The Jiles-Atherton model of magnetic hysteresis was introduced in 1984. This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material. Jiles-Atherton model enables calculation of minor and major hysteresis loops. The original Jiles-Atherton model is suitable only for isotropic materials. However, an extension of this model presented by Ramesh et al. and corrected by Szewczyk enables the modeling of anisotropic magnetic materials.
Contents
Principles
Magnetization
Parameters
Original Jiles-Atherton model considers following parameters:
Extension considering uniaxial anisotropy introduced by Ramesh et al. and corrected by Szewczyk requires additional parameters:
Effective magnetic field
Effective magnetic field
This effective magnetic field is analogous to the Weiss mean field acting on magnetic moments within a magnetic domain.
Anhysteretic magnetization
Anhysteretic magnetization can be observed experimentally, when magnetic material is demagnetized under the influence of constant magnetic field. However, measurements of anhysteretic magnetization are very sophisticated due to the fact, that the fluxmeter has to keep accuracy of integration during the demagnetization process. As a result, experimental verification of the model of anhysteretic magnetization is possible only for materials with negligible hysteresis loop.
Anhysteretic magnetization of typical magnetic material can be calculated as a weighted sum of isotropic and anisotropic anhysteretic magnetization:
Isotropic
Isotropic anhysteretic magnetization
Anisotropic
Anisotropic anhysteretic magnetization
where
It should be highlighted, that typing mistake happened in the original Ramesh et al. publication. As a result, for isotropic material (where
In the corrected form, model for anisotropic anhysteretic magnetization
Magnetization as a function of magnetizing field
In Jiles-Atherton model, M(H) dependence is given in form of following ordinary differential equation:
where
Flux density as a function of magnetizing field
Flux density
where
Vectorized Jiles-Atherton model
Vectorized Jiles-Atherton model is constructed as the superposition of three scalar models one for each principal axe. This model is especially suitable for finite element method computations.
Numerical problems
Two most important computational problems connected with the Jiles-Atherton model were identified:
For numerical integration of the anisotropic anhysteretic magnetization
Further development
Since its introduction in 1984, Jiles-Atherton model was intensively developed. As a result, this model may be applied for the modeling of:
Moreover, different corrections were implemented, especially:
Applications
Jiles-Atherton model may be applied for modeling:
It is also widely used for electronic circuit simulation, especially for models of inductive components, such as transformers or chokes.