Supernodal Analysis Revisited

TL;DR

This paper presents an improved nodal analysis algorithm that simplifies circuit analysis by partitioning equations without complex transformations, making it more accessible for educational purposes.

Contribution

It extends existing algorithms to handle circuits with sources without nullors, avoiding complex graph transformations and additional variables.

Findings

Partitioned nodal equations explicitly in terms of sources and reference nodes.

Eliminated need for preparational graph transformations.

Simplified analysis suitable for teaching environments.

Abstract

In this paper we show how to extend the known algorithm of nodal analysis in such a way that, in the case of circuits without nullors and controlled sources (but allowing for both, independent current and voltage sources), the system of nodal equations describing the circuit is partitioned into one part, where the nodal variables are explicitly given as linear combinations of the voltage sources and the voltages of certain reference nodes, and another, which contains the node variables of these reference nodes only and which moreover can be read off directly from the given circuit. Neither do we need preparational graph transformations, nor do we need to introduce additional current variables (as in MNA). Thus this algorithm is more accessible to students, and consequently more suitable for classroom presentations.