Isotropic / anisotropic soft magnetic material: analytic saturation curve

Presentation

This model defines a nonlinear B(H) dependence for an isotropic material, taking the saturation into consideration.

Mathematical model

This model is composed of a straight line and an arctangent curve.

The corresponding mathematical formula is written as:

where:

• μ₀ is the permeability of vacuum, μ₀ = 4 π 10^-7 H/m
• μ_r is the initial relative permeability of the material (at the origin)
• J_s is the magnetic polarization at saturation T

The shape of this B(H) model is given in the figure below.

Anisotropic material

For an anisotropic material, this model consists in a set of three equations, one per 3D-space direction.

This model is available when the following conditions are satisfied:

• 2D applications (2D plane domain): Magneto Static / Transient magnetic
• regions: magnetic non conducting, solid conductor