Power division ratio on multi-hop WPT considering coupling of the receiver with two couplers

We derive theoretically the power division ratio (PDR) on multi-hop wireless power transfer (WPT) to two receivers coupling with two couplers. The derived expression suggests that the PDR can be controlled by adjusting the load resistance. However, the control range of PDR by adjusting the load resistance of one receiver is limited when a hop count to that receiver is odd number. Therefore we show that the PDR can be controlled by another two methods; control of load resistances of each receiver and control of the load impedance of one receiver. These two methods can control the PDR within coaxial misalignment around the radius of the coupler.