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This paper studies the difference between retro-directive beamforming technique and retroreflective beamforming technique in the context of wireless power transmission applications. In all of our studies, a wireless power receiver broadcasts continuous-wave pilot signal; the wireless power transmitter receives and analyzes the pilot signal; finally, the wireless power transmitter transmits continuous-wave power with phase profile conjugate to that of the received pilot signal. Our study demonstrates that a linear equi-spaced antenna array configuration employed by the wireless power transmitter behaves as a retro-directive beamformer when the wireless power receiver resides in the far-zone of the wireless power transmitter, whereas it behaves as a retro-reflective beamformer when the wireless power receiver is not in the far-zone. This paper further investigates two types of array configurations other than linear equi-spaced array when the wireless power transmitter behaves as a retro-reflective beamformer. One is a V-shaped array, which is obtained by deforming the linear equi-spaced array to a “V” shape. The other is termed “perturbed array:” on the basis of linear equi-spaced array, all the elements’ locations are perturbed randomly. It is particularly interesting to compare the equi-spaced array and perturbed array. When the wireless power receiver resides 5 or 6 wavelengths away, a 6-element equi-spaced array and a 6-element perturbed array produce the same power level at the near-zone focal point, but the maximum far-zone gain associated with the perturbed array is 1 dB lower than the equi-spaced array. All the conclusions drawn in this paper are supported by numerical results as well as experimental results.

RETRO-DIRECTIVE BEAMFORMING VERSUS RETRO-REFLECTIVE BEAMFORMING WITH APPLICATIONS IN WIRELESS POWER TRANSMISSION