Electromagnetic Waveguides and Transmission Lines FRANK OLYSLAGER Department of Information Technology University of Gent CLARENDON PRESS OXFORD 1999
CONTENTS List of symbols xv 1 Introduction 1 1.1 Historical note 1 1.2 Introduction 3 1.3 A brief tour through the book 6 1.4 Maxwell's equations 7 1.5 The Lorentz reciprocity theorem 9 1.6 Waveguide geometry and notation 11 1.7 Classification of waveguides 12 1.7.1 Open and closed waveguides 12 1.7.2 Homogeneous and hybrid waveguides 13 1.7.3 Electric, dielectric and optical waveguides 13 1.7.4 Isotropic, anisotropic, bi-isotropic and bianisotropic waveguides 13 1.7.5 Reciprocal and non-reciprocal waveguides 14 1.7.6 Lossless and non-lossless waveguides 14 1.7.7 One-, two- and three-dimensional waveguides 15 1.8 Exercises 15 2 Transmission lines for quasi-tem fields 17 2.1 Introduction 17 2.2 Homogeneous isotropic waveguides 18 2.2.1 TEM solution 18 2.2.2 Symmetry of circuit parameters 21 2.2.3 Power and field integral 22 2.3 Inhomogeneous isotropic waveguides 23 2.3.1 TEM solution 23 2.3.2 Quasi-TEM solution 24 2.3.3 Validity range 29 2.3.4 Symmetry of circuit parameters 30 2.3.5 Lossless and lossy materials 31 2.3.6 Power and field integral 32 2.4 Inhomogeneous anisotropic waveguides 32 2.4.1 Static solution 32 2.4.2 Quasi-TEM solution 34 2.4.3 Symmetry of circuit parameters 35 2.4.4 Lossless and lossy materials 36 2.4.5 Validity range 37
xii CONTENTS 2.4.6 Power and field integral 37 2.5 Properties of transmission lines 37 2.5.1 Lossless and lossy transmission lines 38 2.5.2 Reciprocal transmission lines 39 2.6 Exercises 39 3 Transmission lines for full-wave fields 41 3.1 Introduction 41 3.2 Modal solutions 42 3.2.1 Three-dimensional waveguides 44 3.2.2 Two-dimensional waveguides 49 3.2.3 One-dimensional waveguides 53 3.2.4 Lossless waveguides 54 3.2.5 Periodic and random waveguides 56 3.2.6 Asymptotic behaviour 59 3.2.7 Waveguides with gain 59 3.2.8 Full Maxwell equations 61 3.3 Properties of eigenmodes in isotropic waveguides 61 3.3.1 Modal relationships 61 3.3.2 Normalization 62 3.3.3 Lossless waveguides 63 3.3.4 Power and field integral 64 3.4 Properties of eigenmodes in transmission lines 65 3.4.1 Modal solutions 65 3.4.2 Modal relationships 66 3.4.3 Lossless transmission line 67 3.4.4 Normalization 68 3.4.5 Power and field integral 68 3.5 Equivalent transmission line model 69 3.6 Determination of the current mode matrix for electric waveguides 71 3.7 The junction of waveguides 73 3.8 The connection of a waveguide to a generator 77 3.9 Properties of waveguide junctions 79 3.10 Power-based transmission line models 83 3.11 Anisotropic and bianisotropic waveguides 86 3.12 Exercises 88 4 Bitransmission lines for quasi-tem fields 93 4.1 Introduction 93 4.2 Homogeneous bi-isotropic waveguides 93 4.2.1 TEM solution 93 4.2.2 Power and field integral 96 4.3 Inhomogeneous bi-isotropic waveguides 97 4.3.1 Static solution 97
CONTENTS xiii 4.3.2 Quasi-TEM solution 99 4.3.3 Symmetry of circuit parameters 102 4.3.4 Lossless materials 104 4.3.5 Power and field integral 105 4.4 Inhomogeneous bianisotropic waveguides 106 4.4.1 Static solution 106 4.4.2 Quasi-TEM solution 108 4.4.3 Symmetry of circuit parameters 110 4.4.4 Lossless materials 110 4.4.5 Power and field integral 111 4.5 Properties of bitransmission lines 111 4.5.1 Lossless and lossy bitransmission lines 112 4.5.2 Reciprocal bitransmission lines 113 4.6 Exercises 113 5 Bitransmission lines for full-wave fields 115 5.1 Introduction 115 5.2 Properties of eigenmodes in bianisotropic waveguides 115 5.2.1 Reciprocity 115 5.2.2 Normalization 118 5.2.3 Bidirectionality 119 5.2.4 Lossless waveguides 123 5.3 Modal solutions 126 5.3.1 Three-dimensional waveguides 126 5.3.2 General bianisotropic waveguides 131 5.4 Properties of eigenmodes in bitransmission lines 132 5.4.1 Modal solutions 132 5.4.2 Reciprocity 133 5.4.3 Normalization 134 5.4.4 Bidirectionality 135 5.4.5 Lossless bitransmission lines 135 5.5 The relation between opposite modes in bitransmission lines 136 5.5.1 Single bitransmission line 137 5.5.2 Perturbational analysis 138 5.5.3 The general case 138 5.6 The relation between opposite modes in bianisotropic waveguides 139 5.7 Bitransmission line models 142 5.7.1 Single reciprocal bitransmission line 142 5.7.2 Single non-reciprocal bitransmission line 149 5.7.3 Coupled reciprocal bitransmission lines 153 5.7.4 Coupled non-reciprocal bitransmission lines 154 5.8 The junction of waveguides 155 5.9 Properties of waveguide junctions 157 5.10 Exercises 160
xiv CONTENTS 6 Fields incident on transmission lines 162 6.1 Introduction 162 6.2 Excitation of eigenmodes 163 6.3 Transmission line representation 169 6.4 Power-based transmission line models 171 6.5 Coupled waveguides 172 6.6 The junction of waveguides 178 6.7 Circuit representation 183 6.8 Quasi-TEM fields 184 6.9 Exercises 186 7 Fields incident on bitransmission lines 187 7.1 Introduction 187 7.2 Excitation of eigenmodes 187 7.3 Transmission line representation 191 7.4 The junction of waveguides 192 7.5 Circuit representation 195 7.6 Exercise 195 8 Mathematics 196 8.1 Introduction 196 8.2 Dyadic analysis 196 8.3 Matrix analysis 197 8.4 Operator analysis 199 8.5 Fourier and Laplace transformations 202 8.6 Cauchy's residue theorem 203 8.7 Integral theorems 204 8.8 The Floquet-Bloch theorem 206 References 211 Index 217