Circuit analysis of frequency splitting phenomena in wireless power transfer systems

The paper treats the wireless power transfer systems with series-series resonators from the point of view of the frequency splitting and bifurcation phenomena. We develop an exact mathematical model of the splitting phenomena (splitting equation) based on the algebraic equation theory, which allows finding exact values of the splitting frequencies. This is extremely useful to setup the magnetic coupling for any connection of the wireless power transfer systems. It is also investigated the variation of the splitting frequencies and the transferred power peaks in function of the magnetic coupling. The exact analysis of the frequency bifurcation phenomena is also studied and the relationship between frequency bifurcation and splitting is elucidated. It is also found an exact mathematical procedure, based on the algebraic equation theory, which allows finding exact values of the bifurcation coupling and the bifurcations frequencies. The theoretical results are validated by numerical simulations based on frequency analysis with different values of the system parameters and by a 10-W prototype with planar spiral coils [10].