Simulation of transmission lines with frequency dependent losses by indirect numerical integration

This paper presents the time domain simulation of multiple coupled transmission lines with frequency dependent conductor (skin effect) and dielectric losses by an indirect numerical integration method. The method is based on an analytical relationship between the continuous and discrete domains, and allows one to recurrently calculate in the time domain a transient response of arbitrary dynamic systems, including time-varying, frequency-dependent, and nonlinear ones. Also, the paper describes the implementation of multiconductor, coupled lines with frequency dependent losses in SPICE3f4. This implementation ties SPICE transient analysis of a transmission line and is more efficient than another approach based on the concept of the numerical Laplace, Fourier transformations and convolution