This paper analyzes the effects of metamaterial slabs with negative permeability when applied to a two-loop wireless power transmission (WPT) system, both in theory and electromagnetic (EM) simulations. The analysis of magnetic flux focusing provided here assumes quasi-magnetostatics or magnetostatics. The slab structures with negative permeability have been realized using the periodically arrayed ring resonators (RRs) at 13.36 MHz. Some examples with ideal lossless slabs of 1, 2, and 3 showed a great enhancement of WPT efficiencies when compared with the free space cases. However, practical lossy slabs made of planar copper RRs did not show significant enhancement of WPT efficiencies due to the relatively high losses in the ring resonator (or in the slab consisting of RRs) near the resonant frequency.

This paper analyzes the effects of a metamaterial slab (or a practical “perfect lens”) with negative permeability applied to a two loop magnetically coupled wireless power transfer (WPT) system at 13.56 MHz, based on theory, full-wave electromagnetic- (EM-) simulations, and measurements. When using lossless slabs with ideal negative permeability in EM-simulations, the WPT efficiencies have been found to be enhanced close to 100% due to the magnetic field focusing. For the case of using a realistic slab made of ring resonators (RR)μr=-1-j0.23withs/d=0.5(s: slab width,d: distance between the transmitting and receiving loops), the WPT efficiency has been found to significantly decrease to about 20%, even lower than that of a free space case (32%) due to the heavy power absorption in the slab. However, some efficiency enhancement can be achieved whens/dis optimized between 0.1 and 0.3. Overall, the significant enhancement of efficiencies when using a lossless slab becomes moderate or only marginal when employing a realistic slab.

In this paper, the effects of a metamaterial slab with negative permeability in a magnetically coupled wireless power transfer system (WPT) in the overall performance are analyzed quantitatively in terms of the effective quality factors of the loop resonators and coupling coefficient considering the slab losses, based on an equivalent circuit. Using the ideal metamaterial slab(lossless slab), the WPT efficiency is improved considerably by the magnetic flux focusing. However, the practical lossy slab made of RRs or SRRs limits the significant enhancement of WPT efficiency due to the relatively high losses in the slab consisting of RRs or SRRs near the resonant frequency. For the practical loop resonator, other than a point magnetic charge, using the practical lossy metamaterial slab in order to improve the transfer efficiency, the width of the slab needs to be optimized somewhat less than the half of the distance between two loop resonators. For the low-loss slab with its loss tangent of 0.001, the WPT efficiency is maximized at 93 % when the ratio of the slab width and the distance between the two resonators is approximately 0.35, compared with 53 % for the case without the slab. The efficiency in case of employing the high-low slab(loss tangent: 0.2) is maximized at 61 % when the slab ratio is 0.25.

This paper presents the analysis of the coupling coefficient(k), Q value of the resonator, and the optimum loaded resistance at Rx for the magnetically coupled wireless power transmission using two loops(resonators). In addition, the metamaterial, conductor, and the relay methods have been used in order to improve the limitation problem of transmission efficiency by using the figure of merit. We have achieved the increase of transmission efficiency about 11～60 % using the proposed methods by analyzing and comparing the results based on EM simulations.

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