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1 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE Nov.; 25(11), ISSN (Print)ISSN X (Online) Slab Analysis of Elements for Efficiencies in Magnetically-Coupled Wireless Power Transfer System Using Metamaterial Slab 김건영 오택규 이범선 Gunyoung KimTaekKyu OhBomson Lee 요약 slab Q-factor.,,.,. RR (Ring Resonator) SRR(Split Ring Resonator),., %( 53 %), 0.2( ), %. Abstract 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 Key words: Efficiency, Flux Focusing, Magnetic Coupling, Metamaterial, Wireless Power Transfer 2013 () (No. NRF-2013R1A2A2A ). (Department of Electronics and Radio Engineering, Kyung Hee University) * (Telecommunication Technology Center, Korea Testing Certification) Manuscript received March 5, 2014 ; Revised September 17, 2014 ; Accepted September 23, (ID No ) Corresponding Author: Bomson Lee ( c Copyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved.

2 Slab. 서론, [1][4].,,.. [2] [3],[4]. thin wire( ), spilt ring resonator ( ), [5].,,. [6]. [3] double-side spiral 27 MHz, 50 cm 17 % 47 %. [4] ring resonator., MHz, 24 cm, 12 cm ( ), 32 % 20 %., [5] slab. slab, slab.,,.. 모델링및분석 1 (magnetostatic) (slab)., d, a b slab s(a + b) slab, θ 1 θ 2 slab, μ r slab. 1 [7]. (1) (1) (d), slab (s), slab (μ r ). (1),,. 2(a)., V, R L,. ( ) magnetic dipole., khz MHz 그림 1. Fig. 1. Focusing of magnetic field coming from point source by a slab with negative relative permeability. 1129

3 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 11, Nov (a) (a) Geometry (b) (b) Equivalent circuit (c) Slab (c) Geometry of slab 그림 2. (slab) slab Fig. 2. Magnetically coupled WPT system using slab with negative relative permeability for magnetic flux focusing, its equivalent circuit, and geometry of slab.,, (1) slab. 2(b) 2(a)., R 1 R 2, L 1 L 2. M,, k. slab R s1 R s2 slab. Slab SRR EM. Rs 1 Rs 2 ( loop ), slab (a b), EM (R 1 + R s1 R 2 +R s2 ). Ring resonator( split ring resonator) 3 metamaterial slab 2(c). KVL I 1, I 2, P in P L., F m slab, (2) (3), b R L R L,opt (R L /R L,opt ),, R L,opt [8]. (4) EM. k EM- (3) (4), [8]. (4) 1130

4 Slab. 시뮬레이션결과 3 EM S-. 3 (a) (b) slab(μ r =1) slab(μ r =1j2)., 5 cm, 0.2 cm, slab, Q-factor 790. 표 1. Table 1. Summary of WPT efficiencies. EM Meas. Slab [%] R L,opt [Ω] j RR RR jj0.23 (at MHz) jj0.23 (at MHz) (r=5.5 cm, d=24 cm, s=12 cm, h=36 cm a=b) (a) slab(μ r =1) (a) Lossless slab(μ r =1) 그림 4. Slab (η L ), slab (η S ), (F m )(r= 5 cm, d=24 cm, s=12 cm, h=60 cm, a=b) Fig. 4. Transfer efficiency(η L ), absorption rate(η S ) in the slab, and figure of merit(f m ) considering slab losses as a function of slab loss tangent(r=5 cm, d=24 cm, s=12 cm, h=60 cm, and a=b). (b) slab(μ r =1j2) (b) Lossy slab(μ r =1j2) 그림 3. Slab EM (r=5 cm, d=24 cm, s=12 cm, h=60 cm, a=b) Fig. 3. Comparison of circuit and EM simulation result according to slab losses(r=5 cm, d=24 cm, s=12 cm, h =60 cm, and a=b). 24 cm, slab 12 cm, 60 cm. slab, R s1, R s Ω, slab R s1 R s Ω. EM. 1 [4] MHz (r) 5.5 cm, (r ring ) 0.1 cm, 1131

5 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 11, Nov Q-factor 473. (d) 24 cm, slab (μ r ) 1. (1) slab (s) 12 cm, slab (h) 37 cm. 1 (slab), ring resonator(rr) MHz 1. 1, slab slab ( ) 32 % 97 % 65 %. RR, [4] 1 (magnetic loss tangent, tanθ m) 0.23., EM slab 32 % 20 % 12 %. slab, 1 slab ( ). 4 slab (η L ), slab (η S ), (F m =kq)., 3, slab 1, slab 12 cm, 60 cm, slab,,. Slab 53 %, slab 100 %, slab 50 %. Slab Rs 1, R s2, (F m ). F m Q-factor, slab 3. Slab. (RR, SRR ). slab. slab, slab. 5 3 slab. Slab.. 1 j0.001( slab), 1j0.2( slab) 0., 53 %., 86 % 33 %., s/d 0.6, slab, s/d %., s/d 0.25 slab, s/d %. slab 1, (1) s/d 0.5. slab, slab. slab, slab 1132

6 Slab slab,..,. References 그림 5., slab (s) (η L ) (r=5 cm, d=24 cm, h=60 cm, a=b). Fig. 5. Transfer efficiency(η L ) as a function of width of slab(s)(r=5 cm, d=24 cm, h=60 cm, and a=b).., 8 %, (μ r =1j0.2) slab 23 %., MRI(Magnetic Resonance Imaging) [9].. 결론., slab. slab Q-factor. Q-factor slab. slab,,. [1] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljacic, "Wireless power transfer via strongly coupled magnetic resonance", Science, vol. 317, no. 5834, pp , Jul [2] X. Zhang, S. L. Ho, and W. N. Fu, "Quantitative design and analysis of relay resonators in wireless power transfer system", IEEE Trans. Magn., vol. 48, no. 11, pp , Nov [3] B. Wang, K. H. Teo, T. Nishino, W. Yerazunis, J. Barnwell, and J. Zhang, "Experiments on wireless power transfer with metamaterials", Appl. Phys. Lett., vol. 98, no. 25, pp (1-3), Jun [4] T. Oh, B. Lee, "Analysis of wireless power transfer using metamaterial slabs made of ring resonators at MHz", JEES, vol. 13, no. 4, pp , Dec [5] J. B. Pendry, "Negative refraction makes a perfect lens", Phys. Rev. Lett., vol. 85, no. 18, pp , Oct [6] N. Garcia, M. Neito-Vesperinas, "Left-handed materials do not make a perfect lens", Phys. Rev. Lett., vol. 88, no. 20, pp (1-4), May [7] M. N. O. Sadiku, Elements of Electromagnetics, Prentice-Hall, Oxford USA, [8],, " ",, 23(9), pp , [9] M. J. Freire, L. Jelinek, R. Marques, and M. Lapine, "On the applications of μ r =1 metamaterial lenses for magnetic resonance imaging", J. Magn. Reson., vol. 203, pp , Dec

7 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 11, Nov : () : () : [ 주관심분야 ] Small Antenna, Metamaterial, Microwave Passive Devices, Wireless Power Transmission : ( ) : () : () : : [ 주관심분야 ] Microwave Antenna, Metamaterials, RF Identification(RFID) Tags, Microwave Passive Devices, Wireless Power Transmisson : () : () ~: [ 주관심분야 ] Antenna, Metamaterials, Microwave Passive Devices, Wireless Power Transmisson 1134

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