Frequency‐dependent modeling of transmission lines using bergeron cells

This paper proposes using Bergeron's equivalent circuit with traveling time equal to the simulation time step as an element for frequency‐dependent modeling of transmission lines for electromagnetic transient (EMT) simulations of power systems. According to the simulation time step used, a transmission line is divided into aforementioned Bergeron's equivalents, each of which is called a ‘Bergeron cell’ in this paper. In this way, the traveling‐wave nature of a line is represented by the cascaded Bergeron cells. Then, the frequency‐dependent loss nature of the line is represented by a matrix partial fraction expansion, and this is inserted at each connection point of the Bergeron cells in the form of a multiphase Norton equivalent. Since the frequency‐dependent loss is modeled in the dimension of impedance, the change of the line length is easily taken into account by a simple multiplication. This methodology thus allows variable‐length modeling and completely avoids modal decomposition in both model identification and EMT simulation stages. The proposed methodology is applied to the frequency‐dependent modeling of overhead and submarine‐cable transmission lines, and its accuracy is assessed.     

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.     

Wave propagation on power cables with special regard to metallic screen design

The high frequency properties of coaxial power cables are modeled using time- and frequency-domain numerical simulations. This is required due to the complex helical structure of the outer metallic screen. The finite element (FEM) and finite difference time domain methods (FDTD) have been employed to study the effect of screen spiralization. It is established that this screen design causes a dependence of the cable high frequency characteristics on the surrounding medium. Analytical model based on modal analysis of wave propagation in coaxial cables confirms the numerical observations     

Proposal of an alternative transmission line model for symmetrical and asymmetrical configurations

This article shows a transmission line model for simulation of fast and slow transients, applied to symmetrical or asymmetrical configurations. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents a practical procedure to model three-phase transmission lines directly in time domain, without the explicit or implicit use of inverse transforms. In three-phase representation, analysis modal techniques are applied to decouple the phases in their respective propagation modes, using a correction procedure to set a real and constant matrix for untransposed lines with or without vertical symmetry plane. The proposed methodology takes into account the frequency-dependent parameters of the line and in order to include this effect in the state matrices, a fitting procedure is applied. To verify the accuracy of the proposed state-space model in frequency domain, a simple methodology is described based on line distributed parameters and transfer function associated with input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust integration procedure to solve the state equations, enabling transient and steady-state simulations. The results obtained by the proposed methodology are compared with several established transmission line models in EMTP, taking into account an asymmetrical three-phase transmission line. The principal contribution of the proposed methodology is to handle a steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behavior, by a practical procedure applied directly in time domain for symmetrical or asymmetrical representations.     

PML absorbing boundary condition for the integral‐based high‐order FV24 FDTD algorithm

An integral equations‐based perfectly matched layers (PML) implementation is presented for the highly phase‐coherent FV24 finite‐difference time‐domain (FDTD) algorithm. The implementation allows including field values off the grid axes in the split‐field PML formulation conserving in the process the continuity and phase coherency of the FV24 algorithm when modeling absorbing boundary conditions (ABCs). It also eliminates the need for cumbersome subgridded low‐order FDTD subregions that until now were required to model PML ABCs within integral‐based high‐order FDTD simulations. The developed approach was numerically tested and found to match the PML behavior of the standard FDTD method at normal wave incidence on ABC boundaries and exceeds it at highly oblique wave incidence. This development serves to improve the capability and practicality of the computationally efficient FV24 algorithm when modeling electrically large structures in 3‐D space. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

On the development of efficient FDTD‐PML formulations for general dispersive media

A novel implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) to terminate the finite‐difference time‐domain (FDTD) algorithm for general dispersive and negative index materials is presented. The proposed formulation also adopts the complex frequency‐shifted (CFS) approach, involves simple FDTD expressions and avoids complex arithmetic. Several FDTD‐PML simulations with different parameters are conducted for the termination of various dispersive media validating the stability, accuracy and effectiveness of the schemes and indicating the advantage of the CFS‐PML. Copyright © 2008 John Wiley & Sons, Ltd.     

Modal decoupling of overhead transmission lines using real and constant matrices: Influence of the line length

The Clarke’s matrix is a well-known real and constant transformation matrix used for modal transformation in three-phase transmission lines modeling. Although modal analysis has been widely discussed in the technical literature on power system modeling, a new content is approached in this research proving that the approximation using an exact and constant modal transformation matrix depends on both the frequency-dependent parameters and transmission line’s length. As an important conclusion, the approach using the Clarke’s matrix leads to more accurate results considering long transmission lines. There are two methods for modal decoupling in power systems modeling. The first uses only a single constant and real transformation matrix during the entire modeling/simulation routine. The second uses the frequency-dependent transformation matrix for parameters decoupling into the propagation modes and the Clarke’s matrix for mode-to-phase transformation of voltage and current values during simulations. The accuracy of these two modeling/simulation processes are evaluated, in the time and frequency domains, based on results obtained from a reference routine that employs the exact frequency-dependent matrix in modal transformations and numerical transforms for simulation in the time domain. The proposed analysis proves that the accuracy of both methods varies with the line length during electromagnetic transient simulations that leads to peak errors up to approximately 10%. The influence of the line length in modal analysis techniques was not approached in previous references on power system modeling, which represents the original contribution of this paper.     

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.     

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.     

Simple and accurate approaches to implement the complex trans‐conductance suited for time‐domain simulators for small‐signal and large‐signal table‐based models

This paper focuses on the implementation of table‐based models of high‐frequency transistors for time‐domain simulators at microwave and mm‐wave frequencies. In this frequency range, the channel is not capable of responding to the excitation instantaneously therefore, a delay‐time exists between the channel response and the channel excitation. This delay is represented by a complex trans‐conductance in terms of circuit elements. The high‐frequency models of transistors are required to have the implementation of complex trans‐conductance, where the complex part accounts mathematically for the delay‐time between the channel response and the channel excitation. This paper presents simple and accurate approaches to incorporate the complex trans‐conductance in both small‐signal and large‐signal table‐based models for time‐domain simulators (MOS‐AK International Meeting. Eindhoven, Netherlands, April 2008). Implementation approach for each model, small‐signal and large‐signal, is presented in separated sections. In the first step, the delay is realized by the introduction of an ideal transmission line between the channel excitation and the channel response. As transmission lines are not generally suitable for time‐domain simulations, a lumped element equivalent network is introduced in the second step. The latter approach is fully compatible with time‐domain simulators but frequency limitation, determined by the delay‐time value itself, is introduced. Then the implementation of the complex trans‐conductance in large‐signal model is introduced. In terms of large‐signal behavior, delay‐time is important to achieve a non‐quasi static model. Yet again there is limitation in terms of the frequency range that is determined by the delay value itself. The methodology is illustrated on the small‐signal and the large‐signal equivalent circuit of a Multi‐Fin MOSFET transistor. Simulations are carried out by Cadence Spectre and Agilent ADS simulators, and comparisons are carried out between the simulation results and the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

A closed‐form equation approach to multi‐port/multi‐zone behavioral modeling of GaN FET Amplifiers

In this paper, a systematic method for the simulation of weakly and mildly nonlinear GaN FET amplifiers is reported. The core of the proposal is a third‐order Volterra‐based behavioral model with multi‐spectral and multi‐node capabilities that is formally derived from a circuit‐level representation. Starting with the equivalent circuit of a typical FET device with thermal power feedback and fading memory, described in terms of its large‐signal functions, closed‐form expressions for the kernels at the gate, drain and thermal nodes are developed up to the third order. The use of these kernels allows the calculation of the responses in the dc, first‐, second‐ and third‐harmonic zones, which are shown to be dependent on the frequency response of the amplifier circuit terminating impedances and thermal filter. The simulation approach has been applied to calculate the nonlinear response of a typical power amplifier circuit, showing the ability of the proposed approach to provide an accurate prediction of multi‐spectral, multi‐node, multi‐bias characteristics, including AM/AM‐AM/PM conversion, spectral regrowth, intermodulation, and temperature rise, under diverse input signal waveforms and bandwidths. These results have been successfully compared with commercial CAD tools based on harmonic balance or envelope simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliable reduced cost modeling and design optimization of microwave filters using co‐kriging

A reliable methodology for accurate modeling of microwave filter is presented. Our approach exploits co‐kriging that utilizes low‐fidelity and high‐fidelity electromagnetic simulation data and combines them into a single surrogate model. Densely sampled low‐fidelity data determine a trend function, which is further corrected by sparsely sampled high‐fidelity simulations. Low‐fidelity electromagnetic data are also enhanced by using a frequency scaling to reduce its misalignment with the high‐fidelity model. With our method, accurate models can be obtained at a fraction of the cost required by conventional approximation models that are exclusively based on high‐fidelity simulations. Three examples of microstrip filters are considered for verification purposes. We also provide comparisons with conventional approximation models and include an application of co‐kriging models for filter design optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Simplified analysis techniques for VLF wave propagation in the earth–ionosphere waveguide

VLF (very low frequency; 3 to 30 kHz) wave propagation in the earth–ionosphere waveguide can be simply analyzed by the method developed in this paper. The finite‐di?erence time‐domain (FDTD) method is used with a conductivity tensor to model the ionosphere, and the applicability is limited to monotonic cases. The proposed method is compared with the wideband method, and it is concluded that the newly developed method can be used as a VLF wave simulator without errors. Conformal FDTD is also introduced to allow for the curvature of the earth's surface, and we have clarified the di?erence between two‐dimensional modeling in Cartesian coordinates and cylindrical coordinates. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 183(1): 25–31, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22302     

Wide‐band modelling of CMOS interconnections and voiding damages with the lumped element LE‐FDTD method

This paper illustrates the application of a lumped element‐finite difference time domain (LE‐FDTD) simulator to the wide‐band modelling of CMOS interconnections. To achieve very accurate results the short‐open calibration (SOC) technique has been adopted. Specific parameters of a CMOS interconnection laterally screened by a stack of metal vias have been extracted in the two cases of an unperturbed and a purposely damaged metal line. The behaviour of void‐like defects in the metal line has been also studied using the fully three‐dimensional capabilities of the simulator. It has been demonstrated that, at least in the simulated cases, only the specific resistance is affected by damaging. Copyright © 2004 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.     

A DC stabilized log‐domain nth‐order multifunction filter based on the decomposition of nth‐order HP filter function to FLF topology

The design of high‐order log‐domain filters can be easily accomplished by transposing already known linear‐domain G_m‐C filter topologies to their counterparts in the log‐domain through the employment of a set of complementary operators. To achieve the G_m‐C filter topologies, the multiple feedback approach is widely used due to its accrued advantages. In this paper a synthesis approach for the development of an nth‐order multifunction log‐domain filter comprising lowpass (LP), highpass (HP) and bandpass (BP) filter functions is proposed. The approach is based on the decomposition of nth‐order HP filter function to follow‐the‐leader‐feedback (FLF) topology. The design is simple and simultaneously achieves nearly all of the chief advantages. The design offers superior performance factors vis‐à‐vis the ones recently reported. To verify the high‐order behavior of the topology, a 5th‐order multifunction filter was designed and the achieved simulated results verify the theory. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

A wave‐front‐time dependent corona model for transmission‐line surge calculations

For transmission‐line surge studies, the inclusion of corona discharge due to high voltage surges is important as well as the inclusion of frequency‐dependent effects. Because the charge‐voltage (q‐v) curve of a lightning surge is different from that of a switching surge, a corona model should reproduce different q‐v curves for different wave‐front times. The present paper proposes a wave‐front time dependent corona model which can express the dependence by a simple calculation procedure as accurately as a rigorous finite‐difference method which requires an enormous calculation time. The simplicity enhances the incorporation of the corona model into a line model, because a large number of models are to be inserted into the line model by discretization. The q‐v curves calculated by the proposed method agrees well with field tests. This paper also proposes an efficient method to deal with nonlinear corona branches in distributed‐parameter line model using the trapezoidal rule of integration and the predictor‐corrector method. © 1999 Scripta Technica, Electr Eng Jpn, 129(1): 29–38, 1999