Analytic and quasi-analytic formulae for MR heads

We present analytic procedures for calculating the magnetostatic and response functions of magnetoresistive (MR) recording heads. To apply these methods we make several simplifying approximations, which have been found to be valid for typical recording head geometries. In particular, we show how to calculate the bias magnetization distribution, ideal transition pulse shape, and frequency response for the unshielded MR (UMR) head. To do this, we summarize methods based on conformal mapping and reciprocity, and present a simpler direct method which produces identical results. We extend this alternate method to find analytic expressions for the saturated bias magnetization.