Fast Realization of the Modal Vector Fitting Method for Rational Modeling With Accurate Representation of Small Eigenvalues

Admittance-based rational modeling of multiport 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; and 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.