Modal equivalent-circuit representation of transmission lines with arbitrary terminations for efficient broadband simulation

A passive and inherently stable Foster equivalent-circuit multiport representation for lossy transmission lines is presented. The convergence is accelerated by appropriate inductances, for which an exact closed-form expression is developed. The order number of the truncated modal circuit is estimated by a simple relation, according to the required signal bandwidth. The accuracy and versatility of the suggested SPICE-compatible equivalent-circuit is demonstrated by examples in frequency and time-domain, including non-linear terminations.