Analytical solution of Everett integral using Lorentzian Preisach function approximation

In this paper, we take in to account the Lorentzian function, already proposed as analytical function approximation in scalar Preisach-type modeling of hysteresis of soft magnetic materials. Preliminarily, we point out the properties of the Lorentzian function and the physical and mathematical meaning of its parameters. Successively, we show how the use of the Lorentzian function approximation allows to solve in complete analytical way the Everett's integral. In particular, we present in the paper the analytical expression in closed form of the first magnetization curve, of the symmetric and non-symmetric minor loops, and of the first- and second-order reversal curves. In addition, we show the use of the complete analytical formulas of the symmetric magnetic loops above-mentioned, applied to a simple identification procedure of the Lorentzian function parameters, by the knowledge of the measured major loop. Finally, in order to show the practical use of the analytical expression found, some computation examples and comparisons with experimental data are shown.