An analytic approach to magnetic speed sensing

To design and optimally layout sensor systems that involve magnetic sensing technologies a fundamental understanding of the underlying physics of magnetic field propagation is often indispensable. This work focuses on magnetic speed sensor layout and comprises an analytical treatment of the feed back of eddy currents that develop in thin layers onto the external magnetic field. The method proposed in this work is based on a connection between infinite integrals of Bessel functions and the complete elliptic integrals and is demonstrated for simple, well-known solutions. In the general case this ansatz provides means to go beyond the usual integral solutions, supplying a basis for further functional understanding of this problem. Connections between skin depth, sensor position, field inhomogeneity and other key parameters are discussed with potentially relevant insights into optimal sensor positioning for chip manufacturers.