The Wave Concept in Electromagnetism and Circuits

Henri Baudrand is Emeritus Professor at the University of Toulouse; INPT, UPS; LAPLACE; ENSEEIHT in France. Mohammed Titaouine is Associate Professor in the Faculty of Technology, University of Batna 2, Algeria. Nathalie Raveu is Professor at the University of Toulouse; INPT, UPS; LAPLACE; ENSEEIHT; CNRS in France.

Preface ix

Chapter 1. General Principles of the Wave Concept Iterative Process  1
Henri BAUDRAND, Med Karim AZIZI, Mohammed TITAOUINE

1.1. Introduction 1

1.2. The iterative wave method  3

1.3. General definition of waves 5

1.4. Application to planar circuits  5

1.5. Applications to quasi-periodic structures 6

1.6. Circuits with localized components 7

1.7. General principles of quasi-periodic circuits 7

1.8. The significance of using auxiliary sources  8

1.8.1. Description of the environment 9

1.9. Unidimensional circuits 9

1.10. Application: transmission line 14

1.11. Comparison of current density for different cell lengths  14

1.12. Bi-dimensional circuits 16

1.13. Two-source bi-dimensional circuits  16

1.14. Three-source bi-dimensional circuits 22

1.15. Validation examples 25

1.16. Lenses and meta-materials 34

1.17. Conclusion  41

Chapter 2. Formulation and Validation of the WCIP Applied to the Analysis of Multilayer Planar Circuits 43
Alexandre Jean René SERRES and Georgina Karla DE FREITAS SERRES

2.1. Introduction 43

2.2. WCIP formulation 45

2.2.1. Multilayer formulation  45

2.2.2. Simulation results 48

2.3. Real and ideal polarizers within planar structures using WCIP  52

2.3.1. Formulation  52

2.3.2. Results 55

2.4. Amplifier structure of compact micro-waves 57

2.4.1. Formulation of the amplifier interface 57

2.4.2. The simulation results  59

Chapter 3. Applications of the WCIP Method to Frequency Selective Surfaces (FSS) 63
Mohammed TITAOUINE and Henri BAUDRAND

3.1. Introduction 64

3.2. Formulation of the iterative WCIP method  65

3.2.1. Determining the diffraction operator 68

3.2.2. Determining the reflection operator  70

3.2.3. The fast modal transform FMT and its inverse FMT−1 72

3.2.4. FSS multilayer devices  72

3.2.5. Multi-level plated FSSs 72

3.3. Application of the iterative WCIP method to different FSSs  74

3.3.1. Dielectric short-circuited FSS rings  74

3.3.2. FSSs charged by lumped elements and active FSSs  76

3.3.3. Multi-frequency band FSSs 79

3.3.4. Double-layer FSS plating  80

3.3.5. Triple-layer plating  82

3.3.6. Thick FSSs 83

3.4. Anisotropic FSS  95

3.5. Measurement system 96

3.6. Conclusion 97

3.7. Acknowledgments 98

Chapter 4. WCIP Applied to Substrate Integrated Circuits: Substrate Integrated Waveguide (SIW) and Substrate Integrated Non-Radiative Dielectic (SINRD) Circuits  99
Nathalie RAVEU and Ahmad ISMAIL ALHZZOURY

4.1. Introduction 99

4.2. Formulation of WCIP for SIC circuits 100

4.2.1. The definition of 103

4.2.2. The definition of 103

4.3. Results for SIW circuits 104

4.3.1. Waveguides  104

4.3.2. Bandpass filter  106

4.4. Results for the SINRD circuits 108

4.4.1. Waveguides  110

4.4.2. Bandpass filter  111

4.5. Conclusion 112

Chapter 5. WCIP Convergence 115
Nathalie RAVEU

5.1. Introduction 115

5.2. Summary of WCIP  116

5.2.1. Representation of homogeneous materials around the interface 117

5.2.2. Description of boundary conditions at the interface 118

5.2.3. System to solve  118

5.3. Improvement of WCIP by mathematical techniques 119

5.3.1. Number of modes/number of meshes 120

5.3.2. GMRES/Richardson 121

5.3.3. Selecting the initial value  122

5.4. Improvement of WCIP by physical considerations 124

5.4.1. Simplification of waves at the interface  124

5.4.2. Choice of reference impedance 125

5.4.3. Boundary conditions on the metallic mesh  126

5.5. Conclusions 127

Chapter 6. Application of WCIP to Diffraction Problems 129
Noemen AMMAR, Taoufik AGUILI and Henri BAUDRAND

6.1. Introduction 129

6.1.1. Diffraction by multilayer cylindrical structures 130

6.1.2. Descriptors for spectral components of reflection operators  132

6.1.3. The modal coefficients ext n Γ and int n Γ  133

6.1.4. Modal coefficients pass n Γ  134

6.1.5. Spatial diffraction operator 136

6.1.6. Excitation source 137

6.1.7. Iterative process  138

6.2. Application 138

6.2.1. Dielectric cylinder diffraction 139

6.2.2. Diffraction by metallic strips  143

6.2.3. Coaxial multi-strip structure  148

6.2.4. Diffraction by two dielectric co-axials  156

6.2.5. Diffraction by structures of any shape 159

6.3. Coupling simulation  160

6.3.1. Different operators involved  162

6.3.2. The case of two pixels on a single fictitious cylinder  163

6.3.3. The case where the two pixels are part of two coaxial cylinders 164

6.3.4. Spatial descriptors of diffraction operators  167

6.3.5. The iterative process 169

6.3.6. Computation of the remote location electric field  169

6.3.7. Application  170

6.4. Conclusion 183

Bibliography  185

List of Authors  195

Index 197