Cover image for Analysis methods for RF, microwave and millimeter - wave planar transmission line structures
Title:
Analysis methods for RF, microwave and millimeter - wave planar transmission line structures
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Publication Information:
New York : John Wiley & Sons, 2000
ISBN:
9780471017509

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30000010048158 TK7876 N48 2000 Open Access Book Book
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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

Prefacep. xi
1 Introductionp. 1
1.1 Planar Transmission Lines and Microwave Integrated Circuitsp. 1
1.2 Analysis Methods for Planar Transmission Linesp. 7
1.3 Organization of the Bookp. 9
2 Fundamentals of Electromagnetic Theoryp. 12
2.1 Maxwell's Equationsp. 12
2.2 Constitutive Relationsp. 14
2.3 Continuity Equationp. 15
2.4 Loss in Mediump. 15
2.5 Boundary Conditionsp. 17
2.6 Skin Depthp. 18
2.7 Power Flowp. 19
2.8 Poisson's and Laplace's Equationsp. 19
2.9 Wave Equationsp. 20
2.10 Electric and Magnetic Potentialsp. 21
2.11 Wave Types and Solutionsp. 23
2.11.1 Wave Typesp. 23
2.11.2 Wave Solutionsp. 24
2.12 Orthogonality Relationsp. 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 Fieldsp. 31
2.12.3 Orthogonality Relations Between Electric and Magnetic Fieldsp. 32
2.12.4 Power Orthogonality for Lossless Structuresp. 35
Referencesp. 37
Problemsp. 37
3 Green's Functionp. 39
3.1 Descriptions of Green's Functionp. 39
3.1.1 Solution of Poisson's Equation Using Green's Functionp. 39
3.1.2 Solution of the Wave Equation Using Green's Functionp. 41
3.2 Sturm-Liouville Equationp. 42
3.3 Solutions of Green's Functionp. 44
3.3.1 Closed-Form Green's Functionp. 44
3.3.2 Series-Form Green's Functionp. 49
3.3.3 Integral-Form Green's Functionp. 53
Referencesp. 56
Problemsp. 56
Appendix Green's Identitiesp. 62
4 Planar Transmission Linesp. 63
4.1 Transmission Line Parametersp. 64
4.1.1 Static Analysisp. 64
4.1.2 Dynamic Analysisp. 66
4.2 Microstrip Linep. 68
4.3 Coplanar Waveguidep. 71
4.4 Coplanar Stripsp. 74
4.5 Strip Linep. 76
4.6 Slot Linep. 78
Referencesp. 80
Problemsp. 81
5 Conformal Mappingp. 85
5.1 Principles of Mappingsp. 85
5.2 Fundamentals of Conformal Mappingp. 87
5.3 The Schwarz-Christoffel Transformationp. 95
5.4 Applications of the Schwarz-Christoffel Transformation in Transmisison Line Analysisp. 98
5.5 Conformal-Mapping Equations for Common Transmission Linesp. 106
Referencesp. 112
Problemsp. 113
6 Variational Methodsp. 120
6.1 Fundamentals of Variational Methodsp. 121
6.2 Variational Expressions for the Capacitance per Unit Length of Transmission Linesp. 123
6.2.1 Upper-Bound Variational Expression for Cp. 124
6.2.2 Lower-Bound Variational Expression for Cp. 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 Domainp. 128
6.3.1 Variational Formulation Using Upper-Bound Expressionp. 128
6.3.2 Variational Formulation Using Lower-Bound Expressionp. 130
6.4 Variational Methods in the Spectral Domainp. 135
6.4.1 Lower-Bound Variational Expression for C in the Spectral Domainp. 135
6.4.2 Determination of C, Z[subscript o], and [varepsilon subscript eff]p. 137
6.4.3 Formulationp. 138
Referencesp. 142
Problemsp. 143
Appendix Systems of Homogeneous Equations from the Lower-Bound Variational Formulationp. 148
7 Spectral-Domain Methodp. 152
7.1 Formulation of the Quasi-static Spectral-Domain Analysisp. 152
7.2 Formulation of the Dynamic Spectral-Domain Analysisp. 162
Referencesp. 176
Problemsp. 177
Appendix A Fourier Transform and Parseval's Theoremp. 186
Appendix B Galerkin's Methodp. 188
8 Mode-Matching Methodp. 191
8.1 Mode-Matching Analysis of Planar Transmission Linesp. 191
8.1.1 Electric and Magnetic Field Expressionsp. 193
8.1.2 Mode-Matching Equationsp. 198
8.2 Mode-Matching Analysis of Planar Transmission Line Discontinuitiesp. 203
8.2.1 Electric and Magnetic Field Expressionsp. 203
8.2.2 Single-Step Discontinuityp. 207
8.2.3 Double-Step Discontinuityp. 211
8.2.4 Multiple-Step Discontinuityp. 214
Referencesp. 221
Problemsp. 222
Appendix A Coefficients in Eqs. (8.62)p. 228
Appendix B Inner Products in Eqs. (8.120)-(8.123)p. 233
Indexp. 237