The SPRIM Algorithm for Structure-Preserving Order Reduction of General RCL Circuits

In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large-scale multi-port RCL networks that arise in VLSI circuit simulation. A popular method of this type is PRIMA. Its main features are provably passive reduced-order models and a Padé-type approximation property. On the other hand, PRIMA does not preserve other structures inherent to RCL circuits, which makes it harder to synthesize the PRIMA models as actual circuits. For the special case of RCL circuits without voltage sources, SPRIM was introduced as a structure-preserving variant of PRIMA that overcomes many of the shortcomings of PRIMA and at the same time, is more accurate than PRIMA. The purpose of this paper is twofold. First, we review the formulation of the equations characterizing general RCL circuits as descriptor systems. Second, we describe an extension of SPRIM to the case of general RCL circuits with voltage and current sources. We present some properties of the general SPRIM algorithm and report results of numerical experiments.