A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications

Abstract

This paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier series with the Laplace–Carson (L-C) transform in the complex domain, utilizing complex time vectors to streamline the computation of the original function. The inverse transformation back into the time domain is achieved using the Cauchy-Heaviside (C-H) method. The second approach applies the Fourier transform (F-Τ) for the transient analysis of a power converter circuit with both passive and active loads. The method of complex conjugate amplitudes is employed for steady-state analysis. Both contributions represent innovative approaches within this study. The process begins with Fourier series expansions and the computation of Fourier coefficients, followed by solving the system’s steady-state and transient responses. The transient states are then confirmed using the Fourier transform. To validate these findings, the analytical results are verified through simulations conducted in the Matlab/Simulink R2023b environment.

Keywords

• Fourier transform
• Laplace–Carson transform
• transient phenomena
• state-space variables
• electrical circuits
• power electronic system