An enhanced perturbation method for analysis of inductance

The inductance of a ferrite cup core inductor is the sum of two parts. One part is the self-inductance of the winding, The other dominant part can be called the residual inductance. We present a mathematical method for calculating the residual inductance from the geometry of the inductor and the permeability μ of the ferrite. The first step in the method is to develop a pair of perturbation series for the residual inductance, one series in powers of 1/μ, and the other series in powers of μ. The final step is to form a Padé approximant based on these series. The Padé approximant yields a uniformly valid approximation, whereas the series may diverge. We describe an application of the method, and discuss its convergence.