On the Feedback of Eddy Currents in Layered Materials for Magnetic Speed Sensing

In this paper, we present a new analytical approach for studying the development and the influence of eddy currents in layered systems of cylindrical symmetry. It is based on the development of a scalar model and exploits a connection between the complete elliptic integral and infinite integrals of Bessel functions to find the solution in an analytic form. The method is specifically designed to help identify the critical model parameters and to understand their functional dependencies. In the context of magnetic speed sensor systems, connections between the feedback of eddy currents and critical parameters, such as penetration depth, lead frame thickness, and the position of the sensitive elements, are investigated, aiming to advocate on sensor layouts to improve signal stability. The developed formalism also bridges the gap between the scalar approach and the well-known off-axis magnetic field of a current loop. In addition, a collection of solutions for infinite integrals of Bessel functions is included of which only a few special cases are found in the literature.