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 , 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, Republic of Korea 報告人 : 碩研電子一甲 MA 林殿朗 Southern 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. Proceedings of the Asia-Pacific Microwave Conference 2011

2 Fig. 1. Geometry of the metamaterial-inspired loop radius10 cm width2 mm thickness0.018 mm

3 Proceedings of the Asia-Pacific Microwave Conference 2011 Fig. 2. Current distribution of proposed loop

4 Proceedings of the Asia-Pacific Microwave Conference 2011 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.

5 Proceedings of the Asia-Pacific Microwave Conference 2011 M, k : coupling coefficient L1 and L2 are the inductances Fig. 4. Equivalent circuit for the magnetically coupled loops considering radiation loss

6 Proceedings of the Asia-Pacific Microwave Conference 2011 Based on Fig. 4, I1 and I2 at a angular resonant frequency 0 ω are obtained as

7 Proceedings of the Asia-Pacific Microwave Conference 2011 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

8 Proceedings of the Asia-Pacific Microwave Conference 2011 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.

9 Proceedings of the Asia-Pacific Microwave Conference 2011 Fig. 5. Photograph of the measurement set-up for WPT The loops shown in Fig. 5 have been fabricated on FR-4 substrate with height 1mm and relative permittivity 4.9.

10 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

11 Proceedings of the Asia-Pacific Microwave Conference 2011 Fig. 10. k and Rr with varying distances

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13 Proceedings of the Asia-Pacific Microwave Conference 2011 CONCLUSION We 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.

14 Proceedings of the Asia-Pacific Microwave Conference 2011 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。