ARTIFICIAL TRANSMISSION LINES FOR RF AND MICROWAVE APPLICATIONS WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING KAI CHANG, Series Editor TexasA&MUniversity Acomplete list of the titles in this series appears at the end of this volume. ARTIFICIAL TRANSMISSION LINES FOR RF AND MICROWAVE APPLICATIONS FERRAN MARTÍN Copyright©2015byJohnWiley&Sons,Inc.Allrightsreserved PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey PublishedsimultaneouslyinCanada Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyany means,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection107 or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,or authorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222Rosewood Drive,Danvers,MA01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.com.Requeststo thePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111River Street,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions. 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Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailable inelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Martín,Ferran,1965– ArtificialtransmissionlinesforRFandmicrowaveapplications/FerranMartín. pages cm. Includesbibliographicalreferencesandindex. ISBN978-1-118-48760-0(hardback) 1. Radiolines. 2. Microwavetransmissionlines. I. Title. TK6565.T73M372015 621.38413–dc23 2015007897 Setin10/12ptTimesbySPiGlobal,Pondicherry,India PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 1 2015 ToAnna, Alba and Arnau CONTENTS Preface xiii Acknowledgments xvii 1 Fundamentals of Planar TransmissionLines 1 1.1 Planar Transmission Lines, Distributed Circuits, and Artificial Transmission Lines, 1 1.2 Distributed Circuit Analysis andMain Transmission LineParameters, 5 1.3 Loaded(Terminated) Transmission Lines, 8 1.4 Lossy Transmission Lines, 16 1.4.1 Dielectric Losses: The Loss Tangent, 19 1.4.2 Conductor Losses: The Skin Depth, 25 1.5 Comparative Analysis of Planar Transmission Lines, 28 1.6 Some Illustrative Applications of Planar Transmission Lines, 31 1.6.1 Semilumped Transmission Lines and Stubs andTheir Application to Low-Pass and Notch Filters, 31 1.6.2 Low-Pass Filters Based on Richard’s Transformations, 39 1.6.3 Power Splitters Based on λ/4 Lines, 40 1.6.4 Capacitively Coupled λ/2 Resonator BandpassFilters, 42 References, 44 2 Artificial Transmission Lines based on Periodic Structures 47 2.1 Introduction and Scope, 47 2.2 Floquet Analysis of Periodic Structures, 48 viii CONTENTS 2.3 The Transfer Matrix Method, 53 2.3.1 Dispersion Relation, 54 2.3.2 Bloch Impedance, 56 2.3.3 Effects of Asymmetry in the Unit Cell through anIllustrative Example, 60 2.3.4 Comparisonbetween Periodic Transmission Lines and ConventionalLines, 62 2.3.5 The Concept of Iterative Impedance, 63 2.4 Coupled Mode Theory, 64 2.4.1 The Cross-SectionMethod and the Coupled Mode Equations, 65 2.4.2 Relation between the Complex Mode Amplitudesand S-Parameters, 69 2.4.3 Approximate Analytical Solutions of the Coupled Mode Equations, 71 2.4.4 AnalyticalExpressions for Relevant Parameters of EBG Periodic Structures, 77 2.4.5 Relation between the Coupling Coefficientand the S-Parameters, 79 2.4.6 Using the Approximate Solutions of the Coupled Mode Equations, 80 2.5 Applications, 86 2.5.1 Applications of Periodic Nonuniform Transmission Lines, 86 2.5.1.1 Reflectors, 86 2.5.1.2 High-Q Resonators, 92 2.5.1.3 Spurious Suppressionin Planar Filters, 93 2.5.1.4 Harmonic Suppression in Active Circuits, 95 2.5.1.5 Chirped Delay Lines, 99 2.5.2 Applications of Reactively LoadedLines:The Slow Wave Effect, 102 2.5.2.1 Compact CPW Bandpass Filters with Spurious Suppression, 105 2.5.2.2 Compact Microstrip Wideband Bandpass Filters with UltrawidebandSpurious Suppression, 108 References, 114 3 Metamaterial Transmission Lines: Fundamentals, Theory, Circuit Models, and Main Implementations 119 3.1 Introduction, Terminology,and Scope, 119 3.2 Effective Medium Metamaterials, 122 3.2.1 Wave Propagation in LH Media, 123 3.2.2 Losses and Dispersion in LHMedia, 125 3.2.3 Main Electromagnetic Properties of LHMetamaterials, 127 3.2.3.1 Negative Refraction, 128 3.2.3.2 Backward Cerenkov Radiation, 129 CONTENTS ix 3.2.4 Synthesis of LH Metamaterials, 131 3.2.4.1 Negative Effective Permittivity Media: Wire Media, 132 3.2.4.2 Negative Effective Permeability Media: SRRs, 136 3.2.4.3 Combining SRRs and Metallic Wires: One-Dimensional LH Medium, 139 3.3 Electrically Small Resonators for Metamaterials andMicrowave Circuit Design, 141 3.3.1 Metallic Resonators, 142 3.3.1.1 The Non-Bianisotropic SRR(NB-SRR), 142 3.3.1.2 The Broadside-CoupledSRR(BC-SRR), 142 3.3.1.3 The Double-Slit SRR (DS-SRR), 143 3.3.1.4 The Spiral Resonator (SR), 144 3.3.1.5 The Folded SIR, 144 3.3.1.6 The Electric LC Resonator (ELC), 145 3.3.1.7 The Open Split-Ring Resonator (OSRR), 146 3.3.2 Applying Duality: Complementary Resonators, 146 3.3.2.1 Complementary Split-Ring Resonator (CSRR), 147 3.3.2.2 Open Complementary Split-Ring Resonator (OCSRR), 149 3.4 Canonical Models of MetamaterialTransmission Lines, 149 3.4.1 The Dual Transmission Line Concept, 150 3.4.2 The CRLH Transmission Line, 154 3.4.3 Other CRLH Transmission Lines, 158 3.4.3.1 The Dual CRLH (D-CRLH) Transmission Line, 158 3.4.3.2 Higher-Order CRLHand D-CRLH Transmission Lines, 159 3.5 Implementation of Metamaterial Transmission Lines and Lumped-Element Equivalent Circuit Models, 162 3.5.1 CL-Loaded Approach, 162 3.5.2 Resonant-TypeApproach, 166 3.5.2.1 Transmission Lines based on SRRs, 167 3.5.2.2 Transmission Lines based on CSRRs, 177 3.5.2.3 Inter-Resonator Coupling: Effects and Modeling, 183 3.5.2.4 Effects of SRR andCSRR Orientation: MixedCoupling, 191 3.5.2.5 Transmission Lines based on OSRRs and OCSRRs, 195 3.5.2.6 Synthesis Techniques, 203 3.5.3 The Hybrid Approach, 204 References, 206 4 Metamaterial Transmission Lines: RF/Microwave Applications 214 4.1 Introduction, 214 4.2 Applications of CRLHTransmission Lines, 215 4.2.1 Enhanced Bandwidth Components, 215 4.2.1.1 Principle and Limitations, 215