A Novel Theoretical Modeling of the Received Power for Phased Array-Based Wireless Power Transfer System in the Near-Field Region

In a phased array-based radio-frequency (RF) wireless power transfer system, the power transfer efficiency can be determined from the transmitted and received power density levels of the individual elements of the array antenna. In this paper, a novel theoretical model to calculate the received power from individual elements of the transmitter array antenna and estimate the received power, specifically in the near-field region is proposed, analyzed, and experimentally validated. The proposed WPT technology utilizes a 2.4 GHz radiative near-field (Fresnel region) power transmission scheme. The calculated results using this analysis have been verified using a complete phased array antenna-based wireless power transfer system. The proposed WPT system consists of a unidirectional $4\times 4$ transmitter array antenna of $2.12~\lambda _{o}\times 2.09~\lambda _{o}$ dimension and a bi-directional receiver antenna of $0.25~\lambda _{o}\times 0.3~\lambda _{o}$ dimension. The proposed methodology is capable of accurately calculating the transmitted and received powers in both Fresnel and Reactive near-field zones, compared to traditional approaches (for example, the Friis path loss model and Goubau equation). This proposed uniform theoretical approach is highly applicable as a tool to calculate the Power Transfer Efficiency (PTE) effectively and reliably in the near-field region.