A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks

Work in the area of model-order reduction for RLC interconnect networks has focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability (Silveira et al., 1996). Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. We address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm (Ruhe, 1994). The scheme reduces to that of (Odabasioglu et al., 1997) when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced order models.