Calculation of the performance of a magnetoresistive permalloy magnetic field sensor

Abstract

Design equations have been developed that predict the performance, in a uniform magnetic field, of a saturated Permalloy flat film magnetoresistor with uniaxial anisotropy. The functional dependence on film dimensions has been determined, of parameters characterizing the performance, including optimal operating point, optimal sensitivity, and range of linearity (one percent) around the optimal operating point. These performance parameters were derived from the device transfer or performance function which, in turn, was determined from a model based on a nonuniform demagnetizing field (NDF). We found that in a uniform field 1) the shape of the normalized performance function depends geometrically only on the film thickness-to-width ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t/w</tex> ; 2) the performance parameters were either linear or hyperbolic functions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t/w</tex> ; and 3) to avoid serious error in predicting performance, the NDF model should be used for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t/w \gsim 1 \times 10^{-4}</tex> . The coefficients for the performance parameter (design) equations are given and, with an upper bound error of ±5 percent, are valid for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t/w</tex> ratios that cover practical device dimensions.