Advances in Emerging Electromagnetics Topics: Metamaterials and Wireless Power Transfer by Brian Benjamin Tierney A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering) in The University of Michigan 2016 Doctoral Committee: Associate Professor Anthony Grbic, Chair Professor Eric Michielssen Professor Kamal Sarabandi Associate Professor Max Shtein c Brian Benjamin Tierney All Rights Reserved 2016 It isn’t the mountains ahead to climb that wear you out, it’s the pebble in your shoe. — Muhammad Ali To my family ii Acknowledgments This thesis would not be possible without the support and guidance of my advisor, Professor Anthony Grbic. Tony, thank you for believing in me and inviting me to join you in Michigan. I couldn’t have asked for a more caring and dedicated advisor. You’ve taught me not only about electromagnetics, but also about how to be a better researcher, writer, and teacher. Your devotion to your work and to your students will always be an inspiration to me. Thank you. I would like to thank the other members of my doctoral committee: Prof. Eric Michielssen, Prof. Kamal Sarabandi, and Prof. Max Shtein. Thank you for your service and for helping to improve this thesis. I would also like to thank all of the professors and research scientists of the Radiation Laboratory. It was an honor and privilege to learn from such a knowledgeable group. Thank you for everything you have taught me. I am also grateful and proud to have spent the past five years studying with the talented students of the Radiation Laboratory. I would especially like to thank Gurkan Gok, Mohammadreza Imani, Amit Patel, and Carl Pfeiffer for mentoring me and accepting me into the research group. I would also like to thank Emre Alan and Lai Wei for offering their friendship on day one and for their constant companionship through the first two years of graduate school. You two made the transition to Ann Arbor so much more enjoyable. I would also like to thank Brian Moore and Andy Meier for three great years as roommates. I would also like to thank the rest of my friends in the RadLab, the EECS department, and the Ann Arbor area. When I moved here, I never thought I would meet such a fantastic group of people. I consider myself extremely lucky to have met you all. It will be tough to leave. Finally, I would like to thank my family. You are the best friends I could have asked for. Thank you for all the laughs we’ve shared throughout the years and for never growing up too much. Thank you for being a model of resilience and responsibility, especially when times were tough. Mom, thank you for your love and support and for always maintaining a great sense of humor. Also, thank you for having one last child iii (me). You can consider this thesis to be your second grandkid. Shaun and Shannon, thank you for being such great role models and for your support throughout the years. Shaun, thank you for getting me into electrical engineering and programming. Feel free to read this thesis to James for a bedtime story. I’m sure it will put him to sleep. Shannon, thank you always letting me hang out during breaks in school. Melissa, thank you for being such a great friend while we were growing up together. Amelia, you’ve been such a great addition to the family. Thank you for always making me feel at home. iv Table of Contents Dedication ..................................... ii Acknowledgments ................................ iii List of Tables ................................... x List of Figures .................................. xi List of Appendices ................................ xvii Abstract ...................................... xviii Chapter 1 Introduction ............................ 1 1.1Metamaterials............................... 1 1.1.1 ANewWorld........................... 1 1.1.2 Shortcomings ........................... 2 1.1.3 Motivation............................. 2 1.2 Wireless Power Transfer ......................... 3 1.2.1 ABriefHistory.......................... 3 1.2.2 Resonant Magnetic Coupling ................... 4 1.2.3 Motivation............................. 4 1.3Goals.................................... 5 1.3.1 Metamaterials: Leaky-Wave Beam Shaping ........... 5 1.3.2 Metamaterials:Beamformers.................. 5 1.3.3 Wireless Power Transfer ..................... 6 1.4 Thesis Outline ............................... 6 Chapter 2 Tailoring Radiation Patterns with Leaky-Wave Antennas 8 2.1ChapterIntroduction........................... 8 2.1.1 Leaky-WaveAntennas...................... 8 2.1.2 Pattern Shaping: Brief Review .................. 8 2.1.3 Pattern Shaping: A New Approach ............... 9 2.1.4 Beam Shaping with Impedance Surfaces ............ 10 2.1.5 Chapter Outline .......................... 10 v 2.2ABriefReviewofApertureFieldAnalysis............... 10 2.2.1 FourierTransformRelations................... 11 2.2.2 GeneratingtheApertureField.................. 12 2.3EigenmodeAnalysis........................... 13 2.3.1 Transverse Resonance Technique ................ 14 2.3.2 Solving for α and β ....................... 16 2.3.3 Impedance Matching ....................... 17 2.3.4 EigenmodeControl........................ 18 2.4 Simple Designs: Prescribing Aperture Fields .............. 19 2.5 Arbitrary Beam Shaping ......................... 21 2.5.1 ApertureFieldMethods..................... 22 2.5.2 A Brief Review of the Orchard-Elliott Method ......... 23 2.5.3 RelatingSpaceFactorstoArrayFactors............ 24 2.5.4 ConstructingtheApertureField................. 25 2.5.5 CompensatingforPatternError................. 27 2.6 Designs for Arbitrary Beam Shaping .................. 28 2.7 Chapter Summary ............................ 29 Chapter 3 A Cascaded, Planar Leaky-Wave Topology ......... 31 3.1ChapterIntroduction........................... 31 3.1.1 ReviewofChapter2 ....................... 31 3.1.2 ANewTopology......................... 31 3.1.3 Chapter Outline .......................... 32 3.2ABriefReviewofLeaky-WavePatternSynthesis........... 33 3.3TheMetasurfaceTopology........................ 35 3.4TheEigenmode(Dispersion)Equation................. 36 3.4.1 RelatingtoSheetAdmittances.................. 38 3.4.2 SpecialCase:IsotropicSheetAdmittances........... 39 3.5PolarizationAnalysis........................... 40 3.5.1 SpecialCase:CircularPolarization............... 41 3.6MetasheetDesign............................. 41 3.7 Design Examples ............................. 44 3.8 Chapter Summary ............................ 47 Chapter 4 An Alternative to Transformation Electromagnetics for Designing Beamformers .......................... 48 4.1ChapterIntroduction........................... 48 4.1.1 Transformation Electromagnetics: History and Shortcomings . 48 4.1.2 AnAlternativetoTransformationElectromagnetics...... 48 4.1.3 Chapter Outline .......................... 49 4.2FEMForwardProblem.......................... 50 4.3 Optimization ............................... 51 4.3.1 MaterialParameters....................... 52 4.3.2 SpatialCostFunction...................... 53 4.3.3 SpectralCostFunction...................... 54 vi 4.3.4 Optimization Algorithm . .................... 54 4.3.5 DesignFlow............................ 57 4.4BeamformerDesign1........................... 57 4.4.1 InitialDesignParameters.................... 58 4.4.2 Stipulated Inputs and Desired Outputs ............. 58 4.4.3 Optimization Results ....................... 59 4.5BeamformerDesign2........................... 60 4.5.1 DesignParameters........................ 61 4.5.2 Optimization Results ....................... 63 4.6 Chapter Summary ............................ 63 Chapter 5 Printed Beamformer Design .................. 64 5.1ChapterIntroduction........................... 64 5.1.1 ReviewofChapter4 ....................... 64 5.1.2 Printed-Circuit Implementation ................. 65 5.1.3 Chapter Outline .......................... 65 5.2 Review: Optimization Design Procedure ................ 66 5.3DesignandFabrication.......................... 68 5.3.1 TensorTransmissionLines.................... 69 5.3.2 ConstructingaCellDatabase.................. 70 5.3.3 DesignGeneration........................ 70 5.3.4 PhaseErrorCorrection...................... 71 5.3.5 Impedance Matching ....................... 73 5.3.6 SimulationofPrinted-CircuitDesign.............. 73 5.4MeasurementResults........................... 74 5.5 Chapter Summary ............................ 76 Chapter 6 Planar Loop Resonators for Wireless Power Transfer .. 77 6.1ChapterIntroduction........................... 77 6.1.1 Non-Radiative Power Transfer .................. 77 6.1.2 LoopResonatorTopologies.................... 78 6.1.3 PlanarAlternatives........................ 78 6.1.4 Chapter Outline .......................... 78 6.2PreviousLoopResonatorTopology................... 79 6.2.1 Coaxial Shielded-Loop Resonators ................ 79 6.2.2 CircuitModel........................... 80 6.2.3 Location of the Ground Slit ................... 82 6.3 Planar Shielded-Loop Resonators .................... 83 6.4 Analytical Modeling ........................... 84 6.4.1 UsefulTransmission-LineEquations............... 84 6.5 Stripline Loop Resonators ........................ 86 6.5.1 Extraction Example ....................... 86 6.5.2 Plated-Stripline Resonator .................... 86 6.5.3 Unplated Stripline Resonator .................. 87 6.5.4 Plated-Stripline Resonator with Shifted Slit .......... 88 vii 6.5.5 ExperimentalResults......................