Scaling law of coupling coefficient and coil size in wireless power transfer design via magnetic coupling

Wireless Power Transfer (WPT), such as magnetic resonant coupling using a magnetic field is being studied and discussed for a wide variety of applications. When the transmission distances are large, very large transmitters and receivers need to be considered. However, in the early stages of an investigation, it might be prohibitive to manufacture and evaluate coils of such a large size. To reduce costs and effort, a scaling law can be used to estimate the WPT efficiency of very large coils using the results of smaller coils. In this paper, a scaling law is proposed that relates the coil size to the coupling coefficient, assuming the ratio between the coil diameter and coil length remains constant. The coupling coefficient is one of the parameters that determine the maximum efficiency of magnetic field WPT. The proposed method was verified by an electromagnetic field simulator and experiment. The results of this study provide an easy method for estimating the WPT efficiency of very large coils.