有损土壤上的多导体传输线的时域分析

将多导体传输线（ＭＴＬ）的土壤复数阻抗拓展为土壤运算阻抗,采用Ｐａｄｅ展开法,提出了计及土壤影响的多导体传输线的时域模型,建立了该模型的时域有限差分（ＦＤＴＤ）算法。通过对计及土壤影响的架空单导体和双导体传输线的波过程计算,表明本文方法的正确性,并可以应用于超高压变电站高压母线和超高压输电线路的瞬态电磁干扰计算。     

Time-domain analysis of lossy active transmission lines using FDTD method

In this paper, an accurate and efficient method for analysis of a GaAs MESFET including frequency-dependent losses of the electrodes in the time domain is presented. The time domain analysis is obtained based on the fully distributed model using finite-difference time-domain (FDTD) technique, with the assumption of the skin effect losses. The time-domain results are verified using the conventional time-domain to frequency-domain (TDFD) solution technique.     

2-D FDTD method for exact attenuation constant extraction of lossy transmission lines

The two-dimensional finite-difference time-domain (2-D FDTD) method is undeniably efficient for full-wave analysis of uniform transmission lines. However, conventional 2-D FDTD method ignores the spatial attenuation along the propagation direction and yields approximate results. We propose a new 2-D FDTD method for extracting exact attenuation constants of lossy transmission lines. In the proposed method, we take the variation of field components with the propagation direction into consideration and describe an iterative process for finding exact attenuation constants. Numerical experiments show that, compared with the conventional 2-D FDTD method, results given by the iterative process agree much better with analytical solutions or measured data.     

不等长非均匀有损耗传输线FDTD瞬态分析

以分析等长均匀无损耗多导体传输线的时域有限差分（FDTD）法为基础,在考虑传输线损耗的情况下,对不等长非均匀多导体传输线进行分析。首先,在考虑传输线损耗的情况下给出传输线上各点电压和电流的迭代计算公式;其次,利用该公式对不等长非均匀有损耗传输线模型进行数值计算和理论分析;最后,通过仿真实验,其结果表明所提计算方法是正确和有效的。该方法对不等长非均匀有损耗传输线的研究提供理论计算参考。     

SPICE implementation of lossy transmission line and Schottky diodemodels

The author describes models for the lossy transmission line and the Schottky diode that are incorporated into the source code of the circuit simulation program SPICE (version 2G.6). The model used for the lossy transmission line was derived by A.J. Gruodis (1979). The DC model for the Schottky barrier diode as shown was formulated by D.B. Estreich (1983). Examples used to verify the models are given     

Modeling of thin wires in a lossy medium for FDTD simulations

An equivalent radius of a thin wire in a lossy medium, represented by the finite-difference time-domain method, is derived using the concept that was proposed to derive an equivalent radius of a thin wire in air. Then, a simple technique to specify an arbitrary radius of a thin wire in a lossy medium is proposed. The proposed technique does not employ locally fine or nonuniform subgrids, but is based on an orthogonal and uniform-spacing Cartesian grid. The validity of the proposed technique is investigated in a transient state, as well as in a quasisteady state, and shown to be satisfactory.     

A SPICE model for incident field coupling to lossy multiconductortransmission lines

An efficient time-domain macromodel for incident field coupling to lossy multiconductor transmission lines is presented. The model takes the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The model is based on the closed-form matrix-rational approximation of the exponential matrix describing telegrapher's equations and semi-analytic rational approximation of forcing functions     

Equivalent circuit modelling of lossy coupled lines using SPICE software

A new skin effect equivalent circuit and a propagation line equivalent circuit for time domain simulation on a single line have been presented in previous work (T. Vu Dinh et al., 1990) SPICE simulations have proved the accuracy and efficiency of the proposed method. This concept is extended for coupled line modelling. A dual line device is analysed as a typical example of the usual cases. The method has successfully been extended to N lossy coupled lines. The results show a good agreement with those obtained by other methods.<>     

Transient response of lossy transmission lines

Transient behaviour of lossy lines has been investigated and clarified. It has been shown that the lossy line terminated with a resistor ? (L/C) behaves similarly to a compensated resistive divider. Compensation occurs not only for distortionless lines, but also for so-called `quasidistortionless? lines.     

Higher-order FDTD(2,4) scheme for accurate simulations in lossy dielectrics

A finite-difference time-domain (FDTD)(2,4) scheme with second-order accuracy in time and fourth-order accuracy in space for the precise solution of Maxwell's equations in lossy dielectrics is presented. Compared with the ordinary FDTD method the novel technique reduces lattice reflection errors, increases the overall accuracy and provides significant computational savings. Numerical results for a waveguide problem indicate the efficiency and robustness of the proposed formulation.     

Sensitivity analysis of lossy coupled transmission lines

An analysis method, based on the numerical inversion of the Laplace transform, is described for the evaluation of the time domain sensitivity of networks that include lossy coupled transmission lines. The sensitivity can be calculated with respect to network components and parameters of the transmission lines. Sensitivity analysis is useful for waveform shaping and optimization. Examples and comparisons with sensitivity determined by perturbation are presented     

Time-domain analysis of lossy coupled transmission lines

A new approach, based on the waveform relaxation technique and fast Walsh transform, is first presented for the analysis of lossy coupled transmission lines (LCTL) with arbitrary terminal networks. The simulation accuracy of the new method can be greatly improved, the disadvantage which always exists in previous methods [1]–[7] can be avoided and a considerable saving in time and memory of CPU is obtained.     

Time-domain analysis of lossy coupled transmission lines

A novel method based on numerical inversion of the Laplace transform is presented for the analysis of lossy coupled transmission lines with arbitrary linear terminal and interconnecting networks. The formulation of the network equations is based on a Laplace-domain admittance stamp for the transmission line. The transmission line stamp can be used to formulate equations representing arbitrarily complex networks of transmission lines and interconnects. These equations can be solved to get the frequency-domain response of the network. Numerical inversion of the Laplace transform allows the time-domain response to be calculated directly from Laplace-domain equations. This method is an alternative to calculating the frequency-domain response and using the fast Fourier transform to obtain the time-domain response. The inversion technique is equivalent to high-order, numerically stable integration methods. Numerical examples showing the general application of the method are presented. It is shown that the inverse Laplace technique is able to calculate the step response of a network. The time-domain independence of the solution is exploited by an efficient calculation of the propagation delay of the network     

FDTD analysis of lossy, multiconductor transmission linesterminated in arbitrary loads

A hybrid method is presented for incorporating general terminations into the solution of lossy multiconductor transmission lines (MTLs). The terminations are characterized by a state-variable formulation which allows a general characterization of dynamic as well as nonlinear elements in the termination networks. The method combines the second-order accuracy of the finite difference-time domain (FDTD) algorithm for the MTL with the absolutely stable, backward Euler discretization of the state-variable representations of the termination networks. A compact matrix formulation of the recursion relations at the interface between the MTL and the termination networks allows a straightforward coding of the algorithm. Skin effect losses of the line conductors as well as the effect of an incident field are easily incorporated into the algorithm. Several numerical examples are given which contain dynamic and nonlinear elements in the terminations. These examples demonstrate the validity of the method and show that the temporal and spatial step sizes can be maximized, thereby minimizing the computational burden     

Time-domain skin-effect model for transient analysis of lossy transmission lines

A skin-effect equivalent circuit consisting of resistors and inductors is derived from the skin-effect differential equations for simulating the loss of a transmission line. A numerical method is used to analyze the transmission-line differential equations and the skin-effect equivalent circuit, yielding a model which relates the new values of node voltages and line currents to their values at the previous time step. Based on this model, a very simple program was written on a desk-top computer for the transient analysis of lossy trammission lines. Two examples are presented. The first example is an analysis of the step and pulse responses of a 600-m RG-8/U coaxial cable. The computed results show excellent agreement with measured data. The second example studies the current at the end of a 12-in 7-Ω strip line under different loading conditions. Very good agreement has been obtained between the calculated steady-state solution and that obtained by the frequency-domain method.     

Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B√s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique     

Rigorous and approximate solutions for the three-conductor lossy transmission lines problem

The coupled first-order linear differential equations governing the voltage and the current on three-conductor lossy (identical) transmission lines are solved by two methods. One method is rigorous, and the other one is approximate and applies in the low- and high-frequency ranges. Although the rigorous solution is a numerical one, the approximate solution consists of explicit expressions that are easy to calculate and give physical insight into the coupling process. Experimental results that are available for two parallel identical lossy wires of finite length situated above a perfectly conducting ground (when only one of the wires is driven by a source) and previously published theoretical results compare satisfactorily with the results obtained by the two methods.<>     

Efficient simulation of interconnect networks withfrequency-dependent lossy transmission lines

Accurate and efficient moment generation methods are important when using moment matching based circuit reduction techniques for the simulation of transients on transmission line networks. A modified matrix exponential method is presented for fast computation of the moments associated with frequency-dependent lossy transmission lines. Numerical examples are given which demonstrate the improved performance of the proposed method with respect to existing techniques     

Transient analysis of lossy parabolic transmission lines withnonlinear loads

The exact analytical expressions of the time-domain step response matrix parameters for the lossy parabolic transmission line are developed, therefore extending the range of problems where Allen's method can be applied for the transient analysis of networks consisting of interconnections of linear distributed elements, lumped linear and/or nonlinear elements, and arbitrary sources. For completeness, similar expressions are derived for the lossless parabolic line. In order to demonstrate the versatility of the techniques presented in this paper, we study the transient response of a lossy parabolic line subjected to the following sets of boundary conditions: 1) a unit step input and a linear load, and 2) a trapezoidal pulse generator and a nonlinear load     

Transients on lossy transmission lines with arbitrary boundary conditions

In this work the problem of transients on a lossy transmission line terminated by an arbitrary, including nonlinear, load is formulated. The tranmission line parameters are the constantsR, L, G, andC. The exact relation between the input and output voltages and currents in the form of two coupled integral equations is derived by the Laplace transform method. It is shown that the kernels of the integral equations may be represented in terms of either Lommel functions or integrals involving zeroth order modified Bessel functions. Simultaneous (numerical) solutions of these integral equations fulfilling the boundary conditions at the input and output of the line yields the input and output voltages and currents on the line. Finally the exact analytical relations in time domain of the voltage and current at an arbitrary point on the line (and the voltages and currents at the input and output terminals) are derived. In all parts, the problem has been formulated in such a way as to impose the causality condition explicitly.