This requires an invasive surgery to hard wire the implanted RF coil out of the body, which limits long term applications since the wires protruding from the skin alter the patient quality of life and run the risk of in fection. Experiments conducted in  report that mice were only able to withstand the i mplanted RF coils for periods up to six months. A less invasive approach to increase NMR sig nal sensitivity is to implant a coil around the ROI that is electrically resonant near the NMR measurement frequency [49 5 7] . The inductive link formed by the external surface coil and the implanted resonator increase the effective
33 coupling to the resonating nuclei through the use of strongly coupled magnetic resonances (SCMR)  . Extensive ana lysis have been performed on inductively coupled coils within NMR applications [59 62] , and have been used to increase the signal sensitivity when assessing the viability of an implanted bio artificial pancreatic t issue construct  in addition to acquiring localized 1 H spectra  , high resolution spectra  , and NMR images. The implantable NMR detection coils are implemented using discrete capacitors s hunted across the terminals of a small inductive coil to form a resonant LC tank. Single turn, double turn, solenoid, and curved coil structures have been implemented on the impla nt side within various magnetic field strengths in conjunction with a variety of external coils, which includ e single turn RF surface coils  , birdcage resonators [52, 57] , rectangular surface coils  , and pha se d array coils  . However, such techn iques rely on discrete components to achieve resonance and thus limit the increase in SNR to a single nucleus within a pre defined magnetic field strength. Of particular importance , however, is the fact that several biologically relevant nuclei can be dete cted with NMR, including 1 H, 19 F , and 31 P, which resonate at specific freque ncies determined by the applied static magnetic field. Thus, these methods are limited in providing a complete metabolic signature that spans multiple nuclei within different magne tic field environments. A multiple frequency NMR coil has implement ed in previous work using an array of varactors and capacitors to remotely switch the resonant frequency of a large NMR detection coil  . However, the size of the electronic prototype is significantly large due to the reliance on discrete components for system implementation. 2.4 Magnetic Compliance The magnetic properties of any equipment used within a high magnetic field environment must be considered since the static magnetic field is generate d using large permanent magnets ,
34 where m agnetic materials will have a strong attraction to the static B 0 with the potential to cause serious injuries. Furthermore, the magnetism of materials near the measurement ROI can alter the uniformity of the applied B 0 , which can introduce artifact s into the NMR measurements and degraded the acquired SNR. The magnetization of a material relates the concentratio n of unpaired electrons within the material to the magnetic dipole that is formed in the presence of an applied magnetic field. There are fo ur classi fications of material magnetism, which are diamagnetism, paramagnetism , s uperparamagneti sm , and ferromagneti sm . The material magnetism is defined in relation to the relative permeability and susceptibility of the material . T he permeability (Âµ) def ines the ability of the material to alter the magnetic flux within the nearby environment. The relative permeability (Âµ r ) of a mat erial is based on the ratio of the material permeability to the permeability of free space ( = 4 x 10 7 m kg s 2 A 2 ) such that: (2 5 ) where the relative permeability of free space is equal to one. The net magnetic field ( ) that occurs when a magnetic field vector ( ) is applied to an isotropic material is: (2 6 ) where is the magnetic field vect or when no material is present. The magnetic susceptibility of a material ( ) is a dimensionless constant that describes the degree of magnetization of a material in response to a n applied mag netic field such that: (2 7 ) The four classifications of material magnetism are summarized in Table 2 1.
35 Table 2 1 . Summary of the classifications of material magnetism . Magneti sm Type Alignment to B 0 Relative Permeability (Âµ r ) Magnetic Susceptibilit y ( ) Diamagnetism Anti P arallel < 1 < 0 Paramagnetism Parallel > 1 > 0 Superparamagnetism Parallel > 1 > 0 F erromagnetism Parallel >> 1 >> 1 2.4 . 1 Diamagnetism Diamagnetism i s described by the quantum pairing of electrons within the molecules of a material having no unpaired electrons; such that the magnetic moments of the electron spins cancel within the paired electron s . The resulting dipole moment vectors align anti paralle l with an applied magnetic field, which results in a weak internal magnetic field within the material that has little effect on the surrounding environment. All materials exhibit diamagnetic properties as a result of containing some number of paired electr ons, thus diamagnetism is defined as materials that do not exhibit both paramagnetic and ferromagnetic properties. Diamagnetic materials have a relative permeability and magnetic susceptibility that are less than one and zero respectively. Examples of di amagnetic materials commonly used in electronic devices include silicon dioxide, g old, s ilver, c opper, and t in. 2.4 . 2 Paramagnetism P aramagnetic materials contain small quantities of unpaired electrons that create a non zero dipole moment in the absence o f an external magnetic field. However, the magnetic moments of the unpaired electrons tend to cancel out due to the random distribution of the electron spins within the material. These magnetic moments align in parallel with an applied magnetic field and g enerate an internal magnetic field in the same direction, resulting in an increase in t he net magnetic field strength.
36 The relative perme ability and susceptibility of paramagnetic ma terial s are both larger than one where the paramagnetic characteristics t end to dominate the diamagnetic properties, as denoted by the larger susceptibility. Commonly used paramagnetic materials in electronic components include a luminum, c hromium, t itanium, and t ungsten. 2.4 . 3 Ferromagnetism Ferromagnetic materials contain lar ge concentrations of unpaired electrons within the material, which have magnetic dipoles that tend to align with the nearby unpaired electrons t o create a strong self magnetic field even in the absence of an external field. In the presence of an applied ma gnetic field, the magnetic moments align to generate a strong self magnetic field in parallel with the static field. Magnetic saturation occurs when the alignment of a large number of unpaired electron spins generates a permanent magnet, where the resultin g magnetic forces are significantly stronger than diamagnetic and paramagnetic materials and can span distances of millimeters. Ferromagnetic materials are commonly referred to as magnetic materials since the susceptibilities are orders of magnitude larger than one and result in attractive forces in th e presence of external magnetic fields. Ferromagnetic materials should not be used within the NMR environment since the distortion to the applied B 0 can alter the acquired measurement s while the resulting attr active forces compromise patient safety. Examples of ferromagnetic materials include iron, iron o xide, nickel, cobalt, and cobalt oxide. 2.4 . 4 Superparamagnetism Superparamagnetic materials are a su b classification of paramagnetism and contain large conce ntrations of unpaired electrons but do not exhibit strong self magnetic fields. However, in the presence of an external magnetic field, the magnetic moments of the unpaired electrons result in large internal magnetic fields similar to ferromagnetic materia ls. Superparamagnetic materials
37 have magnetic susceptibilities that are significantly higher than paramagnetic materials, but are low in comparison to the susceptibilities of ferromagnetic materials. 2.4 . 5 Magnetic Compliance for an Implantable Device The fabrication of most commercial electronic components relies on the use of ferromagnetic materials that are not compatible with the high magnetic field NMR environment. Primary and secondary batteries commonly employ ferromagnetic materials within the batt ery casing while most multi layer ceramic chip (MLCC) capacitors contain i ron, c obalt, i ron o xide, c obalt o xide, and n ickel within the parallel electrodes of the capacitive structure. Nickel and nickel alloys are widely used in electronic components due to the electrical and thermal conductivity of the material in addition to the rigid mechanical properties. Nickel is also commonly used to metal plate the terminals of discrete components for corrosion protection and decreased contact resistance when solderi ng the components. Some companies produce non magnetic MLCC capacitors for NMR and medical applications using a wet process construction to form the capacitive electrodes out of a s ilver p alladium noble metal alloy . Non magnetic terminations consist of non ferromagnetic conductive materials to provide the solder contacts. Ho wever, the energy volume densities of these non magnetic capacitors are inherently low and limit the amount of capacitance that can be used for energy storage within an implanted device. The use of a custom integrated circuit allows for increased system functionality to be implemented within a small footprint while ensuring magnetic compliance, since integrated circuits are fabricated using non ferromagnetic materials such as aluminum, tu ngsten, and silicon.
38 CHAPTER 3 STAGGERED STR ONGLY COUPLED MAGNETIC RESONANT WIRELESS SYSTEM FOR UNIFORM WIRELESS POWER TRANSFER TO A BIOMEDICAL IMPLANT 3.1 Introduction Near field inductive links have been widely used to provide wireless power and data to implanted devices, but are sensitive to coil misalignments and suffer in decreased efficiencies at distances that are on the order of the transmission coil dimensions . While strongly coupled magnetic resonant (SCMR) coils have been used for increased e fficiency in wireless power transfer, the applications have been limited to unidirectional, point to point transmissions [64 67] where a SCMR coil is implemented at both the transmitter and receiver side. However, stringent size constraints within biomedical applications may restrict the area overhead necessary to implement a SCMR around the receiver (RX) coil structure. Additionally, untethered oper ation of the implant can result in large variations in the RX coil location, leading to large fluctuations in the wir eless power transfer efficiency and ultimately unreliable device operation. This Chapter discusses t he implementation of a resonant based wireless transmission system that utilizes two SCMR coil on either side of the transmission (TX) coil for uniform wireless energy transfer to an implanted RX coil. The patient is placed within the inner diameters of the external transmission and SCMR coils, which generate a net magnetic field uniformly and symmetrical ly a cross the region spanning the range of possible implant locations. Summation of the SCMR fields at the RF carrier frequency of operation reduces system sensitivity to coil misalignments and maximizes transmission distance without alteration to the RX coil structure. A brief overview of wireless power transfer using near fie ld inductive links and resonant based systems is provided. Analytical models are developed to model the wireless energy transfer characteristics of 2 coil, 3 coil, and 4 coil systems acro ss a range of RX coil locations.
39 Experimental results are presented to compare the wireless energy transfer characteristics of the staggered SCMR system with a typical 2 coil near field inductive link. 3. 2 Wireless Power Transfer Overview 3.1.1 Near Field Inductive Coupling Non radiative wireless energy transfer has been widely used for wireless power and data telemetry links within a range of applications including radio frequency identification tags [68 70] , batt ery charging platforms [71, 72] , a nd biomedical implants [71, 73 75] , where untethered device operation restricts the use of wired interconnects. Figure 3 1 shows the equivalent schematic of a two coil inductive link consisting of a large TX coil a nd smaller RX coil. Impedance matching capacitors are included on the TX and RX coils to reduce signal reflections within the network and increase power transfer to the load (R L ) . A source voltage ( ) with equivalent source resistance (R S ) drives the impedance matched TX coil, which ge nerates a time varying magnetic field as a result of the alternating current within the inductive element. When a secondary coil is in close proximity to the primary coil, the alternating magnetic fields generate electro motive forces on the inductive secondary coil to produce a time varying voltage across the coil terminals. The degree to which the rate of change of the current within the primary coil induces a voltage potential across the secondary coil is referred to as the coupling coefficient (k). Figure 3 1 . Diagram of wireless power transfer via inductive coupling.
40 Impedance matching techniques have been widely employed to improve the efficiency in wireless power transfer systems [76 78] and typically require capacitors on both the transmitter and receiver. For simplicity, a single element matching network can be implemented using a capacitor with a reactance that is equal but opposite to the in ductive coil at the frequency of interest  . A series capacitor can be implemented on the TX coil to create a band pass circuit that minimizes the electrical impedance at the matched frequency to maximize the induced AC current, and thus the strength of the generated magnetic field. Implementation of a shunt capacitor across the RX coil terminals increases the equivalent impedance at resonance to maximize the induced voltage potential for large resistive loads. 3.1.2 Strongly Coupled Magn etic Resonant Wireless Power Transfer Resonant based wireless power delivery techniques have been shown to significantly increase wireless power transfer efficiency by taking advantage of the magnetic field interactions of electrically resonant coils in c lose proximity to both the driver and load coils [58, 64, 66, 78, 80] . The electrical resonators are typically implemented using an inductive coil with a known capacitance shunted across the coil terminals to form a resonant LC tank, where resonance occurs at the frequency when the reactance of the inductor (L) and capacitor (C) are equal: (3 1 ) When energy is injected into the LC tank, the energy is transferred b etween the two reactive elements in the form of a magnetic field within the inductor and an electric field within the capacitor. The transfer of energy results in a transient sinusoidal voltage and current within the circuit loop at the resonant frequency, where the alternating curre nt within the inductive element generates a time varying magnetic field t hat is used within the resonant based wireless link.
41 Figure 3 2 . Current and magnetic field distribution diagrams and |S11 | simulation of two closely coupled resonant coils. The use of SCMR coils stems from the magnetic field interactions between two closely coupled coils that are electrically resonant at the same frequency. The inductive couplin g between the closely coupled resonators results in both coils generating an individual time varying magnetic field whenever one of the coils is injected with energy, where the resulting net magnetic field is a function of the impedance and proximity of both resonant coils. Coupled mo de theory states that the magnetic field interactions between the two coils occur across the frequency spectrum and result in two modal frequencies of operation: the co rotating and counter rotating frequency modes [58, 60, 81, 82] . Figure 3 2 shows the simulated 1 port S parameter magnitude ( | S11 | ) for an impedance matched transmission coil that is closely coupled to a SCMR coil, where the original TX coil resonance separates into higher and lower order resonances corresponding to the co unter rotating and co rotating modes respectively. The current within both coils is induced in phase at the co rotating frequency to generate an increa sed net magnetic field as a resu lt of the constructive magnetic field interactions between the coils. Within the counter rotating mode, a distorted net magnetic field occurs near the coil geometries
42 as a result of the currents within each coil operating with equal but opposite phases. The magnitude of the frequency split is dictated by the coupling, and thereby distance, between the two resonant coils. 3.1.3 Magnetic Resonance for Increased Wireless Power Transmission A typical resonant based wireless link consists of the 4 coil network shown in Figure 3 3 (a), where the source drives a TX coil with series impedance matching capacitor (C S ) . The RX coil is located at a distance d RX and is also implemented using an inductive coil with impedance matching capacitor (C L ) in addition to an equivalent resistive load (R L ) that is determined by th e application . Both the TX and RX coils are closely coupled to SCMR coils that are electrically resonant at o through shunted capacitors. The TX and RX coils are typically implemented with a smaller turns ratio to leverage the voltage and current step up conversion within the transmitter and receiver coil pair respectively in addition to leveraging the high quality factor of the stand alone resonators within the reflected impedances. (a) (b) Figure 3 3 . D iagram s of wire less power transfer via strongly coupled magnetic resonant ( SC MR) coils ( a) o riented at the TX and RX coil locations and ( b) l ocated equidistant from the TX coil (d SC MR ) for a RX coil located at an arbitrary distance from the TX coil (d RX ). Figure 3 3(b) shows the schematic for a resonant based wireless system to an arbitrarily placed implant, which utilizes two SCMR coi ls that are located at equal distances on either side of the impedance matched TX coil (d SCMR ) . The animal specimen is placed within the i nner -
43 diameters of the strongly coupled coils to generate a net magnetic field uniformly and symmetrically across a volume spanning the range of possible implant RX locations. The resulting net magnetic field increases the transmission distance while reduci ng system sensitivity to the RX location without alteration to the RX coil structure. 3.2 Transmitter and Receiver Coil Design This S ection presents a design approach for the implementation of both the TX and RX coils within a 2 coil inductive link. The c oil geometry, number of turns, and coil location are used to define the transmission power necessary to induce the minimum required voltage across the RX coil as defined by the receiver sensitivity. 3.2 .1 Magnetic Field Link Analysis Energy transfer withi n a wireless system is a direct function of the magnetic field coupling between the coils as it relates to the coil impedances, dimensions, relative locations , and orientations. Figure 3 4 shows a 2 coil wireless link consisting of a RX coil, with dimensio ns and along the X axis and Y axis respectively, that i s located along the Z axis at a distance ( ) from the impedance matched TX coil, with radius . The source voltage ( ) drives the TX coil at the RF carrier fre quency to generate time varying magnetic field s across the RX coil cross sectional area for wireless energy transfer. The magnitude of the time varying magnetic field generated by the TX coil in the Z direction (B Z ) can be ca lculated at the RX coil locati on such that  : (3 2 ) where is the permittivity of free space (4 x 10 7 m kg s 2 A 2 ), is the number of turns in the TX coil, is the AC current amplitude within the TX coil in Amps, and is the distance
44 between the TX and RX coils in cm. Equation 3 2 can be rewritten as a function of the B Z at the RX coil location such that : (3 3 ) where the product of the number of turns and the total current with in the TX coil is defined as the Ampere Turns ( ) metric, which relates the current amplitude that must flow within each turn of the TX coil to generate the necessar y B Z . The voltage induced across the RX coil terminals (V 0 ) can be defined with respect to the magnetic field applied across the RX coil geometry: (3 4 ) where is the operating frequency in Hz , is the orientation angle between the TX and RX coils, and , , and are the number of turns, cross sectional area, and quality factor of the RX coil respectively. Figure 3 4 . Magnetic field link analysis diagra m. Equations (3 3) and (3 4 ) can be combined to define the Ampere T urns required within the TX coil to induce the necessary V 0 across the RX coil terminals : (3 5 )
45 A boundary occurs within equation 3 5 that results in a maximum transmission distance ( ) within a near field inductive link that occurs at approximately of the TX coil radius such that : (3 6 ) 3.3.2 Receiver Coil Geometry Analysis Implantation of a wireless device within the peritoneal cavity of a mouse limits the overall area overhead for implementation of the RX coil used for receiving wireless powe r and data transmissions. The RX coil is constrained to 2.5x11mm 2 planar area on a 1.6mm thick printed circuit board (PCB) to allow for adequate space for the NMR detection coil and integration of subsequent electronics. Inductive coils are commonly implem ented using multiple turns of conductive wire or the conductive traces within the PCB design itself . Figure 3 5 shows layout diagrams for a PCB planar coil, PCB solenoid coil, and hand wound wire coils where the coil parameters are summarized in Table 3 1 . The PCB planar coil consists of a 6 turn rectangular coil within the top PCB copper layer with equivalent 45.3mm 2 coil surface area, which would be soldered orthogonal to the main PCB of the implant device. The solenoid PCB coil is implemented with paral lel top and bottom layer traces that are conn ected on alternating ends with vias to form a 5 turn solenoid coil with 18.0mm 2 coil surface area. Two versions of a wire wrapped coil are analyzed using Litz wire with 710 Âµm and 180Âµm overall wire diameter wher e the number of turns is determined by a 2.4mm notch within the PCB edge, resulting in 3 turns and 13 turns respectively. Table 3 1 . Summary of the receiver coil structures . Coil Type X dim (mm) Y dim (mm) Cross Section Area (mm 2 ) Number of Turns Bz ( ÂµWb/m 2 ) Coil 1 Planar PCB 10.13 4.47 45.3 6 0.43 Coil 2 Solenoid PCB 10.16 1.67 18.0 5 1.38 Coil 3 710Âµm Litz Wire 10.29 1.64 16.9 3 2.32 Coil 4 180Âµm Litz Wire 10.29 1.64 16.9 13 0.54
46 (a) (b) (c) Figure 3 5 . Layout diagrams of the receiver coil structure for a ( a) PCB planar coil, ( b) PCB solenoid coil, and ( c) Litz wire wrapped coil. Using equation (3 5) and a receiver input sensitivity of 200mV , magnetic fields of 0.43ÂµWb/m 2 , 1.38ÂµWb/m 2 , 2.32ÂµWb/m 2 , and 0.54ÂµWb/m 2 must be induced across the PCB planar coil, PCB solenoid coil, 710Âµm Litz wire wrapped coil, and 180Âµm Litz wire wrapped coil structure s respectively. Figure 3 6 shows the calculated transmitter Ampere Turns versus transmission distance for TX coil radii rangi ng from 1cm to 4cm. When the TX to RX coil distance exceeds the boundary, the required Ampere Turns increases significantly. While the planar PCB coil and the 180Âµm Litz wire wrapped coil require the lowest magnetic field strengths across the RX coil geometries, the solenoid PCB coil is chosen for the receiver coil structure due to the decreased assembly complexity, reduced profile height, adequate inductance, and the moderate magnetic field required for wire less power transmission. T he coil was fabricated in a 2 layer PCB process, Figure 3 7(a), and has an i nductance and AC
47 (a) (b) (c) (d) Figure 3 6 . Simulated TX coil Ampere Turns versus transmission distance for various TX coil radii using the (a) PCB planar coil, (b) PCB solenoid coil, and Litz wire wrapped coils with overall wire diameters of (c) 710 Âµm and (d) 180Âµm . 3.3.3 Transmitter and Strongly Coupled Magnetic Resonant Coil Design Design of the external coils used for wireless power transmission must take into account the overall geometry and TX coil structure to ensure sufficient inductance and resonant quality factor for wireless energy transfer to the untethered RX coil. Using equation (3 5), a 5 turn PCB solenoid coil with 18.0mm 2 coil surface area, 200mV RX sensitivity, and a transmission distance of d RX = 1cm would require approximately 0.2 Ampere Turns for a TX coil with 1cm r adius, which equates to 0.2Amps of current (33dBm) within a 1 turn TX coil. Increasing the number of TX coil turns to N = 3 and N = 6 would reduce the required transmission power to 23dBm and 17dBm respectively .
48 Measurements were take n on four mice to determine the average animal dimensions, as summarized in Table 3 2, to ensure the external coils can accommodate a mouse within the inner diameter of the staggered TX and SCMR coils. For an average mouse body height and width of 2.4cm an d 3.5cm respectively, a minimum TX coil inner diameter of 35mm would result in the optimal wireless power transfer boundary to occur around 12.4mm on either side of the TX coil. The external bore coil was implemented using the conductive copper traces to f orm a single layer coil with 45mm diameter. Figure 3 7(b) shows the fabricated PCB external coil that is designed with custom footprints across the inductor terminals to allow for implementation as a TX coil or SCMR coil through the soldering of a separate matching network PCB or discrete capacitor respectively. The fabricated PCB bore coil has a measured inductance of 930nH with corresponding AC resistance of 700 at 13.56MHz . Table 3 2 . Measured average mouse dimensions of four mice . Body Height Length Body Length w/ Tail Body Width Ear Canal to Abdomen 2.4cm 9.5cm 18.5cm 3.5cm 5.75cm (a) (b) Figure 3 7 . Photographs of the PCB ( a) R eceiver coil and ( b) E xternal bore coil. 3. 3 Wireless Power Transfer Analysis This S ection discusses the analysis and modeling of 2 c oil, 3 coil, and 4 coil wireless systems. Analytical models are presented to define t he mutual inductance between the coils
49 within the wireless link as a function of coil geometry and location. Circuit network theory is presented for the multi coil topologies to capture the wireless energy transfer characteristics across RX coil placement. The equivalent input impedance and wireless transm ission voltage gain are derived in addition to power transfer metrics that are used to characterize the wireless systems. 3.3 . 1 Mutual Inductance Modeling In this Section, models are developed to estimate the mutual inductance between the TX, SCMR, and RX coils. The mutual inductance between two circular coils (i.e. TX and SCMR coils) can be modeled as two co planar and co axial coils located at a distance of as shown in Figure 3 8 (a). (a) (b) Figure 3 8 . Mutual inductance modeling diagrams for (a) Two external circular coils and (b) An external circular coil and the PCB solenoid RX coil. The mutual inductance between two coils ( ) can be modeled using the Neumann Formula such that: (3 7 ) where is the permeability of free space, and are differential current element s d efined along the geometries of coil 1 and c oil 2 respectively, and is the magnitude of the relative
50 position vector between and . The line integrals along the geometries of both coils within equation (3 7 ) relate the equivalent mutua l inductance to the relative geometry, orientation, and location of both coils. For c oil 1, the location of along the coil windings can be geometrically represented with a relative position vector ( ) of a circle: (3 8 ) where is the coil radius and is the relative angle to be integrated along the coil geometry from 0 to 2 . The differential current element that results from current flowing wit hin the coil can be defined by different iating with respect to such that: (3 9 ) The location of along the c oil 2 windings can be represented with relative position vector ( ): (3 10 ) where is the c oil 2 radius and is the relative angle to be integra ted along the coil geometry from 0 to 2 . The differential current element along the c oil 2 geometry can be derived as: (3 11 ) T he magnitude of the relative position vector can be defined as the difference of the coil 1 and c oil 2 relative position vectors such that : (3 12 ) The mutual inductance can be derived using e quations ( 3 7) (3 12 ) as: ( 3 13 ) where N 1 and N 2 are the number of turns within coils 1 and 2 respectively.
51 The solenoid RX coil can be modeled with as an ellipse with major and minor radii of and respect ively, as shown in Figure 3 8 (b). The location of the differential current element along the c oil 2 windings can be represented by the Cartesian equation of an ellipse with relative position vector ( ): (3 14 ) Where the differential current element can be derived as: (3 15 ) T he magnitude of the rel ative position vector can be defined as: (3 16 ) E q uations (3 7) (3 9), and (3 14 ) (3 1 6 ) can be combined to relate the mutual inductance between an external circular coil and the solenoid RX coil as: (3 17 ) For given coil dimensions and orientations, equation s ( 3 13 ) and (3 16 ) can be solved n umerically through the use of applied numerical computation software for execution of the elliptical integration that results within the equation s . Two port S parameter measurements were acquired on two external bore coils as the coil separation was incre ased from 1cm to 10cm in 1cm increments. The mutual inductance was extracted from the measurements at 13.56MHz, as shown in Figure 3 9(a), based on the equivalent Z 21 parameter. The measurements were repeated for an external b ore coil and the PCB solenoid coil across a 0cm to 10cm coil separation with 1cm increments as shown in Figure 3 9 (b). The modeled mutual inductance s follow the measured results closely with a Â±18.4% and Â±17.5% percent error across the coil separation range for the Bore to Bore and Bor e to RX
52 experiments respectively. The Bore to RX coils have a measured 7.5nH mutual inductance when the RX coil is locate d in the inner diameter of the b ore coil while the Bore to Bore coils have measured mutual inductances of 51.2nH, 29.2nH, and 19.1nH fo r 3cm, 4cm, and 5cm coil separations respectively. (a) (b) Figure 3 9 . Modeled and measured mutual inductances between two coils as a function of coil separation for (a) Two external circular coils and (b) An external ci rcular coil and the PCB solenoid RX coil. 3.3 . 2 Wireless System Network Theory In this Section, circuit models are developed using network theory to analyze the energy transfer characteristics of 2 coil, 3 coil, and 4 coil systems. Measured results are co mpared with the models to characterize the equivalent TX coil input impedance and TX to RX wireless voltage gain for each wireless topology. 184.108.40.206 Two coil wireless system : 1 TX coil and 1 RX coil A typical near field inductive link can be modeled as th e 2 coil network shown in Figure 3 10 , where the source voltage with equivalent source resistance (Not Shown) drives an impedance matched TX coil (L 1 ) with parasitic resistance (R 1 ). For simplicity, input impedance matching was implemented with a single el ement network consisting of a series capacitor (C 1 ) to maximize the current within the TX coil at the operating frequency of interest. The mutual
53 inductance between the TX coil and RX coil (L 2 ) is modeled with series inductors ( 12 and 21 ) with equivale nt impedances of 12 such that where k is the coupling coefficient between the coils. The parasitic resistance of the RX coil is modeled with resistor R 2 with shunt capacitor (C 2 ) for impedance matching and a n equival ent resistive load ( R L ). Ignoring the impedance matching capacitors and resistive load, t he wireless network can be analytically modeled by a network matrix defined by: (3 18 ) where and are the voltages across and respectively while and are the currents within the respective inductors. The equivalent two port Y parameters can be extracted from the network matrix in equation (3 1 8 ) for conversion into the preferred two port network parameters, specifically the two port ABCD parameters as it allows for the addition of the series and shunt capacitive matching networks through the cascading of the equi valent ABCD parameters as described in Appendix A . Figure 3 10 . Schematic of a 2 coil wireless system. such that: (3 19 )
54 (3 20 ) where Z TX is the equivalent impedance of the TX coil such that and Z RX is the equi valent impedance of the RX coil as defined by: (3 21 ) Due to the small coupling coefficient between the TX and RX coils, the input impedance of the wireless network can be es timated as the equivalent impedance of the TX coil alone : (3 22 ) The wireless voltage transfer gain can be defined with respect to the output voltage ( ) and the load c urrent within R L such that : (3 23 ) Two port S parameter s were acquired on a 2 coil system using th e PCB fabricated TX and load. Capacitive impedance matching was implemented using a series 150pF and shunt 1nF capacitor on the TX and RX coil resistively for operat ion at 13.56MHz. Figure 3 11 shows the measured and modeled input impedance of the TX coil and the wireless voltage transfer function when the RX coil is located in the inner diameter of the TX coil (d RX = 0cm). The input impedance is matched at appr oximately 13.7MHz where a null and zero cross ing in the input impedance magnitude and phase occur respectively , while the wireless transfer voltage gain has a 14.1dB peak.
55 (a) (b) Figure 3 11 . Measured (solid) and modeled (dashed) metrics of a 2 coil system: (a) TX coil input impedance m agnitude and phase and (b) V oltage gain for d RX = 0cm and R L 220.127.116.11 Three coil wireless system : 1 TX coil , 1 SCMR coil , and 1 RX coil A resonant based 3 coil wireless system can be modeled using the schematic in Figure 3 12 , where the TX coil (L 1 ) is closely coupled to a SCMR coil (L 2 ) that is electrically resonant through shunt capacitor (C 2 ). Impedance matching is implemented for the TX coil and RX coil (L 3 ) using series capacitor (C 1 ) and shunt capacitor (C 3 ). The parasitic resistances of the TX, SCMR, and RX coils are modeled with resistors R 1 , R 2 , and R 3 respectively. The mutual inductances between coils are implemented with series inductive elements to model cross coupling withi n the 3 coil system . Ignoring the input and output matching networks , the wireless system can be represented by a network matrix defined by: (3 24 ) where , , and are the voltages across , , and respectively while , , and are the currents w ithin the respective inductors. The equivalent two port parameters of the wireless system, with inclusion of the impedance matching networks, can be modeled using equation (3 24 ) and the methods described in Appendix A .
56 Figure 3 12 . Schematic of a 3 coil resonant based wireless system. The equivalent input impedance can be extracted through loop analysis on the 3 coil system, where the RX coil is ignored as a result of the sufficiently small coupling coefficient, such that: (3 25 ) where Z TX is the equivalent impedance of the TX coil such that and Z SCMR is the equivalent impedance of the SCMR coil as defined by . The wireless voltage transfer gain can be extracted from loop analysis on the full 3 coil system such that: (3 26 ) where is the equivalent impedance at the load such that . S parameter measurements were acquired on a 3 coil system to extract the input impedance for the SCMR coil, which was resonated near 13.56MHz us ing a 150pF discrete capacitor. Figure 3 13 shows the measu red and modeled input impedance of the TX coil in addition to the wireless voltage transfer function when the RX coil is located within the inner diameter of the TX coil (d RX = 0cm) for TX to SCMR coil distances of 3cm, 4cm, and 5cm. T he measured and
57 modeled results show that the original 13.7MHz resonant frequency split s into higher and lower order resonances as a result of the strongly coupled TX and SCMR coils, where the magnitude of the frequency split increases for smaller TX to SC MR coil distances . The input impedance magnitude has nulls at both the co rotating and counter rotating frequency modes, where the lower frequency peak has a larger magnitude as a result of the currents operating in phase within the closely coupled coils. Additionally, the voltage transfer at the lower resonant frequency has increased magnitude compared to the higher frequency mode. The phase of the input impedance has a positive slope zero crossing at both frequency modes, where a negative slope zero cross ing occurs at the original impedance matched frequency. While the input impedance phase has a positive zero crossing at the higher order resonance, the currents within the coupled coils have equal and opposite phase s resulting in destructive magnetic field interactions . (a) (b) Figure 3 13 . Measured (solid) and modeled (dashed) metrics of a 3 coil system: (a) TX coil input impedance magnitude and phase and (b) V oltage gain for d RX = 0cm and R L 18.104.22.168 Four coil wireless system : 1 TX coil , 2 SCMR coils , and 1 RX coil The resonant based 4 coil system consisting of staggered SCMR coils on either side of the TX coil can be modeled using the schematic in Figure 3 14 . The TX coil (L 1 ) is clos ely coupled to two SCMR coils (L 2 and L 3 ) , which are spaced equidistant on either side of the TX coil. The TX coil and RX coil are impedance matched with series capacitor (C 1 ) and shunt capacitor (C 4 )
58 respectively while the SCMR coils are resonated through shunt capacitors (C 2 and C 3 respectively). The parasitic resistances of the TX coil, both SCMR coils, and RX coil are modeled with series resistors R 1 , R 2 , R 3 , and R 4 respectively. The cross coupling between coils within the 4 coil system is modeled with series inductances with equivalent impedances based on the mutual inductance between each coil. Ignoring the input and output matching networks, the 4 coil wireless system can be represented by a network matrix defined by: (3 27 ) where , , , and are the voltages across , , and respectively while , , , and are the currents within the respective inducto rs. Figure 3 14 . Schematic of a 4 coil resonant based wireless system. Loop analysis can be performed on the 4 coil system to extract the equivalent input impedance, ignoring the RX coil, as: (3 28 )
59 w here and are the equivalent impedances of the L 2 and L 3 SCMR coils respectivel y. Assuming the SCMR coils have identical impedances and are spaced equi distan t from the TX coil , such that and , equation (3 28 ) can be rewritten as: (3 29 ) While t he voltage transfer gain can be extracted from loop analysis on the 4 coil system , it becomes very cumbersome as a result of the increased number of coils, where calculation of the voltage gain from the two port parameters is recommended. S parameter measurements were acquired on a 4 coil system to extract the input impedance using two SCMR coils spaced 3cm, 4cm, and 5cm from the TX coil. The TX, RX, and SCMR coils were resonated using 150pF, 1nF, and 150pF capacitors respectively . Figure 3 15 shows the measured and modeled input impedance of the TX coil and the wireless voltage transfer function when the RX coil is located in the inner di ameter of the TX coil (d RX = 0cm). Similar to the 3 coil topology, the 13.7MHz resonant frequency split s into higher and lower order resonan ces as a result of the magnetic field interactions between the TX and SCMR coils. The magnitude of the frequency spl it i s larger than the 3 coil system for t he same TX to SCMR coil spacing as a result of the magnetic field interactions between an increased number of closely coupled resonant coils. Nulls and zero crossings with positive slopes occur in both the TX coil i nput impedance magnitude and phase respectively at the split resonant modes, where a zero crossing with negative slope occurs within the input impedance phase near the original resonant frequency. The peak wireless voltage transfer occurs at the lower reso nant frequency mode associated with the co rotating frequency.
60 (a) (b) Figure 3 15 . Measured (solid) and modeled (dashed) metrics of a 4 coil system: (a) TX coil input impedance magnitude and phase and (b) V oltage gain fo r d RX = 0cm and R L 3.3 . 3 Wireless Power Transfer Metrics In this Section, various metrics are defined to characterize the energy transfer characteristics of a wireless two port system. The power transfer efficiency ( ) is defined as the ratio of the real power deli vered to the load ( ) and the real power delivered into the wireless network ( ) such that: (3 30 ) where , , , and are the 2 port ABCD network parameters of the wireless system and is the equivalent load impedance. The voltage gain ( ) of a wireless system is important within applications requiring minimum voltage sensitivity at the receiver input and is defined as the ratio of the voltage across the load ( ) and the voltage at the input port ( ): (3 31 ) The power transfer characteristics o f the wireless network can be modeled using the diagram in Figure 3 16 , where the source drives the device under test (DUT), in this case the multi coil wireless system, with input and output impedance matching networ ks. The load is modeled with
61 an equival ent impedance Z L . Impedance mismatches at the input and output of the DUT result in signal reflections that diminish the overall power transfer from the source to the load. Thus, t he power at each node can be defined based on the power available from the s ource (P AVS ), power at the input of the DUT (P IN ), available power at the output of the DUT (P AVN ), and the power delivered to the load (P L )  . Figure 3 16 . Power transfer diagram for a device under test (DUT) with input and output matching netw orks. The reflection coefficients at both the source ( ) and load ( ) relate the signal reflections that occur within the network as a result of impedance mismatches with respect to the network characteristic impedance ( ): (3 32 ) (3 33 ) w here and are the source and load impedances respectively . A reflection coefficient of magnitude 1 or 1 is associated with total impedance mismatch, which results in full signal reflection. Alternatively, no si gnal reflection occur s for reflection coefficients with zero magnitude. The reflection coefficients at the input ( ) and output ( ) ports of the DUT are functions of the signal reflections that occur at the load and source respectively: (3 34 )
62 (3 35 ) where S11, S21, S12, and S22 are the two port S parameters. The power transfer between each node within the system can be extracted from two port S parameter measurements. The transducer power gain (G T ) relates the power transfer within the total system by taking into account mismatches at both the input and output impedance matching networks. The transducer power gain is defined as the ratio of the power delivered to the load ( ) and the power available from the source ( ): . (3 36 ) The available power gain (G a ) re lates the power transfer from the source generator to the output of the DUT by ignoring mismatches within the output impedance matching network. The available power gain is defined as the ratio of the power available from the network ( ) and the power available from the source ( ): (3 37 ) The operating power gain (G p ) ignores impedances mismatches at the input and is defined as the ratio of the power delivered to the load ( ) and the power into the DUT ( ): (3 38 ) Maximum power transfer occurs when both the input a nd output matching networks are the complex conjugate of the source and load impedances respectively. The maximum power gain ( ) is defined as: (3 39 ) where K is the Rollett stability factor which defines a system as being stable when K > 1:
63 (3 40 ) is the defined as . 3.4 Experimental Results Experimental results are presented in this Section to characterize the wireless energy performance of the 2 coil and 4 coil topologies. Measurements are presented to illustrate the change in equivalent input impedance as a result of electrically resonant coils operatin g in the strongly coupled region. S parameter measurements were acquired across a range of RX coil location s for the 2 coil inductive link and the stagger ed 4 coil system with TX to SCMR coil spacing of 3cm, 4cm, and 5cm. The analytical models are compared with the measured results. 3.4.1 Strongly Coupled Magnetic Resonant Effect on Equivalent Input Impedance The presence of a SCMR coil in close proximity to an inductive TX coil affects the equivalent TX coil impedance as a result of the reflected impedanc e of the closely coupled electrical resonator. To demonstrate this effect, one port S parameter measurements were acquired on an impedance match TX coil as a SCMR coil, resonant at the same frequency , was moved from a distance of 100cm to 5cm, as shown in Figure 3 1 7 . The PCB bore coils are used as the TX and SCMR coils, where a series impedance matching capacitor is implemented on the TX coil while the SCMR coil is resonated using a capacitor shunted across the coil terminals. When the coil coupling is we ak, at distances larger than 7cm, there is a single peak in the measured | S11 | that is a result of the equivalent reactance s of the TX coil and series matching capacitor. As the SCMR coil is moved incrementally closer to the TX coil, the coils begin to ent er the strongly coupled region where the single | S11 | peak begins to split into higher and lower resonances associated with the counter rotating and co rotating frequency modes. The magnitude of the frequency split is directly related to the distance betwe en the coils as it relates
64 to the equivalent mutual inductance within the coil pair. It is also important to note that the frequency split is asymmetric about the original operating frequency, where the higher order resonance has increased sensitivity to t he coil coupling. (a) (b) (c) Figure 3 17 . Impedance matched TX coil and SCMR coil inductive link (a) Schematic, (b) Photograph, and (c) |S11| measurements across coil spacing . 3.4.2 Wireless Power Transfer Characte ristics of 2 Coil and 4 Coil Systems To characterize the wireless power transfer across transmission distance, two port S parameters were acquired for the 2 coil and 4 coil systems as the RX coil was moved from a distance of 10cm to 10cm from the TX coil in 1cm increments as shown in Figure 3 18 . The one layer PCB bore coil was used as the TX and SCMR coils, which were electrically resonated using 150pf capacitors for a 13.7MHz resonant frequency. The solenoid PCB RX coil was impedance matched using a 1nF capacitor shunted across the coil terminals. The equivalent wireless power transfer efficiency ( ) and voltage gain (A V ) was extracted for each topology for a 1k resistive load, while the maximum
65 power gain (G MAX ) was calculated to remove impedance mismatches at the input and ou t put for arbitrary source and load impedances. Figure 3 19 shows the mea sured and modeled metrics for each topology, where the metrics were calculated at the co rotating frequency for the SCMR topologies. (a) (b) Figure 3 18 . Wireless power transfer experimental set up for the ( a) 2 coil and ( b) 4 coil systems. Figure 3 20 shows the modeled wireless , A V , and G MAX for both coil topolog ies . The two coil system achieves the highest and A V of 4.7% and 13.9dB respectively when the RX coil is located within th e inner diameter of the TX coil, while the peak G MAX decreases up to 1dB within the SCMR system s . The decrease in the wireless energy transfer metrics at d RX = 0cm is most likely a result of degenerative magnetic field interactions that occur within the inner diameter of the TX coil. The addition of the staggered SCMR coils broadens the wireless ene rgy transfer over a larger range of receiver locations and increases the maximum transmission distance for a given receiver sensitivity. For a required wireless power transfer of 30dB, the 3cm, 4cm, and 5cm staggered SCMR topologies increases the maximum transmission distance by 62.5%, 87.5%, and 100% respectively over the 2 coil topology.
66 (a) (b) (c) (d) Figure 3 19 . V ), and maximum power gain (G MAX ) v ersus receiver coil placement for the (a) 2 coil system and 4 coil syst em with TX to SCMR coil spacing of (b) 3cm, (c), 4cm, and (d) 5cm. (a) (b) (c) Figure 3 20 . Comparison of the modeled (a) wireless power transfer ef gain (A V ), and (c) maximum power gain (G MAX ) versus receiver coil placement. 3.5 Conclusion A wireless energy transfer system was experimentally validated to increase the wireless energy transfer to an arbitrarily placed RX coil for use in biomedical studies. The topology
67 utilizes staggered SCMR coils placed on both sides of the TX coil at equal distances to generate a uniform magnetic field across the range of possible RX coil locations. Analytical models of the mutual inductance and circuit network theory were developed and compared with experimental results. Measurements were acquired on 2 coil and 4 coil systems with di fferent TX to SCMR coil spacing to characterize the wireless energy transfer characteristics of each topology. The 4 coil wireless system broadens the wireless energy transfer metrics over possible RX coil locations while increasing the maximum transmissi on distance up to a factor of two for a given receiver input sensitivity.
68 CHAPTER 4 A WIRELESSLY PROGRAMMABLE IMPLANT FOR INCREASED SIGNAL SENSITIVITY OF NUCLEAR MAGNETIC RESONANCE MEASUREMENTS 4.1 Introduction This C hapter discusses the analysis , design, and implementation of a wirelessly controlled implant for increased signal sensitivity of nuclear magnetic resonance (NMR) measurements on a bio artificial pancreas post implantation . The research motivation and background are provided, including a description of previous work. A system overview of the NMR acquisition system and the wirelessly controlled implan t are presented. The design of the implant electronics is discussed along with the implementation and assembly of the finalized device. Measurements are presented to characterize the performance of the wireless implant, which include 1 H NMR images acquired in 4.7T ( = 200MHz) and 11.1T ( = 470MHz) magnetic field ( B field ) environments using tissue equivalent gel phantoms and small animal studies. 4.2 Motivation and Background Bio engineered pancreatic tissue constructs show great potential as a viable treatment for insulin dependency within t ype 1 diabetes without the need for immunosuppressive medication [20, 21] . The micro encapsulated tissue cells coated in a semi permeable alginate based membrane [28, 29] , provide physiological blood glucose regulation through the active release of the insulin hormone. In recent studies, artificial tissues have successfully restored normal glycemic states over extended periods using diabetic animal models in quadruped animals [20, 24, 30 33] and no n human primates [30, 34, 35] , and have reduced regression of diabetes complications [32, 33] . Limited human trials show promise in the ability to treat diabetic patients [36, 37] , however further long term studies and development to the tissue construct structure are required to increase the efficacy and durability of the cells  .
69 One of the key issues in the development of bio artificial organ s ubstitutes is the ability to monitor the construct post implantation  . Techniques using NMR imaging and spectroscopy have been developed to assess bio artificial pa ncreatic cells through non invasive visualization and metabolic characterization [38, 39] to provide information pertaining to construct functionality, viable cell number  , membrane integrity, cell organization and growth patterns, and metabolic activity  . However, the ability to isolate the NMR response within the region of interest (ROI) is limited by the low sensitivity of NMR  , small cell densities associated with the micro encapsulation approach  , and deep tissue implantat ion sites, where adequate signal sensitivity is achieved through increased cell diameters that are not physiologically relevant for in vivo implementation. A direct method for increasing NMR signal sensitivity is to include an electrically resonant coil a round the implanted tissue construct [49, 50] . When acquiring the NMR response using an external surface coil, the inductive link formed with the implanted coil increases the effective coupling to the resonating nu clei through the strongly coupled magnetic resonant (SCMR) effect  . This is problematic as implantable NMR coils rely on discrete components to achieve resonance, thus limiting the increase in SNR to a single nucleus within a pre defined B field. Of particular importance, however, is the fact that several biologically relevant nuclei can be detected with NMR, including 1 H, 19 F, and 31 P, which resonate at specific frequencies determined by the applied B field. Thus, there is a need to develop an active resonator capable of increasing NMR signal sensitivity across a wide frequency range to enable detailed visualization at multiple NMR frequencies and B fields. 4.3 NMR Acquisition with the Implanted Probe Figure 4 1 shows the s ystem architecture for acquisition of NMR measurements using the implanted probe, which houses the bio artificial tissue construct within the inner diameter of a
70 resonant NMR detection coil (L NMR ) . The implant is designed for implantation within the perito neal cavity of a mouse, which limits the overall dimensions to a 15x20x5mm 3 volume including a bio compatible polydimethylsiloxane (PDMS) encapsulation. The external surface coil, used for NMR signal acquisition, is inductively coupled to L NMR to improve measurement signal sensitivity by increasing the coupling between the resonating nuclei and the external coil. Figure 4 1 . System diagram for NMR acquisition through an inductive link between a NMR surface coil and the wirele ssly powered implant. While near field inductive links have been widely used for wireless power delivery [1 4], energy transfer efficiency is highly sensitive to receiver coil placement and degrades over distances comparable to the transmit coil dimension s. While resonant based systems have been shown to provide increased efficiencies [5, 6], applications have been limited to point to point energy transfer over fixed distances and require additional volume overhead for the receiver coil structure. The wire less power and data link is implemented using two planar coils consisting of an impedance matched transmission (TX) coil and a SCMR coil, which are co aligned with a solenoid receiver coil (L RX ) on the implanted device as discussed in Chapter 3 . The matchi ng network for the wireless power/data TX coil consists of a series non magnetic chip capacitor to maximize current through the TX coil the resonant frequency. The wireless link is operated within the co rotating mode, where currents are induced in phase w ithin the coupled coils to generate a uniform field distribution with decreased sensitivity to implant coil placement. The
71 external coils are sized to adhere to the cylindrical form factor of the magnet bore through placement of the animal specimen within the inner diameter of the RF coils. NMR and RF channel isolation is realized through orthogonal orientation of the coil pairs, which ensures device reliability by minimizing the unintended pick up of NMR transmissions that can exceed 1kW. Additional isolat ion is obtained through operation of the RF carrier frequency (~80MHz) outside of the NMR frequency band of interest (190MHz 470MHz). The impedance matching network for the NMR excitation/acquisition surface coil is implemented with trimmable variable c apacitors in a tune and differential match configuration. After the implant resonance is wirelessly programed, the NMR impedance matching network is manually adjusted to match the co rotating frequency operating frequency of interest for maximum signal acquisition . A 3D printed fixture, Figure 4 2, accommodates the multi coil system through placement of the sedated animal in the prone position such that the abdomen is oriented above the NMR surface coil for incre ased coupling to the implanted device. Figure 4 2 . Diagram of the experimental set up for acquisition of in vivo NMR measurements using the wirelessly powered implanted device. The implant system diagram is shown in Figure 4 3, which consists of L NMR , a custom IC, L RX with impedance matching capacitor, and discrete capacitors (C S ) for energy storage. The IC
72 contains an integrated digital capacitor (D Cap) that is shunted across L NMR to form a parallel LC tank, where resonance is controlled by the D Cap output capacitance using a 10 bit digital word. Wireless programmability of the device is enabled through an integrated receiver front end consisting of an envelope detector, clock/data recovery (CDR) circuitry, and finite state machine (FSM) with latch memory to extract the data payload from the RF transmissions coupled to L RX . An on chip power management unit (PMU) harvests energy from the dedicated inductive link to charge C S and provide continuous power to the implant througho ut NMR signal acquisition. Figure 4 3 . System diagram of the imp lantable device consisting of a power management unit (PMU), envelope detector (Env.), clock/data recovery (CDR) circuitry with reference oscillator (osc ), finit e state machine (FSM), and digitally programmable capacitor (D Cap) for selective resonance of the NMR detection coil (L NMR ). With the exception of discrete non magnetic capacitors, all components were integrated within the IC or embedded into the PCB its elf. This highly integrated approach is required since most commercial off the shelf components such as surface mount devices, IC packages, as well as primary and secondary batteries are restricted within NMR environments due to the reliance on ferromagnet ic materials such as Nickel, Iron, Cobalt, and their respective alloys. The large concentrations of unpaired electrons within these materials generate a strong self magnetic field that propagates into the surrounding area and distorts the uniformity of the applied B field, resulting in measurement artifacts and attractive forces that cause animal discomfort and severe health hazards. Additionally, a highly integrated approach minimizes the overall volume
73 overhead for implantation while increasing the mechan ical rigidity and durability of the device to ensure reliable operation after undergoing large forces during bio artificial cell centrifuging, high temperature chamber sterilization, and subsequent implantation. 4.4 Circuit Implementation 4.4.1 Multi Reso nant NMR Detection Coil Implantable NMR detection coils are implemented as resonant LC tanks, where resonance occurs at the frequency where the reactances of the inductive and capacitive elements are equivalent in magnitude such that: (4 1 ) where is the coil inductance, is the capacitance, and is the resonant frequency in Hertz. When the LC tank is excited at the resonant frequency, energy is transferred between the reactive ele ments in the form of a magnetic field within the inductor and an electric field across the capacitor plates. Replacing the discrete chip capacitor with a variable capacitor allows for selective control of the LC tank resonant frequency through the tuning o f the capacitive element. An implantable detection coil used for NMR acquisition on a bio artificial pancreas in  consists of a 20nH single turn copper sheet coil (1.2cm diameter, 2mm height) connected to a discrete chip ca pacitor for resonance at 470.1 MHz. Using a similarly sized 20nH inductive coil, a selectively resonant coil would require a capacitive tuning range from 5.7pF to 35pF in order to resonate the coil across the 11.1T NMR frequencies associated with the 1 Hydro gen, 19 Fluorine, and 31 Phosphorous isotopes (470MHz, 442MHz, and 190MHz respectively) as shown in Figure 4 4. It is important to note that the change in resonant frequency with respect to the change in capacitance is dependent upon the tuning region, where a 5pF change in capacitance from 5 pF to 10pF results in a 147MHz change in the resonant frequency while the same change in
74 capacitance from 40pF to 45pF results in a 10MHz change in the resonant frequency. Thus, the resonant frequency range must be taken into account with respect to the required capacitive tuning resolution. Figure 4 4 . Resonant frequency ( ) versus output capacitance of a LC tank consisting of a 20nH inductor and variable capacitor . Capacitor arrays have been widely used to prov ide precise digital control of capacitance s within electronic systems. Figure 4 5 (a) shows a schematic of a digital capacitor (D Cap) array consisting of multiple branches of increasing capacitor sizes in series with MOSFET switches. The equivalent output capacitance ( ) is controlled through the switching of different combinations of the capacitive br anches by applying a digital voltage to the gates of the respective MOSFET switches. When the D Cap is connected across the L NMR terminals , a LC tank is formed with a resonant frequency ( ) that is controlled through the selection and fine tuning of . Two loss mechanisms result from the replacement of a discrete capacitor with the D Cap array as illustrated in Figure 4 5 ( b ). The first is due to resistive losses associated with the effective series resistance (ESR) of the transistor switches, denoted by R , while the second loss mechanism arises from the finite frequency resolution that results from discrete capacitive step sizes associated with a digital approach, denoted by F . The total fractional loss in quality
75 factor can be defined as the sum of R /Q tank and f /Q tank , where Q tank is the unloaded quality factor of the resonant tank. (a) (b) Figure 4 5 . (a) Schematic of a digitally controlled capacitor (D Cap) array and (b) Q degradation associated wit h D R ) and discrete frequency step f ). Each branch of the D Cap array can be implemented using unit sized branches consisting of unit sized capacitors (C u ) and unit sized MOSFET switches. The minimum and maximum capacitance of th e D Cap array ( and respectively) can be expressed as and respectively, where is the parasitic contributions of each transistor switch in the OFF state and is the total number of unit sized bran ches. and correlate to the minimum and maximum achievable resonant frequencies of the tunable LC tank respectively where the ratio of and can be defined as: (4 2 ) where is the time constant of the unit sized branches (defined as ) and is the technology time constant whic h accounts for the intrinsi c device parasitics (defined as ) . Equation (2) shows that the selection of , transistor switch size, and technology node directly limit the capacitive tuning range of the D Cap. The result ing degradation in quality factor due to resistive losses can be expressed as:
76 (4 3 ) Additionally, for a minimum capacitance step size ( ), the fractional frequency resolution ( ) for a specific can be expressed as: (4 4 ) where is the capacitance necessary to resonate the LC tank at . The corresponding degradation in quality factor due to finite capacitance resolution can be approximated by: (4 5 ) Equations (4 2) (4 5) illustrate that the and maximum number of unit sized branches are defined by the required resonant frequency tuning range and technology node, while is selected based on the re quired . Since the switch is inversely proportional to both the switch siz e and parasitic capacitance , the basic design challenge is determi ning a sizing strategy for the D C ap that yields a sufficiently low ESR to meet the desired Q constraints of the tank while minimizing the total parasitic ca pacitance so as not to limit . For a 130nm CMOS technology node, the of a minimum sized transistor is a pproximately 2.7 with 0.36fF parasitic drain capacitance for a of 0.97ps. Analysis of the achievable f or swept values of and shows that a of 190MHz ( ) requires and larger than 55 are at a 2.5pF margin below , Figure 4 6(a). For a target of 30, the specified sizing requirements would result in 35%
77 and 58% degradation at 190MHz and 470MHz respectively as shown in Figure 4 6(b) and (c) respectively . Thus, a ty pical binary weighted approach is inherently limited in providing the necessary frequency tuning range without significant reduction in and . This is a result of the inherent tradeoff between the channel resistance and parasitic capacitance introduced by the transistor switches. (a) (b) (c) Figure 4 6 . Contour plots for the D Cap (a) maximum capacitance (C max ) and degradation in resonant tank quality factor (Q R /Q tank ) at (b) 190MHz and (c) 4 70MHz for swept values of unit sized capacitance (C u ) versus transistor switch ON resistance (R ON ). To mitigate the limitations of a binary weighted approach, the D Cap is separated into two sub arrays (coarse & fine tuning) sized with distinct . The D Cap array in Figure 4 7 (a) is designed to resonate a 20nH coil across a frequency range spanning the 11.1T NMR frequencies of 31 P (190MHz), 19 F (442MHz), and 1 H (470MHz), which includes the 4.7T 1 H frequency (200MHz). The array is co mprised of capacitive banks implemented with multiple branch elements consisting of unit sized capacitors ( ) and grounded MOSFET switches, Figure 4 7(b), for 10 bit control of the output capacitance ( ). was chosen as and for the coarse and fine tuning sub arrays respectively with unit sized transistor sizing of corresponding to . This sizing approach yields an increase in
78 capacitive tuning range up to 48pF, low side and high si de frequency tuning resolutions of 170kHz and 2.7MHz respectively, and 35% to 21% Q degradation at 190MHz and 470MHz respectively. (a) (b) Figure 4 7 . Schematics of the (a) digital capacitor (D Cap) array used for selec tive L NMR resona nce and (b) u nit size capacitive bank. 4.4.2 Receiver The receiver consists of an envelope detector and clock/data recovery (CDR) circuit to perform on off keyed (OOK) amplitude demodulation and system clock synchronization of non return to zero (NRZ) data encoded RF pulses that are coupled to L RX with simulated 80mV input sensitivity. The envelope detector in Figure 4 8(a) consists of a 4 stage voltage multiplier and 50nA referenced hysteretic comparator for extraction and comparison of t he baseband envelope (V ENV ) and low pass filtered running average (V AVG ). Since the input voltage level is between 0 mV 210mV, the comparator in Figure 4 8(b) utilizes a PMOS input pair with cross coupled NMOS load to ensure input transistor region of opera tion for accurate comparison of the low voltage input signals. The comparator is designed for 53dB open loop gain with 135kHz bandwidth while the positive feedback within the cross coupled load provides 30mV of input
79 referred hysteresis to prevent glitches in output signal transitions. The input current is amplified by a factor of within the second stage, which is followed by a 3 stage inverter chain to generate the rail to rail output for use in the digital CDR circuitry. (a) (b) Figure 4 8 . Schematic of the a) E nvelope detector front en d and b) L ow power hysteretic comparator. The all digital CDR in Figure 4 9(a) performs system clock synchronization and data extraction from the NRZ envelope over a 5kbit/s 250kbit/s data rate range. At start up, the CDR oversamples the incoming data s tream during a preamble training sequence using a 2.4MHz reference clock that is generated by an on chip oscillator. Once the average period length has been determined, a divided down version of the reference clock is selected from a divide by two toggle f lip flop chain for a 10x oversampling rate. A synchronous delay line is used for digital phase sampling of the incoming data for bit extraction and clock synchronization
80 using a 10 bit majority level comparison within the sampling window. The digital logic control algorithm calculates running averages between the NRZ data transitions to adaptively compensate the sampling window for robust operation in the presence of data rate and clock variability. (a) (b) Figure 4 9 . Sys tem d iagram and schematic of the a) A ll digital clock/ data recovery circuitry and b) R ail to rail 2.4MHz reference oscillator. The 2.4MHz rail to rail oscillator is implemented with a buffered 3 stage inverter chain controlled by two dynamic feedback path s operati ng out of phase, as shown in Figure 4 9(b). A V GS referenced bias generator mirrors a reference current through nodes V N and V P to charge known and matched capacitances (C 1 and C 2 ) at the gate of transistors N1 and N2 respectively. When the ramped voltage of the active branch approaches the respective transistor threshold voltage (V th ), the current induced at node V ctrl inverts the output clock, thus resetting the capacitor voltage and activating the other feedback path. Transistor gating and symme tric layout ensures non overlapping operation of the dual feedback paths to reduce clock variability and power consumption. Thick oxide devices within the inverter output stages further reduce short circuit current associated with clock phase transitions f or a 250nA current dissipation from a 1V supply.
81 A synchronous first in first out shift register with FSM control logic performs serial to parallel data depacketization of the 10 bit digital payload with 3 bit cyclic redundancy check ( CRC : x 2 + x 1 + 1 fun ction ) for bit error detection. Upon successful depacketization, the digital capacitive value is stored into latch memory and the PMU is flagged to enter a low power state by shutting down the receiver. The packet structure consists of 3 bit start and stop bits, 3 bit CRC bits, and the 10 bit data payload with dummy bits. The memory used to store the digital capacitive value is implemented with ten master slave latches in parallel to capture the data payload on the rising edge of the loading signal, LD data . The supply voltage of the latches is connected directly to the external energy storage capacitor so the stored digita l value will be retained during low power operation . 4.4.3 Power Management Unit The PMU in Figure 4 10 extracts energy from the RF transm issions to support sustained wireless operation throughout NMR acquisition . The PMU consists of a RF DC converter, voltage clamp, power on reset (POR) pulse generation circuit, and RF DC enabled switch. Wireless signals coupled to the tuned L RX coil pass t hrough the RF DC converter input stage, consisting of a 9 stage voltage multiplier, to boost the signal amplitude and convert the alternating signal into a larger DC current. The magnitude of the charging and reverse leakage currents associated with the voltage multiplier are dependent upon the number of cascaded stages, capacitor sizing, and diode device characteristics in addition to the frequency an d power level of the input signal. A single stage half wave rectifier is shown in Figure 4 11(a) where di ode D1 conducts current to charge the voltage across c apacitor C1 to an amplitude of approximately V in when the input sinusoid amplitude is negative. In the following positive phase, the voltage at the anode of diode D2 is pushed to approximately 2 V in , cau sing it to turn on and charge capacitor C2 .
82 Figure 4 10 . Schematic of the power management unit . Cascading multiple stages of the half wave rectifier results in a linear increase in the rectified output voltage such that: (4 6 ) where V out is the rectified DC output voltage, N is the number of cascaded stages, V in is the input voltage amplitude, and V diode is the forward conducting voltage drop associated with t he diode elements. Optimization of the multiplier is important in obtaining large conversion efficiencies especially at higher operating frequencies because of the limited switching speed and voltage losses associated with each diode device. (a) (b) Figure 4 11 . Schematics of a RF DC converter ( a) Single stage and ( b) C harge transfer model. The charge transfer between the voltage multiplier and load can be modeled as in Figure 4 11(b) where I CHARGE is the forward conducti ng current of the voltage multiplier, I LEAK is the
83 leakage current of the reverse biased diodes, and I LOAD and V OUT are the load current and voltage respectively. In order to maintain a constant output voltage, the average current supplied by the multiplie r has to be equivalent to the average load current for a given period of time such that: (4 7 ) where T is the period of the RF carrier frequency. While the load current is a function of the output voltage, the charge and leakage currents v ary as a function of the input voltage and are dependent upon the input voltage magnitude and types of diode devices. For a given supply vo ltage and load current, the necessary input power to the multiplier can be determined as the sum of the load power and the power dissipated in each diode: (4 8 ) where the power dissipation of a diode is defined as : (4 9 ) where I diode is the current conducted by the diode. It is evident that using diode devices capable of conducting an equivalent amount of current with a reduced forward voltage drop would allow for increased power efficiency. However, any increase in reverse leakage curre nt of the diode must be considered since it results in charge loss during the inactive cycles. Diode connected low V th NMOS transistors are implemented as the diode elements in the RF DC converter to leverage the increased switching speed of these devices for reduced losses within the signal conversion path. The devices are sized with a minimum channel length and large channel width (W/L = 100Âµ/120n) to increase the device current handling capability while further reducing losses in the signal conversion p ath associated w ith the device ON resistance. While low V t h devices allow for increased switching speeds, the reverse leakage current
84 associated with these devices is significantly higher. However, the increase in reverse leakage current is negated through the RF DC enabled switch , as discussed later in this Section, which disconnects the output of the voltage multiplier from the storage capacitor whenever the device has been fully charged and programmed. The charge transfer capacitors are implemented with 4pF metal insulator metal structures for 20% target efficiency within a 70MHz 500MHz frequency range. The PMU employs an active clamping circuit for overvoltage protection and supply regulation using voltage detection, signal conditioning, and current si nking branches. The bypass transistor is sized with large channel width such that the current dissipation is exponentially proportional to the supply voltage exceeding a 1V threshold. MOSFET capacitors are implemented at the voltage multiplier output for o n chip energy storage and RF signal filtering. The POR pulse generation circuit consists of a pull up latch and mono stable circuit to generate a pulse at the gate of N1 whenever power is supplied to the RF DC converter during start up conditions. The pul l up latch utilizes four inverter stages with an 8pF MOS capacitor to increase the node charging profile for a delay in the inverter chain signal path, resulting in a delayed CMOS high level signal at the input of the mono stable circuit. Positive feedback is introduced through a PMOS transistor to latch the output signal once it has transitioned to the high state. When the input of the mono stable circuit is pulled high, the AND gate output signal transitions to the supply voltage level until the input sig nal propagates through the buffered signal path to create a pulse at the AND gate output. The delayed signal path is implemented with 3 inverters with low W/L ratios (W/L=200nm/2Âµm) to have significantly decreased drive strengths and 2pF MOS capacitors to ensure a sufficient delay between the input and output of the mono stable circuit, and thus ensuring a sufficient pulse width.
85 The RF DC enabled switch separates the receiver (V RX ) and storage capacitor (V CAP ) supply voltages into two voltage domains. The circuit consists of a power gating PMOS switch P1, cross coupled inverter latch, and two pull down transistors to control and store the operating state. During start up, the mono stable POR circuit generates a 3Âµs pulse at the gate of a pull down transisto r , activating the PMOS switch and connecting V RX to V CAP . In this state, the receiver is operational while the RF DC converter charges the external storage capacitors. When data is loaded into the internal memory using signal LD, the RF DC latch st ate is t oggled and P1 is opened ; only the cross coupled latch and memory remain active. The bulk of P1 is tied to V CAP to reduce reverse leakage current and prevent latch up during low power operation. After programming the output capacitance, t he system can be co ntinuously powered through out NMR acquisition through the transmission of a continuous wave RF signal to reactivate the RF DC enabled switch. 4.5 Implant Assembly and Encapsulation The assembled implant is shown in Figure 4 12(a), which measures 1.7x1.3cm 2 , and is designed with a rounded form factor to alleviate mechanical stress on the surrounding tissue post implantation. The IC was fabricated in a 0 .13Âµm CMOS process with 1 .5x0.7mm 2 die area, Figure 4 12(b), which is wire bonded chip on board to reduce parasitic contributions and area overhead associated with packaging while ensuring magnetic compliance. The non magnetic discrete components consist of the L RX impedance matching capacitor and a bank of six 220nF energy storage capacitors that are incorpor ated within the PCB edge for device profile reduction. Both L NMR and L RX are fabricated within the 2 layer PCB to increase mechanical rigidness while reducing the discrete component count for decrease d assembly complexity and proce ss variability between de vices.
86 (b) (a) (c) Figure 4 12 . (a) Assembled implant device, (b) Die micrograph, and (c) C ross section diagram of the PDMS coated implant device. The selectively resonant L NMR coil consists of a single turn copper trace with 1cm diameter and 30mil trace width to form an 18nH planar coil ( = 45 ), where a cavity within the inner diameter was included to accommodate the bio artificial organ. For implementation of L RX , parallel top and bottom layer traces are con n ected on alternating ends with vias to form a 150nH solenoid coil within the PCB as discussed in Chapter 3 . L RX is embedded at an orthogonal orientation w ith respect to L NMR to ensure physical isolation through coil decoupling. Preliminary NMR measurement s show B field distortion around the exposed PCB pads as a result of the electroless Nickel immersion Gold finish; however the distortion is localized and does not extend into the ROI . The device is coated in 5mm of PDMS gel using a multi step molding proc ess , as described in Appendix B , to ensure biocompatibility and formation of the cavity used to hold the bio artificial organ as shown in the device cross section in Figure 4 12(c) . Prior to PDMS gel curing,
87 the mold is placed in a vacuum degassing chamber to remove air bubbles within the viscous PDMS gel. This ensures NMR measurement integrity since a non uniform coating results in magnetic susceptibility variations within the surrounding area that can alter the applied B field homogeneity. Due to the high thermal expansion coefficient of PDMS, the gel is cured at room temperature for 24 hours to prevent mi cro fractures within the PCB copper traces and solder connections. 4.6 Experimental Results 4.6.1 Preliminary D Cap NMR Results For acquisition of prelim inary NMR measurements, a stand alone D Cap structure was fabricated in a 0.13Âµm CMOS process as shown in Figure 4 13 . The 10 bit digital input of the D Cap was hard wired using ribbon cable to apply the DC voltages at the MOSFET gates for selective contro l of the output capacitance. The output impedance of the D Cap was measured using an E5071C Network Analyzer with calibrated GSG RF probes (GGB Industries) . The D Cap has a measured capacitive tuning range of 5.4pF 57.2pF with a 51fF resolution, where 3 bond pads were used to interface to the capacitive node for a reduction in the effective bond wire inductance Figure 4 13 . Die micrograph of the digital capacitor (D Cap) array . A tissue equivalent gel phantom consisting of 6 4.1% deionized water, 32.0% Sucrose, 2.3% TX 151 solidifying powder, and 1.6% KCl was created for NMR imaging experiments. A
88 coaxial HP85070B dielectric probe was used to measure the complex permittivity of the gel phantom as defined as  : (4 10 ) where is relative permittivity and is the out of phase loss factor of the material. The conductivity of the tissue can be calculated based on the permittivity of free space and the frequency of interest in radians/second ( such that: (4 11 ) The dielectric properties of various tissues and organs within the body can be calculated based on the frequency of operation using  to determi ne other average dielectric values within the abdomen. The gel phantom was measured to have dielectric properties similar to the average abdomen of a mouse  ( and contains an abundance of the 1 H isotope, thus mimicking an in vivo situation while pro viding a uniform imaging medium. The D Cap was wirebonded to a test PCB to characterize the increase in SNR provi ded by the capacitive output. The D Cap output node was connected to a 20nH single turn copper sheet coil that wa s coated in a bio compatible Polydimethylsiloxane (PDMS) gel. Decoupling capacitors were implemented at the digital input nodes using non magne tic chip capacitors to provide stable voltage levels at the inputs of the transistor switches. NMR image acquisition was per formed within an 11.1T magnetic field environment using an impedance matched NMR surface coil at 470MHz. A multi spin echo imaging pulse sequence (6cm FOV, 1mm slice thickness, 256x256 matrix size, 50kHz Sweep Width, 9ms TE, sinc3 RF Pulse, and 2000Âµs RF Pulse Length) was performed on the tissue equivalent phantom using the surface coil alone, Figure 4 14(a) . The PDMS coated copper sh eet coil (connected to the hard wired D Cap) was inserted into the gel phantom approximately 9mm away from the external NMR surface coil. The implant coil was programmed to resonate above 470MHz and the NMR
89 surface coil was tuned and matched to optimize th e co rotating frequency of the inductive link at 470MHz. The multi spin echo pulse sequence was then repeated with the resonant PDMS coated coil , Figure 4 14(b) . The SNR within a ROI located 9mm from the surface coil was measured to be 16 V/V (24.1dB) and 2 6 V/V (28.3dB) using the surface coil alone and the surface coil with the resonant hard wired coil respectively. Thus, inclusion of the PDMS coated coil connected to the D Cap increased the acquired SNR by approximately 60% (4.2dB) . (a) (b) Figure 4 14 . Coronal plane NMR images of a tissue equivalent gel phantom at 470MHz (11.1Tesla) using a NMR surface coil (a) only and (b) with the PDMS coated copper sheet coil connected to the hard wired D Cap. 4.6.2 Oscillator Performan ce For oscillator characte rization, a stand alone test structure was fabricated in a 0.13Âµm CMOS process , including the bias current reference and start up circuitry. An Agilent 54832D mixed signal oscilloscope and Agilent N9020A MXA signal analyzer were u sed to measure the jitter and phase noise performance of the oscillator respectively. The output pad was probed using a GGB Industries Model 34A high not to degrade the oscillator performance by int roducing excessive capacitance through the test set up. The chip was placed within a grounded metal box to act as a Faraday cage to block
90 external electric fields and prevent any external signals from coupling to the test set up. A low current source meter was used to measure the current consumption of the oscillator test structure when provided with a 1V supply voltage. (a) (b) (c) (d) Figure 4 15 . Measured oscillator (a) Output spectrum, (b) J itter performance, ( c) Phase noise, and (d) F requency and current dissipation of 17 samples. The oscillator produces a stable 2.3 MHz rail to rail square wave clock signal with 103kHz standard deviation measured over 17 samples . Figure 4 15 shows the measured (a) output power s pectrum, (b) jitter performance, (c) phase noise, and (d) frequency and current histograms over measured samples . The oscillator has a measured 84dBc/Hz phase noise at 100kHz offset and 8ns peak to peak jitter performance (1.8%).
91 The oscillator, bias, an d startup circuit ry consume 387 nA from a 1V supply . The figure of merit (FOM) of the oscillator can be calculated using  : (4 12 ) where is the oscillation frequency in Hz, is the phase noise offset in Hz, and P osc i s the power dissipated by the oscillator expressed in Watts. For an oscillation frequency of 2.3MHz, with phase noise of 84.73 dBc/Hz at a 100kHz offset, and 387nW power dissipation, the oscillator has a FOM of 176dB which is comparable with other current ly published low power oscillators. (4 13 ) (4 14 ) Simulated power performance show the oscillator dissipates 64% of the total power, the current reference dissip ates 34%, and the start up circuitry dissipates 2% of the power during normal operation. The power dissipation can be reduced further by decreasing the reference bias current and increasing the current mirror rati os to obtain the same oscillation frequency . 4.6.3 Device Wireless Performance GGB Industries Model 34A high impedance probe s were used for receiver characterization, where the receiver is capable of demodulating AM data streams over a 70MHz 500MHz carrier frequency range with 100% modulation ind ex. After completion of the preamble training sequence, the CDR selects a r eference clock approximately 10 times faster than the i ncoming data rate to perform data payload extraction and clock synchronization over a range of 5k bit/s 250kbit/s data rate s. The system dissipates 1 7ÂµA from a 1V supply, which is dominated by the
92 reverse leakage current of the low V th NMOS devices within the RF DC converter. Upon successful data payload extraction, toggling of the RF DC enabled switch reduces system current dis sipation to approximately 50nA from a 1V supply . Figure 4 16 shows the measured transient waveform s of the two internal supply voltages throughout the charging, programming, and low power phases. Two digital multi meters were used to measure the supply vol tages referenced to the PCB ground plane. The charging phase begins by transmitting a continuous wave signal while the RF DC voltage multiplier converts the received AC signal to charge both supply voltages to approximately 1V. Figure 4 16(b) shows a zoome d in version of the measured voltages during start up conditions. T he voltage multiplier quickly charges V RX until the RF DC enabled switch is activated, where t he V RX charging profile de creases once it is connected to the large energy storage capacitors. In the programming phase, a NRZ data packet with 32 bit preamble (generated by an Agilent 33120A arbitrary waveform generator) is used to modulate a 100MHz carrier signal provided by a HP E4421B ESG series RF signal generator . A fter programming the device, a continuous RF signal can be transmitted to active the RF DC enable switch and provide wireless power to the device througho ut the NMR measurements . The selectivity of the device resonance was characterized using a network analyzer (Agilent E5071C) for a cquisition of 1 port S parameter measurements on a broadband coil that was loosely coupled to the L NMR coil, Figure 4 17. The device can selectively resonate L NMR across a 153MHz 490MHz frequency range through complete wireless control, which includes th e 11.1T NMR frequencies of 1 H, 19 F, and 31 P as well a s the 4.7T 1 H frequency.
93 (a) (b) (c) Figure 4 16 . Measured transient waveforms of the V RX and V CAP supply voltage s during the (a) charge, program, and low power pha ses and (b) charging phase start up conditions. (c) Measured current dissipation before and after programming the device. (a) (b) Figure 4 17 . Measured resonances of the device L NMR when wirelessly powered and programmed to selectively resonate at the (a) 11.1T NMR frequencies and (b) full frequency range .
94 4.6.4 Tissue Equivalent Phantom NMR Measurements A 3D printed module was designed to position the implant device and multi coil wireless system at predetermined location s and orientations to reduce variability in the experimental set up. Spin echo images were acquired within 4.7T (200MHz) and 11.1T (470MHz) B fields in the absence of the implant device, Figure 4 18 (a) and (c) respectively. The implant was then placed at a 1cm depth within the gel phantom and wirelessly programmed to resonate above the 1 H NMR frequency within the respective field strength. Adjustment of the NMR console impedance matching network was performed to optimize the co rotating mode of the resonant inductive link. B field shimming and power calibration procedures were performed using standard protocols followed by acquisition of spin echo images, Figure 4 18 (b) and (d). (a) (b) (c) (d) (e) (f) Figure 4 18 . 1 H NMR images acquired on a tissue equivalent gel phantom using a surface coil alone and surface coil inductively coupled to the wirelessly programmed implant device within (a, b) 4.7T and (d, e) 11.1T magnetic field strengths respectively. Acquired sign al to noise ratio (SNR) versus transmission power for (c) 4.7T and (f) 11.1T magnetic f ield strengths.
95 The NMR transmission power was swept within each experiment to extract the peak SNR within the ROI ( measured values are shown in Figure 4 18 (c ) and (d) f or 4.7T and 11.1T B field strengths respectively). The acquired SNR was calculated as the ratio of the mean ROI signal level and the standard deviation of the acquired noise floor  . NMR image acquisition using the surface coi l alone resulted in a SNR of 43.4 V/V (32.7dB) and 34.8 V/V (30.8dB) within 4.7T and 11.T B fields respectively while inclusion of the wirelessly programmed implant resulted in acquired SNR of 104.8 V/V (40.4dB) and 63.7 V/V (36.1dB) respectiv ely for a 140% (7 .7dB) and 80% (5.3dB) increase in acquired SNR in comparison to the surface coil alone. 4.6.5 Bio Artificial Pancreas I n V ivo NMR Measurements A micro encapsulated bio artificial pancreatic tissue construct was placed within the inner diameter of the PDMS coated implant device using the procedures in  with a 2.2x10 7 cells/mL cell density, Figure 4 13( a). The device was implanted within the peritoneal cavity of a 34g mouse that was anesthetized with Isoflurane throughout NMR acquisition. The animal was placed in the prone position within the inner diameter of the RF coils to supply wireless data and pow er while the NMR excitation/acquisition surface coil was oriented below the abdomen of the mouse to form the inductive link with the implanted device, Figure 4 19 (b). (a) (b) Figure 4 19 . Photograph of the a) PDMS coated devi ce with bio artificial pancreas and (b) experimental set up for in vivo NMR acquisition.
96 Multi slice gradient echo images were acquired for both 4.7T and 11.1T B fields using the same procedures employed in the gel phantom studies. Gradient echo image s (2000Âµs pulse width, 5 averages) were ac quired in an 11.1Tesla magnetic field strength , where Figure 4 20 shows multiple slices of the coronal, sagittal, and axial planes of the acquired NMR images. High resolution measurements were acquired for increasi ng image resolutions of 128x128, 256x256, and 512x512 as shown in Figure 4 21 (a) (f) respectively within 4.7T and 11.1T magnetic field strengths with acquir ed SNR is summarized in Table 4 1. When the image resolution is increased, the size of each voxel ( or pixel) spans a smaller number of resonating nuclei. Thus, an increase in image resolution by a factor of two should degrade the acquired SNR by a factor of four ( 12dB) since the noise floor rem ains constant across imaging resolution s . However, the meas urements show decreased signal sensitivity by a factor of approximately two ( 6dB) between image resolutions, suggesting the implant provides increased SNR at higher image resolutions within a range of 50% (3.5dB) to 73% (4.8dB) enhancement. (a) (b ) (c) Figure 4 20 . Acquired NMR images of the in vivo artificial pancreas with the wirelessly programmed implant at 470MHz (11.1Tesla) for the (a) c oronal, (b) sagittal, and (c) axial planes.
97 (a) (b) (c) (d) (e) (f) Figure 4 21 . 1 H NMR images acquired on a bio artificial pancreas using the implant ed device for image resolutions of 128x128, 256x256, and 512x512 in ( a c) 4.7T and (d f ) 11.1T magnetic field strengths. Table 4 1 . Signal to noise ratio (SNR) summary for 1 H NMR images on the tissue equivalent gel phantom and small animal studies in 4.7T and 11.1T magnetic fields. 4.7 Conclusion A wirel ess implant and NMR system architecture have been experimentally validated to increase the signal sensitivity of NMR measurements at multiple frequencies and field strengths. Through complete wireless operation, the device can selectively resonate a NMR de tection coil
98 across a 190MHz 470MHz frequency range spanning multiple NMR nuclei within 4.7T ( 1 H 200MHz) and 11.1T ( 31 P 190MHz, 19 F 442MHz, 1 H 470MHz) B field s . The device has a 1.3x1.7cm 2 form factor where a high level of system integration is used to e nsure biocompatibility and magnetic compliance for animal safety. Embedded coil design in conjunction with a multi coil wireless system ensures NMR and RF channel isolation while the SC M R based wireless powering scheme provides stable energy transfer acros s the device location for sustained reliable operation during NMR acquisition. Wireless programmability is enable through an integrated receiver front end for 5kbit/s 250kbit/s AM demodulation over 70MHz 500MHz carrier frequencies utilizing an envelope detector front end and all digital oversampling clock/data recovery circuitry . The system reference clock is generated using a 387 nW 2.4MHz on chip reference oscillator with 1.8% measured jitter performance for a 176dB FOM. Logic controlled transistor gat ing reduces device current dissipation from 17ÂµA during data demodulation to a 50nA standby current. Device performance was characterized through NMR measurements o n a tissue equivalent gel phantom, which resulted in increased SNR by a factor of 2.4 (7.7dB ) and 1.8 (5.3dB) within 4.7T and 11.1T B fields respectively. High resolution NMR images obtained within small animal studies provided SNR enhancement at increased resolutions in excess of 50% (3.5dB) within the ROI.
99 CHAPTER 5 AN IMPLANTABLE NMR ACQUISIT ION COIL FOR INCREASED SIGNAL DETECTION OF NUCLEAR MAGNETIC RESONANCE MEASUREMENTS 5.1 Introduction The acquired signal sensitivity in nuclear magnetic resonance (NMR) imaging and spectroscopy is dictated by the sensitivity and concentration of the measur ed nuclei, applied magnetic field (B field) strength, surrounding tissue properties, and design of the RF coil used for NMR signal acquisition. Since the penetration depth of an inductive coil is a function of the coil dimensions, the acquired NMR signal s ensitivity is inherently limited within applications using deep tissue implants. An invasive method to increase the acquired signal to noise ratio (SNR) is to implant the NMR excitation/ acquisition coil within the tissue of the specimen to decrease the ph y sical spacing between the acquisition coil and the region of interest (ROI) [46 48] . These methods have been shown to provide increased NMR signal sensitivity, however the hard wired implanted coils are limited wit hin long term applications since the wires protruding from the body are a site for possible infection and alter the patient quality of life  . This Chapter discusses a wireless NMR acquisition receiver coil for the non invasive monitoring of a bio artificial pancreas post implantation using NMR measurement techniques . The ability to implem ent a wirelessly operated NMR acquisition coil increases the acquired NMR signal sensitivity while requiring a minimally invasive surgery. The implant consists of an inductive NMR coil, implanted around the region of interest (ROI ), which is connected to a highly integrated system for the amplification, demodulation, and digitization of the NMR signal response for wireless transmission to an external base station. The system allows for wireless powering and programmability of the device to adjust the system metrics to enable increased signal sensitivity at multiple NMR frequencies. This Chapter presents the desi gn and
100 measurement results of the intermediate frequency to base band demodulation and amplification circuitry within the wireless acquisition coil . 5 .2 Wireless NMR Acquisition Coil System Overview Figure 5 1 shows the proposed system architecture for the implantable NMR acquisition coil, which houses the bio artificial pancreas within the i nner diameter of a programmable resonant coil (L NMR ) as previo usly discussed in Chapter 4. NMR excitation is performed through standard procedures using the external NMR surface coil, where specific RF pulse sequences are transmitted to generate the excitation B fields within the ROI to cause the nuclear spins to res onate about the static B field. Acquisition of the free induction magnetic field that is generated by the resonating nuclei is performed by the implanted wireless NMR coil. The implant is wirelessly powered and programmed through a secondary inductive link between an external base station and an inductive transmit/receive coil (L TX/RX ). During NMR acquisition, the implant amplifies and converts the NMR s ignals that are induced across the resonant NMR coil (L NMR ) into a digital representation and transmits t he digitized waveforms to the external base station through the secondary inductive link A high level of integration within the implant circuitry reduces the overall volume overhead while limiting the use of commercial off the shelf components to ensure ma gnetic compliance of the device . Figure 5 1 . System diagram for NMR acquisition using the implanted wireless NMR acquisition coil.
101 The implant system diagram is shown in Figure 5 2, where the circuit blocks implemented within Chapter 4 are highlighted. The device is wirelessly powered and programed through RF signals coupled to L TX/RX , which is physically isolated from L NMR through orthogonal coil orientation and operation at a carrier frequency outside of the NMR frequency ba nd of interest (190MHz 470MHz). A power management unit (PMU) extracts energy from the wireless transmissions to charge external capacitors for use as the system supply voltage. Figure 5 2 . System diagram of the wireless N MR acquisition coil. Before NMR excitation, the implant is wirelessly programmed to operate for acquisition at a specific NMR frequency. A receiver front end (RX) connected to L TX/RX performs demodulation and data depacketization to enable wireless program mability of the implant, where system tunability is implemented through control of an on chip oscillator and a digitally programmable capacitor (D Cap). The D Cap is shunted across L NMR to provide selective resonance of the acquisition coil to increase the voltage induced at the NMR frequency of interest. The programmable oscillator is used as the carrier signal within a radio frequency to intermediate frequency demodulation circuit. The oscillator frequency is programmed at , w here is the NMR frequency of interest and is the intermediate frequency in radians/second.
102 The digital microcontroller activates the NMR acquisition chain after the system has been wirelessly programmed for operation at a specified NM R frequency. The NMR acquisition chain consists of a radio frequency to intermediate frequency (RF to IF) demodulation front end, intermediate frequency to baseband (IF to BB) demodulation, and analog to digital conversion (AD C). The free induction magneti c field generated by the resonating nuclear spins within the ROI couples to the L NMR coil, which is subsequently demodulated, amplified, digitized, and stored into on chip memory throughout the NMR acquisition process. After acquisition of the full NMR sig nal, the microcontroller activates a transmitter (TX) for modulation and transmission of the digitized data to the external base station. (a ) (b) Figure 5 3 . System diagram of the (a) I ntegrated NMR acquisition chain a nd the (b) I ntermediate frequency to baseband (IF to BB) circuit.
103 Figure 5 3(a) shows the demodulation and digitization signal path for acquisition of the free induction NMR signal s . The demodulation front end utilizes a differential voltage to current dem odulation switching circuit where the gates of an input differential pair are connected across the terminals of L NMR . A programmable oscillator is used as the demodulation carrier signal by driving two sets of differential MOSFET pairs within the RF to IF conversion stage. The RF to I F demodulation stage is biased to ensure the resulting AC output current is within the pA to nA range. The demodulation frequency is set based on the NMR measurement frequency of interest to demodulate the NMR signals down to a 13kHz intermediate frequency. An amplification stage is not implemented within the RF to IF conversion front end due to the increased power overhead required to operate a low noise amplifier within the 200MHz 500MHz frequency range. Instead, signal ampl ification is performed at the input of the IF to BB demodulation stage, where a static 13kHz oscillator is used as the IF demodulation carrier signal. The signal is passed through a filter to remove t he up converted high frequency components that result fr om the IF to BB mixer . The baseband signal is then digitized within a single ended analog to digital converter and stored into on chip random access memory (RAM) to be transmitted to the external base station after completion of NMR acquisition. The focus of this Chapter is the analysis and design of the IF to BB circuitry within the wireless NMR acquisition coil. The block diagram is shown in Figure 5 3(b), which consists of a current to voltage amplification front end, second stage voltage amplifier, IQ channel demodulation including the out of phase drive signal generator, and differential to single ended signal converters. A low noise transimpedance amplifier is used as the input stage to convert the differential intermediate frequency current into an e quivalent output voltage. The second stage utilizes a low noise voltage amplifier to provide further amplification of the intermediate -
104 frequency signal. After amplification, the signal is demodulated within two separate channels using discontinuously switc of phase to extract the in phase and quadrature phase components of the resulting baseband signal. A sine to square wave IQ signal generator creates rail to oscillator, operated at the intermediate frequency ( ), for use as the demodulation drive signals within the IQ demodulation stage. Differential to single ended conversion is performed through subtraction of the differential signal pairs to interf ace with the analog to digital converters for digitization of the amplified baseband signals. Low pass filters are implemented at the output of both the I and Q channels to filter the up converted frequency components that result from the demodulation stag e. 5.3 Circuit Design 5.3.1 Transimpedance Amplifier Transimpedance amplifiers are commonly used in photodetection diodes [88, 89] , electric field sensors [90, 91] , and RF receivers [92, 93] , where the detection and amplification of low current amplitudes is required. Transimpedance amplifiers are ideal for piezoelectric lead zircona te titanate (PZT) actuators that rely on the application of a constant DC voltage across the output terminals such that a change in the mechanical properties of the PZT device produces an equivalent AC current proportional to the change in the device capac itance. Additionally, transimpedance amplifiers can be made to have a large current to voltage conversion gain, which makes them ideal for the amplification of AC currents with low amplitudes. This Section discusses the design of a closed loop transimpedan ce amplifier, analysis of the accompanying noise contributions, amplifier offset voltage, and the transimpedance amplifier implementation.
105 22.214.171.124 Closed loop transimpedance a mplifier design The transimpedance amplifier relies on the use of an operational amplifier to direct the input current into a known resistance for conversion of the signal into an equivalent output voltage ( ). A basic single ended transimpedance amplifier structure is shown in Figure 5 4, which consists of an operational amplifier with resistive feedback (R F ). The input current is modeled as a current source ( ) with an equivalent source res istance (R S ), and is connected to the negative terminal of an amplifier. A DC voltage can be applied to the positive terminal of the amplifier to set the common mode voltage of the operational amplifier . Assuming R S >> R F , the AC current produced by the se nsor will flow into the feedback resistance such that the output voltage will be equivalent to: (5 1 ) where A OL and are the open loop voltage gain and dominant pole of the op amp respectively. Thus, R F is used to set the closed loop I/V gain at low f requencies within the single pole system. As R S is increased to be on the same order of magnitude as R F , the input current begins to split between the two resistive paths and degrades the closed loop amplification. Thus, R F should be selected to be at leas t 100 times smaller than the R S of the input current source. Figure 5 4 . Schematic of a basic single ended transimpedance amplifier.
106 Any noise that is generated at the negative terminal of the op amp can be modeled as an equ ivalent voltage source, which will be amplified at the output by a voltage gain of . Assuming R S >> R F , then the equivalent noise voltage gain will be approximately 1V/V. However, the equivalent capacitance at the amplifier input (C IN ), which is the sum of the parasitic capacitance of the current source and the negative op amp terminal input capacitance , introduces a zero into the feedforward path (i.e. the noise voltage gain) such that: (5 2 ) where the zero occurs at . The zero that is introduced by the paras itic capacitances results in a + 9 feedforward path as shown in Figure 5 5(a), while t he dominant pole within op amp produces a 90 amp open loop gain path (A OL within the closed loop system, resulting in effective positive feedb ack and system instability. This can also be analyzed in Figure 5 5(b) with respect to the rate of closure between the A OL and 1/ signal paths, such that |A OL | decreases by 20dB/decade after the op amp dominant pole ( ) and |1/ | increases by 20dB /decade after the feedforward zero ( ) [94, 95] . When |A OL | and |1/ | intersect, such that |AOL| = |1/ |, there is a difference of 40dB/decade between the slopes (i.e. rate of closure) between the two signal paths. This equates to marginal instability as a signal paths. Unconditional stability can be restored within the closed loop system through compensation using a capacitor within the feedback path as shown in Figure 5 5(c). The feedback capacitor (C F ) introduces a pole within the 1/ feedforward path such th at: (5 3 )
107 (a) (b) (c) (d) Figure 5 5 . (a) Schematic and (b) |A OL | and |1/ | transfer functions of a basic transimpedance ampli fier and (c) S chematic and (d) |A OL | and |1/ | transfer functions of a transimpedance amplifier with capacitive compensation. where the pole occurs at while the zero shifts to . Analysis of th e resulting |A OL | and |1/ | in Figure 5 5(d) shows that the feedback capacitor can be used to set such that the rate of closure between the two signal paths is less than 40dB/decade. Also shown are examples of compensated systems that are under, c ritically, and over compensated ( , , and respectively). Critical compensation of the amplifier can be achieved by selecting C F such that occurs at the intersection of |A OL | and |1/ | in an uncompensated system such that |A OL | = |1/ |:
108 (5 4 ) where is the unity gain bandwidth of the op amp. The point at which the magnitudes of the voltage transfer functions inte rsect occurs half way between and such that: (5 5 ) Equations (5 4) and (5 5) can be solved to determine the amount of compensation capacitance required for a c ritically compensated amplifier  : (5 6 ) Thus, for an op amp with a given and , the minimum compensation capacitance required can be calculated based on the target I/V conversion gain as it relates to R F . However, gin due to the by , which occurs a decade before the pole frequency . To ensure stability of the closed loop amplifier across process variation and temperature, C F should be selected larger to provide sufficient pha se margin for unconditionally stability. Inclusion of the compensation capacitor, C F , also affects the current to voltage transfer function of the transimpedance amplifier such that: (5 7 ) Thus, increasing C F to ensure unconditional stability results in decreased current to voltage bandwidth within the closed loop transimpedance amplifier.
109 126.96.36.199 Noise performance considerations Electri cal noise occurs in all electronics as a result of the non ideal characteristics of the charge carriers, which results in random fluctuations in the voltages and currents across frequency throughout the system. When designing amplifiers for detection of lo w amplitude signals, the equivalent noise sources of every component must be taken into account to ensure that the generated noise does not saturate the input signal. When analyzing noise sources, the equivalent noise power is used since the fluctuations o f the charge carriers generate a random signal with an equivalent spectral distribution with positive and negative amplitude s . In the design of a system with multiple cascaded stages, the gain and noise contributions of each stage should be taken into con sideration. The noise factor (F) of a stage relates the amount of noise added by the stage as the small signal passes through such that . The total noise factor of a system with N stages ( ) is defined as: (5 8 ) where (G 1 , G 2 , N 1 ) and (F 1 , F 2 N 1 ) are the equivalent gain and noise factors of each stage. A large gain at the input stage minimizes the equivalent noise contributions of the following stages when referred to the input of the system, while the noise contributio ns of the first stage appear directly at the input without any attenuation. For a transimpedance amplifier with R S >> R F , the noise contributions of the following stages are not significantly attenuated by the transimpedance amplifier as a result of the ap proximate unity gain of the amplifier feedback path . Thus, the transimpedance amplifier and the following voltage amplifier should be carefully designed to minimize the noise contributions of both stages . The two main types of noise sources that should be taken into account when designing such systems are the thermal noise and flicker noise. Thermal noise is present in all electrical
110 components with a resistive or real impedance component and is a result of the random vibrations of the charge carriers with a power spectral density that is flat across frequency. The equivalent thermal noise within a resistor (R) is modeled as a series voltage source with equivalent noise voltage spectral density defined as: (5 9 ) where k is the Boltzmann constant (1.38 x 10 23 m 2 k gs 2 K 1 ), T is the temperature in Kelvin, and is the frequency bandwidth under consideration in Hz. Thermal noise within the channel of MOSFET device s can be modeled as a drain current s ource ( ) as shown in Figure 5 6(a) with equivalent noise spectral density of: (5 10 ) where g m is the transconductance of the MOSFET. The noise source can be input referred to the g ate of the transistor such that: (5 11 ) It should be noted that the noise contributions of a MOSFET device are dependent upon the charge carrier mobility as defined within the transist or g m . Since MOSFETs are majority carrier devices, the noise contributions of a PMOS transistor are smaller than the NMOS counterpart due to the lower mobility of positive charges (i.e. holes) being the majority carrier within the P + channel. Flicker nois e, also known as 1/ noise, occurs at low frequencies and is believed to be caused by charge carriers tunneling into and out of the gate oxide. Flicker noise power is inversely proportional to frequency and is defined as:
111 (5 12 ) where K is a process dependent constant, W and L are the channel width and length respectively, C ox Figure 5 6(b) shows an equivalent n oise current spectrum of a MOSFET device, where the flicker noise decreases linearly with frequency and intersects the equivalent thermal noise at the flicker noise corner frequency ( ) . Increasing the overall gate area of a transistor reduces the equivalent flicker noise power such that the flicker noise corner frequency is reduced by . This is a result of an increase d number of charger carriers being present within a larger MOSFET channel at any given time. Thus, the removal or addition of a charge carrier (as a result of tunneling) is a smaller percentage of the overall number of charges within the channel itself, resulting in smaller fluctuations within the equivalent drain current. (a) (b) Figure 5 6 . (a ) Differential MOSFET pair equivalent noise model and (b) MOSFET noise spectral density. The noise contributions of an op amp can be modeled based on the equivalent input referred noise of the amplifier as shown in Figure 5 7(a), where the op amp is model ed as a noiseless amplifier while the internal noise contributions are input referred as an equivalent noise voltage source ( ) and two noise current sources at each terminal ( and ). This can be further
112 developed for a closed loop di fferential system as shown in Figure 5 7(b) where the errors introduced by the input offset voltage of the amplifier (V IO ), input offset current (I IO ), and input bias current (I IB ) are included within the closed loop amplifier analysis. For a transimpedanc e amplifier where R S >> R F , the input offset voltage of the amplifier has unity gain within the closed loop system. Additionally, the use of a MOSFET input differential pair within the amplifier decreases the input bias currents to negligible values . (a) (b) Figure 5 7 . (a) Input referred noise model for an open loop amplifier and (b) DC offset model of a closed loop amplifier. The equivalent outp ut noise voltage ( ) can be d efined with respe ct to the component values as : (5 13 ) where R eq1 and R eq2 are the equivalent parallel resistances of the source and feedback resistors at the positive and negative terminal respectively, and are the feedback factors, E CM is the common mode noise voltage, and and are the noise voltage s of the source and feedback
113 resistances respectively . The equivalent output noise contribution s of each of the modeled sources are summarized in Table 5 1. Also included is the equivalent output noise contribution s fo r an amplifier in the transimpedance configuration where since R S >> R F . The total eq uivalent input referred noise power ( ) is defined as: (5 14 ) where is the thermal noise power of the source resistance. It is important to note that the feedback factor effects the noise voltage transfer function ( ) and dictates which of the input referred noi se sources ( or ) is the dominant noise source  . For a given feedback resistance (R F ), is the dominant noise source for low values of R S while dominate s at large r values of R S . The thermal noise of R S ( ) is the dominant noise source within intermediate frequencies Table 5 1 . Summary of the noise source s with in a closed loop amplifier A closed loop single ended amplifier can be m odeled using the equivalent circuit shown in Figure 5 8  , where M1 is the input transistor of the amplifier, C gs is the equivalen t gate to -
114 source capacitance of M1, and A 2 is the gain of the subsequent stages within the amplifier itself. The equivalent input referred noise current of the amplifier is: (5 15 ) where and are the charge carrier mobility and overdrive voltage of M1 respectively. If t he input capacitance (C IN ) is equivalent to C gs , the equivalent input referred noise current simplifies to: (5 16 ) Analysis of equation (5 16 ) shows that increasing the gain of the system through a larger feedback resistance (R F ) results in decreased input referred noise current. Additionally, the noise contributions can be further reduced by minimizing the equivalent input capacitance at the inp ut terminal. This is a result of the equivalent input capacitance having an effect on the zero within the noise gain transfer function as shown in Figure 5 5. Figure 5 8 . Noise model for a multi stage op amp with resistive fe edback. 188.8.131.52 Operational amplifier offset voltage The ideal operational amplifier with negative feedback assumes that the voltages at the positive and negative terminals are equivalent such that . Process variation within the
115 fabrication p rocess results in time independent variations in the physical device sizes of the identically drawn input transistor pair of the amplifier  . Mismatches in the feature sizes of the input transistors result in a DC offset voltage occurring between the two terminals as it relates to the threshold voltages of the t ransistor pair. The offset voltage, typically on the order of mV or less, is amplified at the output based on the closed loop DC gain. The DC offset that result s at the output node of the amplifier can have significant effects on the closed loop amp lifier performance and reduce the output signal swing. The DC offset voltage gain for an amplifier in the transimpedance configuration, where R S >> R F , is approximately unity gain such that the DC offset appears at the output with the same magnitude. The variation in the transistor threshold voltage has a random distribution with a standard deviation ( ) that can be estimated using the Pelgrom offset model [100, 101] : (5 17 ) where AVT is the mismatch coefficient and W and L are the transistor channel width and length respectively. AVT is dependent upon the technology node and transistor device, which is determined by the number of doping atoms within the depletion layer (N) such that the statistical variation in determines the matching while control of the net value of determines the threshold voltage  . 5. 3.1.4 Transimpedance amplifier implementation The transimpedance amplifier was implemented using the fully differential configuration in Figure 5 9(a). The feedback resistors (R F1 and R F2 ) were implemented using interleaved polysilicon resistors, each wit 135nA/V. For an op GBW = 30MHz, a feedback capacitance (C F ) of approximately 130fF to 1.2pF would be required to critically compensate the closed loop system for an input
116 capacit ance range from C IN = 1pF to 100pF using equation (5 6 ). The compensation capacitors (C F1 and C F2 ) were implemented using metal insulator metal capacitors in a common centroid layout with equivalent capacitances of 1.3pF, five times larger than the require d amount, to ensure unconditional stability across process variation by setting the pole within the current to voltage conversion path around 23kHz . (a) (b) Figure 5 9 . Schematic of the (a) T ransimpedance amplifier an d (b ) T ransistor level op amp. The op amp is implemented using the folded cascade topology in Figure 5 9(b) to leverage the increased resistance s of the cascoded transistors at the output for increased open loop gain while alleviating the voltage headroom for increased output voltage swing. The casco ded output transistors (M3 M5) ar e biased with the system common mode voltage since the amplification of pA signals results in small signal output voltages with amplitudes in the ÂµV to mV range. The transistor si zes , drain currents (I d ) , and transconductances (g m ) are summarized in Table 5 2. The input transistors in the differential pair (M1 and M2) are implemented with PMOS transistors to decrease the noise co ntributions of the input stage and are sized with W/L vth = 267ÂµV) to reduce the flicker noise corner frequency a decade below the 13kHz frequency of interest. The input transistors are biased in the subthreshold region with low values of g m /I d , also known as weak inversion, where the MOSFET g ate to source DC voltage is smaller than the
117 transistor threshold voltage . Operation in this region allows for a large transconductance to be achieved while minimizing power dissipation where the transconductance (g m ) of a transistor in the subthreshold re gion can be approximated as  : (5 18 ) where I d is the drain current, U T is the thermal voltage approximated as ~ 26mV at room te to surface potential) which is approximated as: (5 19 ) where C ox and C dep are the oxide and depletion capacitances associated with the transistor device type and technology node. is approximately 0.62 for PMOS devices in a 0.13Âµm technology, which is extracted from the technology parameters. The input transistors are biased with I BIAS,P1 = 22.8ÂµA for a transconductance of g m = 283ÂµS . The op amp is designed for an open loop gain of A OL T = 32.5MHz, for a 23kHz closed loop current to voltage bandwidth at a 50pF input capacitance. Table 5 2 . Transimpedance amplifier transistor summary .
118 Common mode feedback (CMFB) is implemented using a four input termi nal amplifier to set the common mode voltage of the output nodes through control of the gate voltages of M7 and M8. The differential output voltage s (V OUT+ and V OUT ) are compared to a 600mV reference using transistors M9 M10 to set the output common mode voltage at half of the supply voltage to ensure common mode stability and increased output dynamic range. The input stage transistors of the common mode feedback amplifier are biased in the subthreshold region with I B IAS,CM = 2.7ÂµA, resulting in a transconductance of g m = 35 .6ÂµS for a common mode closed loop gain of 73.2dB loop gain with 1.9kHz bandwidth. 5.3.2 Voltage Amplifier The second stage of the signal chain consists of a voltage amplifier for subsequent voltag e amplification after current to voltage conversion within the previous transimpedance stage. The noise contributions of the second stage should be min imized since amplification of currents within the pA range at the input of the transimpe dance amplifier p roduce s signals at the input of the second stage within the ÂµV range. The low noise voltage amplifier in Figure 5 10(a) is commonly used in brain machine interfaces, where neural amplifiers must detect small voltage signals within the ÂµV region [103, 104] . The mid band gain of the amplifier is set by the ratio of the fee dback and source capacitors (C F and C S respectively), making the topology ideal for low voltage detection since the reactive elements within the signal path do not have any noise contributions. To ensure unconditional stability, a resistive element has to be shunted across the feedback path to provide negative feedback at DC and low frequencies. This is impl emented using pseudo resistors  , which consist of back to back diode connected PMOS devices. Operation of the transistors in the subthreshold region allows for larg e values of resistances on equivalent resistance is set by the sizing of the PMOS transistors.
119 The closed loop transfer function of the voltage amplifier is: (5 20 ) where C F and C S are the source and feedback capacitors respectively, R F is the equivalent resistance of the pseudo resistors within the feedback path s , and A OL and are the open loop voltage gain and dominant pole of the op amp. The closed loop transfer function has a zero located at DC ( ) and a pole that is set by R F and C F such that , whe re the closed loop bandwidth of the amplifier is set by R F and the op amp open loop characteristics such that and where g m is the transconductance of the amplifier output stage and C L is equivalent load capacitance. C S and C F are implemented using metal insulator metal capacitors in a common centroid layout with capacitance values of 10pF and 100fF respectively to set the mid band gain at approximately 100V/V. C F is implemented using four 400fF capacitors in series for reduced component tolerance as a result of process variation. The PMOS transistors within the pseudo resistors are sized with W/L = 5Âµ/1Âµ for an equivalent resistance of approximately L = 10kHz. (a) (b) Figure 5 10 . Schematic of the (a) Voltage amplifier and (b) T ransistor level op amp.
120 The op amp is implemente d using the fully differential two stage topology in Figure 5 10(b) with the transistor sizing and DC operating parameters summarized in Table 5 3. The input vth = 1.07mV) biased in the sub threshold region with I BIAS,P1 = 4.55ÂµA for an input transconductance of g m = 59.3ÂµS. The transistors are sized with large gate area to reduce the flicker noise corner frequency over a decade below the 13kHz frequency of interest. The second stage consists of transistors M 5 and M 6 (W/L = 100Âµ/1Âµ) in the common source configuration, which are biased in the subthreshold region with a bias current of I BIAS,P2 = 9.5ÂµA for a transconductance of g m = 261 ÂµS. Miller compensation is implemented across the high gain second stage to create a dominant pole within the open loop transfer function through pole splitting, where the resulting poles after compensation can be calculated as  : (5 21 ) (5 22 ) where R 1 and R 2 are the equivalent resistances at the second stage input and ou tput respectively and C 1 and C 2 are the total capacitance s at the input and output of the second stage respectively. The Miller compensation capacitor s were set to C M = 2.3pF to set the dominant pole around = 560Hz while the second pole ( ) occurs well above 60MHz. The op amp has an equivalent open loop gain of A OL T = 4.1MHz. The resulting closed loop transfer function of the voltage amplifier has a mid band gain of 87V/V with a higher cutoff frequency H = 41kHz.
121 Common mode feedback is implemented using a four input termi nal amplifier to set the common mode voltage at the output through control of the gate voltages of transistors M3 and M4. The CMFB amplifier has a closed loop gain of 70dB with 53 7Hz bandwidth. Table 5 3 . Voltage amplifier transistor summary . 5.3.3 I Q Demodulation Stage The circuitry responsible for demodulation of the amplified signal consists of differential chopper switches and a sine to square wave IQ signal generator. The signal generator co nverts a 13kHz sine wave from the reference of phase square waves, which are used to drive the differential chopper switches for IQ demodulation of the amplified signal down to baseband frequencie s. 184.108.40.206 I Q channel demodulation IQ channel demodulation is widely used in wireless RF systems to demodulate an input signal across phase differences between the input signal and the demodulation carrier signal. IQ demodulation consist s of two separate of phase to extract the in phase and quadrature phase components of the demodulated output. The input signal to be demodulated can be represented as a cosine with amplitude occurring at a frequency such that: (5 23 )
122 where is the input signal as a function of time. Demodulation using a single channel, driven by signal with amplitude and frequency , can be expressed as: (5 24 ) where the resulting output signal has signal com ponents located at . Equation ( 5 24 ) can be rewritten to take into account a phase difference between the two signals ( ) such that: (5 25 ) The resulting output amplitude has a dependency on the two signals results in a demodulated amplitude of 0V. Implement ation of an additional extraction irrespective of the input phase. The driving signals of the I and Q channels can be respectively defined as: (5 26 ) (5 27 ) where and are the frequencies of the driving signals such that . The mixed outputs of the I and Q channels c an be respectively defined as: (5 28 ) (5 29 )
123 Equations ( 5 28 ) and ( 5 29 ) allow for the extraction of the in phase (I(t)) and quadrature phase (Q(t)) components of the demodulated signal such that the equivalent output amplitude and phase can be extracted as: (5 30 ) (5 31 ) Thus, equation (5 30 ) and (5 31) can be used to extract the base band signal amplitude across phase differences between the input signal and the demodulation carrier . 220.127.116.11 Chopper demodulation switches Choppers are switching devices that are used to convert an AC signal into higher or lower frequencies through signal mixing techniques [106, 107] . Differential chopper switches are commonly implement ed at both the input and output of an op amp for offset compensation and amplification of low frequency signals that would typically be saturated by the flicker noise of the amplifier under normal operation. The input chopper modulate s the signal to a high er frequency that is out of the flicker noise range of the amplifier. The chopper at the output of the amplifier is driven at the same frequency to demodulate the amplified signal back to the original operating frequency. Filtering is required at the outpu t to remove the up converted signal components which occur at twice the driving frequency. The fully differential choppers are implemented using two sets of transmission gates to alternate the connection between the input and output differential nodes as s hown in Figure 5 11(a) and (b). The choppers are sized with W/L = 5Âµ/120n and are switched through discontinuous operation using rail to rail square waves . Square wave signals are used as the driving signal of the chopper switches as the rail to rail signa ls are have a zero correlation property with a non zero DC offset with respect to the system common mode voltage, assuming
124 50% duty cycle. The choppers effectively multiply the frequency components of both the input ( ) and drive ( ) signals, resulting in output signals at and . The layout of the choppers utilizes matched switch transistors with grounded metal shielding between the signal and cloc k lines to reduce the capacitive clock feedthrough. (a) (b) Figure 5 11 . Differential chopper switch ( a) Symbol and (b) S chematic. 18.104.22.168 Sine to square wave IQ signal generator Two demodulation path of phase to extract the amplitude and phase of the input signal through IQ demodulation. This requires the generation of two sets of square phase a nd quadrature phase components of the demodulated signal. The block level diagram of the sine to square wave IQ signal generator is shown in Figure 5 12, which converts a sinusoidal signal (V DRIVE ) into two rail to nce. V DRIVE is compared to two on chip voltage references (V H and V L ), which are set to be 85% and 15% of the supply voltage (1.02V and 180mV respectively). For simplicity, the reference voltages are generated using on chip polysilicon resistors (R A = R C = B the exact resistor values, the resistors are interleaved to allow for increased control of the resistor ratios.
125 The comparators are implemented using two stage operational amplifiers in open loop con figurations to generate rail to rail pulses (V CMP1 and V CMP2 ) whenever the input signal is larger or smaller than V H or V L respectively. The comparator outputs are combined and passed to rising edge and falling edge toggle flip flops to generate full scale square waves tha of phase (V 45 and V 135 ). The reference voltages set the V C edge transitions to occur at 12.5%, 37.5%, 62.5%, and 87.5% of the V DRIVE period to generate the out of phase square waves with 50% duty cycle. (a) (b) Figure 5 12 . Sine to square wave IQ signal generator (a) Block diagram and (b) T iming diagram . 5.3.4 Differential to Single Ended Conversion The differential I and Q channels are convert ed into single ended representation s to interfac e with single ended analog to digital converters (ADC) after demodulation within the previous chopper stage. The differential to single ended conversion is implemented using the closed loop amplifier in Figure 5 13 (a) , where the single e nded output voltage ( ) is the difference of the two input signals ( and ). The voltage transfer function can be defined through superposition of both input signals such that:
126 (5 32 ) (5 33 ) where R F is the feedback resistance, R S is the source resistance at the negative terminal, and R S1+ and R S2+ are the resista nces that form the AC voltage divider at the positive input terminal. Setting R F = R S = 2R S1+ = 2R S2+ results in unity gain amplification of both signals paths such that . The resistors are implemented using interleaved polysilicon resistors so process variation affects each resistance values equally, where R S and R F while R S1 and R S2 large resistive loading to the previous vo ltage amplifier stage. (a) (b) Figure 5 13 . Schematic of the (a) Differencing amplifier and (b) T ransistor level op amp. The op amp is implemented using the current mirrored operational tran sconductance amplifier in Figure 5 13(b) with the transistor sizing summarized in Table 5 4. The input differential pair is implemented using PMOS devices with W/L = 320Âµ/5Âµ to reduce the noise contributions of the input stage. The input stage is biased wi th I BIASP = 3.8ÂµA while the M2 M3 and M4 M5 current mirrors are implemented with a 1:3 mirror ratio to set the overall
127 transconductance to G m = 155ÂµS. The amplifier was designed for an open loop gain of 60.4dB with a unity T = 14.6MHz. Low pass filtering is implemented at the output of the differencing amplifier to remove the high frequency signal components that result from the up converted mixing product of the demodulation stage, which occur at twice of the V DRIVE frequency (26kHz). The low pass filter is implemented as a single pole RC filter using off chip discrete components. The corner frequency to reduce the voltage attenuation that o ccurs when driving a large resistive load. Table 5 4 . Differencing amplifier transistor summary . 5.4 Experimental Results The IC was fabricated in a 0.13Âµm CMOS process with 1.1x0.8mm 2 die area, Figure 5 14(a). The experimental set up in Figure 5 14(b) was used to characterize the system. The supply voltage is provide d by a 3.6V AA battery, where the necessary 1.2V supply voltage is achieved through a resistor divider with decoupling capacitance to mitigate the noise contributions of typical switching power supplies. The input waveforms were generated using a Rigol DG1 022 arbitrary waveform generator as well as the source output of an Agilent 35670A dynamic signal analyzer (DSA). The frequency spectrum and transient response of the output waveforms were measured using the DSA and an Agilent 54832D oscilloscope respectiv ely. The test board was placed within a grounded metal box to act as a Faraday cage to block external electric fields and
128 prevent any external signals from coupling to the test set up . The system dissipates 150ÂµA from a 1.2V supply when all system componen ts are active. (a) (b) Figure 5 14 . (a) Die micrograph and (b) D iagram of the experimental set up. The differential current at the input of the transimpedance amplifier is generated through an attenuated ba lun. A single ended AC source voltage, generated by the function generator or DSA, was attenuated using a resistive voltage divider (R 1 and R 2 ) to generate a low amplitude AC voltage. A balun, consisting of two Bourns LM NP 1001 B1 transformers, converts t he attenuated single ended signal into a differential voltage across the secondary transformer windings. Resistors R A and R B are placed in series between the balun output and the transimpedance amplifier to generate an equivalent differenti al current, wher e t he input terminals of the transimpedance amplifier serve as an AC ground due to the negative feedback within the closed loop amplifier. Thus, the voltage induced at the balun output generates differential AC currents that are fed into the amplifier inpu t, where the differential input current amplitude is controlled through the single ended input voltage amplitude. The resistances were set to be R 1 = 2 A = R B The voltage division ratio was verified using a high impedance probe to measure the balun output voltage as a function of the input voltage amplitude. The transfer function of both the
129 high impedance probe and the sin gle ended voltage to differential current generator were measured and de embedded from the measurements of the integrated system. 5.4.1 Transfer Function Characterization The Agilent 35670A dynamic signal analyzer (DSA) was used to characteriz e the transf er function of the fabricated system using a frequency swept sine methodology where the output voltage amplitude is measured across the corresponding swept frequency. Figure 5 15 (a) and (b) show the simulated and measured transfer functions for the transi mpedance amplifier and the voltage amplifier respectively with the transfer function results summarized in Table 5 5 . The transimpedance amplifier has a measured 138dB gain (126nA/V) with a 29kHz bandwidth. The voltage amplifier has a measured mid band gai n of 37.1dB (71.6V/V) with 21.8kHz bandwidth L H = 29kHz respectively. (a) (b) Figure 5 15 . Simulated and measured transfer fu nc tions of the (a) T r ansimpedance amplifier and (b) V oltage amplifier. The measurements were repeated to characterize the current to voltage transfer function of the complete system when the chopper demodulators w ere disabled. Figure 5 16 shows the simulate d and measured transfer function s of the complete system , which resulted in a current -
130 to voltage mid L H = 22.3kHz). The system has a measured com mon mode rejection ratio (CMRR) > 10 0dB , w hich was measured using the experimental set up described in Appendix C . A summary of the measured transfer function of the full system is provided in Table 5 5. Figure 5 16 . Simulated and measured transfer function of the co mplete system with chopper demodulation disabled. Table 5 5 . Measured transfer function summary . 5.4.2 Current to Voltage Amplification and Demodulation Measurements To measure the current to voltage conversion and demodulation capabilities of the full system, the DSA was used to m easure the output frequency spectrum of the single ended I and Q channels. A differential amplitude modulated current was supplied to the input with a differential current amplitude of 100pA c m = 50 0Hz, and 100% sine wave modulation index. Figure 5 17 shows the measured output frequency spectrums of one of the single ended channel outputs with and without chopper
131 demodulation and subsequent RC low pass filtering. When the chopper demodulation is disa bled, the input signal is amplified at the output by 1.1nA/V at the same operating frequency as the input signal. When the IQ signal generator is driven by a 1.2V p p sinusoidal signal ( and V CM = 600mV), the amplified output signal is down convert ed to the base band frequencies and up converted to twice the drive signal frequency, resulting in the sideband signals to be converted to equivalent 500Hz, 25 .5 kHz, and 2 6.5 kHz signals. Addition of the RC low pass filter pole around 16kHz, resulting in 12.8dB attenuation of the up converted signal. Figure 5 17 . Measured frequency spectrum of the output voltage ( ) for a 100pA amplitude modulated input current c m = 500Hz , 100% modulation index) and 1.2V p p CM = 600mV) with chopper demodulation disabled without LPF, chopper demodulation enabled without LPF, and chopper demodulation enabled with LPF.
132 Figure 5 18 . Meas ured output amplitude at 500Hz versus phase mismatch between c = 13kHz, m = 500Hz, 100% modulation index) and sinusoidal drive signal (1.075V p p c = 13kHz, V CM = 537.5mV). The output amplitude of the single ended I and Q channels were measured as the phase difference between the differential input current and drive signal was swept from to extract the demodulated amplitude at 500Hz. Figure 5 18 shows the measured results whe n using an ampli tude modulated 10 0pA differential input current setting c = 13kHz, m = 500Hz, and 100% modulation index ) and a 1.075V p p sinusoidal drive voltage ( V CM = 537.5mV ). The measured amplitude varied from 26.5mV to 27.9mV across the total phase difference, resulting in a Â±2.7% error when utilizing the IQ channels in conjunction. 5.4.3 Current to Voltage Gain Measurements To characterize the current to voltage gain and demodulation capabilities of the full system, the DSA was used to measure the single ended voltage spectrums at the I and Q channel outputs while the function generator , with attenuated balun , provided differential input currents across a 1pA 2 nA range. The measurements were conducted for input signals consisting of a continuous wave and amplitude modulated signals in the presence and absence of the chopper demodulation. 22.214.171.124 Continuous wave signal amplification The arbitrary waveform generator was used to provide a 13kHz continuous wave sinusoidal signal at the in put of the differential current generator with demodulation disabled. Figure 5 19 shows the meas ured output voltage amplitude ( ) at 13kHz versus input differential current amplitude ( ). The system has a 1.1nA/V current to voltage gain and saturates around 1n A input current amplitude. Also shown is the measured output voltage frequency spect rum and transient sign al for a differential 10 0pA input current.
133 Figure 5 19 . Measured output voltage ( ) versus input current amplitude ( ) for a 13kHz continuous wave sinusoidal input signal. 126.96.36.199 Amplitude modulated signal amplification The output voltage versus input current amplitude measurements were repeated for an c m = 500Hz, and 100% sine wave modulation index) with the chopper demodulation disabled. Figure 5 20 show s the measured output voltage ( ) at 12.5kHz, 13kHz, and 13.5kHz versus input differential current amplitude ( ) across a 2 pA 1nA current setting. The system has a measured 1.1nA/V current to vol tage gain and saturates around 2 00pA AM input current, which corresponds to a 104pA amplitude at 13kHZ and 51 pA current at 12.5kHz and 13.5kHz. Figure 5 20 . Measured output voltage ( ) versus input current amplitude ( ) at 12.5kHz, 13kHz, 13.5kHz for an amplitude modulated input c m = 500Hz, 100% modulation index).
134 188.8.131.52 Amplitude modulated signal amplification and demodulation c m = 500Hz, and 100% modulation index) with a 1 .2V p p sinusoidal common mode) at the input of the IQ signal generation circuit for chopper demodulation. Figure 5 21(a) shows the measured output voltage ( ) at 500Hz versus input differential current amplitude ( ) across a 1pA 1nA current setting. The system has a measured 0.9nA/V current to voltage gain when the demodulators are active and saturates around 2 00pA input current amplitude s etting, which corresponds to a 104 pA input amplitude at 13kHZ and 51 pA amplitude at 12.5kHz and 13.5kHz. Also shown are the measured frequency spectrums at 500Hz and 26kHz center frequencies in addition to the measured tr ansient output waveforms for a 10 0p A input amplitude current setting. The measurements were repeated in Figure 5 21 (b) with the inclusion of the external RC LPF at the output of both the I and Q channels. The addition of the LPF reduces the output amplitude by 12 .8dB at 26kHz. The attenuati on at the up converted frequencies allows for easy extraction of the 500Hz tr ansient signal as shown in Figure 5 21 (b). (a) (b) Figure 5 21 . Measured output voltage ( ) versus input current amplitude ( ) at 500Hz for c m = 500Hz, 100% modulation index) and 1.2V p p CM = 600mV) (a) without and (b) with low pass filtering.
135 5.4.4 Noise Characterization Measurements Noise char acterization of the fabricated system is performed using the DSA to measure the noise spectral density at the I and Q channel outputs. Figure 5 22(a) shows the input referred noise spectrum ( lifier bandwidth from 6.1kHz to 22.3kHz results in an equivalent input referred noise rms current of approximately 1pA. The equivalent noise voltage ( ) and current ( ) parameters of the system were extracted by measuring the output noise spec trum at 13kHz as a function of source resistance (R S ) using metal film resistors soldered across the amplifier input terminals. The equivalent noise voltage gain was measured at 13kHz for each source resistance to acquire the input referred noise spectral density from the measured output noise spectral density . Figure 5 22(b) shows the input referred noise power density vs. R S where and can be extracted from the input referred noise spectral density at low and high source resistances respectively, resulting in equivalent differential input referred noise voltage and current of = 29.1nV/Hz Â½ and = 177.5fA/ Hz Â½ respectively. (a) (b) Figure 5 22 . Measured (a) Input referred noise spect rum and (b) I nput referred noise power spectral density versus source resistance (R S ) at 13kHz.
136 5.5 Conclusion A highly integrated system was proposed for use as an implantable, wireless NMR acquisition coil for the increased signal sensitivity of NMR measurements . The IF to BB sub system was designed and fabricated in a 0.13Âµm CMOS process, which consists of a transimpeda nce amplifier, voltage amplifier, IQ signal generation circuitry , chopper demodulation switch es , differential to single ended amplifiers , and low pass signal filters . The test chip has 1.1x0.8mm 2 die area and dissipates 150ÂµA from a 1.2V supply when all sy stem components are active. The transimpedance amplifier input stage has a measured 138dB gain (126nA/V) with a 29kHz bandwidth while the second stage voltage amplifier has a measured mid band gain of 37.1dB (71.6 V/V ) with 21.8kHz bandwidth corresponding t o lower and higher L H = 29kHz respectively. The total system has a mid band current to L H = 22.3kHz). The system has an input referred noise volta ge and current of = 29.1nV/Hz Â½ and = 177.5fA/Hz Â½ respectively . The IQ demodulation channels are capable of demodulating the amplified signal to the baseband frequencies with a Â±2.7% error across phase differences between the input and drive signals. The syste m can detect input currents ranging from 1pA up t o 1nA of differential input current at the 13kHz frequency of interest.
137 CHAPTER 6 SUMMARY AND FUTURE WORK 6.1 Summary This body of work investigated the design and implementation of wirelessly controlled , implant able device s to increase the signal sensitivity of NMR measurements for the non invasive monitoring of a bio artificial pancreatic tissue construct. A staggered SCMR wireless power transmission topology was experimentally validated to provide unif orm energy transfer to an arbitrarily placed implant coil for use in biomedical applications. Analytical models were de veloped to compare the wireless energy transfer characteristics of the 4 coil system with a typical near field inductive link. Experiment al measurements on 4 coil and 2 coil systems show that the staggered SCMR topology broadens the wireless energy transfer over an increased range of RX coil locations while increasing the maximum transmiss ion distance up to a factor of two . A wireless impl ant was implemented and experimentally validated to increase the signal sensitivity of NMR measurements at multiple frequencies and magnetic field strengths. The device can selectively resonate across a 190MHz 470MHz frequency range spanning multiple NMR nuclei within 4.7T and 11.1T magnetic fields. The device measures 1.3x1.7cm 2 and was experimentally validated within NMR studies to increase the acquired SNR by 140% (7.7dB) and 80% (5.3dB) within 4.7T and 11.1T magnetic fields respectively. The device wa s also shown to enhance the acquired SNR in excess of 50% (3.5dB) within the region of interest for high resolution images. A highly integrated system was proposed for use as an implantable, wireless NMR acquisition coil to increase the signal sensitivity o f NMR imaging and spectroscopy. The intermediate frequency to baseband demodulation and amplification sub system was fabricated
138 and experimentally validated. The test chip measures 1.1x0.8mm 2 die area and dissipates 150ÂµA from a 1.2V supply . The total sy stem has a mid band voltage gain of 179.9dB (1nA/V) with L H = 22.3kHz) and input referred noise voltage and current spectrum of = 29.1nV/Hz Â½ and = 177.5fA/Hz Â½ respectively . The circuit is able to demodulat e signals across phase mismatches between the input current and drive signals using a two channel IQ demodulation scheme with a Â±2.7% error across phase differences . The circuit is capable of detecting input currents ranging from 1pA to 1nA of differential current at the 13kHz frequency of interest. 6 .2 Future Work Additional steps can be conducted to further progress the research studies covered within this work. NMR measurement studies can be performed using the wirelessly programmable implant to charact erize the increase in signal sensitivity provided by the implant for different nuclei such as Phosphorous and Fluorine . S pectroscopy studies should be conducted to characterize the increase in SNR when acquiring the NMR spectra of different chemical compou nds. Measurements can be acquired using liquid phantoms containing an abundance of the nuclei of interest within a tissue equivalent phantom in addition to small animal studies. I n tegration of an automatic impedance matching (AIM) system [108, 109] with the wirelessly programmable implant would allow for increased measurement sensitivity across a large frequency range without the need to manually tune the impedance matching network of the external NMR acquisition coil. Digital algorithms can be implemented to adjust both the internal and external coil resonances to optimize the complete s ystem for maximum coupling to the resonating nuclei. Further development of the wireless NMR acquisition coil can be carried out to implement a full functioning wireless device . Design and integration of the RF to IF demodulation stage,
139 analog to digital converters, and the transmitter is required to finalize the complete system, allowing for a significant increase in the acquired NMR sensitivity. NMR measurements can be performed to quantify the increase in acquired SNR through NMR studies on tissue equiv alent gel phantoms and small animal studies.
140 APPENDIX A CIRCUIT NETWORK THEORY Analytical modeling of a device under test (DUT) can be realized through network analysis on the respective schematic, which can be summarized by the equivalent matrix equat ion: (A 1 ) where is the vector matrix of the complex voltages across each circuit loop, is the vector matrix of the complex currents within each loop, and is the impedance matrix of the system. It is important to note t hat , , and all contain complex values that are functions of frequency. A two port device under test can be treated as a black box using the equivalent two port network parameters as it relates to , , and . Network parameters are mathematical m atrix representations of the transfer function of a given complex linear system as it relates the voltage and current waveforms at the input and output ports. There exist six network parameter models as defined by different combinations of excitation and m easurement voltage and current waveforms at the input and output ports. The Y network parameters are the simplest to derive through matrix algebra on a device under test since the Y parameters define the port currents as functions of the voltages at each p ort such that: (A 2 ) Thus, the two port Y parameters can be extracted from the presented circuit model by calculating the port currents ( and ) when applying an ideal unit valued excitation voltage at a port and short ci rcuit termination at the other. To determine Y 11 and Y 21 , a unit sized excitation voltage can be applied at the input port by setting the respective voltage to 1V within while the output short circuit termination condition
141 can be modeled by setting the o utput port voltage to 0V within . The complex current values at each port can then be calculat ed through left hand matrix multiplication of to both sides of equation (A 1). The same process can be used to calculate Y 12 and Y 22 by swapping the input and output voltage values within and calculating the resulting port currents. The Y parame ters can then be converted to the preferred two port n etwork parameter format using standard formulas, specifically the two port ABCD representation as it allows for the addition of complex matching networks consisting of shunt and series elements as a res ult of the cascading nature of this format. Series circuit elements can be added to the input and output of the DUT as: (A 3 ) where , , , and are the equivalent two por t ABCD parameters of the total system, , , , and are the two port ABCD parameters for the DUT, and and are the lumped impeda nces of the series elements at port 1 and p ort 2 respectively. Shunt circuit elements can be added to the input and output of the DUT as: (A 4 ) where and are the lumped impedances of the shunted elements at port 1 and p ort 2 respectively. Equations (A 3) and (A 4) can be used sequentially to add more complex matching networks consisting of multiple series and shunted cascaded elements.
142 APPENDIX B PD MS ENCAPSULATION PROCESS Encapsulation of implantable electronics using biocompatible gels prevents the implanted device from having undesirable interactions with the host tissue. The wireless implantable device in Chapter 4 is coated in a biocompatible P DMS gel using a multi step molding process to ensure biocompatibility for implantation while forming a cavity to house the bio artificial pancreas. The cross section of the PDMS coating is shown in Figure B 1(a), which consists of a cylindrical cavity with 0.9cm diameter within the 1cm NMR coil of the implantable device. To hold the bio artificial pancreas in place, 1.25mm thick rims extend over both sides of the internal cavity with a 6mm opening to allow placement of the tissue construct after curing of t he PDMS gel. As a result of the complex cavity configuration, two PDMS samples are adhered together using uncured PDMS gel to form the necessary structure, where the samples are formed using a 3D printed mold as shown in Figure B 1(b). Mechanical t abs were included on either side of the PDMS mold to be used as leverage points to prevent tears within the main structure when releasing the cured samples. (a) (b) Figure B 1 . (a) Cross section of the PDMS encapsulated implant a nd (b) 3D printed mold . The assembled wireless implant is placed on top of 3D printed standoffs that are included in the mold design to hold the PCB 1.25mm above the base of the mold . Uncured PDMS gel was pipetted into the mold s, Figure B 2 (a ), followed b y placement within a vacuum degassing chamber for 5 10 minutes to remove air pockets within the viscous PDMS gel , Figure B 2(b ).
143 Excess PDMS was wiped from the top of the uncured samples to create a uniform surface. The gel was allowed to cure for 24 hou rs at room temperature to prevent micro fractures from occurring within the PCB copper traces and solder connections as a result of the high thermal expansion coefficient of PDMS. The cured samp les were removed from the mold and any excess PDMS was trimmed from the structures , Figure B 2 ( c ). A thin layer of uncured PDMS gel was pipetted onto the sample containing the implantable device, Figure B 2 ( d ), and then placed in a degassing vacuum chamber to remove air pockets within the uncured PDMS. The 1.25mm thi ck layer of cured PDMS was placed on top of the sample containing the implantable device and uncured PDMS was pipetted into the holes resulting from the standoff pegs within the mold , Figure B 2(e) , which was allowed to cure for 24 hours at room temperatur e . The mechanical tabs were trimmed from the cured PDMS with the fin al device shown in Figure B 2 (f ). (a) (b) (c) (d) (e) (f) Figure B 2 . PDMS encapsulation process: (a) Placement of uncur ed PDMS gel, (b) Vacuu m chamber degassing, (c) Cured PDMS layers after release from the sample and trimming of excess PDMS, (d) Placement of a thin layer of uncured PDMS gel, (e) cured PDMS layer adhesion and (f) final PDMS encapsulated device.
144 APPENDIX C COMMON MODE REJECTIO N RATIO MEASUREMENT SET UP The common mode rejection ratio (CMRR) of a fully differentia l amplifier is the ability of the amplifier to reject AC signals that are common to both input terminals . Common mode signals will appear at the output due to imbalanc es within the differential feedforward ( ) and amplifier open loop signal paths as a result of process variation and impedance mismatches. The unbalanced signal paths result in different single ended gain s for each input terminal , such that a common mode signal at both input s produces a voltag e difference across the output terminals. CMRR depicts how much the input common mode signals will be amplified at the output in comparison to the differential signal gain (A d ) such that : (C 1 ) where is the common mode gain of the amplifier . A n ideal amplifier has infinite CMRR and the ability to fully reject common mode signals at the input. The common mode gain of a closed loop voltage amplifier can be measured by shorting the input terminals of the close d loop amplifier and applying a si ngle ended AC voltage while measuring the output voltage amplitude. However, CMRR measurements on a transimpedance amplifier require the generation of AC currents within both input terminals that are equal in magnitude and phase. While a common mode current can be generated by applying a single ended voltage across two resistors (with equal resistances) that are each in series with one of the input terminal s of the transimpedance amplifier, mismatches in the resistor values as a result of component tolerances will produce AC currents with unequal amplitudes. This results in an effective differential current within the input terminals that will be amplified at the output and increase the measured A CM .
145 Figure C 1 . Common mode gain measurement set up . An alternative approach for generating a common mode current is to use the experimental set up in Figure C 1. A current mirror is formed using two ALD1107PBL integrated circuits, where each IC consis t s of four p channel M OSFET devices. Four transistors within a single IC are diode connected to form the mirroring transistors, while the output transistors of the current mirror are formed using two transistors in parallel on the secondary IC for each out put node . The current mirror output is connected to the input of the fully differential transimpedance amplifier to gene rate current s wit h a mirror ratio of 2:1 . A single ended voltage is applied across resistor R 1 to generate a current within the diode co nnected transistors that is mirrored equally into both of the output terminals assuming th e transistors are well matched. The common mode voltage of the applied signal should be small enough with respect to the signal amplitude to ensure the transistors wi thin the current mirror remain active such that the gate to source voltages do not go below the device threshold voltage. Additionally, the difference in the current mirror supply voltage and the transimpedance amplifier input common mode DC voltage should be large enough to ensure the output transistors within the current mirror do not enter the linear region. A dynamic signal analyzer is used to measure the single ended voltage a t the output of the full system to extract the equivalent common mode gain at the frequency of interest. Before acquiring CMRR measurements, a high impedance probe was used to verify the mirrored current
146 amplitude by measuring the resulting AC voltage s when the current s were mirrored i nto large resistive load s .
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156 B IOGRAPHICAL SKETCH Walker Turner received the Bachelor of Science and Master of Science degrees in Electrical and Computer Engineering from the University of Florida in 2009 and 2012 respectively. He received the Doctor of Philosophy degree in Electrical and Computer Engineering from the University of Florida in the spring of 2015 with a focus on wireless power transfer and low power integrated circuit design. His research interests include low power integrated circuit design for wireless, bio medical, and RFID applications.