Semi Analytical Study and Calculation of Magnetic Flux Density Created by Rectangularly Shaped Planar Coils With Rounded Corners

Abstract

In this paper, magnetic flux density induced by a rectangularly shaped single-turn planar coil with rounded corners is investigated. Starting from Biot-Savart law analytical derivations are obtained and contributions of straight edges and rounded corners of a coil to a flux density at a point in a three-dimensional space are formulated. In the derived formula the magnetic flux density generated by a coil with rounded corners is expressed as a function of the coil's geometrical parameters including start and end points of the roundings together with the center of the circles that contain arcs at the corners and observation point coordinates. Magnetic flux density distribution of rectangular coils with different sizes and roundings at the corners were calculated on distinct planes by using the derived formula. Also, FEM based electromagnetic simulations and measurements were done for the same coils. The results obtained in the analytical calculations, FEM calculations and measurements are in a good agreement.