Passive Macromodeling

Name: Passive Macromodeling | Theory and Applications
Brand: Wiley
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Theory and Applications

Stefano Grivet-Talocia Bjorn Gustavsen(Autor*in)

Wiley (Verlag)

Erschienen am 19. Oktober 2015

904 Seiten

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Beschreibung

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.

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Inhalt

Cover
Title Page
Copyright
Dedication
Contents
Preface
Chapter 1 Introduction
1.1 Why Macromodeling?
1.2 Scope
1.3 Macromodeling Flows
1.3.1 Macromodeling via Model Order Reduction
1.3.2 Macromodeling from Field Solver Data
1.3.3 Macromodeling from Measured Responses
1.4 Rational Macromodeling
1.5 Physical Consistency Requirements
1.6 Time-Domain Implementation
1.7 An Example
1.8 What Can Go Wrong?
Chapter 2 Linear Time-Invariant Circuits and Systems
2.1 Basic Definitions
2.1.1 Linearity
2.1.2 Memory and Causality
2.1.3 Time Invariance
2.1.4 Stability
2.1.5 Passivity
2.2 Linear Time-Invariant Systems
2.2.1 Impulse Response
2.2.2 Properties of LTI Systems
2.3 Frequency-Domain Characterizations
2.4 Laplace and Fourier Transforms
2.4.1 Bilateral Laplace Transform and Transfer Matrices
2.4.2 Causal LTI Systems and the Unilateral Laplace Transform
2.4.3 Fourier Transform
2.5 Signal and System Norms*
2.5.1 Signal Norms
2.5.2 System Norms
2.6 Multiport Representations
2.6.1 Ports and Terminals
2.6.2 Immittance Representations
2.6.3 Scattering Representations
2.6.4 Reciprocity
2.7 Passivity
2.7.1 Power and Energy
2.7.2 Passivity and Causality
2.7.3 The Static Case
2.7.4 The Dynamic Case
2.7.5 Positive Realness, Bounded Realness, and Passivity
2.7.6 Some Examples
2.8 Stability and Causality
2.8.1 Laplace-Domain Conditions for Causality
2.8.2 Laplace-Domain Conditions for BIBO Stability
2.8.3 Causality and Stability
2.9 Boundary Values and Dispersion Relations*
2.9.1 Assumptions
2.9.2 Reconstruction of H(s) for s ? C+
2.9.3 Reconstruction of H(s) for s ? jR
2.9.4 Causality and Dispersion Relations
2.9.5 Generalizations
2.10 Passivity Conditions on the Imaginary Axis*
Problems
Chapter 3 Lumped LTI Systems
3.1 An Example from Circuit Theory
3.1.1 Variation on a Theme
3.1.2 Driving-Point Impedance
3.2 State-Space and Descriptor Forms
3.2.1 Singular Descriptor Forms
3.2.2 Internal Representations of Lumped LTI Systems
3.3 The Zero-Input Response
3.4 Internal Stability
3.4.1 Lyapunov Stability
3.4.2 Internal Stability of LTI Systems
3.5 The Lyapunov Equation
3.6 The Zero-State Response
3.6.1 Impulse Response
3.7 Operations on State-Space Systems
3.7.1 Interconnections
3.7.2 Inversion
3.7.3 Similarity Transformations
3.8 Gramians
3.8.1 Observability
3.8.2 Controllability
3.8.3 Minimal Realizations
3.9 Reciprocal State-Space Systems
3.10 Norms
3.10.1 L2 Norm
3.10.2 H8 Norm
Problems
Chapter 4 Distributed LTI Systems
4.1 One-Dimensional Distributed Circuits
4.1.1 The Discrete-Space Case
4.1.2 The Continuous-Space Case
4.1.3 Discussion
4.2 Two-Dimensional Distributed Circuits*
4.2.1 The Discrete-Space Case
4.2.2 The Continuous-Space Case
4.2.3 A Closed-Form Solution
4.2.4 Spatial Discretization
4.2.5 Discussion
4.3 General Electromagnetic Characterization
4.3.1 3D Electromagnetic Modeling
4.3.2 Summary and Outlook
Problems
Chapter 5 Macromodeling Via Model Order Reduction
5.1 Model Order Reduction
5.2 Moment Matching
5.2.1 Moments
5.2.2 Padé Approximation and AWE
5.2.3 Complex Frequency Hopping
5.3 Reduction by Projection
5.3.1 Krylov Subspaces
5.3.2 Implicit Moment Matching: The Orthogonal Case
5.3.3 The Arnoldi Process
5.3.4 PRIMA
5.3.5 Multipoint Moment Matching
5.3.6 An Example
5.3.7 Implicit Moment Matching: The Biorthogonal Case
5.3.8 Padé Via Lanczos (PVL)
5.4 Reduction by Truncation
5.4.1 Balancing
5.4.2 Balanced Truncation
5.5 Advanced Model Order Reduction*
5.5.1 Passivity-Preserving Balanced Truncation
5.5.2 Balanced Truncation of Descriptor Systems
5.5.3 Reducing Large-Scale Systems
Problems
Chapter 6 Black-Box Macromodeling and Curve Fitting
6.1 Basic Curve Fitting
6.1.1 Linear Least Squares
6.1.2 Maximum Likelihood Estimation
6.1.3 Polynomial Fitting
6.2 Direct Rational Fitting
6.2.1 Polynomial Ratio Form
6.2.2 Pole-Zero Form
6.2.3 Partial Fraction Form
6.2.4 Partial Fraction Form with Fixed Poles
6.2.5 Nonlinear Least Squares
6.3 Linearization via Weighting
6.4 Asymptotic Pole-Zero Placement
6.5 ARMA Modeling
6.5.1 Modeling from Time-Domain Responses
6.5.2 Modeling from Frequency Domain Responses
6.5.3 Conversion of ARMA Models
6.6 Prony's Method
6.7 Subspace-Based Identification*
6.7.1 Discrete-Time State-Space Systems
6.7.2 Macromodeling from Impulse Response Samples
6.7.3 Macromodeling from Input-Output Samples
6.7.4 From Discrete-Time to Continuous-Time State-Space Models
6.7.5 Frequency-Domain Subspace Identification
6.7.6 Generalized Pencil-of-Function Methods
6.7.7 Examples
6.8 Loewner Matrix Interpolation*
6.8.1 The Scalar Case
6.8.2 The Multiport Case
Problems
Chapter 7 The Vector Fitting Algorithm
7.1 The Sanathanan-Koerner Iteration
7.1.1 The Steiglitz-McBride Iteration
7.2 The Generalized Sanathanan-Koerner Iteration
7.2.1 General Basis Functions
7.2.2 The Partial Fraction Basis
7.3 Frequency-Domain Vector Fitting
7.3.1 A Simple Model Transformation
7.3.2 Computing the New Poles
7.3.3 The Vector Fitting Iteration
7.3.4 From GSK to VF
7.4 Consistency And Convergence
7.4.1 Consistency
7.4.2 Convergence
7.4.3 Formal Convergence Analysis
7.5 Practical VF Implementation
7.5.1 Causality, Stability, and Realness
7.5.2 Order Selection and Initialization
7.5.3 Improving Numerical Robustness
7.6 Relaxed Vector Fitting
7.6.1 Weight Normalization, Noise, and Convergence
7.6.2 Relaxed Vector Fitting
7.7 Tuning VF
7.7.1 Weighting and Error Control
7.7.2 High-Frequency Behavior
7.7.3 High-Frequency Constraints
7.7.4 DC Point Enforcement
7.7.5 Simultaneous Constraints
7.8 Time-Domain Vector Fitting
7.9 z-Domain Vector Fitting
7.10 Orthonormal Vector Fitting
7.10.1 Orthonormal Rational Basis Functions
7.10.2 The OVF Iteration
7.10.3 The OVF Pole Relocation Step
7.10.4 Finding Residues
7.11 Other Variants
7.11.1 Magnitude Vector Fitting
7.11.2 Vector Fitting with L1 Norm Minimization
7.11.3 Dealing with Higher Pole Multiplicities
7.11.4 Including Higher Order Derivatives
7.11.5 Hard Relocation of Poles
7.12 Notes on Overfitting and Ill-Conditioning
7.12.1 Exact Model Identification
7.12.2 Curve Fitting
7.13 Application Examples
7.13.1 Surface Acoustic Wave Filter
7.13.2 Subnetwork Equivalent
7.13.3 Transformer Modeling from Time-Domain Measurements
Problems
Chapter 8 Advanced Vector Fitting for Multiport Problems
8.1 Introduction
8.2 Adapting VF to Multiple Responses
8.2.1 Pole Identification
8.2.2 Fast Vector Fitting
8.2.3 Residue Identification
8.3 Multiport Formulations
8.3.1 Single-Element Modeling: Multi-SISO Structure
8.3.2 Single-Column Modeling: Multi-SIMO Structure
8.3.3 Matrix Modeling: MIMO Structure
8.3.4 Matrix Modeling: Minimal Realizations
8.3.5 Sparsity Considerations
8.4 Enforcing Reciprocity
8.4.1 External Reciprocity
8.4.2 Internal Reciprocity*
8.5 Compressed Macromodeling
8.5.1 Data Compression
8.5.2 Compressed Rational Approximation
8.5.3 An Application Example
8.6 Accuracy Considerations
8.6.1 Noninteracting Models
8.6.2 Interacting Models, Scalar Case
8.6.3 Error Magnification in Multiport Systems
8.7 Overcoming Error Magnification
8.7.1 Elementwise Inverse Weighting
8.7.2 Diagonalization
8.7.3 Mode-Revealing Transformations
8.7.4 Modal Vector Fitting
8.7.5 External and Internal Ports
Problems
Chapter 9 Passivity Characterization of Lumped LTI Systems
9.1 Internal Characterization of Passivity
9.1.1 A First Order Example
9.1.2 The Dissipation Inequality
9.1.3 Lumped LTI Systems
9.2 Passivity of Lumped Immittance Systems
9.2.1 Rational Positive Real Matrices
9.2.2 Extracting Purely Imaginary Poles
9.2.3 The Positive Real Lemma
9.2.4 Positive Real Functions Revisited
9.2.5 Popov Functions and Spectral Factorizations
9.2.6 Hamiltonian Matrices
9.2.7 Passivity Characterization via Hamiltonian Matrices
9.2.8 Determination of Local Passivity Violations
9.2.9 Quantification of Passivity Violations via Bisection
9.2.10 Quantification of Passivity Violations via Sampling
9.2.11 Frequency Transformations
9.2.12 Extended Hamiltonian Pencils
9.2.13 Generalized Hamiltonian Pencils
9.2.14 Positive Real Lemma for Descriptor Systems
9.3 Passivity of Lumped Scattering Systems
9.3.1 Rational Bounded Real Matrices
9.3.2 The Bounded Real Lemma
9.3.3 Bounded Real Functions Revisited
9.3.4 Popov Functions, Spectral Factorizations, and Hamiltonian Matrices
9.3.5 Passivity Characterization via Hamiltonian Matrices
9.3.6 Determination of Local Passivity Violations
9.3.7 Quantification of Passivity Violations via Bisection
9.3.8 Quantification of Passivity Violations via Sampling
9.3.9 Extended Hamiltonian Pencils
9.3.10 Generalized Hamiltonian Pencils
9.3.11 Bounded Real Lemma for Descriptor Systems
9.4 Advanced Passivity Characterization
9.4.1 On the Computation of Imaginary Hamiltonian Eigenvalues
9.4.2 Large-Scale Hamiltonian Eigenvalue Problems*
9.4.3 Half-Size Passivity Test Matrices
Problems
Chapter 10 Passivity Enforcement of Lumped LTI Systems
10.1 Passivity Constraints for Lumped LTI Systems
10.1.1 Passive State-Space Immittance Systems
10.1.2 Passive State-Space Scattering Systems
10.2 State-Space Perturbation
10.2.1 Asymptotic Perturbation
10.2.2 Dynamic Perturbation
10.2.3 Input-State Perturbation
10.2.4 State-Output Perturbation
10.2.5 A Perturbation Strategy for Passivity Enforcement
10.3 Asymptotic Passivity Enforcement
10.3.1 Immittance Systems
10.3.2 Scattering Systems
10.4 Imaginary Poles of Immittance Systems
10.5 Local Passivity Enforcement
10.5.1 Local Passivity Constraints
10.5.2 Enforcing Local Passivity Constraints
10.6 Passivity Enforcement Via Hamiltonian Perturbation
10.6.1 Hamiltonian Perturbation of Immittance Systems
10.6.2 Hamiltonian Perturbation of Scattering Systems
10.6.3 Hamiltonian Perturbation Strategies
10.6.4 Slopes
10.6.5 Global Passivity Enforcement via Hamiltonian Perturbation
10.7 Linear Matrix Inequalities
10.7.1 Parameterizations
10.8 Computational Cost
10.9 Advanced Accuracy Control
10.9.1 Frequency-Selective Norms
10.9.2 Individual Response Weighting
10.9.3 Bandlimited Norms
10.9.4 Relative Norms
10.9.5 Data-Based Cost Functions
10.10 Least-Squares Residue Perturbation
10.10.1 Basic Residue Perturbation (RP)
10.10.2 Spectral Residue Perturbation (SRP)
10.10.3 Mode-Revealing Transformations
10.10.4 Modal Perturbation (MP)
10.10.5 Robust Iterations
10.11 Alternative Formulations
10.11.1 Passivity Constraints Based on H8 norm*
10.11.2 Iterative Update by Fitting Passivity Violations
10.11.3 Pole Perturbation Approaches
10.11.4 Parameterization via Positive Fractions
10.12 Descriptor Systems*
10.12.1 Perturbation of Generalized Hamiltonian Pencils
10.12.2 Handling Singular Direct Coupling Terms
10.12.3 Proper Part Extraction
10.12.4 Handling Impulsive Terms
10.12.5 Accuracy Control
Problems
Chapter 11 Time-Domain Simulation
11.1 Discretization of ODE Systems
11.2 Interconnection of Macromodels
11.3 Direct Convolution
11.3.1 Equivalent Circuit Implementations
11.3.2 Discussion
11.4 Interfacing State-Space Macromodels
11.4.1 Equivalent Circuit Interfaces
11.5 Interfacing Pole-Residue Macromodels
11.5.1 Scalar Single-Pole System
11.5.2 General Multiport High-Order Systems
11.5.3 Discussion
11.6 Equivalent Circuit Synthesis
11.6.1 Direct Admittance Synthesis
11.6.2 Direct State-Space Synthesis
11.6.3 Sparse Synthesis
11.6.4 Classical RLCT Synthesis*
Problems
Chapter 12 Transmission Lines and Distributed Systems
12.1 Introduction
12.2 Multiconductor Transmission Lines
12.2.1 Per-Unit-Length Matrices
12.2.2 Frequency-Domain Solution via Modal Decomposition
12.2.3 Frequency-Domain Solution in the Physical Domain
12.3 Direct Macromodeling Approaches
12.3.1 Folded Line Equivalent Models
12.4 Lumped Segmentation Approaches
12.4.1 Segmenting
12.4.2 Topology-Based Methods
12.5 Matrix Rational Approximations
12.5.1 Padé Matrix Rational Approximations
12.5.2 Series Expansion into Eigenfunctions
12.6 Traveling Wave Formulations
12.6.1 Voltage Waves
12.6.2 Current Waves
12.6.3 Thévenin and Norton Equivalents
12.6.4 Terminal Admittance from Traveling Wave Model
12.6.5 Modal Traveling Waves
12.7 Lossless Traveling Wave Modeling
12.7.1 Delay Extraction for Lossless MTL
12.8 Traveling Wave Modeling of Scalar Lossy Transmission Lines
12.9 Representations Based on Multiple Reflections
12.9.1 The Delayed Vector Fitting Scheme
12.10 Basic Delay Extraction for Lossy MTL
12.11 Frequency-Dependent Traveling Wave Modeling
12.11.1 Modal Domain
12.11.2 Physical Domain
12.11.3 Delay Extraction and Optimization*
12.12 General Delayed-Rational Macromodeling
12.12.1 Delay Estimation
12.12.2 Passivity Enforcement
12.12.3 Equivalent Circuit Synthesis
12.13 Passivity of Traveling Wave Models*
12.14 Time-Domain Implementation for Traveling Wave Models
12.14.1 The Scalar Lossless Line
12.14.2 The Scalar Lossy Line
12.14.3 Lossy Multiconductor Transmission Lines
12.14.4 Examples
12.15 Discussion
Problems
Chapter 13 Applications
13.1 Modeling for Signal and Power Integrity
13.1.1 Prelayout Analysis of Backplane Interconnects
13.1.2 Full Package Analysis
13.1.3 Full Board Analysis and Simulation
13.1.4 High-Speed Channel Modeling and Simulation
13.1.5 Model Extraction from Measurements
13.2 Computational Electromagnetics
13.2.1 Dynamic Subcell Models in Time-Domain Solvers
13.2.2 Automatic Stopping Criteria for Time-Domain Solvers
13.2.3 VF-Based Adaptive Frequency Sampling
13.3 Small-Signal Macromodels for RF and AMS Applications
13.4 Modeling for High-Voltage Power Systems
13.4.1 Subnetwork Equivalencing
13.4.2 Power Transformer Modeling from Frequency Sweep Measurements
13.4.3 Power Transformer Modeling from Manufacturer's White-Box Model
13.5 Fluid Transmission Lines
13.6 Mechanical Systems
13.7 Ship Motion in Irregular Seas
13.8 Summary
Chapter 14 Summary and Outlook
14.1 Parameterized Macromodels
14.1.1 Parameterized Macromodels with Fixed Poles
14.1.2 Fully Parameterized Macromodels
14.1.3 Higher Dimensional Parameter Spaces
14.2 Open Issues
14.2.1 Optimal Passivity Enforcement
14.2.2 Systems with Many Ports
14.2.3 White-Box Model Identification and Tuning
14.2.4 Transmission Line Models
14.2.5 Delay Systems
14.2.6 Extension to NL Systems
14.2.7 Integration with other solvers
Appendix A Notation
Appendix B Acronyms
Appendix C Linear Algebra
Appendix D Optimization Templates
Appendix E Signals and Transforms
Bibliography
Index
Wiley Series in Microwave and Optical Engineering
EULA

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