Broadband analysis of non-uniform transmission lines with a Foster type circuit model

A passive and inherently stable Foster equivalent-circuit multiport representation for non-uniform, lossy transmission lines is presented. The method is based on an eigenfunction expansion, where the eigenfunctions are determined numerically with the finite difference method (FD). An efficient model-order reduction is achieved by appropriate inductances that are extracted by a quasistatic FD analysis. The order number of the truncated modal circuit is simply estimated, according to the required signal bandwidth. The accuracy and versatility of the suggested SPICE-compatible equivalent-circuit is demonstrated by an example in the time-domain, including non-linear loads.