Time-domain simulation of multiconductor transmission lines with frequency-dependent losses

Abstract

This paper presents a method for the time-domaan simulation of multiconductor transmission lines with frequency-dependent conductor (skin effect) and dielectric losses. The method is based on a traveling wave solution of the transmission line equations in the frequency domain, with time-domain simulation achieved by convolving the transmission line terminal voltages with describing time-domain input and tmnsfer impulse responses derived from the frequencydomain solution. Attention must be given to careful formulation of the frequency-dependent conductor and dielectric losses to assure causality in the transmission line responses. The ezcessive numerical burden of discrete-time convolution is avoided by approzimating the tmnsmission line responses with ezponential series, which may be convolved recursively, making the tmnsmission line solution feasible and practical for large simulations. An implementation of the solution algorithm an the circuit simulation program SPICE is described, and sample results for a microstrip system presented.

An equivalent transmission-line model containing dispersion for high-speed digital lines-with an FDTD implementation

“…By combining these two models we can analyze the frequency-dependence of all four transmission-line parameters. This first-order Debye representation for the distributed transmission-line parameters is analogous to the classical approach of analyzing pulse propagation through lossy materials in which a series of first-order Debye terms are used for frequency dependent permittivity and permeability , see [14] and [23]- [27].…”

“…If the frequency-dependent and of a transmission line are desired, the network model shown in Fig. 1(b (14) The formulation presented in (9) assures that the dc values of and are captured. On the other hand, the behavior of and the behavior of are not guaranteed with this Debye model.…”

Transient Analysis of Lossy Transmission Lines: An Efficient Approach Based on the Method of Characteristics

“…We will concentrate only on the critical aspects related to the treatment of lossy and dispersive lines with the MoC and we will skip the basic derivation. The reader is referred to the relevant literature for further details [1], [7], [11], [17]- [19].…”

Fast Transient Simulation of Lossy Transmission Lines

“…Another category of methods for transmission line simulation approximates the characteristics of transmission lines by rational functions [10][11][12][13][14][15][16][17]. This kind of methods has the advantages that it eliminates the use of FFT or NILT and allows an efficient evaluation of the time domain convolution.…”

“…This kind of methods has the advantages that it eliminates the use of FFT or NILT and allows an efficient evaluation of the time domain convolution. Once the rational function approximation is obtained, recursive convolution [11,[13][14][15][16][17] is used to efficiently evaluate the time-domain convolution in linear time. For this category of methods, higher order rational function approximations are needed when accuracy is the main concern, which would make these methods less efficient or even impractical.…”