Analysis, Experimental Results, and Range Adaptation of Magnetically Coupled Resonators for Wireless Power Transfer

Wireless power technology offers the promise of cutting the last cord, allowing users to seamlessly recharge mobile devices as easily as data are transmitted through the air. Initial work on the use of magnetically coupled resonators for this purpose has shown promising results. We present new analysis that yields critical insight into the design of practical systems, including the introduction of key figures of merit that can be used to compare systems with vastly different geometries and operating conditions. A circuit model is presented along with a derivation of key system concepts, such as frequency splitting, the maximum operating distance (critical coupling), and the behavior of the system as it becomes undercoupled. This theoretical model is validated against measured data and shows an excellent average coefficient of determination <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(R^{2})$</tex> </formula> of 0.9875. An adaptive frequency tuning technique is demonstrated, which compensates for efficiency variations encountered when the transmitter-to-receiver distance and/or orientation are varied. The method demonstrated in this paper allows a fixed-load receiver to be moved to nearly any position and/or orientation within the range of the transmitter and still achieve a near-constant efficiency of over 70% for a range of 0–70 cm.