Title: Retrodirective Antenna Array Approach to Achieve Maximum Theoretical Beam Efficiency in Microwave Wireless Power Transfer

Abstract: Efficient long range wireless power transfer (WPT) is realized if the distance between the source and receiver is less than the Fraunhoffer distance. This distance increases proportionally to the square root of the antenna size so to achieve efficient long range WPT, larger antennas are mandatory, but that comes with difficulty in implementing both the feeding network and beamforming control of the antenna. Several proposed implementations require power-hungry processors rendering implementation impractical. An alternative to reduce usage of digital processing is in the form of retrodirective antenna arrays. Its core operation is to track an incoming signal's direction of arrival and resend it to the same direction. This can be implemented by analog circuits. Retrodirective capability on both the generator and rectenna arrays creates a feedback loop that produces a high efficiency WPT channel. In this paper, we characterize the dynamics of this phenomenon using a discrete-time state-space model based on S-parameters and show that the system can naturally achieve maximum theoretical WPT efficiency. We further confirmed the theoretical analysis through a hardware experiment using a 12-port circuit board with measurable S-parameters mimicking a deterministic wireless channel. The results of the hardware experiment show agreement with the proposed theoretical framework.