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     

Full-wave analysis of coupled lossy transmission lines using multiwavelet-based method of moments

Full-wave analysis for coupled lossy transmission lines with finite thickness is conducted using a multiwavelet-based method of moments (MBMM). We use the multiscalets with multiplicity r=2 as the basis and testing functions, and take the discrete Sobolev-type inner products to discretize the integral equation and its derivative at the testing points. Since the numerical integration is not needed in the testing procedure, the new approach is faster, yet preserves high accuracy due to the derivative sampling. In the new approach, we compute the incoming fields in the spatial domain directly without resorting to the inverse Fourier transform. Hence, the local coordinate system used to perform the Sommerfeld integral is avoided and the computational cost is reduced remarkably. In addition, a coarser mesh can be used owing to the smoothness of the multiscalets. Numerical examples show that the MBMM speeds up the traditional method of moments 3 /spl sim/ 10 times.     

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     

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。     

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     

The generalized method of characteristics for waveform relaxationanalysis of lossy coupled transmission lines

The transient response of lossy coupled transmission lines is simulated by iterative waveform relaxation analyses of equivalent disjoint networks constructed with congruence transformers, fast Fourier transform (FFT) waveform generators, and characteristic impedances synthesized by the Pade approximation. A two order reduction of CPU time and one order savings in computer memory are achieved. A lossy directional coupler is simulated for illustration     

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.     

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.     

Full-wave analysis of integrated transmission lines on layered lossy media

Cohn's method of analysis of the slot line on a dielectric substrate is extended to the case of integrated lines on a lossy inhomogeneous substrate. The slow-wave characteristics of the metal-insulator-semiconductor coplanar waveguide for MMIC applications are calculated and found to be in good agreement with the experiments.     

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.     

Condition of modal analysis in time domain of lossy coupled lines

Modal decomposition in the time domain is shown to be applicable to lossy coupled transmission lines of equal width. It is rigorous for two lines and is a good approximation for more than two lines. This allows a direct time-domain simulation of buses made of microstrip lossy lines on chip or on board in digital circuits     

架空多导体传输线的时域阻抗分析

利用误差函数的拉普拉斯变换，对复深度法得出的频域阻抗直接进行拉普拉斯变换，获得了考虑土壤影响的架空多导体传输线时域自阻抗和互阻抗简单的表达式，通过Timotin公式和Pade变换的结果进行比较，验证了公式的正确性。     

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。     

An analysis of multiple parallel coupled quasi-tem transmission lines

A theoretical analysis of general multiple parallel coupled transmission lines in an inhomogeneous medium is presented. The analysis is based on the generalized telegraphists' equation. It is relatively simple and has the advantage of giving explicit solutions for the properties of the coupled-line system. Considerations are also given to a coupled-line structure whose lines have the same characteristic impedance. Results for two and three coupled lines are found in agreement with those published previously.     

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     

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.     

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.<>     

Rigorous analysis of the propagation characteristics of generallossless and lossy multiconductor transmission lines in multilayeredmedia

The frequency-dependent propagation characteristics of lossless and lossy open coupled polygonal conductor transmission lines in a multilayered medium are determined based on a rigorous full-wave analysis. A boundary integral equation technique is used in conjunction with the method of moments. Losses in conductors and layers are included in an exact way without making use of a perturbation approach. Dispersion curves for the complex propagation constants and impedances are presented for a number of relevant examples and, where possible, compared with published data     

降低有损耦合微带线间串扰的方法分析

为降低和控制有损耦合微带线间的串扰,在强信号线两边各插入了一列用金属填充的、顶端用微带连接的接地孔.利用FDTD方法对该结构进行模拟并利用FEM法进行了验证.模拟结果表明串扰衰减程度与基底介质的损耗、接地孔参数有关.