An Approach to Modeling and Scaling of Hysteresis in Soft Magnetic Materials. I Magnetization Curve

TL;DR

This paper introduces a novel, scalable mathematical model for hysteresis loops in soft magnetic materials, extending the tanh function with a flexible exponential base, and demonstrates its self-similarity and invariance under scaling.

Contribution

It presents a new mathematical model for hysteresis that is self-similar and invariant under scaling, extending existing models with a generalized exponential function.

Findings

Model is self-similar and invariant under scaling.

Extension of tanh with a variable exponential base.

Applicable to modeling hysteresis in soft magnetic materials.

Abstract

A new mathematical model of hysteresis loop has been derived. Model consists in an extansion of tanh($\cdot$) by extanding the base of exp function into an arbitrary positive number. The presented model is self-similar and invariant with respect to scaling. Scaling of magnetic hysteresis loop has been done using the notion of homogenous function in general sense.