An improved three-coil wireless power linkto increase spacing distance and power formagnetic resonant coupling systemXian Zhang1*, Hao Meng1, Bin Wei2, Songcen Wang2 and Qingxin Yang1
Abstract
When wireless power transfer (WPT) technology is used to power the sensor networks, it is necessary to increasethe transmission power and distance. We strictly deduced two necessary conditions for strong coupling by coupledmode theory. Next, the transmission power and efficiency as a function of coupling coefficient and quality factorare derived, and the maximum active power of the load depends on the coupling coefficient between resonators,quality factor of the resonator and the drive power. In order to increase transmission power and distance, animproved three-coil wireless power link is proposed. Meanwhile, an experimental platform was established, and theexperimental results show that the transmission power can reach 120 W at a distance of 2.5 m. This proves that theimproved three-coil wireless power link is very effective.
Keywords: Three-coil wireless power link, Magnetic resonant coupling, Coupled mode theory, Critical strongcoupling, Optimal impedance feed
1 IntroductionThe magnetic resonant coupling wireless power transfer(MRC-WPT) was first proposed by MIT’s team in 2007[1] and is now gaining more spotlights ranging fromcontactless battery charging of consumer electronics [2],electric vehicles [3–5], to biological implanted devices’power supply [6, 7].WPT technology can be categorized according to their
operating frequencies, which are short-range inductivepower transmission (IPT) (at the range of a few hundredkilohertz), mid-range MRC-WPT also known as WiTricity(at the range of several MHz) and long-range directlymicrowave radiation (range above GHz) [8, 9]. Differentfrom other two methods, MRC-WPT operates in strongcoupling state to transfer energy wirelessly via evanescentnon-radiative near field. High-frequency power flowsamong resonators in a mid-range which is on the order ofseveral times the physical size of transmitting or receivingend when system is tuned into resonant state and finally
absorbed by the load. Moreover, it interacts weakly withbiological tissues or other non-resonant objects.In the past two decades, IPT is the mainstream of
WPT and its transmission distance is short. However,MRC-WPT has a significant increase in transmissiondistance. For mid-range applications, MRC-WPT is agood choice to reach a range of meters, which is of greatsignificance for the power supply of wireless sensor net-works [10, 11]. Nevertheless, the transmission power ofMRC-WPT system decreases with increasing transmis-sion distance because the magnetic coupling is relativelysmall at longer distances. Therefore, power transmissionrange needs to be extended to achieve more flexibility.Several methods were previously proposed to accom-
modate power pickups when there is deviation in radialdirection. In [12], a multiphase system is proposed toobtain a wider power delivery zone. In [13], a widepower transmission area is achieved by two transmit-ters. In [14], a cooperative operating coupler featuringtight-strong coupling is proposed to enhance anti-offsetcapability. However, transmission distance cannot beextended in coil axis directions by these methods.In [15–17], superconductor is utilized to reduce the
coil losses and increase transmission distance. But it is
* Correspondence: [email protected] Key Laboratory of Advanced Electrical Engineering and EnergyTechnology, Tianjin Polytechnic University, Tianjin 300387, ChinaFull list of author information is available at the end of the article
very expensive and hard to popularize at the moment. In[18], the transmission distance is adjusted by changingthe driving frequency of power source or controlling theloading effect of transmitting coil and receiving coil.However, the range adaptation is only intended toimprove the performance at short distances whereresonant frequency splitting occurs. The maximumtransmission distance after the critical coupling point isstill limited by the vanishing magnetic coupling.In this paper, we provide an improved three-coil wire-
less power link to maximize the transmission distanceand power at a reasonable level of efficiency. First, thetime domain solution of power exchange between tworesonators is achieved through coupled mode theory.Two key prerequisites of strong coupling are deduced bydiscussing the angular frequency, mode coupling factorand quality factor. After that, the overall transmissionefficiency and the maximum power of the load are ana-lysed. Finally, a three-coil wireless power link containingtwo helix resonators and a device coil was established,and power on the load reached 120 W with transmissiondistance up to 2.5 m. Measured values have an error of± 2.5% compared to theoretical ones.
2 Methods/experimental sectionIt is necessary to increase the load power and to extend thetransmission distance in axial direction for MRC-WPTsystem. Though there is high power over kilowatts and longdistance over several kilometres via micro-wave transmis-sion, it is far from safety and stability compared toMRC-WPT by using the non-radiative near field. Whenthe electrical parameters are fixed, the maximum activepower the load can get depends on the coupling coefficientbetween resonators, quality factor of the resonator and thedrive power. Therefore, if we intend to increase the loadpower, the overall contribution of three parameters aboveshould be concerned.It can be seen from the calculation formula (Q =ωL/R)
of the resonator quality factor that the quality factor canbe improved in two aspects: (1) increasing the ratio ofinductance and resistance and (2) increasing the naturalresonant frequency. In this paper, in order to increase thequality factor of the resonators, the oxygen-free coppertube with smooth surface is relatively nice material, be-cause it has good conductive property and skin effect isreduced to some extent. It should be noted that there isonly limited improvement for the ratio of inductance andresistance. The efficient way to get a larger quality factoris to increase the natural resonant frequency. With partici-pation of the distributed capacitance between coil tubes,the resonant frequency is up to 13.56 MHz with the qual-ity factor of 1100~1500.In our project, high-frequency power is fed directly to
the transmitting resonator. The high-frequency signal is
generated by DDS and amplified by MOS transistor M1and M2, as shown in Fig. 1a. C1 and C2 are used toadjust dead time; D1 and D2 are responsible for free-wheeling; C3~C5 and L1 are responsible for impedancematching. Figure 1b shows the way of feed; Fig. 1c showsthe dashboard of power amplifier. Detailed parametersof improved three-coil wireless power link system areshown in Table 1.
3 Characteristics of MRC-WPT by coupled modetheoryA general configuration of MRC-WPT system is shownin Fig. 2; there are three sections to fulfil the functionsof power coupling, transformation and transmission.Power on resonator a1,2 is acquired through inductivecoupling to achieve the conversion of low voltage/highcurrent and high voltage/low current between resonatorsand source or device coil. Once the system is tuned intoresonant state, power exchanges between the resonatorsthrough EM resonantly coupling which results in a rela-tively low transmission loss by high impedance perform-ance. Va1,2, Ia1,2, Ca1,2 and Ra1,2 are equivalent to voltage,current, capacitance and resistance of resonator a1,2,respectively; I1,2, RS,D and LS,D are current, resistanceand induction of source coil and device coil; VS isdriving voltage; RL is load resistance; MS1, M1,2 and M2D
are mutual induction between the coils. Here, the coup-ling effect between non-resonant source and device coilis ignored.
3.1 Prerequisites for efficient wireless power transferThe coupled mode theory is usually employed to de-scribe the general laws of wave interaction phenomenasuch as optical waves and sound waves. It is very suit-able for modelling the resonant energy exchange. Forthe lossless resonators in a MRC-WPT system, energyexchange between resonators can be described by twodecoupled differential equations as (1) [19].
da1dt
¼ jω1a1 þ κ12a2da2dt
¼ κ21a1 þ jω2a2
8><>: ð1Þ
where the forward rotation mode of resonators isdenoted as a1 and a2 whose second norm has energydimension; ω1,2 are natural resonant angular frequency;κ12 and κ21 are mode coupling factors; and there is a re-lationship with coupling coefficient k which is κ = ωk/2.For passive lossless system, energy exchange occurs be-tween modes and meets conservation for overall energy.Any change of oscillation mode needs to go throughnatural resonant periods under weak coupling, so itcomes to a1(t) =A(t)*exp.[0.5j(ω1 − ω2)t], where A(t) is aslowly varying time domain function. Assume there is an
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 2 of 8
initial condition as Γ{t = 0, a1(t) =A(t); a1(t) = 0}, thesolution can be derived as (2), where ω is the averagevalue of ω1 and ω2.
a1 tð Þ ¼ A 0ð Þ cos Ωtð Þ þ jω1−ω2
2Ωsin Ωtð Þ
h i� e jωt
a2 tð Þ ¼ A 0ð Þκ21 sin Ωtð Þ=Ω � e jωt
(
ð2Þ
Their two eigenvalues are λ12 = ±Ω = [(ω1 − ω2)2/4
− κ12*κ21]0.5. There is the first prerequisite that the max-
imum energy exchange exists unless ω1 = ω2. It is simpleand intuitive but explains why the two circuits have tobe tuned into resonance.For a lossy coupling system, the natural resonant
angular frequency will have an offset, and modifiedresonant angular frequency can be expressed as ω’ 1,2
= ω1,2 (1 + j/2Q1,2). The eigenvalues can be expressed as(3) by Taylor expansion, when the quality factor Q ishigh enough. In general, for more convenient impedancematching, the resonators are designed to be the samesize, resonant frequency and quality factor, so there areQ1 =Q2 =Q and ω1 = ω2 = ω.
λ1;2 ¼ −ωQ
� �� ffiffiffiffiffiffiffiffiffiffiffiffiffi
κ12κ21p ð3Þ
If we intend to obtain a sustaining growth in oscillation,it must meet the condition that there is a positive root andthe item within the radical sign is a real number. In general,the parameters of resonators are designed to be the same,so there are Q1 =Q2 =Q and ω1 =ω2 =ω. And the secondprerequisite is shown as (4) after simplification.
κ12κ21j j >>ω2
4Q2 ð4Þ
The two mode coupling factors denote the energycoupling rate; the two quality factors denote the lossrate. In other words, the resonators with high-qualityfactors are needed to form a low-loss bridge for energyflowing between the source and device.Energy exchange relationship between resonators in
normalization is shown as Fig. 3 in which |a1|2, |a2|
2
and |a1 + a2|2 indicate energy of resonator 1, 2 and
overall system. Presence of quality factor Q makes theoverall energy decays exponentially. Reason of attenu-ation in linear system includes Joule loss and radiation
(a) The structure diagram of three-coil power link
(b) The way of feed (c) The dashboard of power amplifier Fig. 1 Structure diagram of three-coil power link and experimental system. a The working principle of the three-coil wireless charging system.The waveform is generated through the DDS circuit. After multilevel amplification, the power is loaded onto the resonant coil. b The way ofpower loading, which improves the power conversion efficiency by the way of central feeding. The power supply prototype used in theexperiment is shown in c. a The structure diagram of three-coil power link. b The way of feed. c The dashboard of power amplifier
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 3 of 8
loss which can be expressed as absorption and radi-ation of Q value. As shown in Fig. 3a with ω1 = ω2
and different mode coupling factor, though there isalmost 100% energy exchange, it cannot keep sustain-ing and attenuating through several cycles. Usually,the distance between the two resonators is severaltimes of them. So it can be called as loose couplingmode. In Fig. 3b, when angular frequencies differgreatly, most of energy were stored in resonator 1,and the receiver gets very limited energy which is themain reason of decline in transmission power andoverall efficiency, which can be called as weakcoupling mode. As soon as the two requirements aremet, it is working under the strong coupling state inwhich proportion of energy exchange reaches 100%theoretically, as shown in Fig. 3c, which can be calledas strong and tight coupling mode.
3.2 Transmission performance for MRC-WPT systemFor the system as shown in Fig. 2, it is assumed thatenergy between resonators is exchanged only throughM12, and coupling coefficients kij are defined as kij =Mij/(LiLj)
1/2 (i = S, 1, 2; j = 1, 2, D). If k2D is smallenough, equivalent quality factor Q′ of receiver canbe expressed as:
Q0 ¼ QQL
Qþ QLð5Þ
Quality factor reflects the ratio of EM energy stored incircuit and energy consumed in a cycle when in reson-ance. Energy consumption comes from the resonator itselfand load resistance. For high-Q resonator, RD is smallenough to be ignored, and the value of equivalent qualityfactor Q′ is more close to QL. Therefore, active power onthe load PL is
PL ¼ A2
ω0� 4k
212
QL� k212 þ 1= QQLð Þ� �−2 ð6Þ
So when resonance occurs, PL is a multivariate func-tion of excitation power, resonant angular frequency,coupling coefficient and quality factor. Figure 4 showsthe variation of normalized PL with load quality factorand coupling coefficient, wherein logarithmic coordi-nates are used to facilitate observation except z-axis.When operating frequency is kept constant, PL is notalways increasing with k12, but reaches maximum undera certain condition which is the critical couplingposition. In general, coupling coefficient changes withthe spacing variation, and other parameters are fixed
Ra1
VS
RS
RL
RD
I1 I2
Ca1
Va1
Ia1
Source Device
a1 a2
Ra2Ca2
Va2
Ia2
LS LD
MS1 M2D
M12
EM Resonant Coupling
Inductive Coupling
Inductive Coupling
IS ID
Fig. 2 Directly field-circuit model of a MRC-WPT system. The analysis of the coupling principle of the field-circuit is shown in Fig. 2. The source coiland device coil are coupled with the resonant coils through inductive coupling, and the resonant coils perform power transmission through EMresonant coupling
Table 1 Parameters of improved three-coil wireless power linksystem
Parameters Resonators Load coil
Materials Copper pipe Silver-plating copper wire
Conductivity (107 S/m) 5.56~6 6.06
Number of turns 4.25 4
Radius of wire (mm) 3 2.5
Radius of the coil(cm) 30 10
Conductor spacing (cm) 6 ± 2.5 –
DC resistance (Ω) 0.046 0.002
Resonant frequency(MHz) 10.1–14.5 –
Quality factor 1000~1500 –
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 4 of 8
values. Thus, the maximum active power obtained bythe load is
PL max ¼ A2
ω0� Q ð7Þ
To derive the transmission efficiency function, we as-sumed that external objects do not participate in energyexchange. Active power consumption result in the losson load power, a1 and a2. While power consumptioncan be divided into Joule losses and radiation losses of acertain dose, both can be embodied by equivalent qualityfactor. So the overall efficiency η can be expressed as:
And the maximum transmission efficiency can beobtained from (8) as:
ηmax ¼ 1−2= 1þ Q=QLð Þ ð9ÞIt can be drawn that linear resonant coupling system
transmission efficiency depends mainly on two factors. Thefirst item Q/QL shows the role of impedance matchingcircuit. Here, the load quality factor is generally less thanthe oscillator quality factor which ensures that transmissionefficiency is always over zero. When QL <<Q, systemefficiency approaches the maximum which indicates poweris all absorbed by the load. When QL =Q, efficiency isalmost zero, indicating that power stored around the load
(a) loose coupling mode
(b) weak coupling mode
(c) strong and tight coupling mode
Fig. 3 Schematic of normalized energy exchanging. Normalized energyexchanging is solved by coupled mode method. In loose couplingmode, the power of the system quickly attenuates to zero. In weakcoupling mode, the rate of energy exchange between the transmitterand the receiving end is very small; it means that the transmittingefficiency is low. In strong and tight coupling mode, the system will workin a highly efficient transmission and low-loss state. a Loose couplingmode. b Weak coupling mode. c Strong and tight coupling mode
Fig. 4 Normalized active power PL as a function of k12 and QL. LEGEND:The abscissa axis is the coupling coefficient k12 and the load qualityfactor QL. They are two important parameters affecting the power. Thenormalized active power PL is displayed on the ordinate axis. It is aunimodal function of the coupling coefficient and the quality factor.Only when both of them get the appropriate value, can the powerreach the maximum
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 5 of 8
in reactive form. The second item k12Q shows the changesof two resonators’ space distance. When distance increases,coupling coefficient is reduced with efficiency decreased.When distance becomes smaller, k12Q increases and theefficiency increases accordingly. The specific variationsbetween efficiency and the two factors are shown in Fig. 5,while efficiency curve of critical state when satisfying (9)and k12Q = 1 are drawn at the same time.
4 Improved three-coil wireless power linkThe coupling mechanism of MRC-WPT system is oftencomposed of four coils which are source coil, two resona-tors and device coil, as shown in Fig. 2. In section III, theenergy exchange between two resonators is mainly ana-lysed by the coupled mode theory. There is also energytransmission between source coil or device coil and reso-nators. In the resonant state, the transmission efficienciesbetween two adjacent coils can be expressed by circuittheory as:
ηS1 ¼P1
PS¼ 1þ k22DQQD
� �k2S1QSQ
1þ k2S1QSQ� �
1þ k22DQQD
� �þ k212Q2
η12 ¼P2
P1¼ k212Q
2
1þ k212Q2 þ k22DQQD
η2D ¼ PL
P2¼ k22DQQD
1þ k22DQQD
� RL
RL þ RDð Þ
8>>>>>>>><>>>>>>>>:
ð10Þ
where QS =ω0LS/(RS + RS′), RS′ is internal resistance ofpower source, QD =ω0LD/(RD + RL). From ηS1 and η2D, itcan be seen that when the quality factor of coils and k12are constant, the increase of coupling coefficients kS1 andk2D contribute to the improvement of the efficiency. How-ever, the source coil and the device coil have the function
of impedance matching which is achieved by adjusting thedistance between the source coil or device coil and theresonators. Two resonators are essential in mid-rangeapplications, and in order to reduce the transmission lossbetween the coils, electrical energy can be directly fed tothe resonator so that the source coil can be omitted.Therefore, an improved three-coil wireless power link isproposed, which consists of a transmitting resonator, areceiving resonator and a device coil. The transmittingresonator and the receiving resonator are symmetrical.For the coupling coefficient k12 between the two resona-
tors, it determines the state of system. Once the couplingcoefficient k12 exceeds the threshold value, frequency split-ting disappears and PL decreases with the reduction of k12.In general, MRC-WPT system is intended to operate in afar enough distance to increase the flexibility of powersupply. Therefore, the remaining method to reduce damp-ing effect is to choose the coils with larger dimension andmore number of turns. However, for helical resonator, thisis also a way to reduce the flexibility of MRC-WPT.Only the characteristic impedance of the coil matches
the output impedance of the power supply; there will beno reflected power. The degree of matching is com-monly measured by the reflectance coefficient, as shownin (11).
Γ ¼ Zo−R0S
Zo þ R0S
ð11Þ
where Zo is the characteristic impedance of the reson-ator. In order to achieve this purpose, the resonatorsadopt γ matching method whose feed position is in thecentre of the coil, and its characteristic impedance can beadjusted until it matches the output impedance of the
Fig. 5 Transmission efficiency η as a function of Q/QL and k12Q. Theabscissa axis is Q/QL and k12Q. For system efficiency, it is related tomany factors. In this paper, we combine the relevant factors to seethe relationship of efficiency more directly
Fig. 6 Transmission efficiency η and power of the load PL as afunction of spacing distance. Transmission efficiency η and powerof the load PL as a function of spacing distance is shown in thisfigure. The transmission efficiency η curves of theoretical value andexperimental value when the frequency can be varied decay withthe increase of distance. When the frequency is constant, there is apeak value of the load PL. The curve shows that the error betweentheoretical calculation and actual measurement is relatively small
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 6 of 8
power supply. The output impedance of the power supplyis generally 50 Ω. Meanwhile, the resonator of receptionside uses the same method to adjust impedance. In thisway, the maximum source power is loaded to resonatorand efficiently transmitted to the load.In order to verify the transmission performance of the
improved three-coil link, a three-coil wireless powertransfer system was established and its transmissionperformance was tested within the distance of 0 to 3 m.Theoretical and experimental values of η and PL as afunction of spacing distance is shown in Fig. 6. Two60-W bulbs connected in parallel are the load whosepower has experienced a process of first increasing andthen decreasing. And the power reaches a maximum of120 W at a distance of 1.5 m. It is the critical couplingpoint when frequency keeps constant. The efficiencycurve shows that the closer two resonators, the higherthe efficiency is when frequency can be varied. However,it will decrease when distance is greater than 1.5 m.When source power is increased to 300 W, it can stillsupply 120 W at 2.5 m under efficiency about 32% fromDC power to the load, as shown in Fig. 7.
5 ConclusionsPrecondition of energy exchange in strong coupling canbe expressed as follows: the angular frequency of resona-tors is equal, and the product of coupling coefficient andquality factor is much larger than 1. We further derivedthat efficiency was constrained by Q/QL and k12Q whichreflect the contribution by electrical structure andspacing distance respectively. The maximum activepower of the load depends on the coupling coefficientbetween resonators, quality factor of the resonator andthe drive power. An improved three-coil wireless powerlink is proposed to maximize the transmission distance
and power at a reasonable level of efficiency. Meanwhile,a centre feed method is applied to resonators to achievegood impedance matching. In order to verify the theory,two 220 V/60 W bulbs are used as load, and MRC-WPTsystem with helical centre feed coils are designed. Exper-iments show that 120 W can be wirelessly transmitted ata distance of 2.5 m which is two times the power, 1.25times the distance and 2.13 times the efficiency of [1]. Inthe future work, we can use this system to supply powerfor wireless sensor networks.
AbbreviationMRC-WPT: Magnetic resonant coupling wireless power transfer; WPT: Wirelesspower transfer
AcknowledgementsThis work was supported by the Science and Technology Project of StateGrid Corporation of China: Research on Electromagnetic Safety Evaluationand Test method of Wireless Charging for Electric Vehicles.
Authors’ contributionsXZ is the main writer of this paper. He proposed the main idea, deduced theperformance of WPT detection, completed the simulation and analysed theresult. HM introduced the algebraic equation of power and efficiency bycoupled mode theory. BW and SW provided experimental environment andcompleted the experiment. QY gave some important suggestions for three-coil wireless power link. All authors read and approved the final manuscript.
Authors’ informationZhang Xian, male, Ph.D., Associate professor of Tianjin Key Laboratory ofAdvanced Electrical Engineering and Energy Technology come from TianjinPolytechnic University (TJPU), Tianjin, China, was born in Hebei, China, onDec 1983. He received the Bachelor degree from Hebei University ofTechnology (HEBUT) in 2009, majoring in Electrical Engineering, and theDoctor Degree in Engineering form HEBUT in 2012. Now, he majors inwireless power transmission and standards in TJPU.Meng Hao was born in Hebei Province, People’s Republic of China, in Apr1990. He received B.S. degree from Hebei University in 2016, majoring inElectrical Engineering. He is currently working toward the M.S. degree inSchool of Electrical Engineering and Automation, Tianjin PolytechnicUniversity. His research interest is wireless power transfer.Wei Bin, male, Ph.D., Professor of engineering, come from China ElectricPower Research Institute (CEPRI), Beijing, China, was born in Hubei, China, on
2.5m
0.2m0.6m
Fig. 7 Wireless power transfer to two 60-W bulbs under interval of 2.5 m. The distance between the transmitting coil and the receiving coil is2.5 m. The receiving end power through the coupling of up to 120 W and successfully lit the two lights
Zhang et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:131 Page 7 of 8
May 1978. He received the Bachelor degree from Changsha University ofScience and Technology in 2002, majoring in Power System andAutomation, and the Doctor Degree in Engineering from HuazhongUniversity of Science and Technology (HUST) in 2007. Now, he majors in inelectric vehicle wireless charging technology and standards in CEPRI.Wang Songcen, male, Ph.D., Senior engineer, comes from China ElectricPower Research Institute (CEPRI), Beijing, China, was born in Hernan, China,on Dec 1979. He received the Bachelor degree from North China ElectricPower University in 2001, majoring in Automation, and the Master andDoctor Degree in Power Electronic from CEPRI in 2010. Now, he works onwireless power transfer and energy storage in CEPRI.Yang Qingxin, male, Ph.D., Professor of Tianjin Key Laboratory of AdvancedElectrical Engineering and Energy Technology come from Tianjin PolytechnicUniversity (TJPU), Tianjin, China, was born in Hebei, China, on Apr 1961. Hereceived the Bachelor degree from Hebei University of Technology (HEBUT)in 1986, majoring in Electrical Engineering, and the Doctor Degree inEngineering form HEBUT in 1997. Now, he majors in Engineeringelectromagnetic field and magnetic technology in TJPU.
Competing interestsThe authors declare that they have no competing interests.
Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Author details1Tianjin Key Laboratory of Advanced Electrical Engineering and EnergyTechnology, Tianjin Polytechnic University, Tianjin 300387, China. 2ChinaElectric Power Research Institute, Beijing 100085, China.
Received: 14 February 2018 Accepted: 10 May 2018
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