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

A method for time-domain simulation of multiconductor transmission lines with frequency-dependent conductor (skin effect) and dielectric losses is presented. The method is based on a traveling-wave solution of the transmission line equations in the frequency domain. Time-domain simulation is achieved by convolving the transmission line terminal voltages with describing time-domain input and transfer impulse responses derived from the frequency-domain 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 excessive numerical burden of discrete-time convolution is avoided by approximating the transmission line responses with exponential series, which may be convolved recursively, making the transmission line solution feasible and practical for large simulations. An implementation of the solution algorithm in the circuit simulation program SPICE is described, and sample results for a microstrip system are presented