Study on Frequency-tracking Wireless Power Transfer System by Resonant Coupling

Wenzhen Fu, Bo Zhang Member IEEE, Dongyuan Qiu Member IEEE

College of Electric Engineering South China University of Technology Guangzhou, P. R. China, 510641

Abstract-Detuning is the application barrier of resonant coupling wireless power transfer. This paper analyzes the effects about inductance variations of launch coil and receiving coil to wireless transmission efficiency from its transmission mechanism and model, and also analyzes detuning mechanism. And thus, it reveals that transmission efficiency has a great affection with inductance of launch coil changing. In order to make sure that wireless power transfer by resonant coupling operates without detuning, a new method of frequency tracking control is came up with, which is, making frequency of transmitting power source tracking with the nature frequency of launch resonant circuit automaticllly. Hence, it avoids detuning and improves transmission efficiency greatly. Finally, a prototype of 1 MHz wireless power transfer system by resonant coupling was made. Experimental results prove this method very well.

I. INTRODUCTION

Wireless power transfer has been a dream of human beings. Many scientists have researched it uninterruptedly but little progress has been made. Untill now,there two kinds of wireless power transfer that one is non-contact electromagnetic induction and another is radio waves transceiver[1-4].They have been studied deeply and usde in daily life, such as electric toothbrushes, cordless home phones and so on[5-7]. Efficiency of non-contact electromagnetic induction can reach to 80% but in a very short distance, just in 1cm. Radio waves can transfer energy in 10m with very low efficiency and only 1mW 100mW power can be transferred. Due to the conflict between transfer efficiency and distance, they are used not in a very wide range. And more,low efficiency results in serious heat problems[8]. Comparatively speaking, wireless power transfer of resonant coupling can transfer energy in 5m and its efficiency can Project Supported by National Natural Science Foundation of China

(NSFC)(50877028) Science Foundation of Guangdong Province

(8251064101000014) Hi-tech research and development program of China(863)

(2007AA05Z200).

to 40%, which will be a new technology with wider using range[9]. In addition, comparing with the contactless electromagnetic induction, resonance coupling uses weak magnetic field but can transfer farther;And comparing with the radio waves, resonance coupling has less dissipated energy during transfering process[10].

However, resonance coupling wireless power transfer is still in its infancy, whose theoretics and experimental analysis are in lacks,especially for efficiency analysis [11-12]. During the wireless power transfer process, resonant frequency maybe change because resonant inductance changes with obstacles (such as magnetic objects,etc.), parasitical parameters,impacts of receiving loop,temperature rising in circuit and so on. Once detuning happens,the efficiency will drop rapidly. Technologies of frequency tracking focusing on CD4046 and all digital PLL have been more mature[13-14], but they can not meet fast tracking in higher than 1MHz.

In order to overcome these problems, focusing on transmission mechanism and model of wireless power transfer by resonant coupling, this paper analyzed its efficiency and detuning mechanism. On this basis, frequency-tracking wireless power transfer system of resonant coupling basing on phase-locked loop 74HC4046 is came up with.Lastly,1MHz frequency-tracking wireless power transfer system by resonant coupling was made and got better results, which would be a very good guide to the future study on wireless power transfer system by resonance coupling.

II. DETUNING MECHANISM AND EFFICIENCY ANALYSIS

A.Detuning mechanism of resonant coupling wireless

Electromagnetic field decayes rapidly with transmission distance increasing,which is very undesirable. Resonant coupling just catches this decayed electromagnetic fields by two resonant loops. When resonance occurred between launch

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loop and receiving loop, most of energy will be transfered from transmitting power source to receiving load[12].

Resonant coupling wireless power transfer system includes not only two LC resonant circuits but also a high frequency transmitting power source and a receiving load. In order to simplify analysis, ignoring high frequency source, transceiver circuits are used as studyed objects directly. Model of resonant coupling is shown in Fig.1, where Vi is high-frequency power source; R1 R2 are parasitical resistances of coils L1,L2; C1, C2 are series resonant capacitors;RL is load; L1, L2 are coils inductance; M is mutual inductance and D is transmission distance.

Vi

R1 R2

C2C1

L1 L2

D

M

I1I2

.

..

.RL

Fig.1 Model of resonant coupling circuit

From Fig.1, when frequency of Vi equals to natural resonant frequency of transceiver circuits,their impedance are at least.Thereby, currents of the loops will be at the most and energy can be deliveryed mostly to receiving loop. On the other hand, energy of transmitting power source will be consumed in the launch circuit itself and its efficiency is very low. That is to say, keeping the frequencies in synchronism without detuning happening is the key point to achieve resonant coupling wireless power transfer.

coil. At the moment, if another coil is put aside it, the magnetic field will also appear around the other coil, which is the reason that the wireless energy transmission is set up between those two coils. Like that, resonance coupling is a special circumstance of non-contectless wireless energy transmission, where the special is: all coils used for resonance coupling operate in resonant state. Resonance occurs when the self-resonant frequency of coils equal to the frequency of AC power supply, when the equivalent circuits of coils in high frequency have the minimum impedance. Then, the most energy will be transferred from the resonant path.

The schematic of resonance coupling wireless energy transmission system was showed in fig.1.It includes two spatial isolated hollow coils: one is LS, which sends the energy inducted from the high frequency power supply; the other is LD, which receives energy from LS. These two coils have the same sizes and operate at the resonant state.

B. Efficiency analysis of resonant coupling

By Fig.1, resonant coupling model of wireless power transfer can be expressed by the following state equation.

1 11 1

22 L 2

2

1( )

10 ( )

R j L j MV C IiIj M R R j L

C

ω ωω

ω ωω

� �+ − −� �� � � �� �=� � � �� � � �� �� � − + + −� �� �

(1)

To simplify analysis, the transceiver loops impedance are written as Z1 and Z2, namely,

1 1 11

1( )Z R j LC

ωω

= + − , 2 2 L 22

1( )Z R R j LC

ωω

= + + − ,

By (1), currents of this two loops can be obtained as follows

1 22

2 11 2

j1j 0( )

iI Z M VI M ZZ Z M

ωωω

−� � � � � �=� � � � � �−+ � �� � � �

(2)

Then, input power Pin of launch circuit and output power Pout on the receiving load RL can be expressed as

22

21 2 ( )

iin

V ZP

Z Z Mω=

+ (3)

2 2L2 2

1 2

( M)[ ( ) ]

iout

V RP

Z Z Mω

ω=

+ (4)

Transmission efficiency is

2L

22 1 2

( )100%

[ ( ) ]M R

Z Z Z Mωη

ω= ×

+ (5)

Taking specific formulas of Z1, Z2 and mutual inductanc

1 2kM L L= (k is coupling coefficients) (5), (5) can be

changed as

21 2 L 2 L 2

2

1 1 2 L 21 2

21 2

1[( k ) ] /{[ ( )]

1 1{[ ( )] [ ( )]

( k ) }} 100%

L L R R R j LC

R j L R R j LC C

L L

η ω ωω

ω ωω ω

ω

= + + − ⋅

+ − ⋅ + + −

+ ×

(6)

From(6),transmission efficiency relates to many factors. If resonant parameters are determinded,resonant capacitor does not change any more, but �, R1 and R2 will change with resonant inductance changing. So resonant inductance is of the most important,which maybe change with its operation environment and some other factors in this system besides

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making errors. So it is too difficult to make actual value of coil inductance equaling to its calculated value exactly,which easily results in detuning. Once detuning happens, resonant coupling efficiency will drop. Therefore, the impact about coil inductance change to efficiency will be mainly analyzed in this paper.

When the frequency is 1MHz, basing on the theory formulas about dual-tube LLC resonant inverter of class E in reference[13], resonant coupling parameters of picture.1 are calculated as:L1=2.35μH,C1=12nF,L2=25μH,C2=1.0nF.

Due to high frequency, hollow coil parasitic resistance included ohm resistance Ro and radiation resistance Rr [10].

0 0o 2 2� 2

l nrRa a

ωμ ωμσ σ

= = (7)

[ ]2 4 20r 3

0

� 2( ) ( )12 3�

r hR nc c

μ ω ωε

= + (8)

Where � is the space permeability; a is the wire radius; r is the coil radius; n is the coil turns ;σ is the conductivity l is the wire length; 0ε is the dielectric constant; h is the coil length; c is the light velocity. For middle distance resonance coupling system, the optimum frequency range is 1 50MHz, then usually Rr� RO from (7) and (8). Coil parasitic resistance is ohm loss Ro mostly. In order to decrease parasitic resistance, the size parameters of hollow coils L1 and L2 are designed as :a1=0.725mm, a2=0.362mm; n1=2, n2=10; r1= r2=5cm. And then, from (7), the parasitical resistances of L1 and L2 are calculated as: R1=0.014� R2=0.139� In order to analyze the immpacts of coils inductance change to efficiency, coupling coefficient k and load RL are fixed firstly(k=0.02 RL=10�). Then, taking parasitic resistance R1, R2 and resonant parameters into (6), relation curves is got in Fig.2, where coil inductance L1 and L2 are independent variables and transmission efficiency is dependent variable.

(a) launch coil (b) receiving coil

Fig.2 Curves of efficiency vs. coil inductance

III. FREQUENCY-TRACKING SYSTEM

A. Principle of tracking control

Frequency-tracking resonant coupling system is shown in Fig.3,where it includes three parts, high frequency inverter, LC resonant couling and frequency-tracking control.

Dual-tube LLC resonant inverter of class E is selected as high-frequency inverter. Characters of this inverter are as follows: firstly, high-frequency transformer is instead by resonant inductance directly, which will reduce transformer loss and increase transmission distance.Secondly,the efficiency of this topology is very high because switches operate on ZVS and ZCS states. Finally but not last, two switches operate without dead time so that it is very fit for high frequency.

Eenergy is delivered from high-frequency inverter to receiving load by LC resonant coulping circuit. Frequency- tracking control includes currrent detection,differential amplifier,phase compensator and phase-locked loop, which are shown in Fig.3.

Fig.3 System principle diagram of frequency tracking

Control principles are as follows: current transformer has a real-time detection to the launch resonant loop, where detection signal is converted into a signal voltage VD. And then VD is converted into another signal Vp through differential amplifier.Lastly,Vp will be used to compare with a DC bias voltage that is abtained by rectifyingVp. After that,a pulse signal VC is got, which is the input of phase-locked loop and has the same frequency with the detection current. Herence, frequency-tracking control to launch resonant loop is realized.

B. Method of frequency tracking

(1) High-frequency current detection Real-time current detection is needed in frequency-

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tracking system. In the article, frequency of wireless power transfer system is 1MHz, so it must use high-frequency performance core for making current transformer to avoid high frequency saturation. Due to launch resonant circuit is not connected to the ground directly, detected current is a differential signal, which can not be sent into comparator directly and differential amplifier is need. High-frequency current detection is shown in Fig.4. According to principle of differential amplifier, there are R3=R4, R5=R6.

Fig.4 Circuit of high frequency current detection

(2) Method of phase compensation In actual circuit, some time delay exists in the process of

current detection, MOSFET on/off and so on,which will make resoant voltage delaying a phase to the resonant current and then resonant inveter operates in capacitive state. So phase compensation is needed in this system, which will make sure that high frequency inverter of class E always operates on quasi-resonant states to improve its efficiency.That is, most energy in transmitting power source will be delivered to receiving load. Schematic diagram and waveforms of phase compensation are shown in Fig.5.

(a) Compensation circuit

(b) waveforms

Fig.5 Phase compensation circuit and its waveforms

VP is the ouput voltage of differential ampilifier. Reference voltage Vref has been got through rectifying VP and

then Vref will fluctuate with VP, which will make sure that compensated phase �t does not change with detection current. Regulating adjustable resistance RP, Vref can be changed so that �t will vary flexibly with Vref changing. So,phase compensation is realized. (3) Method of phase-locked control

Phase-locked loop is compose of phase detector (PC1, PC2, PC3), external RC passive filter and voltage-controlled oscillators(VCO), which are seen in the phase-locked circuit of 74HC4046 in Fig.6. Its center frequency of VCO depends on the resistance of pin 11 and capacitance C3; Shifted frequency is determined by the resistance of pin 12,which is, when resistance decreaseing, shifted frequency will increase. In the conditions of frequency1MHz and frequency-tracking range 0.99MHz~1.1MHz, basing on the typical operation curves of 74HC4046, resistance values of pin11,12 and value of capacitor C3 are designed in Fig.6. Output pulse VCOout of phase-locked loop and its input VC are sent into phase detector PC2 to compare.When phase difference exists, a voltage signal is created by PC2, which will control the input of pin 9. And then make the frequency of VCO changing untill the phase difference does not exist.

Fig.6 Control circuit of phase-locked loop

when main circuit comes into operation, coil current can not be established immediately. PWM driveras also does not generate, which results in that whole system can not self-start. In order to solve this problem, it uses the features of74HC4046 for system self-starting, seeing in Fig.6. It is composed of R11, R12, C5 and D1. At the moment of phase-locked loop powered on, capacitorC5 will be short. Then,voltage of pin 9 is in its maximum and will decline from

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this value. At this time, frequency of VCOout falls down from the maximum fmax to the minimum fmin. As long as the natural resonant frequency of LC circuit is in this range, system will enter into be locked automatically.

IV. EXPERIMENTAL VERIFICATION

Basing on the parameters in section B of part II, a prototype of 1MHz frequency-tracking wireless power transfer system by resonant coupling was produced.Power of high frequency dual-tube LLC resonant inverter of class E is about 30W. IRF840 is switches with smaller junction capacitance. High speed integrated PWM driver UCC27325 is used to driving MOSFET, whose driving ability is 4A. A lamp with 25W/110V is used as receiving load. Differential amplifier and comparator use LM318 and LM311 respectively, both of which have high speed characters.High-speed optocoupler 6N137 is used for isolating main circuit and control circuit.

To verify frequency-tracking circuit, regulates size of launch resonant inductance L1, making resonant frequency of launch circuit changing in the trace range of phase-locked loop. In difference frequency, comparator output pulseVC and phase-locked loop output VCOout were measured as in Fig.7.From the picture, it can be seen that VCOout has a good accordance with VC in the trace range designed in this paper.

(a) f=0.993MHz (b) f=1.001MHz

(c) f=1.047MHz (d) f=1.103MHz

Fig.7 Effects of frequency-tracking at different frequencies

VD, VP, VC were also measured as shown in Fig.8, where it can be seen that they are consistent with theory analysis.

Fig.8 Output voltages of detection,amplifier and comparator

At the same parameters, output voltages of load in frequency tracking and no frequency tracking were seen in Fig.9, where transmission distances are all 3cm and DC input of inverter is 30V/1.0 A. In frequency tracking, from Fig.9(a), output voltage is a sine wave,which effective value is 106.8V and frequency was measured as 995.392kHz; In no frquency tracking, from Fig.9(b),it has a little distortion, where effective value is 68.7V and frequency is 1.000MHz. From that, experimental result with frequency tracking is better than that of no frequency tracking.

(a) Frequency tracking (b) No frequency tracking

Fig.9 Output voltage waveforms of receiving load

In addition, when transmission distance are 3cm, 5cm, 10cm, 15cm, 20cm respectively, their transmission efficiency curves are shown in Fig.10 basing on the output voltages measured in frequency tracking and no frequency tracking. From Fig.10, it can be seen that efficiencies of frequency tracking are all better than those of no frequency tracking at the same transmission distance. It proves the effectiveness of frequency tracking to avoid detuning once again and follows up the theory analysis.

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Frequency tracking

No frequency tracking

0

20

40

60

80

100

3 5 10 15 20 Distance(cm)

Effic

ienc

y(%

)

Fig.10 Efficiency curves in different distance

V. CONCLUSIONS

This paper focuses on the theory analysis of resonant coupling wireless power transfer, finding that efficiency has a big drop when launch coil inductance changes a little but varys smally when the receiving coil inductance changes the same ratio. Based on this, frequency-tracking technology is implemented on resonant coupling wireless power transfer system. Experimental results verified that transmission efficiency of frequency tracking is higher than that of no frequency tracking, which sloved the problem of efficiency droping when detuning. It is propitious to popularize and apply this kind of technology furtherly.

ACKNOWLEDGEMENT

The authors wish to thank all of the reviewers for their constructive comments, based on which the passage has been improved.

REFERENCES

[1] J. J. Hirai, T. W. Kim and A. Kawamura. “Wireless Transmission of

Powerand Information for Cableless Linear Motor Drive”. IEEE

transactions on Power Electronics, Vol. 15, No. 1, pp. 21-27, 2000.

[2] A. Esser and H. C. Skudelny. “A New Approach to Power Supplies

for Robots”. IEEE Transactions on Industry Applications, Vol. 27,

No. 5, pp.871-875, 1991,

[3] Y. Wu, L. G.Yan and S. G. Xu. “Study on Coupling Characteristics of

Contactless Power Supply System for Moving Apparatus”. Advanced

Technology of Electrical Engineering and Energy, Vol. 24, No. 3,

pp.5-85, 2005.

[4] J. Heikkinen, P. Salonen and M. Kivikoski. “Planar Rectennas for

2.45GHz Wireless Power Transfer”. Radio and wireless conference,

Denver co, USA, 63-66, 2000.

[5] W. Q.Zhou, H. Ma and X. N. He. “Frequency Analysis of a Current

Source Inductively Coupled Power Transfer System Based on

Dynamic Circuit Equations”.Proceedings of the CSEE, Vol. 28, No.

3, pp. 119-124, 2008.

[6] L.Wang, M.Chen and D. H. Xu. “The Engineering Design of

Contactless Emergency Power Supply in Maglev”. Proceedings of

the CSEE, Vol. 27, No. 18, pp. 67-70, 2007.

[7] M. Chen, D. Y. Zhou and D. H. Xu. “Contactless Power Supply of

Maglev Using Harmonic Injection Method”. Proceedings of the CSEE,

Vol. 25, No. 6, pp. 104-108, 2005.

[8] M. Soljacic. “Wireless Energy Transfer Can Potentially Recharge Laptops,

Cell phones without Cords” Report in San Francisco Massachusetts

Institute of Technology, 2006

[9] A. Karalis, J. D. Joannopoulos and M. Solja�i�. “Efficient Wireless

Non- radiative Mid-range EnergyTransfer”. Annals of Physics, Vol.

008, No. 323, pp.34-48, 2008

[10] M. Solja�i�, A. Kurs andA. Karalis, “Wireless Power Transfer via

Strongly Coupled Magnetic Resonances”. Sciencexpress, Vol. 112,

No. 6, pp.1-10, 2007.

[11] M. Solja��, E. H. Rafif and A. Karalis. “Coupled-mode Theory for

General Free-space Resonant Scattering of Waves” Physical Review,

Vol. 75, No.5, pp.1-5, 2007.

[12] A. Karalis, J. D. Joannopoulos and M. Solja�i�. “Efficient Wireless

Non- radiative Mid-range Energy Transfer”. Annals of Physics, Vol.

3, No. 23, pp34-48, 2008.

[13] W. H. Dong. “Topology Study of A New Dual-tube ultra

High-frequency Induction Heating Power Supply Circuit”. Zhejiang

University, 2006.

[14] L. S .Xiong and Y. J. Quan. “Application of CD4046 in Induction

Heating Power Source” Electric welder Vol. 6, No. 14, pp14-16,

2000.

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