Numerical model of Hall sensor at the source of a rectangular magnet field

Hall sensors play an important role in magnetic sensing. In recent years, many sensors and electronic products applied to industrial production and daily life have been developed based on Hall sensors. The performance of Hall sensors is based on the measurement of Hall voltage induced by the magnetic field distribution of the magnet. The theoretical model of Hall voltage related to the magnetic field which is the key to design detection devices based on Hall sensors has been studied. For the rectangular permanent magnet that is completely magnetized in a certain direction, starting from the molecular circulation model and the Bio-Safari theorem, the analytical expression of the magnetic field component in space is derived. Then, based on the Hall effect theory, it is deduced that under the magnetic field excited by the rectangular magnet, the accurate analytical expression of the Hall element relative to the Hall voltage of the magnet at any position in space is calculated. Furthermore, the correctness of the theoretical formula is verified by experiments. This paper illustrates the laws of variation and difference of Hall voltage during space movement of Hall elements relative to magnets along the X, Y, and Z axes. Our work may provide magnetic detection theory guidance for multidimensional force perception and spatial displacement detection.