Analytic solutions for double-element shielded magnetoresistive heads

New analytic solutions are presented for idealized mathematical models of d ouble-element shielded magnetoresistive (MR) magnetic recording heads. Two types of heads are considered, represented by poles of either equal or oppo site magnetic potentials, each in the presence of an infinitely permeable u nderlayer. The solutions for heads without underlayers are special cases of the more general results. Typical field plots and spectral response functi ons are given and comparisons are made with published approximate solutions .