High Frequency Nonlinear Modeling of Magnetic Sheets using Polynomial Expansions for Eddy-current Field

Abstract

Cauer realizations of the complex permeability of magnetic sheets can provide powerful means for the homogenization methods applied to the laminated magnetic sheets. The derivations of Cauer realizations are based on the recurrence formula of Bessel functions because the formula provides continued-fraction expansion of complex permeability, which corresponds to Cauer I realization. However, the physical meaning of Cauer I realization is not clearly understood, whereas Cauer II realization is interpreted as the direct discretization of magnetic materials. This paper reveals that the Cauer I realization is also derived by the polynomial expansions of eddy current fields in the magnetic sheets. Through this technique, the physical meaning of Cauer I realization is clarified. The proposed method is combined with the play model, the modeling method for the nonlinear and hysteresis properties of magnetic sheets. Simulations are performed and compared with the experimental results and finite element analysis.