Advanced Time Domain Modeling for Electrical Engineering

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
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