A general approach to circuit equations

Abstract

AbstractComputer‐aided circuit analysis is a complex procedure which may be roughly divided into three steps. the first stage is device modelling, where quantitative properties of the participating electronic devices are determined. In the second step the circuit's topology in conjunction with the device equations is exploited in order to formulate a linearized nonsingular equation set. Eventually the equation set is solved iteratively in the third phase, yielding a solution vector of circuit variables.This paper deals with the second and third steps, where diverse sparse matrix methods are employed. Its aim is to provide a general mathematical form by which most matrix manipulation techniques can be described, thus enabling their classification on a theoretical level. Usually these methods are presented descriptively rather than strictly mathematically.The paper introduces a matrix reduction operator from which a general matrix operator equation is deduced. This operator equation can be used to describe entire analysis approaches. After some necessary definitions, the purpose of this paper is illustrated by studying several classical examples rather than giving many mathematical proofs. the selected examples involve some well‐known linear equation set solution methods as well as several typical equation set transformations.