Application of different saturation curves in a mathematical model of hysteresis

Zdzisław Włodarski (Maritime University, Szczecin, Poland)
Jadwiga Włodarska (University of Technology, Szczecin, Poland)
Andrzej Brykalski (University of Technology, Szczecin, Poland)



The increase of the accuracy of a mathematical model of hysteresis by the choice of the optimum saturation curve for a given material.


Hysteresis loops of typical soft magnetic materials are approximated with the help of the Taka´cs magnetization model using different saturation curves. The quality of approximations is determined by the deviation of computed magnetic induction amplitudes, iron losses, apparent remanences and coercivities from the measured values.


By the proper choice of saturation curve, the relative inaccuracy of approximations can be reduced with reference to the original model based on tangent hyperbolic function.

Research limitations/implications

The accuracy of approximations worsens close to saturation because of the excessive rise of magnetization due to the linear term of the model. This effect should be minimized by the application of complex saturation curves using greater number of parameters.

Practical implications

Owing to the convenient analytical form and increased accuracy, the model equations can be used in simpler practical evaluations of hysteresis effects and for teaching purposes.


Presented form of model equations enables approximation of hysteresis loops and the evaluation of main characteristics of magnetic materials on the basis of any saturation curve.



Włodarski, Z., Włodarska, J. and Brykalski, A. (2005), "Application of different saturation curves in a mathematical model of hysteresis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 4, pp. 1367-1380.

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