Sinusoidal B

Assuming both that B is sinusoidal with time, t, and that the value of H is derived from the original B-H curve, H_e, representing the effective magnetic field, can be calculated.

The derivation of the effective H_e is based on the equivalence of averaged energy between using original, non-sinusoidal H field and the effective sinusoidal field H_esin(wt). That is,

with , the above expression becomes

Allowing a = wt and extracting H_e, simplifying yields

or

where B_m corresponds to the last point on the original B-H characteristic (in the saturation portion) and which is made equal with p/2.

The above equation is used to derive an effective (B_m, H_e) characteristic for the frequency domain simulation. This process is required to be performed only once for a particular B-H curve. During the simulation, H_e is determined for a specific B_m such that an equivalent permeability can be computed as the ratio B_m / H_e and used in the calculations.