Fast realization of the modal vector fitting method for rational modeling with accurate representation of small eigenvalues

Abstract

Admittance-based rational modeling of multi-port systems is prone to error magnification in applications with high-impedance terminations. This problem is overcome by the modal vector fitting method (MVF) which is formulated in terms of modal components with inverse least-squares weighting by the eigenvalue magnitude. A direct realization of MVF is very demanding in computation time and memory requirements. This paper overcomes the performance deficiency via three steps: 1) the required number of MVF iterations is reduced by precalculating an improved initial pole set via conventional vector fitting with inverse magnitude weighting, 2) the pole identification step is calculated in an efficient manner by solving for only the few essential unknowns while exploiting the sparse matrix structure, 3) the residue identification step is calculated efficiently by a row-wise solution procedure that takes advantage of symmetry. The approach is demonstrated to give large savings for the modeling of a frequency-dependent network equivalent.