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In this article, we introduce a general analytical procedure to unambiguously characterize a metasurface through its lumped circuital equivalent in resonant inductive Wireless Power Transfer (WPT) applications. The proposed model incorporates the finite extent of the slab, as well as the WPT near field operative regime and the presence of the particular driving/receiving coils arrangement, providing quantitative and easy-to-handle parameters which can be manipulated to achieve WPT performance enhancement. We first develop the theoretical background aimed at the lumped parameters extraction, which reveals, for WPT applications, more accurate and robust with respect to the conventional sub-wavelength homogenization theories based on infinite slab extent and impinging plane wave hypotheses. We provide some general guidelines for the design of metasurfaces for WPT performance enhancement based on the derived circuit model; afterwards, we numerically design a test-case consisting of two resonant coils (driver and receiver, respectively) with an interposed passive metasurface to verify the developed theory. Finally, we show some measurements performed on a fabricated prototype, that present an overall excellent agreement with both the lumped model and the numerical simulations.
Brizi et al. (Wed,) studied this question.