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

CAD tools and research in the area of reduced-order modeling of large linear interconnect networks have evolved from merely finding a Pade approximation for the given network transfer function to finding an approximate transfer function that preserves such circuit-theoretic properties of the network as stability, passivity, and RLC synthesizability. In particular, preserving passivity guarantees that the reduced-order models will be well-behaved when embedded back in the circuit where the interconnect network originated. While stability can be ascertained by studying the poles of the reduced-order transfer function, passivity depends on both the poles and zeros of the network driving-point impedance. In this paper, we present a novel method for studying the zeros of reduced-order transfer functions and show how it yields conclusions about passivity and synthesizability. Moreover, in order to obtain a guaranteed-passive reduced-order model for multiport RC networks, a new algorithm based on the Arnoldi iteration is presented. This algorithm is as computationally efficient as the one used to generate guaranteed-stable reduced-order models [1].