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 e!ective 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^p with 0<p<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 frequencydependent dielectric losses and lines with normal and anomalous skin-e!ect. Numerical simulations are carried out for illustration.