A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits

TLDR

Pade‑based reduced‑order models are standard for accelerating coupled circuit–interconnect simulations, yet they can remain unstable even when derived from stable RLC circuits, whereas congruence transforms such as the Arnoldi algorithm have been shown to produce guaranteed stable and passive ROMs for certain RC circuit classes. This work introduces a computationally efficient coordinate‑transformed Arnoldi algorithm that generates arbitrarily accurate and guaranteed stable reduced‑order models for RLC circuits. The method applies a coordinate transformation within the Arnoldi framework to produce stable ROMs while maintaining high accuracy. Illustrative examples confirm that the new algorithm achieves superior stability and computational efficiency compared to existing approaches.

Abstract

Since the first papers on asymptotic waveform evaluation (AWE), Pade-based reduced order models have become standard for improving coupled circuit-interconnect simulation efficiency. Such models can be accurately computed using bi-orthogonalization algorithms like Pade via Lanczos (PVL), but the resulting Pade approximates can still be unstable even when generated from stable RLC circuits. For certain classes of RC circuits it has been shown that congruence transforms, like the Arnoldi algorithm, can generate guaranteed stable and passive reduced-order models. In this paper we present a computationally efficient model-order reduction technique, the coordinate-transformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reduced-order models for RLC circuits. Examples are presented which demonstrates the enhanced stability and efficiency of the new method.