The SPRIM algorithm for structure-preserving order reduction of general RCL circuits

Abstract 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.

Parameterized Model Order Reduction

This Chapter introduces parameterized, or parametric, Model Order Reduction (pMOR). The Sections are offered in a prefered order for reading, but can be read independently. Section 5.1, written by Jorge Fernández Villena, L. Miguel Silveira, Wil H.A. Schilders, Gabriela Ciuprina, Daniel Ioan and Sebastian Kula, overviews the basic principles for pMOR. Due to higher integration and increasing frequency-based effects, large, full Electromagnetic Models (EM) are needed for accurate prediction of the real behavior of integrated passives and interconnects. Furthermore, these structures are subject to parametric effects due to small variations of the geometric and physical properties of the inherent materials and manufacturing process. Accuracy requirements lead to huge models, which are expensive to simulate and this cost is increased when parameters and their effects are taken into account. This Section introduces the framework of pMOR, which aims at generating reduced models for systems depending on a set of parameters