Analytical approximations for the magnetic readback signal with application to pulse slimming equalization

The two-parameter arctangent formula is shown to represent a realistic model for the output of a ferrite head. The parameters are estimates of the gap width and head-to-medium separation for the case of a thin medium and ferrite head. As the ratio of gap width to separation approaches zero, the arctangent function approaches the Lorentzian. The accuracy of the arctangent approximation is evaluated by comparing it with actual flux transition responses, as well as with responses generated by a self-consistent two-dimensional physical model of the magnetic process. The Fourier transform of the two-parameter formula is a simple analytic expression providing a good approximation to the head frequency spectrum. The simpler one-parameter Lorentzian approximation, although adequate in many applications, yields optimistic results for pulse-slimming equalization in low-noise environments.