Passive Macromodeling

Offers an overview of state of the art passive macromodeling techniques with an emphasis on black-box approaches

This book offers coverage of developments in linear macromodeling, with a focus on effective, proven methods. After starting with a definition of the fundamental properties that must characterize models of physical systems, the authors discuss several prominent passive macromodeling algorithms for lumped and distributed systems and compare them under accuracy, efficiency, and robustness standpoints. The book includes chapters with standard background material (such as linear time-invariant circuits and systems, basic discretization of field equations, state-space systems), as well as appendices collecting basic facts from linear algebra, optimization templates, and signals and transforms. The text also covers more technical and advanced topics, intended for the specialist, which may be skipped at first reading.

• Provides coverage of black-box passive macromodeling, an approach developed by the authors

• Elaborates on main concepts and results in a mathematically precise way using easy-to-understand language

• Illustrates macromodeling concepts through dedicated examples

• Includes a comprehensive set of end-of-chapter problems and exercises

Passive Macromodeling: Theory and Applications serves as a reference for senior or graduate level courses in electrical engineering programs, and to engineers in the fields of numerical modeling, simulation, design, and optimization of electrical/electronic systems.

Stefano Grivet-Talocia, PhD, is an Associate Professor of Circuit Theory at the Politecnico di Torino in Turin, Italy, and President of IdemWorks. Dr. Grivet-Talocia is author of over 150 technical papers published in international journals and conference proceedings. He invented several algorithms in the area of passive macromodeling, making them available through IdemWorks.

Bjørn Gustavsen, PhD, is a Chief Research Scientist in Energy Systems at SINTEF Energy Research in Trondheim, Norway. More than ten years ago, Dr. Gustavsen developed the original version of the vector fitting method with Prof. Semlyen at the University of Toronto. The vector fitting method is one of the most widespread approaches for model extraction. Dr. Gustavsen is also an IEEE fellow.

Auteur
Stefano Grivet-Talocia, PhD, is an Associate Professor of Circuit Theory at the Politecnico di Torino in Turin, Italy, and President of IdemWorks. Dr. Grivet-Talocia is author of over 150 technical papers published in international journals and conference proceedings. He invented several algorithms in the area of passive macromodeling, making them available through IdemWorks.

Bjørn Gustavsen, PhD, is a Chief Research Scientist in Energy Systems at SINTEF Energy Research in Trondheim, Norway. More than ten years ago, Dr. Gustavsen developed the original version of the vector fitting method with Prof. Semlyen at the University of Toronto. The vector fitting method is one of the most widespread approaches for model extraction. Dr. Gustavsen is also an IEEE fellow.

Contenu

Preface xix

1 Introduction 1

1.1 Why Macromodeling? 1

1.2 Scope 4

1.3 Macromodeling Flows 6

1.3.1 Macromodeling via Model Order Reduction 6

1.3.2 Macromodeling from Field Solver Data 7

1.3.3 Macromodeling from Measured Responses 8

1.4 Rational Macromodeling 9

1.5 Physical Consistency Requirements 11

1.6 Time-Domain Implementation 15

1.7 An Example 16

1.8 What Can Go Wrong? 17

2 Linear Time-Invariant Circuits and Systems 23

2.1 Basic Definitions 24

2.1.1 Linearity 24

2.1.2 Memory and Causality 26

2.1.3 Time Invariance 26

2.1.4 Stability 27

2.1.5 Passivity 28

2.2 Linear Time-Invariant Systems 28

2.2.1 Impulse Response 29

2.2.2 Properties of LTI Systems 32

2.3 Frequency-Domain Characterizations 33

2.4 Laplace and Fourier Transforms 34

2.4.1 Bilateral Laplace Transform and Transfer Matrices 34

2.4.2 Causal LTI Systems and the Unilateral Laplace Transform 36

2.4.3 Fourier Transform 36

2.5 Signal and System Norms 37

2.5.1 Signal Norms 38

2.5.2 System Norms 41

2.6 Multiport Representations 44

2.6.1 Ports and Terminals 44

2.6.2 Immittance Representations 45

2.6.3 Scattering Representations 46

2.6.4 Reciprocity 48

2.7 Passivity 49

2.7.1 Power and Energy 50

2.7.2 Passivity and Causality 51

2.7.3 The Static Case 52

2.7.4 The Dynamic Case 53

2.7.5 Positive Realness Bounded Realness and Passivity 54

2.7.6 Some Examples 56

2.8 Stability and Causality 59

2.8.1 Laplace-Domain Conditions for Causality 61

2.8.2 Laplace-Domain Conditions for BIBO Stability 62

2.8.3 Causality and Stability 62

2.9 Boundary Values and Dispersion Relations 64

2.9.1 Assumptions 64

2.9.2 Reconstruction of H(s) for s + 65

2.9.3 Reconstruction of H(s) for s j 65

2.9.4 Causality and Dispersion Relations 67

2.9.5 Generalizations 68

2.10 Passivity Conditions on the Imaginary Axis 70

Problems 71

3 Lumped LTI Systems 73

3.1 An Example from Circuit Theory 74

3.1.1 Variation on a Theme 76

3.1.2 Driving-Point Impedance 77

3.2 State-Space and Descriptor Forms 77

3.2.1 Singular Descriptor Forms 77

3.2.2 Internal Representations of Lumped LTI Systems 79

3.3 The Zero-Input Response 80

3.4 Internal Stability 81

3.4.1 Lyapunov Stability 81

3.4.2 Internal Stability of LTI Systems 83

3.5 The Lyapunov Equation 84

3.6 The Zero-State Response 87

3.6.1 Impulse Response 88

3.7 Operations on State-Space Systems 89

3.7.1 Interconnections 90

3.7.2 Inversion 91

3.7.3 Similarity Transformations 91

3.8 Gramians 91

3.8.1 Observability 92

3.8.2 Controllability 93

3.8.3 Minimal Realizations 95

3.9 Reciprocal State-Space Systems 95

3.10 Norms 97

3.10.1 *L*2 Norm 98

3.10.2 H Norm 99

Problems 100

4 Distributed LTI Systems 103

4.1 One-Dimensional Distributed Circuits 104

4.1.1 The Discrete-Space Case 104

4.1.2 The Continuous-Space Case 106

4.1.3 Discussion 109

4.2 Two-Dimensional Distributed Circuits 111

4.2.1 The Discrete-Space Case 112

4.2.2 The Continuous-Space Case 114

4.2.3 A Closed-Form Solution 116 4.2.4 Spatial Disc...