Efficient Modal Network Model for Nonuniform Transmission Lines Including Field Coupling

A passive and inherently stable Foster-type multiport equivalent-circuit representation for nonuniform, lossy transmission lines is presented within the validity range of quasi-TEM mode propagation. The approach is based on the eigenfunction expansion. Convergence of the infinite modal representation is accelerated by quasistatic inductances. The required modal and quasistatic analyses are implemented numerically with the method of finite differences (FD) utilizing the same FD operator. The model order of the equivalent circuit is estimated by a linear relation with respect to the required bandwidth. Without increasing significantly the complexity of the model, the influence of an external electromagnetic field is considered by equivalent field sources, which are also calculated by an FD algorithm. The efficiency and applicability of the suggested SPICE compatible model is compared with the ladder network and is demonstrated by examples in frequency and time domain, including nonlinear terminations.