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This book covers the theoretical problems of modeling electrical behavior of the interconnections encountered in everyday electronic products. The coverage shows the theoretical tools of waveform prediction at work in the design of a complex and high-speed digital electronic system. Scientists, research engineers, and postgraduate students interested in electromagnetism, microwave theory, electrical engineering, or the development of simulation tools software for high speed electronic system design automation will find this book an illuminating resource.
List of contents
Acknowledgements xi
Introduction xiii
Chapter 1. Theoretical Foundations of Electromagnetism 1
1.1. Elements of the theory of distributions applied to electromagnetism 1
1.1.1. Choosing a presentation of the foundations of electromagnetism 1
1.1.2. Linear modeling of physical laws and Green's kernels 2
1.1.3. Accounting for the "natural symmetries" of physical laws 31.1.4. Motivation for using the theory of distributions 4
1.1.5. Quick review of the theory of distributions 5
1.1.6. Application to electromagnetism 9
1.2. Vector analysis review according to the theory of distributions 11
1.2.1. Derivation of discontinuous functions defined on R 11
1.2.2. Derivative of linear mappings 12
1.2.3. Derivation of discontinuous functions on a surface in 3 12
1.2.4. Derivation of vector distributions in 3 13
1.2.5. Algebra of the operator ?n 13
1.3. Maxwell's equations according to the theory of distributions 14
1.3.1. Symmetries and duality in electromagnetism 14
1.3.2. The symmetry laws of distributions in electromagnetism 14
1.3.3. Application to the first couple of Maxwell's equations 15
1.3.4. Behavior law of materials by means of the theory of distributions 19
1.3.5. Application to the second couple of Maxwell's equations 19
1.3.6. Charge density, current density, continuity equations 20
1.3.7. Integral form of Maxwell's equations 22
1.4. Conclusion 24
Chapter 2. Full Wave Analysis 25
2.1. Discontinuities in electromagnetism 25
2.1.1. Initial and boundary conditions according to the theory of distributions 25
2.1.2. Electromagnetic images, incident and reflected fields 28
2.1.3. Method of moments for the numerical computation of electromagnetic fields 29
2.2. Potentials in electromagnetism 33
2.2.1. Scalar and vector potentials, duality between electrical and magnetic potentials 33
2.2.2. Lossy propagation equations, the Lorentz gauge 35
2.2.3. Green's kernels for harmonic electromagnetic waves in heterogenous media 39
2.3. Topology of electromagnetic interferences 42
2.3.1. Introduction 42
2.3.2. Topological modeling of electromagnetic interferences 43
2.3.3. Partitioning the electrical network in respect of electromagnetic interferences 45
2.3.4. The tree of electromagnetic interferences and the problem of loops 46
2.4. Conclusion 50
Chapter 3. Electromagnetism in Stratified Media 51
3.1. Electrical and magnetic currents in stratified media 52
3.1.1. Scope of the theory, defining stratified media 52
3.1.2. Integral formulation of the current derivative versus time: general case 53
3.1.3. Integral formula of the current derivative relative to space in the direction of the vector potential 61
3.1.4. Duality between electrical and magnetic currents in lossless media 63
3.2. Straight stratified media 67
3.2.1. Scope 67
3.2.2. Lossy propagation equations and the variational approach 67
3.2.3. Spectral analysis of the longitudinal field 71
3.2.4. From Maxwell's equations to transmission line equations 76
3.2.5. Generalized transmission line matrix equation 79
3.2.6. Non-existence of the TM and TE modes separately 81
3.2.7. Electrical (or magnetic) currents 84
3.3. Conclusion 84
Chapter 4. Transmission Line Equations 85
4.1. Straight homogenous dielectric media with lossless conductors 86
4.1.1. Hypothesis 86
4.1.2. Electrical current formulae in TM mode of propagation 86
4.1.3. Magnetic current formulae in TE mode of propagation 89
4.1.4. Spectral analysis of electromagnetic fields 89
4.1.5. Modal analysis of electrical current and lineic charge 96
4.1.6. Modal analysis of scalar and vector potentials 101
4.1.7. Transmission line with distributed sources corresponding to a waveguide 103
4.2. TEM mode of wave propagation 104
4.2.1. Defining the TEM mode and the transmission lines 104
4.2.2. Basic existence condition of a TEM propagation mode 10
About the author
Stephane Charruau is the author of
Electromagnetism and Interconnections: Advanced Mathematical Tools for Computer-aided Simulation, published by Wiley.
Summary
This book covers the theoretical problems of modeling electrical behavior of the interconnections encountered in everyday electronic products. The coverage shows the theoretical tools of waveform prediction at work in the design of a complex and high-speed digital electronic system.
