International Journal of Antennas and Propagation

Volume 2015, Article ID 840135, 7 pages

http://dx.doi.org/10.1155/2015/840135

## Effects of Metamaterial Slabs Applied to Wireless Power Transfer at 13.56 MHz

^{1}Department of Electronics and Radio Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 446-701, Republic of Korea^{2}Telecommunication Technology Center, Korea Testing Certification, 22 Heungan-daero, 27 Beon-gil, Gunpo-si, Gyeonggi-do 435-862, Republic of Korea

Received 16 October 2014; Revised 5 January 2015; Accepted 19 January 2015

Academic Editor: Francisco Falcone

Copyright © 2015 Gunyoung Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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) with (*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 when is 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.

#### 1. Introduction

The concept of WPT was conceived by N. Tesla in 1914, but, until recently, it had not been developed to any commercial application due to its low efficiency. In 2007, a magnetically coupled WPT system based on coupled mode theory (CMT) was first demonstrated [1], and following that paper, various types of resonators have been proposed to enhance the WPT efficiencies. However, an ongoing problem is the limited maximum efficiency determined by a given system figure of merit, which is defined by the product of a magnetic flux coupling coefficient and resonator quality factor [2]. One approach to overcome this limit is to use a metamaterial slab between the two loop resonators. The realization of media having negative permittivity and permeability has become feasible after Pendry et al. proposed a method using an array of thin wires [3] in 1998 and split ring resonators (SRRs) [4] in 1999. In [5], a perfect lens was proposed and it was theoretically shown that a transverse electromagnetic wave generated from a point source and incident on a metamaterial slab with and is focused in the slab and refocused at a point in the other side of the slab. It was also suggested that a longitudinal quasi-magnetostatic field can be focused by a slab and its dual case may also be possible with an slab. Loss effects of SRR were already examined in [5] and some new structures were proposed in [6, 7] to decrease losses in the resonators for the medium. Nevertheless, a slab with at 63.87 MHz was applied to magnetic resonance imaging [8–10] resulting in a considerable enhancement of MRI images. Besides, there have been some initial trials of employing metamaterial slabs in WPT problems to enhance efficiencies. In [11], it was reported that even with a realistic magnetic loss tangent of 0.1, the WPT efficiency with a slab can be an order of magnitude greater than free space efficiency. The experiments with a slab made of double-side spiral resonators [12] showed that power transfer efficiency of a WPT system could be improved from 17% to 47%. In a recent review paper [13], many promising features of metamaterial slabs for WPT problems were summarized. Another approach in WPT is to use relays, of which main function is to guide the magnetic flux from a Tx resonator to an Rx resonator. The configuration and design methods of relays are usually simpler than those of the metamaterial slab. It was reported in [14] that although conventional wireless electric systems can only achieve about 10% efficiency over a 30 cm distance, the efficiency of the relayed system can reach up to 46%. In fact, in a separate work, we could also observe that if a simple loop resonator is used as a relay, the efficiency is considerably enhanced typically by three to four times compared with that of the free space case. The working mechanisms of metamaterial slabs (focusing) and relays (guiding) are completely different [5, 14]. In our analysis and examinations, the enhanced WPT efficiencies reported in [12, 13] seem to be due to the effect of the guided magnetic flux by a relay, not due to the focused magnetic fields by a metamaterial slab, considering that the thickness of the used slab in [12] is much thinner than that theoretically required in [5].

In this paper, we examine the effects of a practical “super-lens” when applied to a typical WPT problem, sticking to the theory of focusing fields in [5] as much as possible. A metamaterial slab made of ring resonators is placed between a Tx loop resonator and an Rx loop resonator to focus quasi-static magnetic fields and enhance the efficiencies. In the first place, a simple design equation is derived for the cases of using slabs with arbitrary negative permeability, based on [5, 15]. Based on this formula, two loop WPT systems at 13.56 MHz employing lossless metamaterial slabs with effective permeability of −1, −2, and −3 are examined in terms of coupling coefficients and WPT efficiencies. Then, a near-isotropic slab consisting of planar-type ring resonators (referred to as an isotropic RR slab) is designed and fabricated to have (evaluated later to be due to losses on the ring resonators) at 13.56 MHz. The measured WPT efficiencies are compared with the full-wave simulation results based on the same slab and an ideal isotropic slab with (irrespective of frequency). The effects of a practical “perfect lens” are quantitatively discussed in terms of an optimum load in the Rx loop, coupling coefficients, effective -factors of the loop resonators considering slab losses, and efficiencies.

#### 2. WPT System Using Lossless Metamaterial Slabs

Figure 1 shows a simple WPT system consisting of two loop resonators and a metamaterial slab placed between them. At the very low frequencies used in WPT systems (i.e., from several MHz down to kHz), the system size is usually very small compared with the wavelength. Thus, quasi-magnetostatics may be adopted. The loop is loaded with a chip capacitor for resonance at a design frequency. The loop resonator may also be understood as a small magnetic dipole consisting of and . Since the magnetic fields from the loop (or magnetic dipole) are dominantly in the longitudinal direction in the near field, they may be approximated as those from a point magnetic charge as shown in Figure 2. Based on this approximation and the proper boundary conditions for the magnetostatic fields [15], we can obtain where is the incident angle, is the refraction angle, is the distance between the two loops (), is the height of the slab determined to capture as much magnetic field from the loop as possible, and is the relative effective permeability usually realized with ring resonators (RR) or split ring resonators (SRRs). Note that must be negative to satisfy (1). The sum of and is the width () of the slab. The focusing of the fields from the loop mainly depends on the permeability (not on the permittivity) of the slab since magnetic fields are dominant in the near region of the loop.