Isotropic soft magnetic material: Rayleigh parabola curve + straight line

Presentation

In cases of low magnetic fields, this model defines a B(H) dependence for an isotropic material, taking the Raleigh zone into consideration.

Mathematical model

This model is comprised of a parabola and a straight line.

The corresponding mathematical formula is written as follows:

B(H)=μ₀μ_riH + (μ_rf - μ_ri)H²/2H_j → if H < H_j

Β(Η)=μ₀μ_rfΗ-μ₀(μ_rf - μ_ri)Η_j/2 → if H > H_j

where:

• μ₀ is the permeability of vacuum, μ₀ = 4 π 10^-7 H/m
• μ_ri is the initial relative permeability (at the origin)
• μ_rf is the final relative permeability (at the junction point of the parabola and the straight line)
• H_j is the magnetic field at the junction point of the parabola and the straight line

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