Robust reduced-order modelling of distributed linear networks

Foster's canonical form provides a causal bridge between the transfer function representation of the characteristics of a distributed structure and both time-domain and frequency-domain non-linear circuit simulation. It is particularly advantageous in modelling bandpass-like characteristics. In the modelling procedure, a transfer function having Foster's canonical form is fitted to measured or simulated data which may not have an inherent pole-zero description. Even if there is a good transfer function representation, the number of poles required for a reasonable fit is not known a priori which can lead to poor models that may cause convergence problems during either fitting or simulation. In this study, an extension of Foster's model is developed and a robust procedure for fitting the transfer function to data without a priori knowledge of the number of poles is presented. A robust stamp for implementation of the model in a transient circuit simulator is developed.