Finding the Harmonic Contents of Periodic Square Wave

Abstract

This paper presents an analysis of the harmonic content in a periodic square wave. Three methods are employed to evaluate the harmonic characteristics: Fourier series decomposition, Crest Factor (CF), and Total Harmonic Distortion (THD). The Fourier series method decomposes the square wave signal into its direct current (DC) component, cosine, and sine terms. The second method, CF, is used as an initial indication of the presence of harmonics in the signal, where a CF value greater than 1 suggests a signal with harmonics. Finally, the THD method is utilized, which includes both the Fundamental THD (THDF) and the Root Mean Square THD (THDR), quantifying the degree of harmonic distortion in the signal. For the case studied, where the square wave has an amplitude of 1, the CF is found to be 1, the THDF is 46.1%, and the THDR is 41.9%. These results suggest that the square wave contains significant harmonic distortion. The paper highlights the importance of understanding harmonic content in power systems, particularly in the context of nonlinear loads that introduce distortion in voltage and current waveforms. The findings contribute to the broader understanding of harmonic effects on system performance, which can lead to issues such as overheating, protection malfunctions, and reduced power quality.