Analytic nonlinear correction to the impedance boundary condition

The linear impedance boundary condition is based on the solution of Maxwell´s equations for a slab of conducting material with a constant permeability and a given tangential surface magnetic field. The permeability is assumed high enough that the eddy currents are confined to a narrow thickness near the surface. By solving these equations for a similar geometry but with a nonlinear B-H curve, the losses obtained were compared with the linear losses and a correction factor obtained. This correction factor is a function of the surface magnetic field and can be implemented in finite element programs. Using this approach, the stray losses obtained with a finite element program were in good agreement with the tested losses for a variety of transformers.