Mathematical modelling of frequency-dependent hysteresis and energy loss of FeBSiC amorphous alloy

The aim of this paper is to present a novel mathematical model of frequency-dependent magnetic hysteresis. The major hysteresis loop in this model is represented by the ascending and descending curve over an arctangent function. The parameters of the hysteresis model have been calculated from a measured hysteresis loop of the FeBSiC amorphous alloy sample. A number of measurements have been performed with this sample at different frequencies of the sinusoidal excitation magnetic field. A variation of the coercive magnetic field with the frequency has been observed and used in the modelling of frequency-dependent hysteresis with the proposed model. A comparison between measured and modelled hysteresis loops has been presented. Additionally, the areas of the obtained hysteresis loops, representing the energy loss per unit volume, have been calculated and the dependence of the energy loss on the frequency is shown. Furthermore, two models of the frequency dependence of the coercivity and two models of the energy loss separation have been used for fitting the experimental and simulation results. The relations between these models and their parameters have been observed and analysed. Also, the relations between parameters of the hysteresis model and the parameters of the energy loss separation models have been analysed and discussed.