Model of the hysteresis loop of soft-magnetic amorphous alloys with the usage of a modified linear fractional function

Modelling the hysteresis loop is necessary when creating various electrical devices containing ferromagnetic elements, or when studying the physical processes occurring in these elements. The model of the hysteresis loop is optimal for use when, firstly, it provides a description of the loop branches with sufficient accuracy, and, secondly, the parameters of which have a clear physical meaning, and the behavior of which can be predicted, which is typical for interpolation models. The paper proposes an interpolation model of the hysteresis loop, which ensures the coincidence of theoretical and experimental curves at the tops of the hysteresis loop, and at the points of residual induction and coercive force. To describe the descending and ascending branches of the hysteresis loop, a modified linear fractional function was used to describe the contribution to the induction of irreversible magnetization reversal processes, and the Langevin function for the reversible contribution. The adequacy of the model has been established by comparing the calculated and experimental data obtained in low and high magnetic fields, using the example of three amorphous soft magnetic alloys — based on iron, cobalt and iron-cobalt. The model was verified using an analysis of variance based on calculating the residual variance of magnetic induction and the Fisher criterion. The resulting model provides a sufficiently high-quality approximation of the values of magnetic induction with an error not exceeding the measurement error, and its application doesn’t require complex calculations or the development of a special computer program.

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