Zeros and passivity of Arnoldi-reduced-order models for interconnect networks

Abstract

CAD tools and research in the area of reduced-ordermodeling of large linear interconnect networks have evolvedfrom merely finding a Pad' e approximation for the givennetwork transfer function to finding an approximate transferfunction that preserves such circuit-theoretic propertiesof the network as stability, passivity, and RLC synthesizability.In particular, preserving passivity guarantees thatthe reduced-order models will be well-behaved when embeddedback in the circuit where the interconnect networkoriginated. While stability can be ascertained by studyingthe poles of the reduced-order transfer function, passivitydepends on both the poles and zeros of the networkdriving-point impedance. In this paper, we present a novelmethod for studying the zeros of reduced-order transferfunctions and show how it yields conclusions about passivityand synthesizability. Moreover, in order to obtain aguaranteed-passive reduced-order model for multiport RCnetworks, a new algorithm based on the Arnoldi iteration ispresented. This algorithm is as computationallyefficient asthe one used to generate guaranteed-stable reduced-ordermodels [Coordinate-transformed Arnoldi for generating guranteed stable reduced-order models for RLC circuits].