Circuit simulation using state space equations

This paper proposes a method to recast the classic circuit simulation algorithm to maximize parallelism by formulating the circuit equations as state variable equations and using an integration method such as Runge Kutta as the foundation to break the time dependencies. A brief introduction to the SPICE algorithm and previous attempts to exploit parallelism is given. The implementation of the new algorithm for both linear and non-linear circuits is presented and results are compared with the traditional method. The opportunities for extracting parallelism are discussed.

I. Introduction

Circuit simulation remains a vital tool for the design of integrated circuits. As transistors decrease in size with each generation of CMOS technology, their variability is increasing, so there is a need to characterize digital systems at the circuit level. Conventional algorithms, such as those used in SPICE, have many features that are inherently sequential and that have proved very difficult to parallelize. With the speed of conventional processors limited to less than 4GHz, it is essential that parallel algorithms are found.