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Summary
Summary
A one-stop reference to the
major techniques for analyzing
microwave planar transmission line structures
The last two decades have seen important progress in the development of methods for the analysis of microwave and millimeter-wave passive structures, which contributed greatly to microwave integrated circuit design while also stimulating the development of new planar transmission lines. This timely and authoritative work introduces microwave engineers to the most commonly used techniques for analyzing microwave planar transmission line structures.
Designed to be easily accessible to readers with only a fundamental background in electromagnetic theory, the book provides clear explanations of the theory and applications of Green's function, the conformal-mapping method, spectral domain methods, variational methods, and the mode-matching methods. Coverage for each method is self-contained and supplemented with problems and solutions as well as useful figures.
In addition to providing detailed formulations of the methods under discussion, this highly practical book also demonstrates how to apply the principles of electromagnetic theory to the analysis of microwave boundary value problems, customize methods for specific needs, and develop new techniques. Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures is an excellent working resource for anyone involved in the design and engineering of RF, microwave, and millimeter-wave integrated circuits.
Author Notes
Cam Nguyen, PhD, is a professor in the Department of Electrical Engineering at Texas A&M University.
Table of Contents
Preface | p. xi |
1 Introduction | p. 1 |
1.1 Planar Transmission Lines and Microwave Integrated Circuits | p. 1 |
1.2 Analysis Methods for Planar Transmission Lines | p. 7 |
1.3 Organization of the Book | p. 9 |
2 Fundamentals of Electromagnetic Theory | p. 12 |
2.1 Maxwell's Equations | p. 12 |
2.2 Constitutive Relations | p. 14 |
2.3 Continuity Equation | p. 15 |
2.4 Loss in Medium | p. 15 |
2.5 Boundary Conditions | p. 17 |
2.6 Skin Depth | p. 18 |
2.7 Power Flow | p. 19 |
2.8 Poisson's and Laplace's Equations | p. 19 |
2.9 Wave Equations | p. 20 |
2.10 Electric and Magnetic Potentials | p. 21 |
2.11 Wave Types and Solutions | p. 23 |
2.11.1 Wave Types | p. 23 |
2.11.2 Wave Solutions | p. 24 |
2.12 Orthogonality Relations | p. 28 |
2.12.1 Orthogonality Relations Between [psi superscript h subscript mn](x, y) and Between [psi superscript e subscript mn](x, y) | p. 28 |
2.12.2 Orthogonality Relations Between Electric Fields and Between Magnetic Fields | p. 31 |
2.12.3 Orthogonality Relations Between Electric and Magnetic Fields | p. 32 |
2.12.4 Power Orthogonality for Lossless Structures | p. 35 |
References | p. 37 |
Problems | p. 37 |
3 Green's Function | p. 39 |
3.1 Descriptions of Green's Function | p. 39 |
3.1.1 Solution of Poisson's Equation Using Green's Function | p. 39 |
3.1.2 Solution of the Wave Equation Using Green's Function | p. 41 |
3.2 Sturm-Liouville Equation | p. 42 |
3.3 Solutions of Green's Function | p. 44 |
3.3.1 Closed-Form Green's Function | p. 44 |
3.3.2 Series-Form Green's Function | p. 49 |
3.3.3 Integral-Form Green's Function | p. 53 |
References | p. 56 |
Problems | p. 56 |
Appendix Green's Identities | p. 62 |
4 Planar Transmission Lines | p. 63 |
4.1 Transmission Line Parameters | p. 64 |
4.1.1 Static Analysis | p. 64 |
4.1.2 Dynamic Analysis | p. 66 |
4.2 Microstrip Line | p. 68 |
4.3 Coplanar Waveguide | p. 71 |
4.4 Coplanar Strips | p. 74 |
4.5 Strip Line | p. 76 |
4.6 Slot Line | p. 78 |
References | p. 80 |
Problems | p. 81 |
5 Conformal Mapping | p. 85 |
5.1 Principles of Mappings | p. 85 |
5.2 Fundamentals of Conformal Mapping | p. 87 |
5.3 The Schwarz-Christoffel Transformation | p. 95 |
5.4 Applications of the Schwarz-Christoffel Transformation in Transmisison Line Analysis | p. 98 |
5.5 Conformal-Mapping Equations for Common Transmission Lines | p. 106 |
References | p. 112 |
Problems | p. 113 |
6 Variational Methods | p. 120 |
6.1 Fundamentals of Variational Methods | p. 121 |
6.2 Variational Expressions for the Capacitance per Unit Length of Transmission Lines | p. 123 |
6.2.1 Upper-Bound Variational Expression for C | p. 124 |
6.2.2 Lower-Bound Variational Expression for C | p. 125 |
6.2.3 Determination of C, Z[subscript o], and [varepsilon subscript eff] | p. 127 |
6.3 Formulation of Variational Methods in the Space Domain | p. 128 |
6.3.1 Variational Formulation Using Upper-Bound Expression | p. 128 |
6.3.2 Variational Formulation Using Lower-Bound Expression | p. 130 |
6.4 Variational Methods in the Spectral Domain | p. 135 |
6.4.1 Lower-Bound Variational Expression for C in the Spectral Domain | p. 135 |
6.4.2 Determination of C, Z[subscript o], and [varepsilon subscript eff] | p. 137 |
6.4.3 Formulation | p. 138 |
References | p. 142 |
Problems | p. 143 |
Appendix Systems of Homogeneous Equations from the Lower-Bound Variational Formulation | p. 148 |
7 Spectral-Domain Method | p. 152 |
7.1 Formulation of the Quasi-static Spectral-Domain Analysis | p. 152 |
7.2 Formulation of the Dynamic Spectral-Domain Analysis | p. 162 |
References | p. 176 |
Problems | p. 177 |
Appendix A Fourier Transform and Parseval's Theorem | p. 186 |
Appendix B Galerkin's Method | p. 188 |
8 Mode-Matching Method | p. 191 |
8.1 Mode-Matching Analysis of Planar Transmission Lines | p. 191 |
8.1.1 Electric and Magnetic Field Expressions | p. 193 |
8.1.2 Mode-Matching Equations | p. 198 |
8.2 Mode-Matching Analysis of Planar Transmission Line Discontinuities | p. 203 |
8.2.1 Electric and Magnetic Field Expressions | p. 203 |
8.2.2 Single-Step Discontinuity | p. 207 |
8.2.3 Double-Step Discontinuity | p. 211 |
8.2.4 Multiple-Step Discontinuity | p. 214 |
References | p. 221 |
Problems | p. 222 |
Appendix A Coefficients in Eqs. (8.62) | p. 228 |
Appendix B Inner Products in Eqs. (8.120)-(8.123) | p. 233 |
Index | p. 237 |