Linear approximation * exponential function of T

Presentation

This model defines a B(H) behavior law:

• linear (without taking the saturation into consideration)
• for an isotropic material
• through a magnetic susceptibility χ (where χ = μ_r - 1) which decreases in an exponential way when the temperature increases

It can be used for low magnetic fields as long as saturation is not reached.

Mathematical model

This model is based on a straight line equation whose μ_r slope varies with the temperature.

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 the material for T = 0 °C
• coeff(T) is the temperature coefficient function which describes how the magnetic susceptibility χ decreases when the temperature increases

The shape of the B(H) curve for several temperature values is presented in the figure below.