大功率谐振式无线电能传输方法与实验研究
|
摘要
作为无线电能传输技术的一个新的发展方向，磁耦合谐振式无线电能传输技术具有较大的传输距离、较高的传输功率和效率以及无辐射性和穿透性等优势，它的出现使该技术成为国内外学者研究的热点问题之一。目前很多国内外的学者在这方面展开研究，也取得了很大进展，但是还有很多问题尚未解决，例如无线电能传输理论有待突破，传输功率和效率有待提高等。
本文正是基于这些问题展开研究的，首先利用耦合模理论研究了电能无线传输的规律和有效传输的必要条件，利用互感理论分析了电能无线传输的基本特性。其次为了提高电能传输的功率，提出了大功率无线电能传输方法。最后设计实验电路进行相关的实验研究。本文的主要研究工作如下：
（1）基于耦合模理论建立了振荡系统的传输模型和数学方程，对无损、有损振荡系统分别建立方程并求解，由其简正模的分析得到能量有效交换和传输的必要条件。
（2）利用耦合模方程并综合考虑阻抗损耗和辐射损耗情况下得出系统的传输效率方程，由效率方程的表达式进一步推导工作效率和损耗效率与系统参数的关系。建立了多用户和带中继线圈的无线电能传输耦合模方程，通过拉普拉斯变换和拉普拉斯反变换解出方程得到其简正模。
（3）作为耦合模理论的补充和延伸，建立了利用互感理论分析无线电能传输技术的基本特性的方法。首先对无线电能传输系统进行等效得出其电路模型和简化电路，给出简化电路的方程式，解出该方程式得到负载侧的归一化电压表达式和其频率响应特性，即频率分裂特性和分裂规律。
（4）根据在一定范围内接收电压最大值不随耦合因数的减小而降低的特性，定义了有效传输范围的概念。结合距离（包括轴向距离和径向距离）或方向与耦合因数的关系，进一步推导得出了无线电能传输的距离特性和方向特性，即虽然距离和方向发生改变但是只要系统仍处于“过耦合”状态，负载接收电压的最大值就有可能保持不变。
（5）针对大功率无线电能传输的需要，提出提高无线电能传输功率所涉及的三个基本问题（大功率高频电源、阻抗匹配、谐振频率稳定性问题）以及由于功率提高带来的电磁辐射与电磁兼容问题。
（6）设计磁耦合谐振式无线电能传输的实验系统，具体包括功率放大电路、阻抗匹配电路、发射与接收系统等，实现了能量的有效大功率无线传输。随后利用实验电路对本文所提的理论进行了具体分析和验证，包括频率特性、距离特性、方向特性等方面的实验。
本文的研究不仅包括磁耦合谐振式无线电能传输技术的传输机理、传输条件等，还系统分析了无线电能传输的基本特性，以及发射与接收系统电气参数对传输性能的影响。本文的研究成果为无线电能传输技术在轨道交通（电动汽车）、物联网（无线传感网）、医疗设备、特种设备（矿山机械、移动机器人、自动导航车、水下设备等）、便携式电子产品等方面的应用奠定了理论基础。
As a new development trend, wireless power transfer via coupled magnetic resonances hasmore merits: delivering higher power at longer ranges and with more efficiency, non-radiative,penetrability, which has became one of the hotspot researches by domestic and internationalscholar. The progress of technology in the field of wireless power transfer via coupled magneticresonances in the last few years is remarkable, but there are more questions is unsolved, such asthe mechanism,power and efficiency of wireless power transfer.
In order to solve these questions, the transfer laws and necessary condition were studied bycoupled mode theory(CMT) and the transfer fundamental characteristics were analyzed bymutual inductance theory firstly. Then for improving the wireless transfer power, the way oftransfering high power in wireless power transfer system was presented. In the end, experimentcircuit was designed and the experiment results verified the right of the key theoretical analysis.
Main points of this paper as follows:
(1)Transfer model and mathematics equations of oscillation system baesd on CMT wereestablished. The lossness and loss system were analyzed by mathematics equations and thenecessary condition of energy exchange and transferring was yielded by its normal mode.
(2)Considering impedance loss and radiation loss, the equation of teansfer efficiency wasobtained, by which the relationship between working efficiency (or loss efficiency) and wirelesspower transfer system paramerers was derived. Mathematics equations of wireless powertransfer on multi-users and with relay coils were established and its normal mode was obtainedby laplace transform and inverse laplace transform.
(3)Fundamental characteristics on wireless power transfer were analyzed by mutualinductance theory. Circuit model and its simplified circuit of wireless power transfer systemwere presented.Then the frequency characteristic including frequency splitting and its lays wasproposed by the describing of normalized voltage of load coils.
(4)The concept of effective transfer range was defined, which means the range that themaxim receiving voltage didn t become smaller with the decreasing of coupling factor.Thecharacteristic of transfer range and orientation were proposed using the relationship between thetransfer range(or the orientation) and coupling factor. The maxim receive voltage don t becomesmaller with the changing of transfer range or orientation, if the wireless power transfer is understrong coupling.
(5)In order to meet the high power of wireless power transfer, three basic questionsincluding big power with high frequency, impedance matching and stability resonant frequencywere proposed. The electromagnetic radiation and electromagnetic compatibility (EMC) ofhigher power in wireless power transfer system must not be neglected.
(6)Experiment system of wireless power transfer including power amplifier, impedancematching circuit, transfer system and receiver system was designed.Then the key theoreticalanalysis on wireless power transfer was verified, such as the characteristic of transfer range,orientation and frequency, etc.
Not only the transfer mechanism and transfer condition of wireless power transfer viacoupled magnetic resonances, but also its fundamental characteristics were presented in thispaper. The research achievement in this paper lays a theoretical foundation for the application ofwireless power transfer technology in rail transit（e.g. electric vehicle）, internet of things（e.g.wireless sensor network）, medical equipment，special equipment（e.g. mine machinery，mobile robot，automatic navagation car,submersed equipment, etc）, portable electronic productsetc.
本文正是基于这些问题展开研究的，首先利用耦合模理论研究了电能无线传输的规律和有效传输的必要条件，利用互感理论分析了电能无线传输的基本特性。其次为了提高电能传输的功率，提出了大功率无线电能传输方法。最后设计实验电路进行相关的实验研究。本文的主要研究工作如下：
（1）基于耦合模理论建立了振荡系统的传输模型和数学方程，对无损、有损振荡系统分别建立方程并求解，由其简正模的分析得到能量有效交换和传输的必要条件。
（2）利用耦合模方程并综合考虑阻抗损耗和辐射损耗情况下得出系统的传输效率方程，由效率方程的表达式进一步推导工作效率和损耗效率与系统参数的关系。建立了多用户和带中继线圈的无线电能传输耦合模方程，通过拉普拉斯变换和拉普拉斯反变换解出方程得到其简正模。
（3）作为耦合模理论的补充和延伸，建立了利用互感理论分析无线电能传输技术的基本特性的方法。首先对无线电能传输系统进行等效得出其电路模型和简化电路，给出简化电路的方程式，解出该方程式得到负载侧的归一化电压表达式和其频率响应特性，即频率分裂特性和分裂规律。
（4）根据在一定范围内接收电压最大值不随耦合因数的减小而降低的特性，定义了有效传输范围的概念。结合距离（包括轴向距离和径向距离）或方向与耦合因数的关系，进一步推导得出了无线电能传输的距离特性和方向特性，即虽然距离和方向发生改变但是只要系统仍处于“过耦合”状态，负载接收电压的最大值就有可能保持不变。
（5）针对大功率无线电能传输的需要，提出提高无线电能传输功率所涉及的三个基本问题（大功率高频电源、阻抗匹配、谐振频率稳定性问题）以及由于功率提高带来的电磁辐射与电磁兼容问题。
（6）设计磁耦合谐振式无线电能传输的实验系统，具体包括功率放大电路、阻抗匹配电路、发射与接收系统等，实现了能量的有效大功率无线传输。随后利用实验电路对本文所提的理论进行了具体分析和验证，包括频率特性、距离特性、方向特性等方面的实验。
本文的研究不仅包括磁耦合谐振式无线电能传输技术的传输机理、传输条件等，还系统分析了无线电能传输的基本特性，以及发射与接收系统电气参数对传输性能的影响。本文的研究成果为无线电能传输技术在轨道交通（电动汽车）、物联网（无线传感网）、医疗设备、特种设备（矿山机械、移动机器人、自动导航车、水下设备等）、便携式电子产品等方面的应用奠定了理论基础。
As a new development trend, wireless power transfer via coupled magnetic resonances hasmore merits: delivering higher power at longer ranges and with more efficiency, non-radiative,penetrability, which has became one of the hotspot researches by domestic and internationalscholar. The progress of technology in the field of wireless power transfer via coupled magneticresonances in the last few years is remarkable, but there are more questions is unsolved, such asthe mechanism,power and efficiency of wireless power transfer.
In order to solve these questions, the transfer laws and necessary condition were studied bycoupled mode theory(CMT) and the transfer fundamental characteristics were analyzed bymutual inductance theory firstly. Then for improving the wireless transfer power, the way oftransfering high power in wireless power transfer system was presented. In the end, experimentcircuit was designed and the experiment results verified the right of the key theoretical analysis.
Main points of this paper as follows:
(1)Transfer model and mathematics equations of oscillation system baesd on CMT wereestablished. The lossness and loss system were analyzed by mathematics equations and thenecessary condition of energy exchange and transferring was yielded by its normal mode.
(2)Considering impedance loss and radiation loss, the equation of teansfer efficiency wasobtained, by which the relationship between working efficiency (or loss efficiency) and wirelesspower transfer system paramerers was derived. Mathematics equations of wireless powertransfer on multi-users and with relay coils were established and its normal mode was obtainedby laplace transform and inverse laplace transform.
(3)Fundamental characteristics on wireless power transfer were analyzed by mutualinductance theory. Circuit model and its simplified circuit of wireless power transfer systemwere presented.Then the frequency characteristic including frequency splitting and its lays wasproposed by the describing of normalized voltage of load coils.
(4)The concept of effective transfer range was defined, which means the range that themaxim receiving voltage didn t become smaller with the decreasing of coupling factor.Thecharacteristic of transfer range and orientation were proposed using the relationship between thetransfer range(or the orientation) and coupling factor. The maxim receive voltage don t becomesmaller with the changing of transfer range or orientation, if the wireless power transfer is understrong coupling.
(5)In order to meet the high power of wireless power transfer, three basic questionsincluding big power with high frequency, impedance matching and stability resonant frequencywere proposed. The electromagnetic radiation and electromagnetic compatibility (EMC) ofhigher power in wireless power transfer system must not be neglected.
(6)Experiment system of wireless power transfer including power amplifier, impedancematching circuit, transfer system and receiver system was designed.Then the key theoreticalanalysis on wireless power transfer was verified, such as the characteristic of transfer range,orientation and frequency, etc.
Not only the transfer mechanism and transfer condition of wireless power transfer viacoupled magnetic resonances, but also its fundamental characteristics were presented in thispaper. The research achievement in this paper lays a theoretical foundation for the application ofwireless power transfer technology in rail transit（e.g. electric vehicle）, internet of things（e.g.wireless sensor network）, medical equipment，special equipment（e.g. mine machinery，mobile robot，automatic navagation car,submersed equipment, etc）, portable electronic productsetc.
引文
[1]延宏,刘莉.中国科协“五个10”系列评选结果揭晓[N].科技日报,2008.12.17.
[2] Tesla, N. Apparatus for transmitting electrical energy. U.S. patent number1,119,732, issued inDecember1914．
[3] Esser A，Skudelny H C. A new approach to power supplies for robots[J].IEEE Transactions on IndustryApplications,1991,27(5):871-875.
[4] Manolatou C, Khan M J, Fan Shanhui,et al．Coupling of modes analysis of resonant channel add-dropfilters[J]．IEEE Journal of Quantum Electronics,1999,35(9):1322-1331．
[5] Hirai J J，Kim T W，Kawamura A．Wireless transmission of power and information for cableless linearmotor drive[J]．IEEE transactions on Power Electronics,2000,15(1):21-27．
[6]任立涛.磁耦合谐振式无线能量传输功率特性研究[D].硕士论文.哈尔滨：哈尔滨工业大学，2009.
[7] Abel E, Third S M. Contactless power transfer-An exercise in topology[J]. IEEE Transaction onmagnetic,1984,20(5):1813-1815.
[8]韩腾,卓放,王兆安等.非接触电能传输系统频率分岔现象研究[J].电工电能新技术.2005,24(2):44-47.
[9] G.A.Covie, J.T.Boys, M.L.Kissin, etal. A three-Phase induetive Power transfer system for roadway-power transfer [J]. IEEE Trans.on Industrial Eleetronies，2007,54(6):3370-3378.
[10] J.T.Boys, G.A.Covie, G.A.Elliort. pick-up transformer for ICPT applications[J]. Electronies Letters,2002,38(21):1276-1278.
[11] G.A.Elliott, G.A.Covie, D.KaePrzaak, etal. A new concept: Asymmetrical pick-ups for inductively coupled power transfer monorail systems[J]. IEEETrans. on Magnetics,2006,42(10):3389-3391.
[12] J.T.Boys, G.A.Covic,A.W. Green. Stability and control of inductively coupled power transfer systems[J].IEEE Proeeedings-Electric Power Applications,2000,147(l):37-43.
[13] C.S.Wang，G. A. Covic, O.H.Stielau. Power transfer capability and bifurcation phenomena of Iooselycoupled induetive power transfer systems[J]. IEEE Trans. on Industrial Eleetronics,2004,51(l):145-157.
[14] Chang-Yu Huang, J.T.Boys,G.A. Covic, etal. Practical considerations for designing IPT system for EVbattery cllarging[J]. Vehicle Power and Propulsion Conferenee,2009:402-407.
[15] N.A.Keeling,G.A.Covie,J.T.Boys. A unity-power-factor IPT pick-up for high-power applications[J].IEEE Trans. on Industrial Electronics,2010,57(2):744-751.
[16]朱俊.探秘电动汽车的无线充电技术[J].交通与运输,2012（1）:26-27.
[17]朱俊.电动汽车的无线充电技术[J].汽车工程师,2011（12）:50-52.
[18] http://tech.sina.com.cn/d/2010-11-09/08084843495.shtml.
[19] http://news.bitauto.com/qyxw/20110608/0805380250.html.
[20] Liu X.,Hui S.R.Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery ChargingPlatform[J].IEEE Transaction on Power Electronics,2008,23(1):455-463.
[21]武瑛，严陆光，徐善纲.运动设备无接触供电系统耦合特性的研究[J].电工电能新技术,2005,24（3）:5-8.
[22]孙跃，王智慧，戴欣，苏玉刚，李良.非接触电能传输系统的频率稳定性研究[J].电工技术学报,2005，20（6）:56-59.
[23]徐晔,马皓.串联补偿电压型非接触电能传输变压器的研究[J].电力电子技术,2008,42（3）：4-5,11.
[24]高金峰，徐磊.并联谐振型非接触供电平台的频率控制与设计[J].郑州大学学报,2006,27（4）：66-70.
[25]毛赛君.非接触感应电能传输系统关键技术研究[D].硕士论文,南京:南京航空航天大学,2006.
[26] Zhang,XJ,Zhang H,Chen BL.Narrow width pulsed and high peak power supply circuit of laserdiode[C].6th InternationSymposium on Test and Measurement,Jun01-04,2005,vols1-9:3071-3073.
[27]张青.谐振耦合式无线输电多载系统建模及特性研究[D].硕士论文,广州:华南理工大学,2011.
[28]韩腾,卓放,闫军凯,刘涛,王兆安.非接触电能传输系统频率分叉现象研究[J].电工电能新技术,2005,24（2）:44-47,76.
[29] Li H L,Hu A P,Covic G A,etal.Optimal coupling condition of IPT sysytem for activeing maximumpower transfer[J].Electronics Letters,2009,45(1):76-77.
[30] GLASER P．Power From the Sun．Its Future［J］.Science,1968,162（11）：857-861．
[31]胡大璋,周兆先.微波输送电能的新技术[J].电子科技导报,1996,(12):1-4.
[32]张小壮.磁耦合谐振式无线能量传输距离特性及其实验装置的研究[D].硕士论文,哈尔滨：哈尔滨工业大学,2009.
[33] http://www.eeworld.com.cn/dygl/2011/1012/article_7482.html.
[34] M.Ali,G.Yang,R.Dougal.A Miniature Packaged Rectenna for Wireless Power Transmission and DateTelemetry[C].IEEE International Workshop on Antenna Technology Small Antennas and NovelMetamaterials,Mar.2006:225-228.
[35]张猛.微波无线电能传输与通信系统的研究[D].硕士论文,杭州：浙江大学，2004.
[36] BROWN W．Status of the Microwave Power Transmission Components for the Solar Power Satellite［J］．IEEE Transactions on Microwave Theory and Techniques，1981，29（12）：1319-1327．
[37] Andre Kurs, Aristeidis Karalis, Robert Moffatt, etal. Wireless Power Transfer Via Strongly CoupledMagnetic Resonances[J]. Science.2007,317(6):83-86.
[38] Alanson P. Sample, David A. Meyer, Joshua R. Smith. Analysis, Experimental Results, and RangeAdaptation of Magnetically Coupled Resonators for Wireless Power Transfer [J]. IEEE tansactions onindustrial electronics,2011,58(2):544-554.
[39] Aristeidis Karalis, J. D. Joannopoulos, and Marin Soljacic. Wireless Non-Radiative Energy Transfer.The AIP Industrial Physics Forum,2006.1.
[40]冯慈璋,马西奎.工程电磁场导论[M].北京:高等教育出版社,2000.
[41] http://www.google.com.hk/imglanding.
[42] Fei Zhang, Xiaoyu Liu, Steven A. Hackworth, Robert J. Sclabassi, and Mingui Sun.In Vitro and In VivoStudies on Wireless Powering of Medical Sensors and Implantable Devices[C].2009IEEE/NIH LifeScience Systems and Applications Workshop,2009:84-87.
[43] Xiaoyu Liu, Fei Zhang, Steven A. Hackworth, Robert J. Sclabassi,Mingui Sun. Modeling andSimulation of a Thin Film Cell for Power Transfer to Medical Devices and Implants[C],2009IEEEInternational Symposium on Circuits and Systems,2009:3086-3089.
[44] Xiaoyu Liu, Fei Zhang, Steven A. Hackworth, Robert J. Sclabassi, Mingui Sun.Wireless Power TransferSystem Design for Implanted and Worn Devices[C] Proceedings of the IEEE35th Annual NortheastBioengineering Conference,2009:1-2.
[45] Zhang Fei,Hackworth Steven A., Fu Weinong, Sun, Mingui.The Relay Effect on Wireless PowerTransfer Using WiTricity[C].14th Biennial IEEE Conference on Electromagnetic FieldComputation,2010:1.
[46] Wang Junhua, Ho S.L., Fu W.N.,Sun Mingui.Analytical design study of a novel witricity charger withlateral and angular misalignments for efficient wireless energy transmission[C]. IEEE Transactions onMagnetics,2011:47(10):2616-2619.
[47] Junhua Wang, Jiangui Li, S. L. Ho, W. N. Fu, etal．Analytical study and corresponding experiments for anew resonant magnetic charger with circular spiral coils[C]. Journal of Applied Physics,2012,111(7).
[48] http://www.52solution.com/article/articleinfo/id/80010144/page/3.
[49] Imura Takehiro,Uchida Toshiyuki,Hori Yoichi.Experimental Analysis of High Efficiecy Power TransferUsing Resonance of Magnetic Antennas for the Near Field-Geometry and Fundamental Characteristics[C].IEEE Japan Industry Applications Society Conference,2008:539-542.
[50] Imura Takehiro, Okabe Hiroyuki,Hori Yoichi. Basic Experimental Study on Antennas of Wireless PowerTransfer for Electric Vehicle by using Magnetic Resonant Coupling[C].Vehicle Power and PropulsionConference,2009:936-940.
[51] Beh TeckChuan,Kato Masaki,Imura Takehiro. Basic Study on Improving Efficiecy of Wireless PowerTransfer via Magnetic Resonance Coupling Based on Impedance Matching[C]. IEEE InternationalSymposium on Industrial Electronics2010,2010:2011-2016.
[52] http://biz.ppsj.com.cn/2010-10-28/2969342259.html.
[53] http://emc.ofweek.com/2012-02/ART-8320058-11000-28597792.html.
[54] http://www.pcworld.com.cn/Article/ShowArticle.asp?ArticleID=6734.
[55] http://tech.cn.yahoo.com/ypen/20120111/808800.html.
[56] http://www.eeworld.com.cn/szds/2011/1228/article_3499.html.
[57]赵彪,陈希有,于庆广.用于非接触电能传输的自适应谐振技术原理[J].电工电能新技术,2010,29（2）:33-37.
[58]马官营,颜国正.基于电磁感应的消化道内微系统无线能量传输问题研究[J].生物医学工程杂志，2008,25(1):61-64.
[59]翟渊，孙跃，戴欣，苏玉刚，王智慧.磁共振模式无线电能传输系统建模与分析[J].中国电机工程学报,2012,32(12):155-160.
[60]杨庆新，陈海燕，李阳等.电磁-机械同步共振无线传能与转换方法研究（批准号：50977062）.
[61]杨庆新，陈海燕，徐桂芝等.无接触电能传输技术的进展[J].电工技术学报,2010,25（7）：6-13.
[62]张献，杨庆新，陈海燕，李阳，等.电磁耦合谐振式传能系统的频率分裂特性研究[J]，中国电机工程学报,2012,32(9):167-172.
[63]张献，杨庆新，陈海燕，李阳，等.电磁耦合谐振式无线电能传输系统的建模、设计与实验验证[J].中国电机工程学报,2012,32(21):153-158.
[64] Zhang Xian，Yang Qingxin，Chen Haiyan，Li Yang，Yan Zhuo. The application of non-contact powertransmission technology (NPT) in the modern transport system[C]. Mechatronics and Automation(ICMA),2010International Conference on,2010,2010:345-349.
[65] Zhang Xian，Yang Qingxin，Chen Haiyan，Li Yang，Yan Zhuo. Analysis of A Novel Near-fieldNon-radiative Wireless Power Transmission System[C]. CASE2011,2011:1-4.
[66] Zhang Xian,Yang Qingxin，Li Yang. Numerical analysis on electromagnetic characteristics of laminatedcore joints of power transformer[C].2010International Conference on Computer and informationApplication,2010:67-70.
[67] Zhang Xian, Yang Qingxin, Chen Haiyan. Investigation on contactless power transmission ofelectromaganetic-mechanical synchronous resonance[C].The Secand International Conference onElectromagnetic Field Problems and Applications,2012.
[68] Zhang Xian,Yang Qingxin,Chen Haiyan. Direct Field-circuit coupled Analysis and CorrespondingExperiments of Electromagnetic resonant Coupling System. International Magnetics Conference2012.
[69] Zhuo Yan, QingxinYang, Haiyan Chen, Chao Zhang, Guizhi Xu. Modeling and Experimental Analysisof Helical Resonator for Wireless Power Transmission System[C].The International Conference onElectrical and Control Engineering(ICECE2010),2010:3886～3889.
[70] Zhuo Yan, Chao Zhang, Haiyan Chen, Qingxin Yang, Sumei Yang. Simulation Analysis on DetachableTransformer in Contactless Electrical Energy Transmission System[C]. International Conference onElectrical Machines and Systems(ICEMS2010),2010:1777～1780.
[71] Zhuo Yan, Chao Zhang, QingxinYang, Haiyan Chen, Guizhi Xu. Design and Analysis of ResonantCoupling Wireless Power Transmission System[C],201014th Biennial IEEE Conference onElectromagnetic Field Computation.
[72] Zhang Xian,Yang Qingxin,Chen Haiyan. A Novel Two-port Network Model and ExperimentalValidation for Resonantly Coulping Power Transmission System[C]. The Sixth International Conferenceon Electromagnetic Field Problems and Applications,2012.
[73]杨庆新，李阳，等.无线电能传输实验系统[P].申请号：201010532425.9
[74]李阳,杨庆新,牛萍娟,田会娟.基于无线电能传输技术的LED室内台灯[P].申请号：201210164092.8
[75]张献，杨庆新，等，电动车智能在线充电系统[P].申请号：201110350760.1.
[76]张献，杨庆新，等，一种智能脉冲式无线电能传输装置[P].申请号：201220011291.0.
[77]张献，杨庆新，等，家庭便携式无线充电装置[P].申请号：201110350956.0.
[78]张献，杨庆新，等，一种智能脉冲电磁推送发射装置[P].申请号：201210007360.5.
[79]张献，杨庆新，等，深水下水文测量无线供电系统[P].申请号：201210052453.X.
[80]朱春波.基于平面磁芯的电动汽车磁共振式非接触充电技术研究（批准号：51277037）.
[81]朱春波.基于磁耦合谐振的无线传感器无线供电技术研究（批准号：51077019）.
[82]陈乾宏.电动汽车高效率、高可靠性无线供电的关键技术研究（批准号：51507009）.
[83]李云辉.基于特异材料的非辐射无线能量传输技术研究（批准号：51007064）.
[84] Chunbo Zhu, Chunlai Yu, Kai Liu, Rui Ma. Research on the Topology of Wireless EnergyTransferDevic[J].IEEE Vehicle Power and Propulsion Conference(VPPC), Sept.3-5,2008.
[85] Chunbo Zhu, Kai Liu, Chunlai Yu, Rui Ma, Hexiao Chen, Simulation and Experimental AnalysisonWireless Energy Transfer Based on Magnetic Resonance[C].IEEE Vehicle Power and PropulsionConference(VPPC), Sept.3-5,2008.
[86]曲立楠.磁耦合谐振式无线能量传输机理的研究[D].哈尔滨工业大学.2010.
[87]朱春波,于春来,毛银花,陈清泉.磁共振无线能量传输系统损耗分析[J].电工技术学报.2012，27（4）：13-17.
[88]朱春波等.磁耦合谐振式无线能量传输装置[P].申请号:200810064667.2
[89]朱春波等.带有增强器的磁耦合谐振式无线能量传输装置[P].申请号:200810136892.2
[90]黄学良.谐振耦合式无线传输理论深化研究及其在电动汽车无线充电技术中的应用（批准号：51177011）.
[91]袁小芳.电动汽车非接触感应充电的智能建模与控制研究（批准号：61104088）.
[92] Tan Linlin, Huang Xueliang, Li Hui, Huang Hui. Study of Wireless Power Transfer System ThroughStrongly Coupled Resonances.2010International Conference on Electrical and ControlEngineering.2010.
[93]黄辉,黄学良,谭林林,丁晓辰.基于磁场谐振耦合的无线电力传输发射及接收装置的研究[J].电工电能新技术,2011,30(1):32-35.
[94]张建华,黄学良,邹玉炜,柏杨.利用超声波方式实现无线电能传输的可行性的研究[J].电工电能新技术,2011,30(2)：66-69，74.
[95]强浩，黄学良，谭林林，吉青晶，赵家明.基于动态调谐实现感应耦合无线电能传输系统的最大功率传输[J].中国科学，2012，42（7）：830-837.
[96]傅文珍,张波,丘东元,等.自谐振线圈耦合式电能无线传输的最大效率分析与设计.中国电机工程学报,2009,29(18):21-26.
[97] Wenzhen Fu, Bo Zhang, Dongyuan Qiu. Study on Frequency-tracking Wireless Power Transfer Systemby Resonant Coupling. IPEMC2009.
[98]傅文珍,张波,丘东元.频率跟踪式谐振耦合电能无线传输系统研究.变频器世界.2009(08):41-46.
[99] Jun Zhao,Guizhi Xu,Chao Zhang,Yang Li,Xian Zhang,Qingxin Yang,Ying Li,Hongli Yu.The Design andResearch of a New Kind Small Size Resonator Used in Magnetic Coupling Resonance Wireless EnergyTransmission System[C].the International Magnetics Conference (INTERMAG2012).
[100] Jun Zhao, Guizhi Xu, Chao Zhang, Xiaowei Wan.Research on Electromagnetic Radiation to HeadFrom Head Implantable Coil Powered via Witricity[C].The6th International Conference onBioinformatics and Biomedical Engineering (ICBBE2012).
[101] Jun Zhao, Guizhi Xu, Chao Zhang,Wei Zhang, Xuan Li.A Contrastive Studies between MagneticCoupling Resonance and Electromagnetic Induction in Wireless Energy Transmission[C].The SixthInternational Conference on Electromagnetic Field Problems and Applications (ICEF2012).
[102]闫卓.基于磁谐振耦合的多用户无线电能传输技术研究[D].博士论文.天津：河北工业大学，2011.
[103]张献.基于电磁-机械同步共振的无线电能传输与转换方法研究[D].博士论文.天津：河北工业大学，2012.
[104]谢翔,张春,王志华.生物医学中的植入式电子系统的现状与发展[J].电子学报,2009,32(03):462-467.
[105]甘丽,闵永泉.脑深部电刺激的作用机制及其在精神疾病治疗中的应用[J].立体定向和功能性神经外科杂志.2006,(05):314-317.
[106]卓勇.生物体内置电装置的外部供电模式研究[D].博士论文，重庆：重庆大学.2007.
[107] D. Kondziolka, D. Whiting, A. Germanwala, et al.Hardware-related complications after placement ofthalamic deep brain stimulator systems.Stereotact Funct Neurosurg,2002,79(3-4):228-33.
[108]张文亮，武斌，李武峰等.我国纯电动汽车的发展方向及能源供给模式的探讨[J].电网技术,2009,33(4):l-5.
[109]赵小坤.电动汽车感应充电技术[D].硕士论文.哈尔滨：哈尔滨工业大学，2009.
[110]李昆鹏.电动汽车动力蓄电池无线充电技术的智能化研究[D].天津：河北工业大学硕士论文，2011.
[111] H.Haus. Waves and Fields in Optoelectronics. Prentice-Hall,Englewood Cliffs, J,1984.Hermann.A.Haus著,陈东培译.光电子学中的波和场.上海翻译出版公司.1990年11月第1版,209-244.
[112] Seung-Hwan Lee, Robert D. Development and Validation of Model for95%Efficiency220WWireless Power Transfer over a30cm Air-gap [J]. IEEE Transactions on IndustryApplications,2011,47(6)：2495-2504.
[113] Aristeidis Karalis, J.D.Joannopoulos, Marin Soljacic. Efficient Wireless Non-radiative Mid-rangeEnergy transfer[J]. Annals of Physics,2008,32（3）:34-48.
[114]刘修泉，曾昭瑞，黄平．空心线圈电感的计算与实验分析[J]．工程设计学报，2008，15(2)：149~153.
[115]陈抗生.电磁场与电磁波[M].北京：高等教育出版社,2007.
[116] M.M.拉德马内斯.射频与微波电子学[M].北京：科学出版社,2006.
[2] Tesla, N. Apparatus for transmitting electrical energy. U.S. patent number1,119,732, issued inDecember1914．
[3] Esser A，Skudelny H C. A new approach to power supplies for robots[J].IEEE Transactions on IndustryApplications,1991,27(5):871-875.
[4] Manolatou C, Khan M J, Fan Shanhui,et al．Coupling of modes analysis of resonant channel add-dropfilters[J]．IEEE Journal of Quantum Electronics,1999,35(9):1322-1331．
[5] Hirai J J，Kim T W，Kawamura A．Wireless transmission of power and information for cableless linearmotor drive[J]．IEEE transactions on Power Electronics,2000,15(1):21-27．
[6]任立涛.磁耦合谐振式无线能量传输功率特性研究[D].硕士论文.哈尔滨：哈尔滨工业大学，2009.
[7] Abel E, Third S M. Contactless power transfer-An exercise in topology[J]. IEEE Transaction onmagnetic,1984,20(5):1813-1815.
[8]韩腾,卓放,王兆安等.非接触电能传输系统频率分岔现象研究[J].电工电能新技术.2005,24(2):44-47.
[9] G.A.Covie, J.T.Boys, M.L.Kissin, etal. A three-Phase induetive Power transfer system for roadway-power transfer [J]. IEEE Trans.on Industrial Eleetronies，2007,54(6):3370-3378.
[10] J.T.Boys, G.A.Covie, G.A.Elliort. pick-up transformer for ICPT applications[J]. Electronies Letters,2002,38(21):1276-1278.
[11] G.A.Elliott, G.A.Covie, D.KaePrzaak, etal. A new concept: Asymmetrical pick-ups for inductively coupled power transfer monorail systems[J]. IEEETrans. on Magnetics,2006,42(10):3389-3391.
[12] J.T.Boys, G.A.Covic,A.W. Green. Stability and control of inductively coupled power transfer systems[J].IEEE Proeeedings-Electric Power Applications,2000,147(l):37-43.
[13] C.S.Wang，G. A. Covic, O.H.Stielau. Power transfer capability and bifurcation phenomena of Iooselycoupled induetive power transfer systems[J]. IEEE Trans. on Industrial Eleetronics,2004,51(l):145-157.
[14] Chang-Yu Huang, J.T.Boys,G.A. Covic, etal. Practical considerations for designing IPT system for EVbattery cllarging[J]. Vehicle Power and Propulsion Conferenee,2009:402-407.
[15] N.A.Keeling,G.A.Covie,J.T.Boys. A unity-power-factor IPT pick-up for high-power applications[J].IEEE Trans. on Industrial Electronics,2010,57(2):744-751.
[16]朱俊.探秘电动汽车的无线充电技术[J].交通与运输,2012（1）:26-27.
[17]朱俊.电动汽车的无线充电技术[J].汽车工程师,2011（12）:50-52.
[18] http://tech.sina.com.cn/d/2010-11-09/08084843495.shtml.
[19] http://news.bitauto.com/qyxw/20110608/0805380250.html.
[20] Liu X.,Hui S.R.Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery ChargingPlatform[J].IEEE Transaction on Power Electronics,2008,23(1):455-463.
[21]武瑛，严陆光，徐善纲.运动设备无接触供电系统耦合特性的研究[J].电工电能新技术,2005,24（3）:5-8.
[22]孙跃，王智慧，戴欣，苏玉刚，李良.非接触电能传输系统的频率稳定性研究[J].电工技术学报,2005，20（6）:56-59.
[23]徐晔,马皓.串联补偿电压型非接触电能传输变压器的研究[J].电力电子技术,2008,42（3）：4-5,11.
[24]高金峰，徐磊.并联谐振型非接触供电平台的频率控制与设计[J].郑州大学学报,2006,27（4）：66-70.
[25]毛赛君.非接触感应电能传输系统关键技术研究[D].硕士论文,南京:南京航空航天大学,2006.
[26] Zhang,XJ,Zhang H,Chen BL.Narrow width pulsed and high peak power supply circuit of laserdiode[C].6th InternationSymposium on Test and Measurement,Jun01-04,2005,vols1-9:3071-3073.
[27]张青.谐振耦合式无线输电多载系统建模及特性研究[D].硕士论文,广州:华南理工大学,2011.
[28]韩腾,卓放,闫军凯,刘涛,王兆安.非接触电能传输系统频率分叉现象研究[J].电工电能新技术,2005,24（2）:44-47,76.
[29] Li H L,Hu A P,Covic G A,etal.Optimal coupling condition of IPT sysytem for activeing maximumpower transfer[J].Electronics Letters,2009,45(1):76-77.
[30] GLASER P．Power From the Sun．Its Future［J］.Science,1968,162（11）：857-861．
[31]胡大璋,周兆先.微波输送电能的新技术[J].电子科技导报,1996,(12):1-4.
[32]张小壮.磁耦合谐振式无线能量传输距离特性及其实验装置的研究[D].硕士论文,哈尔滨：哈尔滨工业大学,2009.
[33] http://www.eeworld.com.cn/dygl/2011/1012/article_7482.html.
[34] M.Ali,G.Yang,R.Dougal.A Miniature Packaged Rectenna for Wireless Power Transmission and DateTelemetry[C].IEEE International Workshop on Antenna Technology Small Antennas and NovelMetamaterials,Mar.2006:225-228.
[35]张猛.微波无线电能传输与通信系统的研究[D].硕士论文,杭州：浙江大学，2004.
[36] BROWN W．Status of the Microwave Power Transmission Components for the Solar Power Satellite［J］．IEEE Transactions on Microwave Theory and Techniques，1981，29（12）：1319-1327．
[37] Andre Kurs, Aristeidis Karalis, Robert Moffatt, etal. Wireless Power Transfer Via Strongly CoupledMagnetic Resonances[J]. Science.2007,317(6):83-86.
[38] Alanson P. Sample, David A. Meyer, Joshua R. Smith. Analysis, Experimental Results, and RangeAdaptation of Magnetically Coupled Resonators for Wireless Power Transfer [J]. IEEE tansactions onindustrial electronics,2011,58(2):544-554.
[39] Aristeidis Karalis, J. D. Joannopoulos, and Marin Soljacic. Wireless Non-Radiative Energy Transfer.The AIP Industrial Physics Forum,2006.1.
[40]冯慈璋,马西奎.工程电磁场导论[M].北京:高等教育出版社,2000.
[41] http://www.google.com.hk/imglanding.
[42] Fei Zhang, Xiaoyu Liu, Steven A. Hackworth, Robert J. Sclabassi, and Mingui Sun.In Vitro and In VivoStudies on Wireless Powering of Medical Sensors and Implantable Devices[C].2009IEEE/NIH LifeScience Systems and Applications Workshop,2009:84-87.
[43] Xiaoyu Liu, Fei Zhang, Steven A. Hackworth, Robert J. Sclabassi,Mingui Sun. Modeling andSimulation of a Thin Film Cell for Power Transfer to Medical Devices and Implants[C],2009IEEEInternational Symposium on Circuits and Systems,2009:3086-3089.
[44] Xiaoyu Liu, Fei Zhang, Steven A. Hackworth, Robert J. Sclabassi, Mingui Sun.Wireless Power TransferSystem Design for Implanted and Worn Devices[C] Proceedings of the IEEE35th Annual NortheastBioengineering Conference,2009:1-2.
[45] Zhang Fei,Hackworth Steven A., Fu Weinong, Sun, Mingui.The Relay Effect on Wireless PowerTransfer Using WiTricity[C].14th Biennial IEEE Conference on Electromagnetic FieldComputation,2010:1.
[46] Wang Junhua, Ho S.L., Fu W.N.,Sun Mingui.Analytical design study of a novel witricity charger withlateral and angular misalignments for efficient wireless energy transmission[C]. IEEE Transactions onMagnetics,2011:47(10):2616-2619.
[47] Junhua Wang, Jiangui Li, S. L. Ho, W. N. Fu, etal．Analytical study and corresponding experiments for anew resonant magnetic charger with circular spiral coils[C]. Journal of Applied Physics,2012,111(7).
[48] http://www.52solution.com/article/articleinfo/id/80010144/page/3.
[49] Imura Takehiro,Uchida Toshiyuki,Hori Yoichi.Experimental Analysis of High Efficiecy Power TransferUsing Resonance of Magnetic Antennas for the Near Field-Geometry and Fundamental Characteristics[C].IEEE Japan Industry Applications Society Conference,2008:539-542.
[50] Imura Takehiro, Okabe Hiroyuki,Hori Yoichi. Basic Experimental Study on Antennas of Wireless PowerTransfer for Electric Vehicle by using Magnetic Resonant Coupling[C].Vehicle Power and PropulsionConference,2009:936-940.
[51] Beh TeckChuan,Kato Masaki,Imura Takehiro. Basic Study on Improving Efficiecy of Wireless PowerTransfer via Magnetic Resonance Coupling Based on Impedance Matching[C]. IEEE InternationalSymposium on Industrial Electronics2010,2010:2011-2016.
[52] http://biz.ppsj.com.cn/2010-10-28/2969342259.html.
[53] http://emc.ofweek.com/2012-02/ART-8320058-11000-28597792.html.
[54] http://www.pcworld.com.cn/Article/ShowArticle.asp?ArticleID=6734.
[55] http://tech.cn.yahoo.com/ypen/20120111/808800.html.
[56] http://www.eeworld.com.cn/szds/2011/1228/article_3499.html.
[57]赵彪,陈希有,于庆广.用于非接触电能传输的自适应谐振技术原理[J].电工电能新技术,2010,29（2）:33-37.
[58]马官营,颜国正.基于电磁感应的消化道内微系统无线能量传输问题研究[J].生物医学工程杂志，2008,25(1):61-64.
[59]翟渊，孙跃，戴欣，苏玉刚，王智慧.磁共振模式无线电能传输系统建模与分析[J].中国电机工程学报,2012,32(12):155-160.
[60]杨庆新，陈海燕，李阳等.电磁-机械同步共振无线传能与转换方法研究（批准号：50977062）.
[61]杨庆新，陈海燕，徐桂芝等.无接触电能传输技术的进展[J].电工技术学报,2010,25（7）：6-13.
[62]张献，杨庆新，陈海燕，李阳，等.电磁耦合谐振式传能系统的频率分裂特性研究[J]，中国电机工程学报,2012,32(9):167-172.
[63]张献，杨庆新，陈海燕，李阳，等.电磁耦合谐振式无线电能传输系统的建模、设计与实验验证[J].中国电机工程学报,2012,32(21):153-158.
[64] Zhang Xian，Yang Qingxin，Chen Haiyan，Li Yang，Yan Zhuo. The application of non-contact powertransmission technology (NPT) in the modern transport system[C]. Mechatronics and Automation(ICMA),2010International Conference on,2010,2010:345-349.
[65] Zhang Xian，Yang Qingxin，Chen Haiyan，Li Yang，Yan Zhuo. Analysis of A Novel Near-fieldNon-radiative Wireless Power Transmission System[C]. CASE2011,2011:1-4.
[66] Zhang Xian,Yang Qingxin，Li Yang. Numerical analysis on electromagnetic characteristics of laminatedcore joints of power transformer[C].2010International Conference on Computer and informationApplication,2010:67-70.
[67] Zhang Xian, Yang Qingxin, Chen Haiyan. Investigation on contactless power transmission ofelectromaganetic-mechanical synchronous resonance[C].The Secand International Conference onElectromagnetic Field Problems and Applications,2012.
[68] Zhang Xian,Yang Qingxin,Chen Haiyan. Direct Field-circuit coupled Analysis and CorrespondingExperiments of Electromagnetic resonant Coupling System. International Magnetics Conference2012.
[69] Zhuo Yan, QingxinYang, Haiyan Chen, Chao Zhang, Guizhi Xu. Modeling and Experimental Analysisof Helical Resonator for Wireless Power Transmission System[C].The International Conference onElectrical and Control Engineering(ICECE2010),2010:3886～3889.
[70] Zhuo Yan, Chao Zhang, Haiyan Chen, Qingxin Yang, Sumei Yang. Simulation Analysis on DetachableTransformer in Contactless Electrical Energy Transmission System[C]. International Conference onElectrical Machines and Systems(ICEMS2010),2010:1777～1780.
[71] Zhuo Yan, Chao Zhang, QingxinYang, Haiyan Chen, Guizhi Xu. Design and Analysis of ResonantCoupling Wireless Power Transmission System[C],201014th Biennial IEEE Conference onElectromagnetic Field Computation.
[72] Zhang Xian,Yang Qingxin,Chen Haiyan. A Novel Two-port Network Model and ExperimentalValidation for Resonantly Coulping Power Transmission System[C]. The Sixth International Conferenceon Electromagnetic Field Problems and Applications,2012.
[73]杨庆新，李阳，等.无线电能传输实验系统[P].申请号：201010532425.9
[74]李阳,杨庆新,牛萍娟,田会娟.基于无线电能传输技术的LED室内台灯[P].申请号：201210164092.8
[75]张献，杨庆新，等，电动车智能在线充电系统[P].申请号：201110350760.1.
[76]张献，杨庆新，等，一种智能脉冲式无线电能传输装置[P].申请号：201220011291.0.
[77]张献，杨庆新，等，家庭便携式无线充电装置[P].申请号：201110350956.0.
[78]张献，杨庆新，等，一种智能脉冲电磁推送发射装置[P].申请号：201210007360.5.
[79]张献，杨庆新，等，深水下水文测量无线供电系统[P].申请号：201210052453.X.
[80]朱春波.基于平面磁芯的电动汽车磁共振式非接触充电技术研究（批准号：51277037）.
[81]朱春波.基于磁耦合谐振的无线传感器无线供电技术研究（批准号：51077019）.
[82]陈乾宏.电动汽车高效率、高可靠性无线供电的关键技术研究（批准号：51507009）.
[83]李云辉.基于特异材料的非辐射无线能量传输技术研究（批准号：51007064）.
[84] Chunbo Zhu, Chunlai Yu, Kai Liu, Rui Ma. Research on the Topology of Wireless EnergyTransferDevic[J].IEEE Vehicle Power and Propulsion Conference(VPPC), Sept.3-5,2008.
[85] Chunbo Zhu, Kai Liu, Chunlai Yu, Rui Ma, Hexiao Chen, Simulation and Experimental AnalysisonWireless Energy Transfer Based on Magnetic Resonance[C].IEEE Vehicle Power and PropulsionConference(VPPC), Sept.3-5,2008.
[86]曲立楠.磁耦合谐振式无线能量传输机理的研究[D].哈尔滨工业大学.2010.
[87]朱春波,于春来,毛银花,陈清泉.磁共振无线能量传输系统损耗分析[J].电工技术学报.2012，27（4）：13-17.
[88]朱春波等.磁耦合谐振式无线能量传输装置[P].申请号:200810064667.2
[89]朱春波等.带有增强器的磁耦合谐振式无线能量传输装置[P].申请号:200810136892.2
[90]黄学良.谐振耦合式无线传输理论深化研究及其在电动汽车无线充电技术中的应用（批准号：51177011）.
[91]袁小芳.电动汽车非接触感应充电的智能建模与控制研究（批准号：61104088）.
[92] Tan Linlin, Huang Xueliang, Li Hui, Huang Hui. Study of Wireless Power Transfer System ThroughStrongly Coupled Resonances.2010International Conference on Electrical and ControlEngineering.2010.
[93]黄辉,黄学良,谭林林,丁晓辰.基于磁场谐振耦合的无线电力传输发射及接收装置的研究[J].电工电能新技术,2011,30(1):32-35.
[94]张建华,黄学良,邹玉炜,柏杨.利用超声波方式实现无线电能传输的可行性的研究[J].电工电能新技术,2011,30(2)：66-69，74.
[95]强浩，黄学良，谭林林，吉青晶，赵家明.基于动态调谐实现感应耦合无线电能传输系统的最大功率传输[J].中国科学，2012，42（7）：830-837.
[96]傅文珍,张波,丘东元,等.自谐振线圈耦合式电能无线传输的最大效率分析与设计.中国电机工程学报,2009,29(18):21-26.
[97] Wenzhen Fu, Bo Zhang, Dongyuan Qiu. Study on Frequency-tracking Wireless Power Transfer Systemby Resonant Coupling. IPEMC2009.
[98]傅文珍,张波,丘东元.频率跟踪式谐振耦合电能无线传输系统研究.变频器世界.2009(08):41-46.
[99] Jun Zhao,Guizhi Xu,Chao Zhang,Yang Li,Xian Zhang,Qingxin Yang,Ying Li,Hongli Yu.The Design andResearch of a New Kind Small Size Resonator Used in Magnetic Coupling Resonance Wireless EnergyTransmission System[C].the International Magnetics Conference (INTERMAG2012).
[100] Jun Zhao, Guizhi Xu, Chao Zhang, Xiaowei Wan.Research on Electromagnetic Radiation to HeadFrom Head Implantable Coil Powered via Witricity[C].The6th International Conference onBioinformatics and Biomedical Engineering (ICBBE2012).
[101] Jun Zhao, Guizhi Xu, Chao Zhang,Wei Zhang, Xuan Li.A Contrastive Studies between MagneticCoupling Resonance and Electromagnetic Induction in Wireless Energy Transmission[C].The SixthInternational Conference on Electromagnetic Field Problems and Applications (ICEF2012).
[102]闫卓.基于磁谐振耦合的多用户无线电能传输技术研究[D].博士论文.天津：河北工业大学，2011.
[103]张献.基于电磁-机械同步共振的无线电能传输与转换方法研究[D].博士论文.天津：河北工业大学，2012.
[104]谢翔,张春,王志华.生物医学中的植入式电子系统的现状与发展[J].电子学报,2009,32(03):462-467.
[105]甘丽,闵永泉.脑深部电刺激的作用机制及其在精神疾病治疗中的应用[J].立体定向和功能性神经外科杂志.2006,(05):314-317.
[106]卓勇.生物体内置电装置的外部供电模式研究[D].博士论文，重庆：重庆大学.2007.
[107] D. Kondziolka, D. Whiting, A. Germanwala, et al.Hardware-related complications after placement ofthalamic deep brain stimulator systems.Stereotact Funct Neurosurg,2002,79(3-4):228-33.
[108]张文亮，武斌，李武峰等.我国纯电动汽车的发展方向及能源供给模式的探讨[J].电网技术,2009,33(4):l-5.
[109]赵小坤.电动汽车感应充电技术[D].硕士论文.哈尔滨：哈尔滨工业大学，2009.
[110]李昆鹏.电动汽车动力蓄电池无线充电技术的智能化研究[D].天津：河北工业大学硕士论文，2011.
[111] H.Haus. Waves and Fields in Optoelectronics. Prentice-Hall,Englewood Cliffs, J,1984.Hermann.A.Haus著,陈东培译.光电子学中的波和场.上海翻译出版公司.1990年11月第1版,209-244.
[112] Seung-Hwan Lee, Robert D. Development and Validation of Model for95%Efficiency220WWireless Power Transfer over a30cm Air-gap [J]. IEEE Transactions on IndustryApplications,2011,47(6)：2495-2504.
[113] Aristeidis Karalis, J.D.Joannopoulos, Marin Soljacic. Efficient Wireless Non-radiative Mid-rangeEnergy transfer[J]. Annals of Physics,2008,32（3）:34-48.
[114]刘修泉，曾昭瑞，黄平．空心线圈电感的计算与实验分析[J]．工程设计学报，2008，15(2)：149~153.
[115]陈抗生.电磁场与电磁波[M].北京：高等教育出版社,2007.
[116] M.M.拉德马内斯.射频与微波电子学[M].北京：科学出版社,2006.