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Hysteresis loop reversing by applying Langevin approximation

Jeno Takacs (Department of Engineering Science, University of Oxford, Oxford, UK)



The purpose of this paper is to model one of the unsolved problems of magnetism, the reversal of hysteresis loops, in an analytical way. The mathematical models, describing the multiphase steel used in engineering practice, without any exception, are unsuited to provide a way to reverse the hysteretic process. In this paper, a proposal is put forward to model it by using analytical expressions, applying the reversal of the Langevin function. This model works with a high accuracy, giving useful answers to a long unsolved magnetic problem, the lack of reversibility of the hysteresis loop. The use of the proposal is shown by applying the reversal of Langevin function to a sinusoidal and a triangular waveform, the two most frequently used waveforms in research, test and industrial applications. Schematic representations are given for the wave reconstruction by using the proposed method.


The unsolved reversibility of the hysteresis loop is approached by a simple analytical formula, providing close approximation for most applications.


The proposed solution, applying the reversal of Langevin function, to the problem provides a good practical solution.

Research limitations/implications

The simple analytical formula has been applied to a number of loops of widely different shapes and sizes with excellent results.

Practical implications

The proposed solution provides a missing mathematical tool to an unsolved problem for practical applications.

Social implications

The solution proposed will reduce the work required and provide replacement for expensive complex test instrumentation.


To the best of the authors’ knowledge, this approach used in this study is the first successful approach in this field, irrespective of the required waveform, and is completely independent of the model used by the user.



Takacs, J. (2017), "Hysteresis loop reversing by applying Langevin approximation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 4, pp. 850-858.



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