Advanced Time Domain Modeling for Electrical Engineering

Description

Time domain modeling is a fascinating world which brings together several complex phenomena and methods of essential interest to engineers. This book is a reference guide which discusses the most advanced time-domain modeling methods and applications in electromagnetics and electrical engineering. The book starts by clearly explaining why time-domain modeling may be worth doing; then, it provides guidelines about why some choices must be made among the principal modeling approaches and next guides the reader through the state of the art in time domain modeling, concerning either numerical and analytical methods, and applications. Finally, it highlights areas for future time-domain modeling research. The book is a collection of chapters written by leading research groups in the fields, following a logical development set out by the editor. Topics covered include finite element methods in time domain with applications to low-frequency problems; transient analysis of scattering from composite objects using late-time stable TDIEs; the transmission-line modeling method, partial element equivalent circuit method in time-domain; unconditionally stable time-domain methods; time-domain linear macromodeling, analytical techniques for transient analysis; the application of the finite-difference time-domain (FDTD) technique to lightning studies; modeling of lightning and its interaction with overhead conductors; transient behaviour of grounding systems; and statistics of electromagnetic reverberation chambers and their simulation through time domain modeling. Cover Contents About the editor Preface 1 Introduction to time-domain electromagnetics 1.1 Differential form of Maxwell’s equations 1.2 Integral form of Maxwell’s equations 1.3 Constitutive relations 1.4 Discontinuities and singularities 1.5 Initial conditions, boundary conditions, and causality 1.6 Fundamental theorems 1.6.1 Uniqueness theorem 1.6.2 Equivalence theorem 1.7 Wave equations 1.8 Transient uniform plane waves 1.9 Electromagnetic potentials and gauge transformations 1.9.1 Coulomb gauge 1.9.2 Lorenz gauge 1.9.3 Hertzian potentials 1.10 Potentials in unbounded media: retarded potentials 1.11 Time-domain dipole fields in free space 1.12 Volume integral representations of the fields 1.13 Surface integral representations of the fields 1.14 Time-domain far fields 1.15 Time-domain reciprocity and energy theorems 1.15.1 Reciprocity theorems 1.15.2 Poynting’s theorem and electromagnetic momentum 1.15.3 Time-domain optical theorem References 2 Finite-difference time-domain method Abstract 2.1 Impact of the finite-difference time-domain method (FDTD) 2.2 The FDTD algorithm 2.2.1 Discretization of Maxwell’s equations 2.3 CPML 2.4 Implementation 2.5 Subcell algorithms 2.5.1 Subcell models 2.5.2 Subcell for PEC objects 2.5.3 Subcell for thin-wires 2.5.4 Conformal grid for dielectrics 2.6 Summary References 3 Finite-element methods in time domain with applications to low-frequency problems 3.1 Quasistatic field formulations 3.1.1 MQS: A - j-formulation 3.1.2 MQS: A -formulation 3.1.3 EQS: j-formulation 3.2 Space discretization using finite elements 3.2.1 Function spaces 3.2.2 Weak formulation for MQS 3.2.3 Weak formulation for EQS 3.2.4 Initial-value and steady-state problems 3.3 Implicit time-stepping methods 3.3.1 Stability 3.3.2 Runge–Kutta methods 3.3.3 Application to the Eddy current problem 3.4 Solution of TP problems 3.4.1 Multi-harmonic diagonalization of cyclic systems 3.5 PnT integration methods 3.5.1 Parareal for IVPs 3.5.2 Multirate Parareal for IVPs 3.5.3 Parareal for TP problems 3.6 Numerical examples 3.6.1 Induction machine 3.6.2 Coaxial cable 3.7 Conclusions Acknowledgement References 4 Transient analysis of scattering from composite objects using late-time stable TDIEs 4.1 Introduction 4.2 Problem statement 4.3 Discretization and evaluation of inner products 4.3.1 Accurate evaluation of retarded potential integrals 4.3.2 Quasi-exact integration schemes 4.3.3 Integration on curvilinear elements 4.3.4 Separable expansion 4.3.5 Truncation error 4.3.6 Incorporation into method of moments scheme 4.3.7 Efficient evaluation of scalar potential 4.3.8 Extension to higher order space–time Galerkin scheme 4.3.9 Interpolation properties 4.4 Results 4.5 Summary 4.6 Acknowledgments References 5 Transmission-line modeling method—TLM 5.1 Introduction 5.1.1 Modeling for CEM 5.1.2 Classification of CEM and TLM 5.2 The basic TLM building elements 5.2.1 Lumped and distributed models of systems 5.2.2 TLM models in one dimension 5.2.3 TLM models, integration algorithms, and wave digital filters 5.3 TLM models in three dimensions 5.3.1 Mapping of fields to circuits in 3D 5.3.2 Scatter and connect in TLM for irregular meshes 5.3.3 TLM scattering in the modal domain and the unstructured mesh 5.3.4 Boundaries in TLM 5.3.5 Dispersion in TLM 5.3.6 TLM and other computational EM methods 5.4 Dealing with complexity in TLM 5.4.1 General principles of embedding fine objects in TLM 5.4.2 Embedded multi-conductor cables 5.4.3 Fractional boundaries 5.4.4 Embedding complex materials 5.4.5 Embedding arbitrarily shaped objects 5.4.6 Behavioral models 5.4.7 Near-field scans 5.4.8 TLM and stochastic models 5.5 Concluding remarks References 6 Partial element equivalent circuit method in time-domain 6.1 Integral formulation of Maxwell’s equations 6.1.1 Basis functions for the surfaces 6.1.2 Basis functions for volume currents 6.1.3 Dielectrics modeling 6.1.4 Enforcement of Kirchhoff’s voltage and current laws 6.1.5 DC solution 6.2 Computation of partial elements 6.3 Time-domain formulation 6.3.1 Quasi-static PEEC formulation 6.3.2 Improved MNA PEEC formulation 6.3.3 Delayed PEEC formulation 6.3.4 Temporal basis functions 6.4 Model order reduction of PEEC models 6.4.1 MOR of quasi-static PEEC models 6.4.2 MOR of delayed PEEC models 6.5 Examples 6.5.1 Stability analysis 6.5.2 Conductive coupling 6.5.3 Microstrip line 6.5.4 Radiated coupling 6.6 Conclusions References 7 Unconditionally stable time-domain methods 7.1 Introduction 7.2 ADI-FDTD algorithm 7.3 LOD-FDTD Algorithm 7.4 PML implementation 7.5 Iterative approach to reduce the splitting error 7.5.1 Iterative ADI-FDTD algorithm 7.5.2 Iterative LOD-FDTD algorithm 7.6 Extension to complex dispersive media 7.7 Split step, Leapfrog ADI, and hybrid-implicitexplicit FDTD methods 7.8 Further unconditionally stable time-domain methods 7.9 Summary and conclusions Acknowledgment References 8 Time-domain linear macromodeling 8.1 The macromodeling framework 8.1.1 The main objective 8.1.2 Black-box modeling: intrusive vs non-intrusive 8.2 Vector Fitting 8.2.1 Rational barycentric forms 8.2.2 The generalized Sanathanan–Koerner iteration 8.2.3 The basic VF scheme 8.2.4 Stability and realness 8.2.5 VF for multiport systems 8.2.6 State-space realizations 8.2.7 SPICE synthesis 8.3 Passivity 8.3.1 Checking passivity 8.3.2 Enforcing passivity 8.3.3 An example 8.4 Parameterized macromodels 8.4.1 Structure of parameterized models 8.4.2 The parameterized SK iteration 8.4.3 Enforcing stability 8.4.4 Descriptor realizations 8.4.5 Checking passivity 8.4.6 Enforcing passivity 8.5 Applications 8.5.1 A signal interconnect 8.5.2 An integrated inductor 8.6 Conclusions References 9 A charged particle traveling along the axis of a circular waveguide 9.1 Preliminary remarks 9.2 Solution in the laboratory frame 9.3 Evaluation of the integral 9.3.1 The factorization of the Bessel function J0(x) 9.3.2 The factorization of the modified Bessel function I0(x) 9.3.3 Evaluation of the zeros 9.3.4 The expansion of the integral 9.3.5 Acceleration of the convergence 9.3.6 An example 9.4 Solution in the particle frame 9.5 Transformation in the laboratory frame 9.6 Concluding remarks References 10 Analytical techniques for transient analysis 10.1 Cagniard-de Hoop method 10.1.1 Generalities 10.1.2 Thin metal sheet excited by a vertical dipole 10.1.3 Free-standing graphene sheet 10.2 Double-deformation method 10.3 Haddon leaky-mode method 10.4 Felsen–Niu unconventional spectral synthesis 10.5 Time-domain exact image theory References 11 The application of the finite-difference time-domain (FDTD) technique to lightning studies 11.1 Fundamentals of the FDTD method 11.1.1 FDTD basic equations in different coordinate systems 11.1.2 FDTD algorithm for LEMP simulations 11.2 Application 11.2.1 Lightning electromagnetic fields at close, medium, and far ranges 11.2.2 Lightning electromagnetic fields propagation over mountainous terrain 11.2.3 Lightning electromagnetic field propagation in the EIWG and its interaction with the lower D-region ionosphere 11.3 Conclusion and summary References 12 Modeling of lightning and its interaction with overhead conductors 12.1 Specification of channel-base current 12.2 Return-stroke models 12.2.1 Bruce–Golde (BG) model 12.2.2 TCS model 12.2.3 TL model 12.2.4 Modified TL with linear current decay with height (MTLL) model 12.2.5 Modified TL with exponential current decay with height (MTLE) model 12.3 Electromagnetic fields generated by lightning 12.3.1 General solution 12.3.2 Solutions for a vertical lightning channel 12.3.3 The effect of finite ground conductivity 12.4 Field-to-line coupling models 12.4.1 Taylor, Satterwhite, and Harrison model 12.4.2 Agrawal, Price, and Gurbaxani model 12.4.3 Rachidi model 12.5 Analytical solutions for lightning-induced voltage calculations 12.5.1 Step-function channel-base current 12.5.2 Linearly rising channel-base current References 13 Transient behaviour of grounding systems 13.1 Introduction of the transient behaviour of grounding systems 13.2 Discharge characteristics of soil under a lightning surge 13.2.1 Soil ionisation process 13.2.2 Method for observing soil discharge 13.2.3 Discharge characteristics of soil under lightning 13.2.4 Discussion of discharge characteristics of soil under lightning 13.3 Frequency variation of soil electrical parameters 13.3.1 Method for measuring frequency variation of soil electrical parameters 13.3.2 Frequency variation of soil resistivity and permittivity 13.4 Time-domain methods to simulate the transient behaviour of grounding grids 13.4.1 Equivalent circuit 13.4.2 Scalar electric potential in multilayer soil 13.4.3 Frequency-independent model 13.4.4 Soil ionisation effect 13.4.5 Determination of initial state for each time-step 13.5 Validation and application 13.5.1 Comparison with published results 13.5.2 Comparison with field test References 14 Statistics of electromagnetic reverberation chambers and their simulation through time domain modeling 14.1 Introduction to electromagnetic RCs 14.1.1 Stochastic description versus deterministic solution of the electromagnetic wave equation 14.1.2 Random plane wave spectrum 14.1.3 Modal theory 14.1.4 About the relevance of full-wave simulations for RC 14.2 Numerical modeling of RCs 14.2.1 Numerical modeling using 3-D solvers of Maxwell’s equations 14.2.2 Geometrical optics approximation 14.3 Time-domain simulations using theory of images and ray-tracing 14.3.1 Introduction 14.3.2 Image theory of elementary currents 14.3.3 Application to cavities 14.3.4 Preliminary result example 14.4 Simulation of RCs through image theory 14.4.1 Assessment of the loss coefficient 14.4.2 Current source in arbitrary orientation and rectangular components of electric field 14.4.3 Stirring process 14.4.4 Time domain results 14.4.5 Frequency domain results 14.5 Discussion 14.6 Acknowledgments References 15 Analysis of a class of dynamical systems with applications to power conversion circuits 15.1 Introduction 15.2 An overview on dynamical systems: basic principles 15.2.1 Modeling: vector fields 15.2.2 Phase portraits 15.2.3 Equilibrium points and stability of planar linear systems 15.3 Equilibrium points in nonlinear planar systems and their stability analysis 15.3.1 Linearization 15.3.2 Basic concepts for bifurcation analysis 15.4 Floquet theory for stability analysis of limit cycles 15.5 Dynamic behavior of Filippov control systems and concept of sliding mode motion 15.5.1 A simple example of Filippov system: the double integrator with relay feedback 15.5.2 Equivalent control within sliding mode region 15.6 Application to a resonant power converter 15.6.1 System description and modeling 15.6.2 The dynamics on the escaping sliding region 15.6.3 The crossing switching dynamics: simulations from the switched model 15.6.4 Determination of crossing limit cycles and their stability analysis 15.6.5 Nonsmooth limit cycle bifurcations 15.6.6 Summary of the bifurcation scenario in the PRC under ZCS control 15.7 Acknowledgments References 16 Pure time domain multiconductor transmission line formalism 16.1 Time domain electromagnetic field equations 16.2 Time-domain MTL equations 16.2.1 MTL currents and voltages 16.2.2 Governing equation of i/z 16.2.3 Governing equation of i/z 16.2.4 MTL conservation laws 16.3 Skin effect in the time domain 16.4 Frequency-domain MTL equations References 17 Shielding in time domain 17.1 Rationale: when a direct TD approach is mandatory, when convenient 17.2 Reference standards and commonly used FD approaches 17.2.1 NSA 94-106 setup 17.2.2 IEEE Std 299 setup 17.3 Local figures of merit in TD: when they are sufficient 17.4 Global figures of merit in TD: when they are recommended 17.5 Statistical approach 17.5.1 When it is useful 17.5.2 Statistical analyses 17.6 Results 17.7 A word of caution: the influence of load on the shielding performance References Index Back Cover