Superposition principle in linear networks with controlled sources

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.