Inductance calculation for the curved rectangular coil

Wireless power transmission and charging technologies for smart devices, small robots and electric vehicles using the magnetic coupling have been available commercially [1]. And most of wireless charging pads sold in the markets have a planar shape. Therefore, 3-Dimensional wireless charging technology should be needed to improve the consumer product convenience. For 3D wireless charging, it is common to use multiple transmitting coils. And the shape of the transmitting coils is designed to conform to that of the transmitter system. In this case, the performances of the coils and the important design parameters determining the system efficiency can be varied with the shape. In this paper, the inductance calculation for a curved coil in 3D wireless charging is proposed and the comparison results with EM simulation is shown.