Fourier Transforms and Their Use in Electrical Circuit Analysis

Abstract

This paper investigates Fourier series and Fourier transforms as fundamental tools for electrical circuit analysis with an emphasis on bridging mathematical theory and practical applications. An analytical applied approach is adopted in which periodic and non-periodic signals are represented in the frequency domain to facilitate the analysis of circuit responses to various voltage and current excitations. The study presents the mathematical foundations of Fourier series and Fourier transforms, followed by the frequency domain analysis of RLC circuits and an examination of key phenomena associated with spectral analysis. To enhance practical insight, Mathcad was employed to generate graphical representations of the signals corresponding to each series and to demonstrate the effect of the number of harmonics on waveform reconstruction accuracy. The results demonstrate that Fourier based analysis, when supported by graphical visualization offers a clearer and more efficient interpretation of circuit behavior compared with conventional time-domain methods. Moreover, this approach provides a comprehensive framework for the design and analysis of electronic circuits, electrical filters, communication systems, and signal processing applications.