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

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 by the finite difference method (FD). An efficient model order reduction is achieved by appropriate inductances that are extracted with the same FD operator. 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 terminations.