Gain expressions for capacitive wireless power transfer with one electric field repeater

In this paper, the use of a repeater element between the transmitter and the receiver of a capacitive wireless power transfer system for achieving larger transfer distances is analyzed. A network formalism is adopted and the performance described by using the three power gains usually adopted in the context of two-port active networks. The analytical expressions of the gains as function of the network elements are derived. Assuming that the parameters of the link are given and fixed, including the coupling factors between transmitter, repeater and receiver, the conditions for maximizing the different gains by acting on the network terminating impedances (i.e., load and internal source conductance) are determined. The analytical formulas are verified through circuital simulations.