Mutual inductance calculation of movable planar coils on parallel surfaces

Recent developments of wireless battery charging platform have prompted the requirements to investigate the mutual inductance between a movable planar coil and the fixed planar coil on the charging platform. The wireless battery charging platform must allow the load to be placed anywhere on the charging surface. Therefore the relative position between the movable energy-receiving coil and the energy-transmitting coils on the charging platform must be flexible. In this paper, an extended formula is proposed for the mutual inductance calculation for two coaxial or non-coaxial planar spiral windings sandwiched between two double-layer substrates. It can quickly determine the mutual coupling of two planar windings that can have different relative positions and distance between them. This new calculation method provides a new and useful tool for determining the mutual inductance of a movable planar coil and the fixed planar coil on the wireless battery charging platform. The theory has been favorably tested and compared with practical measurements and also finite-element analysis.