MATEC Web of Cofereces, 008 ( 05) DOI: 0.05/ mateccof/ 05008 C Owed by the authors, published by EDP Scieces, 05 Efficiecy Aalysis of Wireless Power Trasmissio for Portable Electroics Xigpig Xu, Chuaxiag Yu, Yuxi Zhag, Ma Zhag & Haotia Hu School of Electrical Egieerig, Chogqig Uiversity, Chogqig, Chia ABSTRACT: With the portable electroics becomig more ad more popular, a model of wireless power trasmissio for geeral portable electroics was preseted based o the priciples of magetic resoace trasmissio. Ad that trasferrig the model to a equivalet circuit was possible to calculate. The characteristics of the system ad the optimal coditios were aalyzed, ad the ifluece of the trasmissio efficiecy for the Couplig factor ad the Quality factor was discussed. The theory aalysis ad simulatio i MATLAB show that the performace of the system ca be optimized by adjustig the couplig factor betwee the trasmitter couplig coils. Furthermore, the feasibility of this theory was prove by experimets. Thus, this paper provides a useful referece to improve the wireless power trasmissio for portable electroics. Keywords: portable electroics; wireless power trasmissio; magetic couplig resoace; efficiecy INTRODUCTION I November 006, a assistat professor of departmet of physics i MIT, Mari Soljacic, first proposed magetic couplig resoat WPT techology o the BBS i AIP idustrial physics. Ad i Jue 007, usig the techology, he successfully lit a 60-watt light bulb i the distace of.3 meters. Efficiecy is as high as 96% at a distace of 75 cm. The ews seems to igite the ethusiasm of scietists. With the portable electroic products (such as TVs, laptops, cell phoes, ad so o) were more ad more popular, people's lives become more coveiet. At the same time, the traditioal power supply of these devices cause a lot of icoveiece to people, such as the limited power supply, power trasmissio ad other security risks. I order to effectively address the shortcomigs of traditioal wired power supply i recet years, the wireless power trasmissio (WPT) has attracted much attetio of researchers at home ad abroad []. Curretly, the wireless power trasmissio mode icludig: the resoace magetic couplig type, the electromagetic iductio type, ad the electromagetic radiatio type. Amog them, the resoat magetic couplig techique was the use of o-radiative electromagetic ear-field regio achievig eergy trasmissio. Compared with the other two types, it has advatages such as low difficulty desig, high trasmissio efficiecy, log trasmissio distace, o radiatio ad high security features. So this type of wireless power trasmissio system has received more attetios ad researches [-3]. I order to obtai a stable system performace, the trasmitter ad the receiver i the systems usually use the same parameters, symmetrical resoator to achieve excellet performace [4-5]. However, it ows a very arrow rage of applicatios of the study because of the actual trasmissio distace ad equipmet size. I the referece [6], the author preseted the magetic couplig of the resoace system made by differet size ad asymmetric resoators without the theoretical poit of view of the workig mechaism, ad optimizatio of system performace; the refereces [7-8] are preseted to adjust the distace betwee the trasmitter ad receiver to achieve impedace matchig system, thereby improve the trasmissio efficiecy. However, four coils i the system separated from each other eed to keep the same distace, besides, the load impedace should also remai the same. So it was ot for the actual electroic products. Referece [9] shows that the professor TC Beth had use the wireless power trasmissio i electric automobile, studyig the receive coil resoace frequecy ad system frequecy which were caused by mismatch problem. Impedace matchig was put forward to adjust the coil resoace frequecy. Besides, the electromagetic aalysis ad test was carried o to coclude a parameter desig method. Scholars such as Seug-Hwa LEE proposed a equivalet circuit model of the magetic couplig resoat WPT system i the referece [0]. Ad the fiite elemet aalysis shows that the circuit model is a effective model which icludig the ifluece of ski effect ad proximity effect based o a high frequecy system. All above has helped to promote the progress of wireless power trasmissio. This paper presets a suitable portable electroic products magetically coupled resoat couplig wireless power trasmissio system model to fill up the deficiecy metioed earlier [-]. The trasmissio characteristics of the system were aalyzed, the expressios of the trasmissio efficiecy were derived, the system performace was optimized, ad the impact of the quality factor ad the couplig factor for trasmissio efficiecy was discussed. Fially, the This is a Ope Access article distributed uder the terms of the Creative Commos Attributio Licese 4.0, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Article available at http://www.matec-cofereces.org or http://dx.doi.org/0.05/mateccof/05008
MATEC Web of Cofereces optimum coditios i the system were give. The Matlab simulatio shows that whe the coil Q factor is determied, the system trasmissio efficiecy optimizatio ca be realized by adjustig the couplig factor betwee the trasmitter coils. aalysis. SYSTEM MODEL AND CIRCUIT ANALYSIS The model of wireless power trasmissio system for portable electroic products was show i Figure. There were four compoets of the system cosist of the drive coil (Drive Coil), the trasmit coil (TX Coil), the receivig coil (RX Coil) ad the load coil (Load Coil). Trasmittig ad receivig coils were called resoator. Whe eergy was trasmitted, they were i a resoace state. The resoat frequecy ad the atural frequecy of the coil were the same. As show i Figure, the trasmittig termial was the same with the traditioal four resoat wireless power trasmittig, amely the drivig coil was formed as the sigle-tur coil, ad the multi-tur trasmitter coil was made of axial spiral coil. But the receivig termial of the receivig coil ad loadig coil i a plaar spiral were fixed together ad they are ot the same size with the trasmitter coil [3-4]. Thus, the coil size is i accordace with the size of the electrical equipmet. Figure. Model of wireless power trasmissio that suitable for portable electroics To simplify the aalysis, oly four coils eergy trasfer were aalyzed [5]. I accordace with the priciple of magetic couplig ad the resoace circuit theory, each of coils may be equivalet to RLC circuit system. So it is obvious that we ca obtai the equivalet circuit model show i Figure. I the Figure, AC was a high-frequecy sigal source, L, L, L3 ad L4 were the equivalet iductace of the four coils; RL was the load resistace; R, R, R3 ad R4 were loss resistace of the coils; C, C, C3 ad C4 were the sum of a parasitic capacitace ad tued compesatio capacitor; M, M3 ad M34 were the mutual iductace betwee adjacet coils. Sice o cross couplig betwee the adjacet, weak, low-impact coils, the cross mutual iductace M3, M4 ad M4 were ot cosidered i the process of Figure. Equivalet circuit of wireless power trasmissio I Figure, K was preseted as the couplig factors betwee the Drive coil ad the TX coil, K3 was preseted as the couplig factors betwee the TX coil ad the RX coil, K34 was preseted as the couplig factors betwee the RX coil ad the Load coil. They were maily determied by coil iductace, coil turs ad the distace amog coils. Assume ω was the agular frequecy i the system. By Kirchhoff's voltage law (KVL), we ca obtai that[6]: i Z Z Z3 Z4 Vs i Z Z Z3 Z 4 0 i3 Z3 Z3 Z33 Z34 0 i4 Z4 Z4 Z43 Z44 0 () Wherei: R jl m () Zm Z j C m jmm m, Mm km Lm L Wherei, m was resoat coil umerals,, m {,,3,4}; R was preseted as the -th coil of equivalet resistace; L was preseted as the -th coil equivalet iductace; C was the -th tuig capacitace value; M m ad k m were respectively the mutual iductace ad the couplig coefficiet betwee the m-th coil ad the -th coil. Whe the system was i steady-state operatio, it was show as follows: ω,, 3, 4 LC m jl 0 m,,,3,4 jc (3) (4) Igore the cross-couplig factor k4, k3, k4, the formula () ca be simplified as follows: i R jm 0 0 Vs i jm R jm3 0 0 i3 0 jm3 R3 jm34 0 i4 0 0 jm34 R4 0 (5) 008-p.
ICETA 05 Takig the quality factor L Q ad equatio () R ito the equatio (5), it was show as follows: i i k3qq3 k34qq 3 4 Vs k QQ k34qq 3 4 Vs R kqq k34qq 3 4 k3qq3 RR kqq k34qq 3 4 k3qq 3 i k k QQ Q QV 3 3 s 3 RR 3 kqq k34qq 3 4 k3qq 3 kk3k34 QQ QQ3 QQ 3 4V i4 s RR 4 kqq k34qq 3 4 k3qq 3 (6) Expressio (7) of trasmissio efficiecy i the system was obtaied by equatio (6). I additio, the loadig coil was usually a sigle coil, ad R4 was much less tha L4. It was possible for formula (7) to do approximatio as show i formula (8): [k 3Q Q3k 34Q3Q 4] (7) (kqq )(k3qq 3)(k34Q3Q 4) (kqq )(k 34Q3Q 4) k 3Q Q 3 ir R [ k Q Q k Q Q ] 4 L L Ui s RL R4 3 3 34 3 4 (kqq )(k 3QQ 3)(k34Q3Q 4) 34 3 4 3 3 (k Q Q )(k Q Q ) k Q Q 3 PERFORMANCE ANALYSIS AND OPTIMI- ZATION OF SYSTEM (8) Accordig to the formula (8), it is show that whe the load was determied, the eergy trasfer efficiecy was determied by the couplig factor ad the quality factor. I order to further study the trasmissio efficiecy of the optimized coditios, we respectively aalyzed the trasmissio efficiecy with the ifluece of the couplig factor ad the quality factor. 3. Impacts o the efficiecy ad optimizatio of the quality factor Figure shows that the drive coil is coected to the power supply ad the load coil is coected to the load. The quality factor Q, Q4 was very small due to RS ad RL. I the practical applicatio, load coils were limited by size of the apparatus, which makes Q4, the size level, be geerally less tha ; the quality factor Q, Q3 was relatively idepedet, the self-resistors R ad R3 were small, so Q, Q3 was usually much greater tha Q, Q4. I additio, whe the system was workig properly, the trasmitter ad the receiver were i a state of strog couplig, ad the couplig factor meets k, k34 >> k3. This time, the formula (8) ca do the followig approximatios: ( k QQ )( k QQ ) ( k QQ )( k Q Q )(9) 34 3 4 34 3 4 (k Q Q )(k Q Q ) k Q Q (k Q Q )(k Q Q ) 34 3 4 3 3 34 3 4 3 3 34 3 4 3 3 (0) k Q Q k Q Q k Q Q () At last, the equatio (8) ca be approximated as follows: k Q Q () 3 3 k3qq3 From the equatio (), we ca kow that the trasmissio efficiecy was proportioal to formula k 3 Q Q 3. So, whe k3 was determied, the trasmissio efficiecy was oly relied o the value of Q, Q3. Sice that: k N N r r 0 m m m (3) 3 LLd m m Wherei: μ0 was the permeability of vacuumnm, N was the circle umber of coil m, ; rm, r was the radius of coil m, ; dm was the distace of coil m, ; Lm, L was the iductace value of coil m, ad m, {,,3,4}. It comes to a coclusio from formula (3) that whe the distace d3 was determied i practical applicatio, we ca improve the efficiecy of trasmissio through chagig the parameter of coil to get high trasmissio efficiecy. To further illustrate the impact of the quality factor Q of the trasmissio efficiecy, we make Vs = 5V, ω = 7.5306 rad/s, R = 0, Q =00, Q3 =00, k = 0., k3 = 0.5, k34 = 0.5, ad the, we obtai the relatio curve through formula (8) show i Figure 3. Next step, we make Vs = 5V, ω = 7.5306 rad/s, R = 0, Q = 0.8, Q4 = 0.8, k = 0., k3 = 0.5, k34 = 0.5, ad the, we obtai the relatio curve through formula (8) as show i Figure 4. As show i Figure 3, the efficiecy affected by quality factor Q was very small. With the chage of Q4, there will be a peak efficiecy. However, whe Q4 was betwee the value of ad 0, it chaged little. It ca be see from Figure 4 that the trasmissio efficiecy is obviously icreased with the chage of quality factor Q, Q3. So, while i the actual desig of wireless power trasmissio system, the resoace frequecy meets the requiremets uder the premise, 008-p.3
MATEC Web of Cofereces the bigger value of quality factor Q ad Q3, the better. This was much of value i the followig aalysis. It is obviously see from the formula (3) ad (4) that whe the efficiecy is declied with the chage of the equipmet distace d3 ad directio i practice applicatio, we ca adjust the distace d i the trasmittig termial to optimize the trasmissio efficiecy. 4 SIMULATION ANALYSIS AND EXPERIMENT VERIFICATION 4. Simulatio aalysis I order to verify the optimizatio aalysis metioed earlier, the simulatio aalysis by Pspice, the wireless power trasmissio system model, was doe. Simulatio circuit was show i Figure 5. The simulatio system was based o SPICE software. Figure 3. Relatio curve betwee Q, Q4 ad η Figure 5. Simulatio model of magetically coupled resoat wireless power trasmissio system Chage the value of iductace, capacitace ad resistace i the circuit to obtai the resoat state. At the same time, differece quality factors Q were obtaied, which was the key poit. The, differet value with differet efficiecy is show i Table. Figure 4. Relatio curve of Q, Q3 ad η 3. Impacts o the efficiecy ad optimizatio of couplig factor I practical applicatios, whe the wireless power trasmissio system desig was completed, the quality factor Q to Q4 were the fixed value. I additio, the receivig coil ad loadig coil secured together i this wireless power trasmissio system that we study, so k34 was also a fixed value. Therefore, the trasmissio efficiecy was oly iflueced by k, k3 idicated i the formula (8). Take the derivative of formula (8) by k3 to obtai the maximum trasmissio efficiecy. The k ad k3 eed to meet the formula (4) show as follows: k Q Q 3 3 QQ k34qq 3 4 k (4) Table. Results of simulatios (k=0.8, k3=0.3, k34=0.8, RL=50 Ω) Q Q Q 3 Q 4 f/mhz η/% 0.63 37 338 0.3.0 35 0.63 55 338 0.3.0 5 0.63 37 6 0.3.0 5 0.63 37 6 0.3.0 30 0.63 55 55 0.3.0 65 0.63 37 338 0.3.0 38 0.63 55 6 0.3.0 6 We ca see from Table that the trasmissio efficiecy chagig with the quality factor Q was satisfied well with the theory aalysis metioed earlier. As show i Figure 6, whe Q to Q4 were determied ad k3 was chageable, we obtai the curve of the trasmissio efficiecy. I order to facilitate comparative aalysis, we measured the correspodig trasmissio efficiecy whe the couplig factors were chaged ad fixed. As show i Figure 6, whe k was a fixed value ad k3 was icreased to a certai value, the trasmis- 008-p.4
ICETA 05 sio efficiecy will be rapidly decreased. However, the trasmissio efficiecy will be cotiued to icrease through chagig k. This was because there will be a frequecy splittig icreased with k3 whe k was a fixed value detuig the system ad leadig to a sharp declie i trasmissio efficiecy. If chagig k o the system is to realize the real-time adjustmet, the the frequecy splittig pheomeo does ot occur, ad it ca effectively improve the trasmissio efficiecy. Coclusio was cosistet with the theoretical aalysis. I practical applicatios, it ca effectively icrease the trasmissio distace ad the trasmissio efficiecy of eergy by maual adjustmet or automatic adjustmet of the distace betwee the trasmitter coils to fid the poit of maximum efficiecy. Figure 7. Test system of wireless power trasmissio Keep other coditios such as circuit, coils ad k34 uchaged ad chagig k ad k3, we measured the iput ad output powers ad calculated trasfer efficiecy. The result was show i Figure 7 ad Figure 8. Figure 6. Curves of trasmissio efficiecy 4. Experimet verificatio Set up four coils of the wireless power trasmissio apparatus as show i Figure 7. I the system, the trasmissio termial ad the receive termial were itegrated ispective for there was o ifluece o the experimet result accordig to the aforemetioed aalysis. This trasmissio circuit was charged by full bridge iversio with power MOS trasistors IRF640 which were cotrolled by MOS driver UCC744. Ad the receive coil was coected to diode rectificatio, icludig capacitor filterig. The load was high power LED. The WPT system was simplified so as to decrease the amout of work i the experimet, but it was eough for the accuracy of the result. Figure 8. Trasmissio efficiecy of experimetal value compared with the theoretical value whe k was fixed Figure 9. Trasmissio efficiecy of experimetal value compared with the theoretical value whe k was chaged 008-p.5
MATEC Web of Cofereces From Figures 7 ad 8, there was a little deviatio betwee the experimetal data ad the simulatio data. It was acceptable as the actual system stray iductace ad stray capacitace existed, ad takig ito accout the o-stadard coil widig. Moreover, the resoat frequecy of the parameter of the actual system was about 993 khz after costatly adjustig, while the actual use of resoat frequecy was.0mhz i the simulatio metioed earlier. Take ito accout the tolerace limits, the results of the experimet will ot cause much error. 5 CONCLUSION This paper was maily for portable electroic products, researchig magetic resoace couplig wireless power trasmissio system model, aalyzig the model topology of the system deeply, discussig the relevat factors affectig the efficiecy. Ad the, the relatioship was obtaied amog the coil quality factor, couplig factor ad the trasmissio efficiecy, ad optimized coditios i performace of this system which was aalyzed, ad the relatioal expressio was give. Fially, verificatio through simulatios ad experimets show that it ca effectively improve the system trasmissio efficiecy for the wireless power trasmissio techology i portable electroic products by adjustig the couplig factor of the coils i trasmitter termial. It has laid a theoretical foudatio. REFERENCES [] SAMPLE A P, MEYER D A, & SMITH J R. 0. Aalysis, experimetal results, ad rage adaptatio of magetically coupled resoators for wireless power trasfer. IEEE Trasactios o Idustrial Electroics, 58(): 544-554. [] KURS A, KARALIS A. & MOFFATT R, et al. 007. Wireless power trasfer via strogly coupled magetic resoaces. Sceic-express, 37(5834): 83-86. [3] Jiaxu Wu, Juyog Wu. & Yu Zhag, et al. 0. Experimetal Research o Wireless Power Trasmissio Based o Magetic Couplig Resoat Theory. Moder Electric Power, 9(): 4-8. [4] Wezhe Fu, Po Zhag. & Dogyua Qiu, et al. 009. Maximum efficiecy aalysis ad desig of self-resoace couplig coils for wireless power trasmissio system. Proceedigs of the CSEE, 9(8): -5. [5] Yua Zhai, Yue Su. & Xi Dai, et al. 0. Modelig ad aalysis of magetic resoace wireless power trasmissio systems. Proceedigs of the CSEE, 3(): 55-60. [6] ISHIZAKI T. & AWAI D F I. 0. A ovel cocept for -dimesioal free access wireless power trasfer system usig asymmetric couplig resoators with differet sizes. IMWS, IEEE MTT-S Iteratioal, (3): 43-46. [7] DUONGTP, LEE J. W. 0. Experimetal results of high-efficiecy resoat couplig wireless power trasfer usig a variable couplig method. IEEE Microwave ad Wireless Compoets Letters, (8): 44-444. [8] K. Scheurle, A. Schitzer. & J. Krammer et al. 04. Stellewert. Der Galaktographie zur Abklärug pathologischer Sekretio i der komplemetäre Mammadiagostik. Der Radiologe, 54(). [9] Teck C B, Imura T. & Kato M, et al.00. Basic study of improvig efficiecy of wireless power trasfer via magetic resoace couplig based o impedace matchig. IEEE Iteratioal Symposium o Idustrial Electroics. Bari, Italy: IEEE, pp: 0-06. [0]Seug-Hwa L. & Lorez R D. 0. Developmet ad validatio of model for 95%-efficiecy 0-W wireless power trasfer over a 30-cm air gap. IEEE Tras. o Idustry Applicatios, 47(6):495-504. []Y.-H. Kim, S.-Y. Kag. & M.-L. Lee, et al. 009. Optimizatio of wireless power trasmissio through resoat couplig. Proceedigs of the Compatability ad Power Electroics, (5): 46 43. []Chubo Zhu, Kai Liu, Chulai Yu, Rui Ma. & Hexiao Cheg. 008. Simulatio ad experimetal aalysis o wireless eergy trasfer based o magetic resoaces. Harbi: IEEE Vehicle Power ad Propulsio Coferece, pp: -4. [3]Sukyu K, Myughoi K. & Kyougchoul K, et al. 0. Aalytical expressios for maximum trasferred power i wireless power trasfer systems. IEEE Iteratioal Symposium o Electromagetic Compatibility. Log Beach, USA: IEEE, pp: 379-383. [4]Gabriele Gradi, Maria K Kazimierczuk, Atoio Massarii. & Ugo Reggiai. 999. Stray capacitaces of sigle-layer soleoid air-core iductors. IEEE Trasactios o Idustry Applicatios, 35(5): 6-66. [5]Chulai Yu, Regui Lu, Yihua Mao, Litao Re. & Chubo Zhu. 009. Research o the Model of Magetic-Resoace Based Wireless Eergy Trasfer System. Dearbor, MI: Vehicle Power ad Propulsio Coferece, pp: 44 48. [6]Thuc P D. & Jog-Wook L. 0. Experimetal results of high-efficiecy resoat couplig wireless power trasfer usig a variable couplig method. IEEE Microwave ad Wireless Compoets Letters, (8): 44-444. 008-p.6