The Optimum Layout for Giant Magneto-Resistive Angle Sensors

360° angle sensors use small permanent magnets attached to the shaft. The magnet is polarized perpendicularly to the axis of rotation, and a magnetic field sensor is placed underneath on the axis. The sensor circuit consists of two orthogonal bridges having four giant magneto-resistive (GMR) elements. In a prior work it was shown that even though the magnetic field sensor may be calibrated perfectly, still significant angle errors may result from assembly tolerances of magnet and sensor. This work investigates how shape and size of the GMRs affect this error. Optimum layouts for GMRs fulfill three constraints: (i) the centers of gravity of all GMRs of both bridges lie on the axis of rotation; (ii) the sum over the deviation moments of all GMRs of each bridge circuit vanishes; and (iii) the sums over the moments of inertia around two perpendicular axes in the die surface are equal. Examples of optimized layouts are given. Layout and assembly tolerances interact to give an overall angle error, which is expanded into a second-order Taylor series. Monte Carlo simulations show that optimum layout reduces typical angle errors significantly and worst case angle errors moderately. For Gaussian distributed assembly tolerances with standard deviations of 0.1 mm and 1° and cylindrical magnets with 5 mm diameter 99.7% of all systems have errors less than +/-0.41°. Magnets with 10 mm diameter have only +/-0.16° error. It is shown that magnetic angle sensors are more robust against eccentricities of the shaft than many optical encoder systems.