Superposition principle in linear networks with controlled sources

TL;DR

This paper clarifies the applicability of the superposition principle in linear circuits with dependent sources, providing an intuitive approach suitable for educational purposes and addressing recent debates on the topic.

Contribution

It offers a general, didactic interpretation of superposition in circuits with controlled sources, expanding the understanding beyond traditional views.

Findings

Superposition applies to linear circuits with dependent sources when properly interpreted.

The paper provides a clear method to turn off controlled sources in circuit analysis.

An educational approach to superposition enhances teaching of electric circuit theory.

Abstract

The manuscript discusses a well-known issue that, despite its fundamental role in basic electric circuit theory, seems to be tackled without the needful attention. The question if the Principle of Superposition (POS) can be applied to linear networks containing linear dependent sources still appears as an addressed point unworthy to be further discussed. Conversely, the analysis of this point has been recently re-proposed [5,6] and an alternative conclusion has been drawn. From this result, the manuscript provides an alternative approach to such issue from a more general point of view. It is oriented to clarify the issue from the didactic viewpoint, rather than provide a more efficient general technique for circuit analysis. By starting from a linear system of equations, representing a general linear circuit containing controlled sources, the correct interpretation of turning off the controlled elements in terms of circuit equivalent is provided, so allowing a statement of the POS for linear circuits in a wider context. Further, this approach is sufficiently intuitive and straightforward to fit the needs of a Basic Electric Circuit Theory class.