How to make theoretically passive reduced-order models passive in practice

This paper demonstrates that, in general, implementations of circuit reduction methods can produce unstable and nonpassive models even when such outcomes are theoretically proven to be impossible. The reason for this apparent contradiction is the numeric roundoff inherent in any finite-precision computer implementation. This paper introduces a new variant of the symmetric, multiport, Pade via Lanczos algorithm (SyMPVL) that, even in practice, is guaranteed to produce stable and passive models for all the circuits characterized by pairs of symmetric, positive semidefinite matrices. The algorithm is based on a new band Lanczos process with coupled recurrences. A number of circuit examples are used to illustrate the results.