Global modeling of nonlinear circuits using the finite‐difference Laguerre time‐domain/alternative direction implicit finite‐difference time‐domain method with stability investigation

This paper describes a new unconditionally stable numerical method for the full‐wave physical modeling of semiconductor devices by a combination of the finite‐difference Laguerre time‐domain (FDLTD) and alternative direction implicit finite‐difference time‐domain (ADI‐FDTD) approaches. The unconditionally stable method by using FDLTD scheme for the electromagnetic model and semi‐implicit ADI‐FDTD approach for the active model leads to a significant decrease in the full‐wave simulation time. Numerical simulations of an example transistor and a power amplifier show the efficiency of presented method for the full‐wave simulation of mm‐wave active circuits. Copyright © 2012 John Wiley & Sons, Ltd.     

Transient analysis of printed lines using finite‐difference time‐domain method

Comprehensive studies of ultra‐wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full‐wave 3D finite‐difference time‐domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_r = 1) and with (ϵ_r > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Physical interpretations of the simulation results are discussed in the paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Electromagnetic radiation from vertical dipole antennas near air–lossy soil interface—a finite‐difference time‐domain simulation

Radiation from vertical dipole antennas, which are located over or under the surface of lossy earth, is analysed by the finite‐difference time‐domain (FDTD) method in cylindrical coordinates. A novel generalized perfectly matched layer (PML) has been developed and used for the truncation of the lossy soil. In order to decrease the memory requirements and for having an accurate modelling, an efficient ‘non‐uniform’ mesh generation scheme is used. The excitation is considered in the form of sine carrier modulated by Gaussian pulse (SCMGP) and in each time step, computation is limited to that part of the mesh where the radiated pulse is passing (computational window). This could considerably reduce the required CPU time. In this manner, large‐scale problems can be solved and the values of radiated field at far distances (up to 500λ₀ in this work) can be obtained directly by the FDTD method. The frequency‐domain results are calculated from the obtained time‐domain results by taking the Fourier transform. The spatial distributions of the amplitude and phase of radiated field are shown in illustrations for different types of soil and different positions of antenna. The influence of the lossy soil on dipole's admittance is also shown. Copyright © 2005 John Wiley & Sons, Ltd.     

A three‐dimensional mesh refinement algorithm with low boundary reflections for the finite‐difference time‐domain simulation of metallic structures

We present a method for including areas of high grid density into a general grid for the finite‐difference time‐domain method in three dimensions. Reflections occurring at the boundaries separating domains of different grid size are reduced significantly by introducing appropriate interpolation methods for missing boundary points. Several levels of refinement can be included into one calculation using a hierarchical refinement architecture. The algorithm is implemented with an auxiliary differential equation technique that allows for the simulation of metallic structures. We illustrate the performance of the algorithm through the simulation of metal nano‐particles included in a coarser grid and by investigating gold optical antennas. Copyright © 2009 John Wiley & Sons, Ltd.     

Extending the enlarged cell and uniformly stable conformal techniques to modeling curved conductors in two‐dimensional high‐order finite‐difference time‐domain algorithms

The critical tool of modeling irregularly shaped perfect conductors is developed for the extended‐stencil high‐order two‐dimensional M24 variant of the finite‐difference time‐domain (FDTD) method. Two standard FDTD conformal approaches are analyzed and successfully extended to work accurately with M24. They both afford higher order convergence with respect to mesh density than a previously developed technique, which better matches M24's characteristics. Both approaches rely on borrowing weighted electromotive forces from nearby extended‐stencil cells to ensure accuracy and numerical stability while the overall algorithm is efficiently operated at the maximum allowable time steps by FDTD and M24 theories. Validation examples demonstrate that M24's amplitude and phase accuracies using coarse numerical meshes were not compromised. Copyright © 2012 John Wiley & Sons, Ltd.     

An overlapping Yee finite‐difference time‐domain method for material interfaces between anisotropic dielectrics and general dispersive or perfect electric conductor media

A novel stable anisotropic finite‐difference time‐domain (FDTD) algorithm based on the overlapping cells is developed for solving Maxwell's equations of electrodynamics in anisotropic media with interfaces between different types of materials, such as the interface between anisotropic dielectrics and dispersive medium or perfect electric conductor (PEC). The previous proposed conventional anisotropic FDTD methods suffer from the late‐time instability due to the extrapolation of the field components near the material interface. The proposed anisotropic overlapping Yee FDTD method is stable, as it relies on the overlapping cells to provide the collocated field values without any interpolation or extrapolation. Our method has been applied to simulate electromagnetic invisibility cloaking devices with both anisotropic dielectrics and PEC included in the computational domain. Numerical results and eigenvalue analysis confirm that the conventional anisotropic FDTD method is weakly unstable, whereas our method is stable. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of proposed thin‐wire model in finite difference time domain method

Thin‐wire approximation in the finite difference time domain (FDTD) method is important in saving computer resources and truncating central processing unit (CPU) time. Previously, thin wires were mainly realized using the true thin wire (TTW) model, in which electric field components along the wire axis are set at zero, and three methods, in which electric field components along the wire axis are also set at zero and the medium around thin wires is replaced depending on wire radius, are hereafter called the RM model. The former is the most conventional and widely used method; however, its resultant radius is 0.23Δs, supposing that the space under consideration is divided by cubic cells with a Δs of the side length of FDTD cells. The first method of the RM model can realize thin wires having a radius of about 0.15Δs under the conditions we used, in which the time interval is set at a value which is slightly less than Δt_c, e.g. 0.9999t_c, where Δt_c is defined by the Courant condition; in the case of a thin wire having a radius less than 0.15Δs, the FDTD computation suffers from numerical instability. The second method can realize a thin wire having a radius of about 10⁻⁴Δs. We need some changes in the numerical electromagnetic analysis program based on the FDTD method to employ these models. The third of the RM model, which has already been proposed by the author and in which the relative permittivity and relative permeability of four FDTD cells closest to a thin wire are replaced according to the radius of the thin wire and Δs, could realize thin wires having a radius of about 10⁻⁶Δs without changing the program and numerical instability. In this paper, the third model is extensively investigated and it is demonstrated that we can deal with a thin wire with a radius of about 10⁻⁹Δs without numerical instability. The maximum difference in the evaluation of the surge impedance of an open‐ended horizontal wire located 5 m above a perfectly conducting ground is less than 5%. We can easily use the third model even though the program, which is available, has no the specific function of thin‐wire approximation. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Higher‐order finite‐difference schemes with reduced dispersion errors for accurate time‐domain electromagnetic simulations

The potential for developing higher‐order finite‐difference time‐domain (FDTD) schemes with reduced phase errors is investigated in the present paper. Using the classic (2,4) FDTD method as the basis of this study, electromagnetic wave propagation is accurately reproduced in the discretized space by replacing isotropic materials with modified, anisotropic in general, ones. The use of such artificial materials improves the simulation's precision significantly around a specific frequency, yet the overall error remains small at a considerably wide bandwidth; therefore, this algorithm can be useful for wideband problems as well. Additionally, it is shown that an even better single‐frequency performance can be attained, when the modified materials are combined with systematically calculated spatial operators. Pursuing a more wideband enhancement of the (2,4) technique, a version realizing more accurate results at almost all frequencies that can be coupled in a staggered grid is derived. Furthermore, novel spatial operators are introduced, with the distinct feature of using extended stencils in more than one directions. It turns out that when such operators are incorporated, a scheme that combines the aforementioned features can be obtained. The theoretical findings of this investigation are verified in a sequence of numerical tests, involving free‐space and guided‐wave propagation, as well as the determination of a cavity's resonant frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Broadband characteristics analysis of semicircle‐type bow‐tie antenna with hole slots

For electromagnetic compatibility, broadband antennas are important for measurements of fast pulse transient electromagnetic phenomena and broadband characteristics due to noise and high‐frequency interference. We analyzed the characteristics of a semicircle type bow‐tie antenna with various slots using the FDTD method. It was shown from the simulation results that the shape and position of the slot influenced greatly the broadband characteristics of the antenna. We confirmed that a semicircle type bow‐tie antenna with a triangle slot was effective for a broadband antenna. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(4): 47–53, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20252     

反激式变换器电磁辐射的FDTD仿真与分析

开关电源电磁辐射发射容易超出EMC标准限值,有必要对其形成机理、特性和预测进行研究。本文在建立电容、变压器、PCB引线、半导体开关等元器件模型基础上,对Flyback开关电源进行了时域有限差分(FDTD)建模,仿真研究了其在开放空间中远场电磁辐射的分布和规律。仿真结果表明开关电源输入/输出电缆是电磁辐射的主要影响因素,并验证了共模电感对远场电磁辐射的抑制作用。     

A modified finite‐difference time‐domain method for analysing field‐to‐transmission line coupling of telecommunication system signals

A modified finite‐difference time‐domain (FDTD) code is presented for the line response characterization of a transmission line illuminated by a Gaussian pulse‐modulated electromagnetic signal. The final expressions are transformed according to the complex‐envelope representation in order to omit the high‐frequency carrier contribution and thus provide an accurate solution of the coupling phenomenon by avoiding the computational burden of the conventional FDTD algorithm. Comparison results between the conventional FDTD method and the modified one are presented, showing the advantages of the novel method. Copyright © 2002 John Wiley & Sons, Ltd.     

A quasi‐planar incident wave excitation for time‐domain scattering analysis of periodic structures

We present a quasi‐planar incident wave excitation for time‐domain scattering analysis of periodic structures. It uses a particular superposition of plane waves that yields an incident wave with the same periodicity as the periodic structure itself. The duration of the incident wave is controlled by means of its frequency spectrum or, equivalently, the angular spread in its constituting plane waves. Accuracy and convergence properties of the method are demonstrated by scattering computations for a planar dielectric half‐space. Equipped with the proposed source, a time‐domain solver based on linear elements yields an error of roughly 1% for a resolution of 20 points per wavelength and second‐order convergence is achieved for smooth scatterers. Computations of the scattering characteristics for a sinusoidal surface and a random rough surface show similar performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Investigation of numerical time‐integrations of Maxwell's equations using the staggered grid spatial discretization

The Yee‐method is a simple and elegant way of solving the time‐dependent Maxwell's equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time‐steps. This is why, during the last decade, the main goal was to construct such methods that are unconditionally stable. This means that the time‐step can be chosen based only on accuracy instead of stability considerations. In this paper we give a uniform treatment of methods that use the same spatial staggered grid approximation as the classical Yee‐method. Three other numerical methods are discussed: the Namiki–Zheng–Chen–Zhang alternating direction implicit method (NZCZ), the Kole–Figge‐de Raedt method (KFR) and a Krylov‐space method. All methods are discussed with non‐homogeneous material parameters. We show how the existing finite difference numerical methods are based on the approximation of a matrix exponential. With this formulation we prove the unconditional stability of the NZCZ method without any computer algebraic tool. Moreover, we accelerate the Krylov‐space method with a skew‐symmetric formulation of the semi‐discretized equations. Our main goal is to compare the methods from the point of view of the computational speed. This question is investigated in ID numerical tests. Copyright © 2005 John Wiley & Sons, Ltd.     

An accurate time‐domain model of transmission lines with frequency‐dependent parameters

Linear lossy two‐conductor transmission line can be modelled as dynamic two ports in the time domain, via the describing input and transfer impulse responses. This convolution technique is very effective when dealing with networks composed of transmission lines with frequency‐dependent parameters and non‐linear and/or time‐varying circuits. The paper carries out an accurate analysis of this model, in the most general case of lines with frequency‐dependent parameters. For such lines it is not possible to evaluate analytically the impulse responses, nor is it possible to catch them numerically, due to the presence of irregular terms, such as Dirac pulses, terms that numerically behave as Dirac pulses, and functions of the type 1/t^ρ with 0 < ρ <1. A simple method is proposed to evaluate exactly all the irregular terms of the impulse responses: once these irregular parts have been extracted, the regular remainders are easily evaluated numerically. This method is applied to analyse lines with frequency‐dependent parameters of practical interest, such as superconductor transmission lines, power lines above a finite conductivity ground, lines with frequency‐dependent dielectric losses and lines with normal and anomalous skin‐effect. Numerical simulations are carried out for illustration. Copyright © 2000 John Wiley & Sons, Ltd.     

Stabilization control of multi‐machine power systems by adaptive power system stabilizer using frequency domain analysis

To improve electric power system transient stability, synchronous generators are generally equipped with controllers such as AVR, PSS, and GOV. Fixed parameter controllers degrade control performance, since various oscillation modes occur depending on system conditions. This paper presents an adaptive power system stabilizer (PSS) using frequency domain analysis for improving the transient stability of a multimachine system. In the proposed method, first, the frequency components of the generator swings are detected by the FFT. The conventional PSS parameters are tuned online by a fuzzy controller and frequency domain analysis. We verify the proposed adaptive PSS using frequency domain analysis, which can damp the generator swings effectively. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 10–20, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10129     

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

A time‐domain method for calculating the band structure of one‐dimensional periodic structures is proposed. During the time‐stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix‐exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix–vector multiplication involved in each time‐step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finite‐difference time‐domain (FDTD) method. The time‐step with which the method runs stably can be much larger than the Courant–Friedrichs–Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large‐scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix‐pruning operation can be very effectively performed. In the numerical experiments for large‐scale quasi‐periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

A numerical scheme is presented for the time‐domain finite‐element modeling of an electrically and magnetically lossy and dispersive medium in the dual‐field domain‐decomposition method. Existing approaches for modeling doubly lossy and dispersive media are extended to the dual‐field case, yielding a general dual‐field domain‐decomposition scheme for modeling large‐scale electromagnetic problems involving such media. A quantitative analysis is performed to estimate the error induced by the modeling of medium dispersion. Copyright © 2012 John Wiley & Sons, Ltd.     

Steady‐state solutions of a voltage source converter with dq‐frame controllers by means of the time‐domain method

A voltage source converter (VSC) is one of the most widely used power converters in a power system. In this paper, a time‐domain‐based accelerated steady‐state method is proposed to solve for a closed‐loop pulse‐width modulated (PWM) VSC with dq‐frame controllers, which is able to account for the harmonic interactions between the converter and the rest of the power network, between the AC and DC sides of a VSC, and between the converter and its controllers. The proposed time‐domain method is based on the modified time‐domain shooting method, where the Jacobian matrix is updated by the quasi‐Newtons method. This will drastically increase the computation efficiency as it avoids re‐evaluating and inverting the Jacobian matrix, whose size is usually very large for a PWM‐VSC due to high number of times of switching. All the results are shown to be consistent with those obtained by a PSCAD/EMTDC model, which has been validated with the experiment in a previous publication. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Modelling of lossy curved surfaces in the 3‐D frequency‐domain finite‐difference methods

A conformal first‐order or Leontovic surface‐impedance boundary condition (SIBC) for the modelling of fully three‐dimensional (3‐D) lossy curved surfaces in a Cartesian grid is presented for the frequency‐domain finite‐difference (FD) methods. The impedance boundary condition is applied to auxiliary tangential electric and magnetic field components defined at the curved surface. The auxiliary components are subsequently eliminated from the formulation resulting in a modification of the local permeability value at boundary cells, allowing the curved 3‐D surface to be described in terms of Cartesian grid components. The proposed formulation can be applied to model skin‐effect loss in time‐harmonic driven problems. In addition, the impedance matrix can be used as a post‐processor for the eigenmode solver to calculate the wall loss. The validity of the proposed model is evaluated by investigating the quality factors of cylindrical and spherical cavity resonators. The results are compared with analytic solutions and numerical reference data calculated with the commercial software package CST Microwave Studio™ (MWS). The convergence rate of the results is shown to be of second‐order for smooth curved metal surfaces. The overall accuracy of the approach is comparable to that of CST MWS™. Copyright © 2006 John Wiley & Sons, Ltd.