Analytical solutions to eddy current and excess losses

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



This paper sets out to develop analytical solution to the hysteresis, eddy current and excess losses using the T(x) model. Based on Steinmetz' postulation, the losses, represented by the area enclosed by the hysteresis loop, are individually formulated in analytical form. The model is applied to sinusoidal and triangular excitation wave forms.


The equivalent interaction fields introduced into the model represent the losses individually by applying the separation and superposition principle.


Contrary to the presently used models, this model describes the hysteresis loop with its natural sigmoid shape and describes the losses individually in simpler mathematical formulation.

Research limitations/implications

Experimental verification will still be needed as to the accuracy of the model and the applicability to the various magnetic materials.

Practical implications

The model presented here gives a more realistic presentation of the hysteresis loop and by using simpler mathematics than other models it is more accessible to the practical user. At the same time with the easy mathematics and its visual presentation it is a great value to people engaged in theoretical research in the field of magnetics.


In contrast with present magnetic loss models, using almost exclusively MSPM with “flat power” loop or the elliptical equivalent loop approximations, these calculations based on the T(x) model of hysteresis and uses realistic shape for the hysteresis loop, resulting in a simpler mathematical formulation.



Takacs, J. (2005), "Analytical solutions to eddy current and excess losses", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 4, pp. 1402-1414.

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