A Contribution to the Application of the Phasor Transform for Solving Electric Circuits

This paper presents an alternative analysis of the fundamental concepts underlying the use of the phasor transform in electric circuit analysis. Traditionally, the phasor transform is employed to determine the steady-state response of circuits composed of passive elements (resistors, capacitors, and inductors) and active sources (voltage and current sources) operating under sinusoidal excitation. Such circuits are essential for analyzing power systems, telecommunications networks, and similar applications. The primary objective of this study is to develop a comprehensive framework for solving electric circuits in the steady state by leveraging the phasor transform, without explicitly introducing the conventional phasor concept as a rotating vector nor using Euler’s identity. Instead, our approach mirrors the strategy of the Laplace transform, thereby unifying the analysis under a single, consistent methodology without the need for additional new concepts.