Passive Macromodeling Theory and Applications

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 char...

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Bibliographic Details
Main Authors Grivet-Talocia, Stefano, Gustavsen, Bjorn
Format eBook
LanguageEnglish
Published Newark Wiley 2015
John Wiley & Sons, Incorporated
Edition1
Subjects
Computer simulation
Electric power systems
Electromagnetic interference
Online AccessGet full text
ISBN1119140951
9781119140955
1118094913
9781118094914
1119140935
9781119140931
DOI10.1002/9781119140931

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Table of Contents:
  • 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
  • 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 H∞ 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
  • 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
  • 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
  • 9.3.11 Bounded Real Lemma for Descriptor Systems
  • 6.7 SUBSPACE-BASED IDENTIFICATION* -- 6.8 LOEWNER MATRIX INTERPOLATION* -- PROBLEMS -- CHAPTER 7: THE VECTOR FITTING ALGORITHM -- 7.1 THE SANATHANAN-KOERNER ITERATION -- 7.2 THE GENERALIZED SANATHANAN-KOERNER ITERATION -- 7.3 FREQUENCY-DOMAIN VECTOR FITTING -- 7.4 CONSISTENCY AND CONVERGENCE -- 7.5 PRACTICAL VF IMPLEMENTATION -- 7.6 RELAXED VECTOR FITTING -- 7.7 TUNING VF -- 7.8 TIME-DOMAIN VECTOR FITTING -- 7.9 z-DOMAIN VECTOR FITTING -- 7.10 ORTHONORMAL VECTOR FITTING -- 7.11 OTHER VARIANTS -- 7.12 NOTES ON OVERFITTING AND ILL-CONDITIONING -- 7.13 APPLICATION EXAMPLES -- PROBLEMS -- CHAPTER 8: ADVANCED VECTOR FITTING FOR MULTIPORT PROBLEMS -- 8.1 INTRODUCTION -- 8.2 ADAPTING VF TO MULTIPLE RESPONSES -- 8.3 MULTIPORT FORMULATIONS -- 8.4 ENFORCING RECIPROCITY -- 8.5 COMPRESSED MACROMODELING -- 8.6 ACCURACY CONSIDERATIONS -- 8.7 OVERCOMING ERROR MAGNIFICATION -- PROBLEMS -- CHAPTER 9: PASSIVITY CHARACTERIZATION OF LUMPED LTI SYSTEMS -- 9.1 INTERNAL CHARACTERIZATION OF PASSIVITY -- 9.2 PASSIVITY OF LUMPED IMMITTANCE SYSTEMS -- 9.3 PASSIVITY OF LUMPED SCATTERING SYSTEMS -- 9.4 ADVANCED PASSIVITY CHARACTERIZATION -- PROBLEMS -- CHAPTER 10: PASSIVITY ENFORCEMENT OF LUMPED LTI SYSTEMS -- 10.1 PASSIVITY CONSTRAINTS FOR LUMPED LTI SYSTEMS -- 10.2 STATE-SPACE PERTURBATION -- 10.3 ASYMPTOTIC PASSIVITY ENFORCEMENT -- 10.4 IMAGINARY POLES OF IMMITTANCE SYSTEMS -- 10.5 LOCAL PASSIVITY ENFORCEMENT -- 10.6 PASSIVITY ENFORCEMENT VIA HAMILTONIAN PERTURBATION -- 10.7 LINEAR MATRIX INEQUALITIES -- 10.8 COMPUTATIONAL COST -- 10.9 ADVANCED ACCURACY CONTROL -- 10.10 LEAST-SQUARES RESIDUE PERTURBATION -- 10.11 ALTERNATIVE FORMULATIONS -- 10.12 DESCRIPTOR SYSTEMS* -- PROBLEMS -- CHAPTER 11: TIME-DOMAIN SIMULATION -- 11.1 DISCRETIZATION OF ODE SYSTEMS -- 11.2 INTERCONNECTION OF MACROMODELS -- 11.3 DIRECT CONVOLUTION -- 11.4 INTERFACING STATE-SPACE MACROMODELS
  • 11.5 INTERFACING POLE-RESIDUE MACROMODELS -- 11.6 EQUIVALENT CIRCUIT SYNTHESIS -- PROBLEMS -- CHAPTER 12: TRANSMISSION LINES AND DISTRIBUTED SYSTEMS -- 12.1 INTRODUCTION -- 12.2 MULTICONDUCTOR TRANSMISSION LINES -- 12.3 DIRECT MACROMODELING APPROACHES -- 12.4 LUMPED SEGMENTATION APPROACHES -- 12.5 MATRIX RATIONAL APPROXIMATIONS -- 12.6 TRAVELING WAVE FORMULATIONS -- 12.7 LOSSLESS TRAVELING WAVE MODELING -- 12.8 TRAVELING WAVE MODELING OF SCALAR LOSSY TRANSMISSION LINES -- 12.9 REPRESENTATIONS BASED ON MULTIPLE REFLECTIONS -- 12.10 BASIC DELAY EXTRACTION FOR LOSSY MTL -- 12.11 FREQUENCY-DEPENDENT TRAVELING WAVE MODELING -- 12.12 GENERAL DELAYED-RATIONAL MACROMODELING -- 12.13 PASSIVITY OF TRAVELING WAVE MODELS* -- 12.14 TIME-DOMAIN IMPLEMENTATION FOR TRAVELING WAVE MODELS -- 12.15 DISCUSSION -- PROBLEMS -- CHAPTER 13: APPLICATIONS -- 13.1 MODELING FOR SIGNAL AND POWER INTEGRITY -- 13.2 COMPUTATIONAL ELECTROMAGNETICS -- 13.3 SMALL-SIGNAL MACROMODELS FOR RF AND AMS APPLICATIONS -- 13.4 MODELING FOR HIGH-VOLTAGE POWER SYSTEMS -- 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 -- 14.2 OPEN ISSUES -- APPENDIX A: NOTATION -- GENERAL SYMBOLS AND ABBREVIATIONS -- NUMERIC FIELDS AND RELATED OPERATORS -- SCALARS, VECTORS, AND MATRICES -- SIGNALS, SYSTEMS, AND TRANSFER FUNCTIONS -- INTEGRALS AND TRANSFORMS -- FUNCTION SPACES -- ELECTROMAGNETIC FIELDS -- CIRCUITS -- APPENDIX B: ACRONYMS -- APPENDIX C: LINEAR ALGEBRA -- C.1 LINEAR SUBSPACES -- C.2 MATRICES -- C.3 LINEAR SYSTEMS -- C.4 EIGENVALUES -- C.5 SINGULAR VALUES -- C.6 VECTOR AND MATRIX NORMS -- C.7 MATRIX TRANSFORMATIONS AND FACTORIZATIONS -- C.8 GENERALIZED EIGENVALUES -- C.9 MATRIX FUNCTIONS -- C.10 THE SHERMANN-MORRISON-WOODBURY LEMMA -- C.11 BLOCK MATRICES
  • Intro -- WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING -- TITLE PAGE -- COPYRIGHT -- DEDICATION -- TABLE OF CONTENTS -- PREFACE -- ABOUT THIS BOOK -- SOME REMARKS ON NOTATION -- ACKNOWLEDGMENTS -- CHAPTER 1: INTRODUCTION -- 1.1 WHY MACROMODELING? -- 1.2 SCOPE -- 1.3 MACROMODELING FLOWS -- 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 -- 2.2 LINEAR TIME-INVARIANT SYSTEMS -- 2.3 FREQUENCY-DOMAIN CHARACTERIZATIONS -- 2.4 LAPLACE AND FOURIER TRANSFORMS -- 2.5 SIGNAL AND SYSTEM NORMS* -- 2.6 MULTIPORT REPRESENTATIONS -- 2.7 PASSIVITY -- 2.8 STABILITY AND CAUSALITY -- 2.9 BOUNDARY VALUES AND DISPERSION RELATIONS* -- 2.10 PASSIVITY CONDITIONS ON THE IMAGINARY AXIS* -- PROBLEMS -- CHAPTER 3: LUMPED LTI SYSTEMS -- 3.1 AN EXAMPLE FROM CIRCUIT THEORY -- 3.2 STATE-SPACE AND DESCRIPTOR FORMS -- 3.3 THE ZERO-INPUT RESPONSE -- 3.4 INTERNAL STABILITY -- 3.5 THE LYAPUNOV EQUATION -- 3.6 THE ZERO-STATE RESPONSE -- 3.7 OPERATIONS ON STATE-SPACE SYSTEMS -- 3.8 GRAMIANS -- 3.9 RECIPROCAL STATE-SPACE SYSTEMS -- 3.10 NORMS -- PROBLEMS -- CHAPTER 4: DISTRIBUTED LTI SYSTEMS -- 4.1 ONE-DIMENSIONAL DISTRIBUTED CIRCUITS -- 4.2 TWO-DIMENSIONAL DISTRIBUTED CIRCUITS* -- 4.3 GENERAL ELECTROMAGNETIC CHARACTERIZATION -- PROBLEMS -- CHAPTER 5: MACROMODELING VIA MODEL ORDER REDUCTION -- 5.1 MODEL ORDER REDUCTION -- 5.2 MOMENT MATCHING -- 5.3 REDUCTION BY PROJECTION -- 5.4 REDUCTION BY TRUNCATION -- 5.5 ADVANCED MODEL ORDER REDUCTION* -- PROBLEMS -- CHAPTER 6: BLACK-BOX MACROMODELING AND CURVE FITTING -- 6.1 BASIC CURVE FITTING -- 6.2 DIRECT RATIONAL FITTING -- 6.3 LINEARIZATION VIA WEIGHTING -- 6.4 ASYMPTOTIC POLE-ZERO PLACEMENT -- 6.5 ARMA MODELING -- 6.6 PRONY'S METHOD
  • C.12 SCHUR COMPLEMENTS -- C.13 HAMILTONIAN MATRICES -- C.14 SPECTRAL PERTURBATIONS -- C.15 SOME USEFUL TOOLS -- APPENDIX D: OPTIMIZATION TEMPLATES -- D.1 NUMERICAL CONDITIONING AND STABILITY -- D.2 UNDERDETERMINED LINEAR SYSTEMS -- D.3 OVERDETERMINED LINEAR SYSTEMS -- D.4 CONVEX SETS AND FUNCTIONS -- D.5 UNCONSTRAINED OPTIMIZATION -- D.6 CONSTRAINED OPTIMIZATION -- APPENDIX E: SIGNALS AND TRANSFORMS -- E.1 ANALYTIC FUNCTIONS -- E.2 RATIONAL FUNCTIONS -- E.3 SIGNALS AND DISTRIBUTIONS -- E.4 LAPLACE TRANSFORM -- E.5 FOURIER TRANSFORM -- E.6 HILBERT TRANSFORM -- E.7 F-TRANSFORM -- E.8 CONTINUOUS-TIME AND DISCRETE-TIME SIGNALS -- E.9 THE DISCRETE FOURIER TRANSFORM -- E.10 NUMERICAL INVERSION OF THE LAPLACE TRANSFORM -- BIBLIOGRAPHY -- INDEX -- WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING -- END USER LICENSE AGREEMENT