Fourier analysis of hysteretic distortions

Abstract

The paper presents the derivation of the Fourier coefficients of the magnetisation wave form in closed form for periodic triangular field excitation. The mathematical model used here to approximate the hysteresis loop applies exponential functions and it is presented briefly in the first part of the paper. This method of calculation is applicable to a group of excitation wave forms, constructed of straight lines, such as square, triangular and trapezoid wave forms. The criteria for the Rayleigh region is given and an appropriate formulation of the Fourier coefficients in closed form for the Rayleigh region is also described. It is shown that the calculation is also applicable to anhysteretic processes both in the saturation and in the “small” signal (Rayleigh) region. The Fourier components of the periodic magnetisation wave form resulting from an anhysteretic magnetisation process are also calculated in closed form for triangular field excitation.