MATEC Web of Conferences 22, 02018 (2015) DOI: 10.1051/matecconf/20152202018 C Owned by the authors, published by EDP Sciences, 2015 Efficiency Analysis of Wireless Power Transmission for Portable Elec- tronics Xingping Xu, Chuanxiang Yu, Yuxin Zhang, Man Zhang & Haotian Hu School of Electrical Engineering, Chongqing University, Chongqing, China ABSTRACT: With the portable electronics becoming more and more popular, a model of wireless power transmission for general portable electronics was presented based on the principles of magnetic resonance trans- mission. And that transferring the model to an equivalent circuit was possible to calculate. The characteristics of the system and the optimal conditions were analyzed, and the influence of the transmission efficiency for the Coupling factor and the Quality factor was discussed. The theory analysis and simulation in MATLAB show that the performance of the system can be optimized by adjusting the coupling factor between the transmitter cou- pling coils. Furthermore, the feasibility of this theory was proven by experiments. Thus, this paper provides a useful reference to improve the wireless power transmission for portable electronics. Keywords: portable electronics; wireless power transmission; magnetic coupling resonance; efficiency 1 INTRODUCTION the actual transmission distance and equipment size. In the reference [6], the author presented the magnetic In November 2006, an assistant professor of depart- coupling of the resonance system made by different ment of physics in MIT, Marin Soljacic, first proposed size and asymmetric resonators without the theoretical magnetic coupling resonant WPT technology on the point of view of the working mechanism, and optimi- BBS in AIP industrial physics. And in June 2007, zation of system performance; the references [7-8] are using the technology, he successfully lit a 60-watt presented to adjust the distance between the transmit- light bulb in the distance of 2.13 meters. Efficiency is ter and receiver to achieve impedance matching sys- as high as 96% at a distance of 75 cm. The news tem, thereby improve the transmission efficiency. seems to ignite the enthusiasm of scientists. With the However, four coils in the system separated from each portable electronic products (such as TVs, laptops, cell other need to keep the same distance, besides, the load phones, and so on) were more and more popular, peo- impedance should also remain the same. So it was not ple's lives become more convenient. At the same time, for the actual electronic products. Reference [9] shows the traditional power supply of these devices cause a that the professor TC Beth had use the wireless power lot of inconvenience to people, such as the limited transmission in electric automobile, studying the re- power supply, power transmission and other security ceive coil resonance frequency and system frequency risks. In order to effectively address the shortcomings which were caused by mismatch problem. Impedance of traditional wired power supply in recent years, the matching was put forward to adjust the coil resonance wireless power transmission (WPT) has attracted frequency. Besides, the electromagnetic analysis and much attention of researchers at home and abroad [1]. test was carried on to conclude a parameter design Currently, the wireless power transmission mode in- method. Scholars such as Seung-Hwan LEE proposed cluding: the resonance magnetic coupling type, the an equivalent circuit model of the magnetic coupling electromagnetic induction type, and the electromag- resonant WPT system in the reference [10]. And the netic radiation type. Among them, the resonant mag- finite element analysis shows that the circuit model is netic coupling technique was the use of non-radiative an effective model which including the influence of electromagnetic near-field region achieving energy skin effect and proximity effect based on a high fre- transmission. Compared with the other two types, it quency system. All above has helped to promote the has advantages such as low difficulty design, high progress of wireless power transmission. transmission efficiency, long transmission distance, no This paper presents a suitable portable electronic radiation and high security features. So this type of products magnetically coupled resonant coupling wireless power transmission system has received more wireless power transmission system model to fill up attentions and researches [2-3]. the deficiency mentioned earlier [11-12]. The trans- In order to obtain a stable system performance, the mission characteristics of the system were analyzed, transmitter and the receiver in the systems usually use the expressions of the transmission efficiency were the same parameters, symmetrical resonator to achieve derived, the system performance was optimized, and excellent performance [4-5]. However, it owns a very the impact of the quality factor and the coupling factor narrow range of applications of the study because of for transmission efficiency was discussed. Finally, the This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152202018 MATEC Web of Conferences optimum conditions in the system were given. The analysis. Matlab simulation shows that when the coil Q factor is determined, the system transmission efficiency opti- mization can be realized by adjusting the coupling factor between the transmitter coils. 2 SYSTEM MODEL AND CIRCUIT ANALYSIS The model of wireless power transmission system for portable electronic products was shown in Figure 1. There were four components of the system consist of the drive coil (Drive Coil), the transmit coil (TX Coil), the receiving coil (RX Coil) and the load coil (Load Figure 2. Equivalent circuit of wireless power transmission Coil). Transmitting and receiving coils were called resonator. When energy was transmitted, they were in a resonance state. The resonant frequency and the natural In Figure 2, K12 was presented as the coupling fac- frequency of the coil were the same. As shown in Fig- tors between the Drive coil and the TX coil, K23 was ure 1, the transmitting terminal was the same with the presented as the coupling factors between the TX coil traditional four resonant wireless power transmitting, and the RX coil, K34 was presented as the coupling namely the driving coil was formed as the single-turn factors between the RX coil and the Load coil. They coil, and the multi-turn transmitter coil was made of were mainly determined by coil inductance, coil turns axial spiral coil. But the receiving terminal of the re- and the distance among coils. ceiving coil and loading coil in a planar spiral were Assume ω was the angular frequency in the system. fixed together and they are not the same size with the By Kirchhoff's voltage law (KVL), we can obtain transmitter coil [13-14]. Thus, the coil size is in ac- that[16]: cordance with the size of the electrical equipment. 1 FVi FVZZZZ FVVs GW1 GW11 12 13 14 GW i ZZZZ 0 (1) GW2 GW21 22 23 24 GW GWi GWZZZZ GW0 GW3 GW31 32 33 34 GW HXi4 HXZZZZ41 42 43 44 HX0 Wherein: I 1 L RjLnn mn (2) jC ZZmn nm J n L K jMmn m n, M mn k mn LL m n Wherein n, m was resonant coil numerals, n, mę {1,2,3,4}; Rn was presented as the n-th coil of equiva- lent resistance; Ln was presented as the n-th coil Figure 1. Model of wireless power transmission that suitable equivalent inductance; Cn was the n-th tuning capaci- for portable electronics tance value; Mmn and kmn were respectively the mutual inductance and the coupling coefficient between the m-th coil and the n-th coil. When the system was in To simplify the analysis, only four coils energy steady-state operation, it was shown as follows: transfer were analyzed [15]. In accordance with the 1 (3) principle of magnetic coupling and the resonance cir- ω + n 1, 2, 3, 4 LC cuit theory, each of coils may be equivalent to RLC mn circuit system. So it is obvious that we can obtain the 1 (4) equivalent circuit model shown in Figure 2. In the jL 0,1,2,3,4 m nn n Figure 2, AC was a high-frequency signal source, L1, jCn L2, L3 and L4 were the equivalent inductance of the Ignore the cross-coupling factor k14, k13, k24, the four coils; RL was the load resistance; R1, R2, R3 and formula (1) can be simplified as follows: R4 were loss resistance of the coils; C1, C2, C3 and FV FV 1 FV C4 were the sum of a parasitic capacitance and tuned i1 RjM11200Vs compensation capacitor; M12, M23 and M34 were the GW GW GW(5) GWi2 GWjM12 R 2 jM 23 0 GW0 mutual inductance between adjacent coils. Since no GWi GW0 jM R jM GW0 cross coupling between the adjacent, weak, GW3 GW23 3 34 GW low-impact coils, the cross mutual inductance M13, HXi4 HX00jM34 R 4 HX0 M14 and M24 were not considered in the process of 02018-p.2 ICETA 2015 L self-resistors R2 and R3 were small, so Q2, Q3 was Taking the quality factor Q n and equation (2) n usually much greater than Q1, Q4. In addition, when Rn the system was working properly, the transmitter and into the equation (5), it was shown as follows: the receiver were in a state of strong coupling, and the coupling factor meets k12, k34 >> k23. This time, the I 22 formula (8) can do the following approximations: 1 kQQ23 2 3 kQQV 34 3 4 s L 222 i1 ()()()(11kQQ kQQ kQQ kQQ )(9) L FV 222 12 1 2 34 3 4 12 1 2 34 3 4 RkQQkQQkQQ1HX11 1212 3434 2323 L L 2 222 kQQkQQV 1 (6) (1 k1212 Q Q )(1 k 3434 Q Q ) k 2323 Q Q Li 12 1 2 34 3 4 s (10) L 2 FV 222 22 L RR1 2HX11 k 12 QQ 1 2 k 34 QQ 3 4 k 23 QQ 2 3 (k Q Q )(k Q Q ) J 12 1 2 34 3 4 L kk12 23 QQ 1 2 QQV 2 3 s Li 22 2 3 FV 222 1 kQQ kQQ 1 kQQ (11) L RR1 3HX11 k 12 QQ 1 2 k 34 QQ 3 4 k 23 QQ 2 3 23233434 2323 L L kkk QQ QQ QQV At last, the equation (8) can be approximated as 12 23 34 1 2 2 3 3 4 s Li4 follows: FV 222 KL RR1 4HX11 k 12 QQ 1 2 k 34 QQ 3 4 k 23 QQ 2 3 kQQ2 Expression (7) of transmission efficiency in the 2323 (12) system was obtained by equation (6).