Analytic saturation curve * exponential function of T

Presentation

This model defines a B(H) behavior law:

• nonlinear (taking the saturation into consideration)
• for an isotropic material
• through a value of the saturation magnetic polarization J_s which decreases in an exponential way when the temperature increases

Mathematical model

This model is a combination of a straight line and an arc tangent curve. In this model, the saturation magnetic polarization J_s decreases in an exponential way when the temperature increases (J_s0 is multiplied by the value of a temperature coefficient COEF(T)).

The corresponding mathematical formula is written:

where:

• μ₀ is the permeability of vacuum; μ₀ = 4 π 10^-7 [H/m]
• μ_r0 is the relative permeability of material (at the origin) for T = 0°C
• J_s0 is the saturation magnetic polarization for T = 0°C [Tesla]
• COEF(T) is the previously described temperature coefficient

The shape of B(H) curve is presented in the figure below.

Example

An example of a B(H) curve dependent on T is presented in the figure below.

It is an analytic saturation curve * exponential function of T with:

T_curie = 720°, C = 100°C