Contents I. Introduction
Modeling of transmission lines in the time-domain is an ongoing challenge for the people involved in the simulation of integrated circuits and/or printed circuit boards at high frequency. The literature on this subject is very rich and can be found e.g. in [2], [3], [4]. Among many methods and approaches we would like to focus on two, which include further references. In the first paper [2], the author presents an approach based on dyadic Green's function and vector fitting of per-unit-length impedance and admittance of transmission line to obtain a Z matrix of transmission line as a two-port. The line impedance and admittance are the sums of rational functions of complex frequency s, which facilitates the transformation to the time-domain and modeling in SPICE. The biggest problem is the necessity to take into account a large number of terms in every entry of the mentioned Z matrix. In [3], the same author has extended the above approach to weakly nonuniform transmission lines. In that case the author used results obtained for uniform case and parametric macromodeling to obtain the approximate Z matrix of the line. In both papers, the presented approach has been extended to the case of a multiconductor line. On the other hand in paper [4], a method was developed to convert of differential telegrapher's equations into integral equations and next to solve them using the method of successive approximation. In that approach, we obtain a first order approximation of the solution in a simple analytical form which is valid for low loss transmission lines. The drawback of that approach was not including the skin effect and dielectric dispersion.
