Approximate Antenna Analysis for CAD A pproxi m at e A nt enna A nal ysi s f or C A D Hubregt J. Visser © 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-51293-7 Approximate Antenna Analysis for CAD Hubregt J. Visser AntennaEngineer,TheNetherlands A John Wiley and Sons, Ltd, Publication Thiseditionfirstpublished2009 ©2009JohnWiley&SonsLtd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ, UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapply forpermissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewith theCopyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor otherwise,exceptaspermittedbytheUKCopyright,DesignsandPatentsAct1988,withouttheprior permissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint maynotbeavailableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.All brandnamesandproductnamesusedinthisbookaretradenames,servicemarks,trademarksor registeredtrademarksoftheirrespectiveowners.Thepublisherisnotassociatedwithanyproductor vendormentionedinthisbook.Thispublicationisdesignedtoprovideaccurateandauthoritative informationinregardtothesubjectmattercovered.Itissoldontheunderstandingthatthepublisheris notengagedinrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceis required,theservicesofacompetentprofessionalshouldbesought. LibraryofCongressCataloging-in-PublicationData Visser,HubregtJ. ApproximateantennaanalysisforCAD/HubregtJ.Visser. p.cm. Originallypresentedasauthor’sthesis–Ph.D. Includesbibliographicalreferencesandindex. ISBN978-0-470-51293-7(cloth) 1.Antennas(Electronics)–Computer-aideddesign.2.Electromagneticfields–Computersimulation. I.Title. TK7871.6.V5692009 621.382’4–dc22 2008041825 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN9780470697160(H/B) Setin10/12ptTimesbySunriseSettingLtd,Torquay,UK. PrintedinGreatBritainbyAntonyRowe. Contents Preface xi Acknowledgments xiii Acronyms xv 1 Introduction 1 1.1 The history of Antennas and Antenna Analysis 1 1.2 Antenna Synthesis 5 1.3 Approximate Antenna Modeling 7 1.4 Organization of the Book 9 1.5 Summary 12 References 13 2 Intravascular MR Antennas: Loops and Solenoids 19 2.1 Introduction 20 2.2 MRI 22 2.2.1 Magnetic Properties of Atomic Nuclei 22 2.2.2 Signal Detection 24 2.3 Intravascular MR Antennas 27 2.3.1 Antenna Designs for Tracking 28 vi CONTENTS 2.3.2 Antenna Designs for Imaging 30 2.4 MR Antenna Model 30 2.4.1 Admittance of a Loop 34 2.4.2 Sensitivity 40 2.4.3 Biot–Savart Law 41 2.4.4 Model Verification 43 2.5 Antenna Evaluation 58 2.5.1 Antennas for Active Tracking 59 2.5.2 Antennas for Intravascular Imaging 65 2.5.3 Antenna Rotation 71 2.6 In Vitro Testing 75 2.6.1 Sensitivity Pattern 75 2.6.2 Tracking 77 2.7 Antenna Synthesis 80 2.7.1 Genetic-Algorithm Optimization 80 2.8 Safety Aspects 86 2.8.1 Static Magnetic Fields and Spatial Gradients 87 2.8.2 Pulsed Gradient Magnetic Fields 88 2.8.3 Pulsed RF Fields and Heating 88 2.9 Conclusions 89 Appendix 2.A. Biot–Savart Law for Quasi-Static Situation 90 References 92 3 PCB Antennas: Printed Monopoles 97 3.1 Introduction 97 3.2 Printed UWB Antennas 99 3.2.1 Ultrawideband Antennas 99 3.2.2 Two-Penny Dipole Antenna 100 3.2.3 PCB UWB Antenna Design 100 3.2.4 Band-Stop Filter 109 3.3 Printed Strip Monopole Antennas 117 3.3.1 Model of an Imperfectly Conducting Dipole Antenna 118 3.3.2 Dipole Antenna with Magnetic Coating 121 3.3.3 Generalization of the Concept of Equivalent Radius 122 3.3.4 Equivalent Dipole with Magnetic Coating 125 3.3.5 Validation 125 CONTENTS vii 3.3.6 Microstrip-Excited Planar Strip Monopole Antenna 127 3.4 Conclusions 135 References 136 4 RFID Antennas: Folded Dipoles 139 4.1 Introduction 139 4.2 Wire Folded-Dipole Antennas 142 4.2.1 Symmetric Folded-Dipole Antenna 142 4.2.2 Asymmetric Folded-Dipole Antenna 144 4.3 Impedance Control 146 4.3.1 Power Waves 147 4.3.2 Short Circuits 150 4.3.3 Parasitic Elements 152 4.4 Asymmetric Coplanar-Strip Folded-Dipole Antenna on a Dielectric Slab 153 4.4.1 Lampe Model 155 4.4.2 Asymmetric Coplanar-Strip Transmission Line 157 4.4.3 Dipole Mode Analysis 166 4.5 Folded-Dipole Array Antennas 169 4.5.1 Reentrant Folded-Dipole Antenna 170 4.5.2 Series-Fed Linear Array of Folded Dipoles 171 4.5.3 Model Verification 172 4.5.4 Inclusion of Effects of Mutual Coupling 174 4.5.5 Verification of Modeling of Mutual Coupling 176 4.6 Conclusions 178 References 179 5 Rectennas: Microstrip Patch Antennas 183 5.1 Introduction 183 5.2 Rectenna Design Improvements 185 5.3 Analytical Models 187 5.3.1 Model of Rectangular Microstrip Patch Antenna 187 5.3.2 Model of Rectifying Circuit 193 5.4 Model Verification 198 5.5 Wireless Battery 200 5.5.1 Single Rectenna 202 5.5.2 Characterization of Rectenna 203 5.5.3 Cascaded Rectennas 204 viii CONTENTS 5.6 Power and Data Transfer 204 5.7 RF Energy Scavenging 211 5.7.1 GSM and WLAN Power Density Levels 211 5.7.2 GSM Mobile Phone as RF Source 215 5.8 Conclusions 216 References 217 6 Large Array Antennas: Open-Ended Rectangular-Waveguide Radiators 221 6.1 Introduction 222 6.1.1 Mode Matching and Generalized Scattering Matrices 222 6.2 Waveguide Fields 224 6.2.1 TE Modes 227 6.2.2 TM Modes 228 6.2.3 Transverse Field Components 229 6.3 Unit Cell Fields 231 6.3.1 TE Modes 232 6.3.2 TM Modes 234 6.3.3 Transverse Field Components 234 6.4 Cross-Sectional Step in a Rectangular Waveguide 236 6.4.1 Boundary Conditions Across the Interface 237 6.4.2 Creation of a Finite System of Linear Equations 239 6.4.3 Matrix Formulation and GSM Derivation 243 6.5 Junction Between a Rectangular Waveguide and a Unit Cell 245 6.5.1 GSM Derivation 246 6.6 Dielectric Step in a Unit Cell 248 6.6.1 GSM Derivation 249 6.7 Finite-Length Transmission Line 251 6.7.1 GSM Derivation 252 6.8 Overall GSM of a Cascaded Rectangular-Waveguide Structure 254 6.9 Validation 256 6.9.1 Initial Choice of Modes 256 6.9.2 Relative Convergence and Choice of Modes 258 6.9.3 Filter Structures 262 6.9.4 Array Antenna Structures 265 6.10 Conclusions 272 CONTENTS ix Appendix 6.A. Waveguide Mode Orthogonality and Normalization Functions 273 Appendix 6.B. Mode-Coupling Integrals for Waveguide-to-Waveguide Junction 277 Appendix 6.C. Unit Cell Mode Orthogonality and Normalization Functions 281 Appendix 6.D. Mode-Coupling Integrals for Rectangular-Waveguide-to-Unit-Cell Junction 282 References 288 7 Summary and Conclusions 293 7.1 Full-Wave and Approximate Antenna Analysis 293 7.2 Intravascular MR Antennas: Loops and Solenoids 295 7.3 PCB Antennas: Printed Monopoles 297 7.4 RFID Antennas: Folded Dipoles 297 7.5 Rectennas: Microstrip Patch Antennas 298 7.6 Large Array Antennas: Open-Ended Rectangular- Waveguide Radiators 299 References 299 Index 301 Preface InderBeschränkungzeigtsicherstderMeister,1 wroteJohannWolfgangvonGoetheon26 June1802.ItisaquotemuchusedinPhDthesestoaccentuateandjustifythecompactnessof athesis.Forthisbook,whichalsoservesthepurposeofaPhDthesis,thisquoteiscompletely unjustified.Ihavetriedtobeaselaborateaspossibleinexplainingtheapproximateantenna modelsdeveloped. Thisbookis the resultof morethan 15 yearsof work in the field of antennamodeling. After working for a number of years on the full-wave modeling of large phased array antennas,I foundthat, fora customer,itisveryhardtowaittilla full-wavecomputercode has been developed.Therefore I started developingso-called ‘engineering’or approximate models in parallel with the full-wave models. These engineering models, which can be producedmuchfaster,butatthe costof reducedaccuracy,can givethe customera preview ofwhatwillbepossible,andmaybeusedtocreate‘predesigns’tobefine-tunedbyapplying thefull-wavemodel.NowadaysIfocuscompletelyondevelopingapproximatemodels.Most ofthetopicsencounteredinthisbookweredevelopedoverthelastfewyears,butsomedate backalmost15years. Thereasonforbeing‘aselaborateaspossible’in explainingtheapproximatemodelsis twofold.First,asayoungengineerfreshfromuniversity,Ifoundithard,whenstartingona newassignment,toworkbackwardsfromarelevantpaperandunderstandallthestepstaken inthedevelopmentofamodel.Inthosedays,Iwouldhavewantedabookthatwouldhave takenmebythehandandexplainedtomeallthenecessarystepstakeninthedevelopmentof 1‘Constraintiswhereyoushowyouareamaster’. xii PREFACE amodel.Withthisbook,Ihavetriedtoaccommodatethiswish.Second,Ihavealwaysbeen intheprivilegedsituationofhavingliteraturesearchfacilitiesandalargetechnicallibraryat myimmediatedisposal.Forthosenotinthisprivilegedsituation,itmaybeveryhardtoget accesstothenecessaryreferences.Therefore,ratherthanjustreferringtothesources,Ihave alsowrittendownalloftheequationsneededforimplementingthemodelintosoftware. Thismayhavetheeffectthatthebookwillbecomeabitdrearyforexperiencedantenna engineers. For the inexperienced antenna engineer, I hope that, referring again to Goethe, the following quote will be appropriate after reading the book: Das also war des Pudels Kern2 [1]. REFERENCE 1.J.W. von Goethe, Faust: Der Tragödie erster und zweiter Teil. Urfaust, Beck Verlag, Munich,Germany,2006. HubregtJ.Visser Veldhoven,TheNetherlands 2‘Sothis,then,wasthekernelofthebrute’.