Thin film recording head efficiency and noise

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Abstract
Analytic formulas for thin film recording head efficiency and thermal noise are presented. Paton’s transmission line model is replaced by two‐dimensional eddy currents in four regions: the coil region, the gap region, and two permeable pole regions. Predicted efficiencies are lower, and close to actual thin film heads. Basically, a four‐region solution is needed because the gap region is a reluctive load on the coil region’s pole reluctance, which lowers the predicted efficiency substantially below that of the unloaded Paton two region (coil and pole) transmission line. Paton efficiency formulas seem to often predict either too high an efficiency, or too low a permeability. For typical head dimensions, the four region efficiency formulas reduces to hand calculator simplicity. Eddy currents in the drive coils and conductive (permalloy) poles can cause the impedance phase angle θ of these heads to hover closer to 45° than to a purely inductive 90° (eddy currents in a permeable, plane slab have 45° average phase angle). Such eddy currents can give an unusual impedance Z( f), and can raise the real part of the head impedance (‖Z‖cos θ) an order of magnitude higher than the dc resistance, and thereby similarly raise the mean‐square thermal noise from the head. Magnetic field formulas from the four‐region eddy current equations are used to calculate this impedance and the excess noise factor.