Non-linear circuit modelling via nodal methods

摘要

We discuss in this paper several interrelated nodal methods for setting up the equations of non-linear, lumped electrical circuits. A rather exhaustive framework is presented, aimed at surveying different approaches and terminologies in a comprehensive manner. This framework includes charge-oriented, conventional, and hybrid systems. Special attention is paid to so-called augmented node analysis (ANA) models, which somehow articulate the tableau and modified node analysis (MNA) approaches to nonlinear circuit modelling. We use a differential—algebraic formalism and, extending previous results proved in the MNA context, we provide index-1 conditions for augmented systems, which are shown to be transferred to tableau models. This approach gives, in particular, precise conditions for the feasibility of certain state-space reductions. We work with very general assumptions on device characteristics; in particular, our approach comprises a wide range of resistive devices, going beyond voltage-controlled ones.