Figure of merit for power loss

Dries van Wageningen and Eberhard Waffenschmidt, Philips Research

A wireless power system is limited by the power losses which appear in the system. This is wasted energy and the losses generate heat, which sets an upper limit of power which can be transferred. Therefore, an optimization strategy aims in minimizing the losses.

The losses can be expressed as loss factor

which is the sum of all losses related to the transferred power. A deeper analysis results in an minimum loss factor, which can be achieved by a given wireless power system, if it is proper matched to load and generator:

 
Which can be reduced to:

(thanks to Esko Strömmer for pointing out this simplification)

The equation is shown graphically in figure 3. The equation is only dependent on the two basic parameters of the wireless power system: The coupling factor k between the receiver and transmitter coil and the system quality factor Q. The system quality factor is the geometrical average of the transmitter’s and receiver’s quality factors.
The equation suggests the product of the system quality factor Q and the coupling factor k as a general figure of merit (FOM). This means, that the system quality factor and the coupling factor determine the performance in an equivalent way. A worse coupling can be linearly compensated by a better quality factor and vice versa.