Calculation of the Reversible Permeability of Gapped Cores from Measured Ring Core Data

Abstract
In ferrite data books the reversible permeability for small excitation levels is usually given vs. external dc magnetic field for different values of the effective permeability. To determine these curves the incremental permeability has to be measured on cores with different air gaps. Due to the grinding of different air gaps the determination of those curves is very costly. Also a judgement of the incremental permeability from ring cores, which are used in the material development, is not possible. In this paper the calculation of the incremental permeability for cores with homogeneous cross section from measured data of ring cores is presented. The reversible permeability vs. dc magnetic field and the amplitude permeability vs. flux density has to be measured. With those data the reversible permeability vs. flux density for the ring core can be calculated. Gans made the assumption that the reversible permeability vs. flux density is a material property. By calculating the drop of the flux density due to an air gap the incremental permeability for a gapped core with homogeneous cross section can be calculated as a function of the external dc magnetic field. Calculated and measured data for E-cores made of the S+M material N87 are in excellent accordance.