Analytic solutions for double-element shielded magnetoresistive heads

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