Broadband foster-type-circuit model of non-uniform and radiating transmission lines

A novel passive, inherently stable and convergence accelerated Foster-type circuit model for non-uniform transmission lines (TLs) including the effect of radiation is presented. The straightforward derivation is based on the solution of the TL equations by finite differences in conjunction with an eigenvector expansion. Radiation losses are included by modal conductances, calculated from the radiated power of the corresponding modal far fields. The model order is estimated by a linear relation referring to the required bandwidth. The definition of the per-unit-length parameters in the case of non-uniform TLs is reviewed and an accurate general expression is developed, so far not found in the literature. The comparison with a more elaborate full-wave reference simulation demonstrates the accuracy and applicability of the suggested SPICE compatible network model in frequency and time domain, including non-linear terminations.