論文探討 : Analysis of wireless power transmission between metamaterialinspired

loops ChungJu Kim#1, Bomson Lee#2 # Department of Electronics and Radio Engineering, College of

Electronics and Information, Kyung Hee University 446-701, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do,

Republic of Korea

kimcj@khu.ac.kr bomson@khu.ac.kr

報告人 : 碩研電子一甲 MA130225 林殿朗

Southern Taiwan UniversitySouthern Taiwan University Department of Electronic Engineering

Abstract This paper models and analyzes the wireless power transmission

(WPT) between two metamaterial-inspired loops employing a generalized equivalent circuit.

The use of the metamaterial-inspired loop is for uniform current distribution along the loop even when the loop circumference is comparable to wavelength.

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Fig. 1. Geometry of the metamaterial-inspired loop

radius 10 cm

width 2 mm

thickness 0.018 mm

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Fig. 2. Current distribution of proposed loop

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Fig. 3. Reflection coefficient of the loop

The radiation resistance at resonant frequency has been found to be about 30 Ù from EM simulation and 32.2 Ù from measurement.

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M , k : coupling coefficient L1 and L2 are the inductancesFig. 4. Equivalent circuit for the magnetically coupled loops considering radiation loss

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Based on Fig. 4, I1 and I2 at a angular resonant frequency 0 ω are obtained as

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If the two loops are identical and assumed to be lossless for simplicity ( R1=R2=0, Rr1=Rr2=Rr, L1=L2 =L, C1=C2, and M=kL), based on the equivalent circuit (Fig. 4) and Sparameters obtained from EM simulation (or measurements), radiation loss rate and transmission rate can be shown to be given by

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For the closely coupled case, where two resonant frequencies are usually shown in the simulated or measured S-parameters, we can easily calculate the coupling coefficient k using equation (5).

Where, and are the high and low frequency of the two resonant frequencies [6].

Once is obtained, the radiation resistance can be extracted from (3) or (4) using a root-finding algorithm.

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Fig. 5. Photograph of the measurement set-up for WPTThe loops shown in Fig. 5 have been fabricated on FR-4 substrate with height 1mm and relative permittivity 4.9.

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Fig. 6. S-parameters when the distance between the two loops are 5 cm

Fig. 7. S-parameters when the distance between the two loops are 10 cm

Fig. 8. S-parameters when the distance between the two loops are 20 cm

Fig. 9. S-parameters when the distance between the two loops are 30 cm

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Fig. 10. k and Rr with varying distances

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CONCLUSIONWe have proposed and analyzed the equivalent circuit for the magnetically coupled WPT between the two metamaterial-inspired loops in terms of radiation factors and coupling coefficient. The current flowing on the metamaterial-inspired loop has been found to be almost uniform even when the loop circumference compared with wavelength is not small. The WPT efficiency when has been found to be about 0.4. The modeling of the WPT using the radiation loss resistances is considered to be valid since the circuit- and EM-simulated results excellently agree with each other. The modeling of the WPT in terms of circuit characterizations gives us sufficient physical insight for the problem.

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心得：這篇 paper讓我了解到無線電力傳輸是用共振方式來傳送能量，有公式分析，且有實例對照說明。